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THE EFFECT OF GROUNDWATER PUMPING ON BASEFLOW IN THE DESCHUTES RIVER OF WASHINGTON STATE

Item

Title

THE EFFECT OF GROUNDWATER PUMPING ON BASEFLOW IN THE DESCHUTES RIVER OF WASHINGTON STATE

Date

2020

Creator

Lee, Eunbi

Identifier

Thesis_MES_2020_LeeE

extracted text

THE EFFECT OF GROUNDWATER PUMPING ON BASEFLOW
IN THE DESCHUTES RIVER OF WASHINGTON STATE

by
Eunbi Lee

A Thesis
Submitted in partial fulfillment
of the requirements for the degree
Masters of Environmental Studies
The Evergreen State College
June 2020

@ 2020 by Eunbi Lee. All rights reserved.

This Thesis for the Master of Environmental Studies Degree
by Eunbi Lee

has been approved for
The Evergreen State College
by

________________________
Dr. EJ Zita
Member of the Faculty

________________________
Date

ABSTRACT
The Effect of Groundwater Pumping on Baseflow in the Deschutes River of Washington
State
Eunbi Lee
Groundwater pumping via wells has been identified as a critical element in groundwater
depletion and consequent hydrologic alterations on numerous streams across the globe.
The deficit in groundwater reduces baseflow, which originates from the groundwater and
contributes to the surface flow, potentially putting the low streamflow at risk during a
low flow period. In Deschutes River in Washington, U.S., the capacity of baseflow has
decreased during the dry season in summer.
This research project utilized two baseflow analyses. First, the ‘natural’ baseflow
without the impact of the withdrawals (W=0), and the ‘impacted’ baseflow including
existing groundwater pumping (W≠0) were compared using two-sample Student’s t-test.
Second, a low flow frequency analysis estimated the times when the currently impacted
baseflow within the stream exceeded and fell below an ecological threshold, or
“environmentally critical baseflow.” Both analyses used baseflow data extracted from
streamflow discharge data measured at the lower Deschutes River (river mile 2.4) near
Tumwater. The total study period is 75 years (1945-2019) with 110 recession periods in
the dry season between June to October.
There was a significant difference between the ‘natural’ and ‘impacted’ minimum
baseflow, signifying that baseflow contribution would have been substantially higher
without the pumping effect. I project that the future baseflow within the stream will
decrease and reach the environmentally critical baseflow (ECB) in 2061. The work
presented here describes anthropogenic impact on the interactive regime between the
groundwater and surface water (quantity) and the ecological function (quality) of the
streams in the Pacific Northwest.

Table of Contents
Chapter 1: Introduction ....................................................................................................... 1
1.1: Description of the Study Area .............................................................................................. 5

Chapter 2: Literature Review .............................................................................................. 7
2.1: Roadmap ............................................................................................................................... 7
2.2: Introduction........................................................................................................................... 7
2.3: Interconnectivity between Groundwater and Surface Water ................................................ 9
2.3.1: Single Water System ...................................................................................................... 9
2.3.2: What is Baseflow? ....................................................................................................... 10
2.3.3: Baseflow as a Major Inflow ......................................................................................... 12
2.4: Low flow Trends and Attributions...................................................................................... 17
2.4.1: Low flow in Pacific Northwest .................................................................................... 17
2.5: Baseflow Recession in the Deschutes ................................................................................. 24
2.5.1: What is Baseflow Recession? ...................................................................................... 24
2.5.2: Baseflow Recession in the Deschutes River ................................................................ 26
2.5.3: Groundwater demand ................................................................................................... 28
2.5.4: Hydrological Impact of Wells in Deschutes River ...................................................... 33
2.5.5: Consequences of Baseflow Recession ......................................................................... 39
2.6: Well Pumping Mechanism.................................................................................................. 46
2.6.1: Cone of Depression ...................................................................................................... 46
2.6.2: Residual Depletion and Lag Effect .............................................................................. 48
2.6.3: Losing and Gaining streamflow ................................................................................... 49
2.7: Baseflow recession analysis................................................................................................ 50
2.7.1: Baseflow Recession Analysis Methods ....................................................................... 50
2.7.2: Linear or Nonlinear Relationship................................................................................. 52
2.7.3: Recession Constant (𝑲 𝒐𝒓 𝒂)....................................................................................... 53
2.7.4: Baseflow Separation Method ....................................................................................... 55
2.8: Frequency Analysis............................................................................................................. 58
2.8.1: Low Flow Parameters in the Deschutes ....................................................................... 58
2.8.2: A Different Frequency Analysis in Washington State ................................................. 59
2.8.3: Environmentally Critical Streamflow .......................................................................... 59
2.9: Conclusion .......................................................................................................................... 63

v

Chapter 3: Methods ........................................................................................................... 66
3.1: Roadmap ............................................................................................................................. 66
3.2: Data Description ................................................................................................................. 66
3.2.1: Basic Concept of Data Analysis................................................................................... 66
3.2.2: Selecting a Streamflow Gauge Station......................................................................... 67
3.2.3: Baseflow Separation and Selection .............................................................................. 68
3.2.4: Well Data ..................................................................................................................... 70
3.3: Formula Development ........................................................................................................ 77
3.3.1: Step 1. Baseflow Recession Analysis .......................................................................... 77
3.3.2: Step 2. Data Preparation and Prediction ...................................................................... 82
3.3.3: Step 3. Withdrawal Impact on Ecological Functions of a River .................................. 91

Chapter 4: Results ............................................................................................................. 96
4.1: Roadmap ............................................................................................................................. 96
4.2: Groundwater withdrawals ................................................................................................... 96
4.2.1: Yearly Groundwater Withdrawals ............................................................................... 96
4.2.2: Concentrated Withdrawal Locations............................................................................ 99
4.3: Model fitness..................................................................................................................... 101
4.3.1: Data preparation ......................................................................................................... 101
4.3.2: Choosing a Model ...................................................................................................... 109
4.4: Baseflow Recession Analysis ........................................................................................... 115
4.4.1: Existing “Impacted” Baseflow Recession.................................................................. 115
4.4.2: Hypothetical “Natural” Baseflow Recession ............................................................. 117
4.4.3: Statistical Analysis on Groundwater Withdrawal Impact .......................................... 117
4.5: Environmentally Critical Baseflow (ECB) ....................................................................... 124
4.5.1: Future Baseflow Recession and Ecological Threshold .............................................. 124
4.5.2: Different Estimation and Interpretation of ECB ........................................................ 125

Chapter 5: Discussion, Limitations & Suggestions, Conclusion .................................... 127
5.1: Discussion ......................................................................................................................... 127
5.2: Limitations and Suggestions ............................................................................................. 131
5.3: Conclusion ........................................................................................................................ 132

Chapter 6: References ..................................................................................................... 136
Chapter 7: Appendices .................................................................................................... 146
vi

Appendix A. Baseflow Composition in the Deschutes River and Washington State. Sinclair &
Pitz, 1999. ....................................................................................................................... 146
Appendix B. Population Projection Compared to 2012. TRPC, 2019. .................................. 146
Appendix C. Total Dwelling Unit Projection in Thurston County. TRPC, 2019. ................. 147
Appendix D. Linear baseflow recession constant (K) ............................................................ 148
Appendix D-1: Linear case .................................................................................................. 148
Appendix D-2: Nonlinear case............................................................................................. 149
Appendix D-3: Nonlinear case with 𝒃 = 𝟏/𝟐 ..................................................................... 149
Appendix E. Selection of Baseflow Recession period (t) ....................................................... 150
Appendix F. Yearly Withdrawal Amount. Data from the Thurston County Water Planning 151
Appendix G. Estimated Maximum Baseflow (Q0) and Recession Period (t) with Three
Methods .......................................................................................................................... 153
Appendix H. Linear and Nonlinear Baseflow Recession Constants ....................................... 155
Appendix I. Estimation of the Future Minimum Baseflow (𝑸𝒕) ............................................ 159
Appendix J. Estimated Minimum Baseflow (Qt) under Impacted and Natural Scenarios. .... 161
Appendix K. The Ratio of Groundwater Withdrawals to the Minimum Baseflow (𝑸𝒕) ........ 165

vii

List of Figures
Figure 1 Study Area ........................................................................................................................ 6
Figure 2 Baseflow: Groundwater Contribution to the Stream. Winter et al., 1999. ....................... 8
Figure 3 Groundwater and surface water system. Winter et al., 1999. ....................................... 10
Figure 4 Schematic groundwater flow and baseflow. Smith, 2010. ............................................. 11
Figure 5 Streamflow height and precipitation. ............................................................................. 12
Figure 6 Hydrograph of surface flow and baseflow of the Deschutes River................................. 14
Figure 7 Baseflow composition of total annual streamflow. ......................................................... 15
Figure 8 Historic and Present Baseflow Composition of the lower Deschutes River. .................. 16
Figure 9 Climate change effect on precipitation and low flow. Tohver & Hamlet, 2010; EPA,
2016. ................................................................................................................................. 21
Figure 10 Modeled timing when an environmental flow limit has been or will be reached for the
first time in streams of the globe. Graaf et al., 2019 ....................................................... 23
Figure 11 Schematic effects of pumping on a water movement. Barlow & Leake, 2012. ............ 25
Figure 12 Components of baseflow. .............................................................................................. 26
Figure 13 Lowest Baseflow in the Deschutes. ............................................................................... 27
Figure 14 Groundwater withdrawal purposes in Thurston County (1985-2015). ........................ 31
Figure 15 Population trend and projection in Olympia-Tumwater-Lacey urban area. TRPC,
2019. ................................................................................................................................. 32
Figure 16 Instream flow of the Deschutes River Basin. Chapter 173-513 WAC, 1988. .............. 34
Figure 17 Trend of surface flow of the lower Deschutes River (1991-2019). Modified from
streamflow data from NWIS. ............................................................................................. 35
Figure 18 Stream Temperatures and salmon habitat standard temperatures. .............................. 42
Figure 19 Hyporheic zone. Winter et al., 1998. ........................................................................... 45
Figure 20 Cone of depression. Gleeson & Richter, 2018. ........................................................... 47
Figure 21 Groundwater depletion and losing surface flow. Barlow & Leake, 2012. .................. 49
Figure 22 Recession Curve, period, and segment. Tallaksen, 1995............................................. 50
Figure 23 Recession Curve, period and segment. Modified from Tallaksen, 1995. ..................... 54
Figure 24 Components of a typical flood hydrograph. Brodie, 2005. ......................................... 56
Figure 25 Continuous pumping and Streamflow reaching the environmental flow limit. Graaf et
al., 2019. ........................................................................................................................... 61
Figure 26 Groundwater withdrawals and baseflow. Modified from Grannemann et al., 2000. ... 67
Figure 27 Surface Streamflow Components. ................................................................................. 69
viii

Figure 28 Baseflow data description and selection. Streamflow data retrieved from NWIS. ...... 70
Figure 29 Aquifer layers in Deschutes River Watershed – Included or Excluded. ....................... 73
Figure 30 Purposes of groundwater withdrawals in Thurston County. ........................................ 76
Figure 31 Model fitness through linear regression. Gan & Luo, 2013........................................ 85
Figure 32 Environmentally Critical Baseflow (ECB) of the Deschutes every 5 years. ................. 94
Figure 33 Relationship between population and groundwater withdrawals in Thurston County. 97
Figure 34 Groundwater Withdrawals by Water Use Purposes. .................................................... 99
Figure 35 Groundwater withdrawal concentrations in the study area of Thurston County ....... 100
Figure 36 Maximum baseflow (𝑸𝟎) of recession periods (1945-2019) estimated from the
trendline and forecast function. ...................................................................................... 103
Figure 37 Recession period (t) of the historic data (1945-2019) and future (2020-2069) estimated
from the trendline and forecast function (2020-2069). ................................................... 106
Figure 38 Trend of recession constants. ..................................................................................... 107
Figure 39 Estimated recession constants (1945-2069) ............................................................... 108
Figure 40 Forecasted future minimum baseflow (𝑸𝒕). ............................................................... 110
Figure 41 Linear regression analysis of the linear and nonlinear model. .................................. 112
Figure 42 Statistical comparisons of the 𝑸𝒕 estimations from the linear and nonlinear model . 113
Figure 43 Residuals analysis of the linear and nonlinear models. ............................................. 114
Figure 44 Recession constant of the linear model (K) and minimum baseflow (𝑸𝒕) (1945-2069).
Streamflow data from NWIS, separated using WHAT. ................................................... 116
Figure 45 Minimum baseflow (𝑸𝒕) and withdrawals (W) (1945-2019). ..................................... 118
Figure 46 Minimum baseflow (𝑸𝒕) comparisons between the Impacted versus Natural scenarios
........................................................................................................................................ 119
Figure 47 Two-sample Student's t-test analysis between Models ............................................... 122
Figure 48 Future Impacted baseflow and ECB (mode, mean, and forecasted of the past records)
........................................................................................................................................ 126

ix

List of Tables
Table 1 Elements associated with low flow in streams of the PNW. Georgiadis et al., 2018. ..... 18
Table 2 Purposes of wells. Dieter et al., 2018. ............................................................................ 28
Table 3 Management action scenarios to reduce stream temperature of the Deschutes River.
Data from DoE, 2015........................................................................................................ 43
Table 4 Aquifer layers in Deschutes River Watershed. Schuster, 2015. ...................................... 72
Table 5 Six cases of modeled future minimum baseflow (Qt) ....................................................... 86
Table 6 Baseflow recession analysis equations under Natural or Impacted scenarios and Linear
and Nonlinear models ....................................................................................................... 90
Table 7 Minimum baseflow (Qt) estimation from different methods and models ....................... 111
Table 8 Statistical comparison between the minimum baseflow (Qt) under the Impacted scenario
(model A) and Natural scenarios (model B, C, and D). .................................................. 123

x

Acknowledgements

There are several groups and individuals whom I acknowledge for their help in
completing this thesis. First and foremost, I would like to thank my husband, Sean
Wood, for his unwavering trust and support that helped me to put this educational pursuit
forth and accomplish it. Thank you for being with me in rain and sunshine all the way
through this program.
This thesis project would not have been possible without the direction and guidance of
my faculty advisor, EJ Zita. Also, I want to thank all the MES faculty for their support.
Especially, I received a great amount of help from the program director, Kevin Francis,
who openly communicated with me in regard to difficulties and successes.
There are several agencies and professionals that I would like to thank. Erica Marbet
from the Squaxin Island Tribe has given me valuable support and guidance from the early
stage of my research and interest in hydrology. Kevin Hansen from Thurston County
Water Planning offered instructive details and data regarding the groundwater
withdrawals that were essential for this project. Scott Malone from the Department of
Ecology provided expert advice on hydrogeologic knowledges. Numerous people were
willing to answer my questions, provided data, and invited me to meetings to broaden my
understanding on the subject matter and I thank them: Brian McTeague from Squaxin
Island Tribe, Kenneth Tabbutt from the Evergreen State College, Jim Pacheco, Lisa
Kean, Joe Witczak from the Department of Ecology, and Nathaniel Kale and Mark
Biever from Thurston County Water Planning.
Finally, I thank my parents for their unchanging support in all the paths I chose in my
life.

xi

Chapter 1: Introduction
Over the past 100 years, human water demand increased almost 8-fold due to the
quadrupling of the global population and continues to rise (Wada et al., 2016).
Socioeconomic developments increasingly put pressure on our freshwater resources with
rising per-capita demands and standards of living (Veldkamp et al., 2017). Pressure on
available freshwater resources has occurred in both water systems: groundwater within
underground aquifers and surface water flowing over the surficial levels. The two water
systems—groundwater and surface water—are hydraulically interconnected, such that
exploitation of one system (e.g., groundwater) inevitably depletes the other system (e.g.,
surface water).
Groundwater is a primary source of freshwater in many parts of the world and
supplies more than one-third of the U.S. population with drinking water 1 (Konikow,
2013). Though seemingly infinite, groundwater is a finite resource that is vulnerable to
depletion due to perpetuated withdrawals (Famiglietti, 2014). Some regions that are
increasingly dependent on groundwater consume groundwater faster than it is naturally
replenished and cause water tables to decline (Rodell et al., 2009). Lowered water tables
disconnect the interaction between groundwater and surface water, deplete the surface
water, and put risk on the ecology of the flowing stream systems (de Graaf et al., 2014).
Recent studies assessed the impact of human activities (e.g., groundwater
pumping) on hydrologic processes between groundwater and surface water 2. The
interaction between groundwater and surface water is a critical element to sustain the

1
2

Globally, groundwater accounts for 30% of available freshwater (Gleick, 1996)
Wang & Cai (2009); Thomas et al. (2013); Gleeson & Richter (2018); de Graaf et al. (2019).

1

ecological functions of a river, wetland, lake, and terrestrial ecosystem (Gleeson &
Richter, 2018). Yet, current groundwater management in some regions has not explicitly
included the potential impacts of groundwater pumping on depleted groundwater storage
and degraded surface water ecology. The lack of management of the impacts of
groundwater pumping on the interactive water systems is relatively riskier in regions with
prolonged droughts and extended low streamflow.
The impact of groundwater pumping on lowering water tables and reducing
surface water leads to detrimentally low streamflow during the dry summertime in the
Pacific Northwest (PNW). Traditionally, summer streamflow in PNW maintained a ‘low
flow’ status from prolonged droughts with little to no precipitation to recharge the surface
flow (Konikow, 2013). The low flow results in degraded water quality with heightened
stream temperature, low dissolved oxygen level, unbalanced pH level, and spreading
diseases (DoE, 2015). With increased groundwater exploitation, the quantity of stored
groundwater and the amount of groundwater contributing to the surface flow (‘baseflow’)
are expected to decrease in urbanized regions (Georgiadis et al., 2018).
The decreasing trend of baseflow in PNW due to perpetuated groundwater
pumping relates to exacerbated low flow and consequent water quality issues. The
Deschutes River in Washington State is faced with a continuous rise in stream
temperature and water quality degradation, most of which have been the focus of studies
on the quality of the stream3. In contrast, there have been relatively fewer studies
regarding the impacts of groundwater withdrawals on reduced baseflow contribution on
3

Deschutes River does not meet water quality standards and is on the Clean Water Act Section 303(d) list
for one or more Total Maximum Daily Load (TMDL) parameters: fecal coliform bacteria, temperature,
dissolved oxygen (DO), pH, or fine sediments (Wagner & Bilhimer, 2015).

2

the surface flow, even though the baseflow is a major source of streamflow during the
low flow period4. The lack of quantitative studies on baseflow may be attributed to the
common perception of ample precipitation in wet seasons (Fall, Winter, and Spring)
recharging low streamflow. However, PNW under rapid urbanization is no longer
exempt from being a naturally sustainable low flow region. Groundwater storage and
baseflow contribution here may be at risk of decreasing below the level that they cannot
sustain minimally required streamflow for the riverine ecosystem 5. Thus, the decreasing
trend of baseflow (‘baseflow recession’) of the Deschutes River should be carefully
monitored and analyzed because the aquifer, which is hydraulically related to the river,
has been exploited. Such groundwater pumping and appropriation have met the fastgrowing demands of burgeoning Thurston County populations and development 6.
A quantitative baseflow recession analysis delineates the impact of groundwater
withdrawals on surface streamflow. The baseflow recession analysis explains the
fluctuating baseflow, which links the effect of groundwater depletion on the surface flow.
Streams in PNW already are faced with both quantity and quality degradation due to
climate change and recurring ocean-atmosphere patterns, such as Pacific Decadal
Oscillation and El Niño‐Southern Oscillation (Georgiadis et al., 2018). Coupled with
climatic elements, the unsustainable groundwater withdrawal practices without
considering the baseflow recession will exacerbate the low flow and ecological functions
on riverine ecosystems. Additionally, analyzing the low flow period, maintained by

4

Baseflow consisted of the surface flow on average 83% of the streamflow between 1945 and 2019 (see
section 2.3.3).
5
Hamlet et al. (2010); Luce & Holden (2009).
6
Thurston County was ranked as the third-fastest growing region in Western Washington (USGS, 2015).

3

mostly baseflow contribution during dry seasons, explains the impact of the baseflow
recession. A frequency analysis explains how the future low flow status will change in
relation to the sustainable level of baseflow contribution to the stream.
The two research questions this study intends to answer are 1) To what extent has
groundwater demand impacted baseflow recession in the lower Deschutes River in
Washington State? and 2) At what point of time in the future will critically low
groundwater supply to the Deschutes River occur? The quantitative baseflow recession
analysis on the Deschutes groundwater system estimates numeric values to describe the
baseflow pattern between 1945 and 2019. The estimated values are categorized into two
scenarios; the “natural” groundwater system is a hypothetical scenario of the baseflow
without groundwater pumping; the “impacted” groundwater system represents the current
baseflow status with groundwater pumping accounted. The “natural” and “impacted”
baseflow are compared to understand the effect of groundwater pumping on the baseflow
contribution to the surface flow. This study hypothesized that the effect of groundwater
withdrawal is significant when the baseflow recession under the “natural” versus
“impacted” scenarios are statistically compared. Finally, the withdrawal impact on
baseflow recession is assessed in a view from whether the baseflow in the future will
sustain a minimum baseflow threshold, or environmentally critical baseflow (ECB,
adopted from Gleeson & Richter, 2013; de Graaf, 2019). Through this study, baseflow
recession elucidates a quantitative effect of groundwater pumping and whether current
withdrawal practice is environmentally sustainable for future streams.

4

1.1: Description of the Study Area
Deschutes River is a 50-mile-long (80 km) river in Washington, United States.
From the Gifford Pinchot National Forest in Lewis County, it flows from southeast to the
northwestern part of Thurston County and empties into Budd Inlet at the southernmost
arm of Puget Sound. The capitol city of Washington, Olympia, is located on the southern
Deschutes River, and the greater-Olympia area, where fast-growing cities, such as
Tumwater, Lacey, and Yelm, rely on the Deschutes River for their development.
The study area includes parts of Thurston County where unconsolidated
sediments are at land surface (510 square miles; figure 1). The unconsolidated layers of
the Puget Sound aquifer represent the geologic units where groundwater interacts with
the surface water of the Deschutes River. The selected study area covers most of the
river’s watershed (162 square miles), except for some areas in the southeast where there
are consolidated sediment layers at the land surface. The range of selected geologic map
layers included Quaternary alluvium (Qa), Pleistocene continental glacial drift (Qgd), and
Pleistocene alpine glacial drift (Qad). The excluded areas include consolidated geologic
layers of Tertiary volcanic rocks (Tv(c)), Tertiary marine sedimentary rocks (Tm), and
Tertiary nearshore sedimentary rocks (Tn) 7. The range of the included geologic layers
are the selected study area (blue area in Fig. 1).
U.S. Geologic Survey (USGS) collected the streamflow data for the lower
Deschutes River, gauged at the station in Tumwater, Washington, 2.4 miles away from
the river mouth (river mile 2.4). I used the collected streamflow data to extract the

7

Geologic map layer source: City of Tacoma, 2019.

5

baseflow contribution from the groundwater aquifer to the stream. This study
demonstrates the impact of groundwater withdrawals on the baseflow, which is a part of
the surface flow. The lower (northern) Deschutes River, toward which the water flows
due to hydraulic gradients, was chosen for this study because it incorporates the
groundwater deficit from its upper stream.
Figure 1
Study Area
ESRI online map layer sources: City of Tacoma, 2019 (geologic unit layers); WSDOT,
2012 (county boundary); Bilhimer, 2014 (Deschutes River).

Note. Light blue: included geologic units (Qa, Qgd, Qad). This area represents the whole
study area. Brown: excluded geologic units (Tv(c), Tm, Tn). The streamflow gauge
station is located on E street, Tumwater, WA.

6

Chapter 2: Literature Review

2.1: Roadmap
This literature review is organized into 8 sections: an introduction, Sections 1-6,
and a concluding summary. The introduction describes the concept of baseflow and its
importance during low flow periods. Section 1 provides a conceptual understanding of
interconnected groundwater and surface water as a single source. Section 2 addresses
low flow trends in the Pacific Northwest region and possible causes of the low flow
phenomenon. Section 3 describes the concept of baseflow recession, and how
groundwater demand and withdrawals can affect the baseflow recession and water
qualities in streams. Section 4 describes the water wells' pumping mechanism. Section 5
explains a baseflow recession analysis in a quantitative way. Section 6 provides a
frequency analysis, for a different perspective to interpret the streamflow depletion in a
low flow period. Finally, the conclusion summarizes why the quantitative analysis of
streamflow is imperative for preserving groundwater and surface water resources.

2.2: Introduction
Streamflow in the Pacific Northwest (PNW) region has been depleted during dry
summertime in recent decades (Georgiadis et al., 2018). While many people may think
that rivers in the PNW sustain significant flow rates due to ample precipitation events in
wet seasons, this is not true in the dry season when surface streamflow is lowered
significantly. Low streamflow ("low flow") is detrimental to the ecological functions of
rivers to sustain aquatic species and natural values of flowing streams (DoE, n.d.). Low
7

flow is a natural phenomenon that occurs in dry seasons, which maintains streamflow
from groundwater contribution during the non-precipitated period. During low flow
periods, groundwater inflow into the surface water system can alleviate low streamflow
and cool streams; the groundwater inflow is referred to as "baseflow" (Fig. 2).
Figure 2
Baseflow: Groundwater Contribution to the Stream. Winter et al., 1999.

Baseflow

Note. Baseflow is denoted with blue arrows (upward) from groundwater to the surface
flow.
Baseflow is a natural regime of hydraulic movement between groundwater–
surface water systems. Baseflow is associated with both quantity and quality of water in
streams. When there is less groundwater available, baseflow decreases within the surface
stream. The reduced baseflow contributes to severely low flow and degraded water
quality in a surface stream. This relationship is important to understand streamflow from
a holistic perspective. Baseflow is a connective system between groundwater and surface
water, where an effect on one system (i.e., groundwater) will have an impact on the other.
Water quality in the Deschutes River in Washington State has brought attention to
environmental and societal issues in the South Puget Sound area. Many studies explored
degraded water qualities (e.g., warm stream temperature, low oxygen retention, and
8

unbalanced pH level). However, there have not been significant studies related to the
trend of changing quantity of baseflow and its effect on the surface water. The effect of
baseflow on the water quality enhancement signifies why we should pay attention to the
fluctuating baseflow trends. Furthermore, the human interception of groundwater via
well pumping has altered the quantity of groundwater and surface water, which entails
possible degradation of the stream quality.

2.3: Interconnectivity between Groundwater and Surface Water
2.3.1: Single Water System
A paradigm shift in the late 20th century increased attention on the
interconnectedness of groundwater and surface water as an integrated body (Winter et al.,
1998). Surface water is the most recognizable source of water in the form of streams,
rivers, lakes, reservoirs, and oceans (Winter et al., 1999). Groundwater, though unseen at
the landscape level, exists underground in saturated zones, filling pores and fractures
between sediment beneath the land surface and forming aquifers (Fig. 3, Barlow &
Leake, 2012). Surface water percolates down through sediment fractures to recharge
groundwater, while groundwater moves upward to contribute to the surface water above
riverbeds (Fig. 3). “Baseflow” constitutes a part of streamflow, contributed from the
groundwater system, and connects the two water systems (Hall, 1968; Tallaksen, 1995).

9

Figure 3
Groundwater and surface water system. Winter et al., 1999.

2.3.2: What is Baseflow?
The surface water system is composed of “baseflow” and “direct runoff”.
Baseflow flows up into surface streams, originating from groundwater below. Direct
runoff flows within streams, primarily from rainfall or artificial recharge which “runs
off” the land surface (Nolan & Hill, 1990). After a precipitation event (e.g., rainfall,
snow, or flood), direct runoff can overwhelm the surface water system (Fig. 4). But the
opposite occurs during low flow periods and drought when there is little to no
precipitation; the surface water we see is mostly baseflow, which seeps from the
underground water into the stream (USGS, n.d.). Below, surface water recharges
groundwater through “infiltration” and “percolation”, which describes the process of
surface water moving vertically down through sedimentary pores of an aquifer and

10

adding to the groundwater. Baseflow flows into the surface flow where it is combined
with direct runoff (or, “surface runoff” below 8) to form the total surface water system.
Figure 4
Schematic groundwater flow and baseflow. Smith, 2010.

Surface water= baseflow + surface runoff

Baseflow maintains surface water when there is no precipitation recharging the
direct runoff on a stream. For example, the Deschutes River in Washington maintained
streamflow above zero even during a severe drought in 2005 with the inflow from the
groundwater (OWSC, 2009; Anderson et al., 2016). Without the baseflow contribution,
the surface water would not have maintained the flow without consistent inflow from
precipitation. In detail, the low flow is exacerbated when high air temperature yields
increased evaporation. Alike many glacier/snowmelt-dominated Washington Cascade
rivers, the glacier retreat due to global warming results in an increasing number of days
with substantially low flow (Pelto, 2011). However, the low flow without precipitation
inflow did not completely dry in the summer of 2005 of the Deschutes River. Most days

8

In this study, “surface runoff” is equivalent to the “direct runoff”.

11

in July showed almost no precipitation (0 inches), but the surface streamflow remained at
least 24 feet high (Fig. 5). The baseflow from the groundwater sustained the low flow.
Figure 5
Streamflow height and precipitation.
Streamflow data retrieved from USGS National Water Information System: Web Interface
(NWIS), gauge station 12080010 near Tumwater. Precipitation data from NOAA.

25.2
25.1
25
24.9
24.8
24.7
24.6
24.5
24.4
24.3
24.2

1.2
1
0.8
0.6
0.4
0.2
0

precipitation (inches)

Gauge height (feet)

Low flow and Precipitation

Time (date)
Gauge height

Precipitation

Note. Blue columns denote daily average gauge height, or the level of the surface flow
reaching in height at the gauging station (USGS 12080010 near Tumwater). The orange
line denotes the amount of rainfall.
2.3.3: Baseflow as a Major Inflow
Baseflow can maintain the minimum surface flows that are required for ecological
functions of a river during “low flow” or prolonged drought period (Hall, 1968;
Tallaksen, 1995; Stuckey, 2006; Gustard & Demuth, 2008). Low flow refers to the phase
when surface streamflow is primarily sustained by baseflow (the groundwater
contribution to the surface flow) during prolonged, but non-drought, dry weather
(Stuckey, 2006; Gleeson & Richter, 2016). Low flow is an important parameter to

12

determine whether the surface flow without precipitation input sustains aquatic species
and intrinsic values (Gleeson & Richter, 2018).
Baseflow is a major inflow to the surface flow during low flow periods assuming
the river maintains streamflow during the absence of precipitation input. Rivers located
in areas with extremely variant precipitation between seasons rely heavily on baseflow
contribution during dry seasons to maintain minimum flows. A hydrograph, describing
the variance in the amount of flow component, of the Lower Deschutes River below (Fig.
6) shows the baseflow component within surface streamflow in dry and wet seasons 9.
Using the web-based hydrograph analysis tool (WHAT), the baseflow component within
the surface flow represents how much groundwater contribution occurs of a water year,
typically between October to next year September. Between 2014 and 2015, the
baseflow (orange) dominates the surface flow (blue) during the dry season. Also, the
direct runoff, which is the other component of the streamflow contributed from mainly
precipitation, decreased in the same dry period.

9

Typically, the dry season is from June to October and the wet season is November to May in Pacific
Northwest (Kormos et al., 2016).

13

Figure 6
Hydrograph of surface flow and baseflow of the Deschutes River.
Streamflow data from NWIS, gauge station 12080010 near Tumwater; baseflow data
separated using a web-based hydrograph analysis tool (WHAT).

Surface flow and Baseflow (2014-2015)
3000

Flow (cfs)

2500
2000
1500
1000
500
10_1_2014
10_14_2014
10_27_2014
11_9_2014
11_22_2014
12_5_2014
12_18_2014
12_31_2014
1_13_2015
1_26_2015
2_8_2015
2_21_2015
3_6_2015
3_19_2015
4_1_2015
4_14_2015
4_27_2015
5_10_2015
5_23_2015
6_5_2015
6_18_2015
7_1_2015
7_14_2015
7_27_2015
8_9_2015
8_22_2015
9_4_2015
9_17_2015
9_30_2015

0

Time (day)
Surface streamflow (cfs)

Base flow (cfs)

Note. The surface streamflow (blue) includes both the baseflow (orange) and direct
runoff (blue area without orange area). Data selected for the water year between October
2014 and September 2015.
The portion of baseflow within the surface flow is dominant during low flow
periods in Pacific Northwest streams. In summer, streams experience peak evaporation
rates from flowing water as well as evapotranspiration from plants due to heightened air
temperature and transpiration process10. The lack of rainfall and heightened
evapotranspiration reduce the surface flow volume; thus, streams in PNW depend on
baseflow to prevent complete depletion (Miller et al., 2016). The Deschutes River
showed a large dependency on baseflow contribution during low flow periods of summer

10

Evapotranspiration is the combined process of water loss through the leaves of plants (transpiration)
and water changes to vapor in the atmosphere (evaporation) (Yang et al., 2016).

14

compared to the average dependency of other streams in Washington State (Fig. 7)
(Sinclair & Pitz, 1999). Sinclair and Pitz (1999) separated the baseflow from the
streamflow component and determined that the average baseflow comprised 69%-86% of
582 Washington State summer stream gauge stations in 1991 (gray bar in Fig. 7). For the
Lower Deschutes River, the baseflow composition within the stream ranged from 74% to
97% in the same period (blue bar in Fig. 7) (Sinclair & Pitz, 1999).
Figure 7
Baseflow composition of total annual streamflow. Data from Sinclair & Pitz, 1999.

Baseflow composition in
Surface flow (%)

Baseflow Composition (1999)
100
80
60
40
20
0
Jun

July

Aug

Sep

Oct

time (month)
Lower Deschutes 12080010 E Street in Tumwater
Upper Deschutes 12079000 near Rainier
Washington State Average of 582 gauging stations

Note. Baseflow composition in the Lower Deschutes River is consistently higher than the
Upper Deschutes River or the average of 582 gauge stations in Washington State. A unit
for flow is cubic feet per second (cfs).
The baseflow has consistently been high during summer in the lower Deschutes
River. On the other hand, direct runoff has been highly variable; the blue column
(surface flow) without the baseflow portion (orange column) fluctuates to a larger degree
(Fig. 8). Baseflow consistently accounts for a large portion of the surface flow; 83% of
15

the streamflow has been baseflow component over 65% of the time between 1945 to
201911. This shows how the groundwater inflow (i.e., baseflow) dominated the surface
water system (i.e., low flow) during the dry season in the Deschutes River. Therefore, we
should understand that the baseflow is a major surface water component during low flow
periods and how it affects the surface water quantity of the Deschutes River.
Figure 8
Historic and Present Baseflow Composition of the lower Deschutes River.
Streamflow data from NWIS gauge station 12080010 near Tumwater; baseflow data
separated using a web-based hydrograph analysis tool (WHAT).

5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
5_1_1945
10_4_1946
3_8_1948
8_11_1949
1_14_1951
6_18_1952
11_21_1953
11_24_1957
4_29_1959
10_1_1960
3_6_1962
8_9_1963
4_13_1991
9_15_1992
2_18_1994
7_24_1995
12_26_1996
5_31_1998
11_3_1999
4_7_2001
9_10_2002
2_13_2004
7_18_2005
12_21_2006
5_25_2008
10_28_2009
4_2_2011
9_4_2012
2_7_2014
7_13_2015
12_15_2016
5_20_2018

Flow (cfs)

Historic and Present Baseflow (1945-2019)

Time (date_year)
Surface flow (cfs)

Base flow (cfs)

Note. Baseflow (orange) from groundwater has consistently been a major component of
the Deschutes surface flow (blue). Units for flows are in cubic feet per second (cfs).

11

Appendix A. Baseflow composition analysis in Lower Deschutes River. Data includes the entire water
year of the Lower Deschutes River.

16

2.4: Low flow Trends and Attributions
2.4.1: Low flow in Pacific Northwest
Low flow phenomena occur in streams in ‘wet’ regions of the Pacific Northwest
(PNW). As noted, low flow is the “flow of water in a stream during prolonged dry
weather” (EPA, 2018). The low flow represents a certain flow rate to regulate minimum
streamflow that should be kept for instream values (EPA, 2018). Typically, the PNW
region is perceived to be free of risks of stream depletion because of ample rainfall
throughout Fall, Winter, and Spring seasons. In other words, even though Summer flow
remains low, the deficit streamflow is expected to be recovered or compensated by the
following precipitation during wet winter (Konikow, 2013).
The perception that ample precipitation during wet winter alleviating the low
streamflow during dry season may be an incomplete analysis on the low flow in PNW
(Konikow, 2013). Summertime flows in PNW streams have deteriorated in recent years
in both Eastern and Western Washington (Georgiadis, 2018). The reasons for streamflow
deterioration can be climatic and anthropogenic; in this study, the attributing factors are
divided into "precipitation", "climate change", and "groundwater exploitation".
2.4.1.1: Attribution 1. Precipitation
An empirical assessment of low flow in Puget Sound streams showed that most
stream flows have deteriorated over the past 63 years on average 12 (Georgiadis et al.,

12

11 out of 13 streams of interest showed moderate to significant deterioration of low flow (Grorgiadis et
al., 2018). 9 streams that showed significant deterioration include NE Stillaguamish near Arlington,
Issaquah Creek near mouth, Deschutes River near Rainier, Deschutes River near Tumwater, South Fork
Snoqualmie, Snoqualmie River near Carnation, Cedar River above Chester Morse Dam, Soos Creek, and
Newaukum Creek. 2 streams with moderate deterioration include North Fork Snoqualmie and Snohomish
near Monrow.

17

2018). Georgiadis, et al. showed that streamflow is positively associated with
precipitation in wet seasons (winter, spring, and some summer wet periods). This means
the low flow is enhanced as the surface water is recharged from the rainfall. On the other
hand, the streamflow in low flow periods is negatively associated with the number of
years (Table 1). The two findings combined indicated that the streams in PNW have
experienced reduced flow in low flow periods, even with the precipitation recharging the
flow (Hamlet, 2010; Luce et al., 2014; Georgiadis et al., 2018).
Table 1
Elements associated with low flow in streams of the PNW. Georgiadis et al., 2018.
(years
)

Mean
Low
Flow

Nisqually
River

72

Puyallup
River near
Orting

84

Gauge
Name

N

Model Coefficients
𝑅

Probability

8.98

0.17

1.37E-02

6.89

0.22

4.42E-02

(cfs)

NF
Stillaguamis
h near
Arlington

87

Issaquah
Creek near
the mouth

52

0.61

0.70

1.11E-11

Deschutes
River near
Rainier

53

0.90

0.67

5.12E-11

Deschutes
River near
Tumwater

40

2.40

0.60

4.05E-06

North Fork
Snoqualmie

71

2.40

0.55

1.01E-10

South Fork
Snoqualmie

53

1.28

0.68

3.14E-11

85

22

0.42

6.17E-09

18

7.61

0.42

Summer
Rain

Spring
Rain

Winter+
Fall Rain

Years of
records

0.027
4.58E-01

0.071
7.37E-03

0.032
2.60E-02

0.005
7.06E-01

0.171

0.162

0.095

0.021

1.71E-02

2.72E-03

1.43E-03

2.71E-02

1.006

0.228

0.110

-0.025

4.54E-08

4.47E-02

1.62E-02

4.79E-02

0.030

0.022

0.008

-0.008

2.19E-04

4.52E-06

1.23E-04

3.02E-08

0.047

0.038

0.006

-0.004

3.51E-04

2.33E-08

2.90E-03

3.26E-05

0.137

0.038

0.006

-0.004

5.83E-03

3.75E-05

5.92E-04

1.71E-02

0.348
1.59E-11
0.148
3.18E-10

0.034
2.64E-01
0.032
1.03E-02

0.022
834E-02
0.008
1.47E-01

-0.005
2.27E-01
-0.010
2.99E-03

1.462

0.045

0.158

-0.110

3.17E-09

Snoqualmie
River near
Carnation
Snohomish
near
Monroe

47

44.92

0.60

5.09E-08

Cedar River
above
Chester
Morse Dam

70

1.12

0.70

2.26E-16

Soos Creek

49

29.40

0.52

1.40E-06

Newaukum
Creek

62

16.30

0.52

8.19E-09

2.86E-09

7.08E-01

1.31E-03

5.86E-03

7.914

2.319

0.717

-0.268

5.81E-15

4.59E-03

3.52E-02

8.72E-02

0.084

0.012

0.005

-0.004

5.82E-15

6.49E-03

2.26E-02

4.45E-03

1.533
2.46E-03
0.722
1.08E-03

1.193
5.53E-07
0.722
7.21E-07

0.119
2.23E-01
0.171
5.36E-04

-0.119
1.10E-02
-0.080
6.45E-05

Note. Green denotes a positive effect on low flows and red a negative effect. Darker
shades denote significance at alpha=0.05.

The result of a multi-year reduction in streamflow indicates that winter
precipitation has not been a ‘solution’ to summer low flow, regardless of the precipitation
input. The effect of precipitation recharging streamflow happens in a short-term period;
instead, the long-term low flow has not been resolved by precipitation. This suggests that
other elements are more likely to affect the deteriorated flow in PNW streams.
2.4.1.2: Attribution 2. Climate Change
Diverse elements of climate change due to anthropogenic effects are associated
with the declining surface flow and increased low flow periods in the PNW. The
elements of climate change include 1) greenhouse effect and increased air temperature, 2)
modified ocean-atmospheric patterns in the Pacific Ocean, and 3) frequent extreme
precipitation events.
First, Luce et al (2013) found that streamflow declines in the rivers of PNW are
more associated with anthropogenic climate change elements, such as the greenhouse
effect, land-use alteration, or groundwater pumping activities, than they are with a trend
19

of precipitation (Luce et al., 2013). They concluded that annual streamflow in the PNW
has shown marked declines while annual precipitation has not changed significantly.
This highlights climate change as a stressor on hydrology in the PNW (Luce et al., 2013).
Second, modified ocean-atmospheric patterns in the Pacific Ocean due to climate
change are associated with declining streamflow in the PNW. The Pacific Decadal
Oscillation, the El Nino Southern Oscillation, and the Pacific North American patterns
(Hamlet & Lettenmaier 2007; Luce & Holden, 2009) increase the seasonal disparity in
streamflow between dry and wet periods, mostly exacerbating low flow phenomena 13.
Lastly, a low flow period prolongs as streamflow decreases via frequent extreme
precipitation events, which result from a combined effect of heightened air temperature
and drier weather patterns from climate change. Historically, a substantially reliable
amount of precipitation and snowpack has replenished low flows in streams of the PNW;
many streams are glacier/snowmelt dependent in PNW (Pelto, 2011). Climate change
has threatened the natural recharge and storage regimes by changing the timing of
snowmelt and the amount of water available to streams (Fig. 9) (EPA, 2016). The
warmer climate contributes to earlier and more concentrated precipitation and snowmelt,
which can cause higher streamflow in wet seasons and lower flows in summer (Hamlet,
2010). In sum, the climate change and its effect on oceanic currents are highly associated

13

The oceanic climate change attributions explain the streamflow disparity in the PNW. The interannual
variability is linearly correlated with climate change variabilities realized through the Pacific Decadal
Oscillation (𝑟 = 0.33, 𝑝 < 0.001), the Pacific North American pattern (𝑟 = 0.3, 𝑝 < 0.001), and the El
Nino-Southern Oscillation (𝑟 = 0.28, 𝑝 < 0.001). Together they explain some (𝑟 = 0.37, 𝑝 < 0.001)
interannual variability in streamflow.

20

with extreme precipitation patterns and increased streamflow disparities: higher flows
during the wet season versus lower flows during the dry season.
Figure 9
Climate change effect on precipitation and low flow. Tohver & Hamlet, 2010; EPA,
2016.

Note. (left) Simulated changes in precipitation
stored as peak snow water equivalent (SWE).
Watersheds in PNW are characterized as rain
dominant (green), mixed rain and snow (red), or
snowmelt dominant (blue). The climate
warming in the PNW results in altering snowdominant watersheds into rainfall watersheds.
(right) Natural surface water availability during
late summer is projected to decline across most
of the PNW. The local direct runoff (shading)
and surface streamflow (colored circles) for the 2040s (compared to the period 1915 to
2006) are expected to decline, associated with the climate change effect.
2.4.1.3: Attribution 3. Groundwater exploitation
Groundwater pumping can explain much of the groundwater storage reduction
and consequent deterioration of low flow during dry periods. Excessive pumping
consumes, intercepts, and depletes groundwater and natural waterways, compromising

21

surface water ecosystems (Lambert, 2019). De Graaf et al. studied the deleterious impact
of groundwater withdrawals on reducing surface flow in agricultural regions of the globe
(Fig. 10; de Graaf et al., 2019). For example, about 15 to 21 percent of surface water in
the globe has already reached the ecological tipping point, such that the streamflow
cannot serve the usual ecological functions due to heavy groundwater pumping (de Graaf
et al., 2019). By 2050, the authors estimate that 42 to 79 percent of pumped watersheds
of major rivers in the globe will have crossed this tipping point (Graaf et al, 2019),
leaving the streams too dry to provide ecological functions, such as healthy habitats for
aquatic-dependent species.
In Pacific Northwest, the increased pumping and reduced surface flow have
caused harm to the anadromous fish populations (Hebert, 2016). In Eastern Washington,
groundwater extraction has already led to large reductions in groundwater storage over
more than 10,000 square miles (Pitz, 2016). Groundwater levels in Eastern Washington
have declined by more than 300 feet in some areas with deeper basalt aquifers (Burns et
al., 2019). Reduced groundwater storage and discharge (i.e., baseflow) greatly affects the
ecological function of a river system.

22

Figure 10
Modeled timing when an environmental flow limit has been or will be reached for the
first time in streams of the globe. Graaf et al., 2019

Note. (top) The first time at which environmental flow limits have been, or will be,
reached, by year, averaged per sub-watershed 14. Red denotes streams that have already
reached the flow limits; blue denotes the streams that are projected to reach the limits by
2010. (bottom) Global distribution of estimated first times at which environmental flow
limits have been, or will be, reached, under different projection models. Over half of the
studied streams are projected to reach flow limits around 2030-2045.
Groundwater pumping and its effect on reducing streamflow during a low flow
period are not limited to agricultural regions, such as the Eastern Washington region. In

14

Environmental flow limits refer to the streamflow at a level to sustain the ecological functions of a
stream.

23

Western Washington, increased groundwater pumping from population growth has
stressed the groundwater storage and surface flow, especially during low flow in the
summertime. Here, the increased groundwater pumping is assumed to directly reduce the
baseflow during dry seasons. Pitz (2016) argued that groundwater pumping may
deteriorate the summertime low flow and baseflow more than consequences due to
climate change (Pitz, 2016). Already, Western Washington groundwater dynamics (i.e.,
storage and discharges, baseflow) faces reduced annual recharge due to climate change
effects15. More extreme precipitation and drier low flow period imply that the amount of
groundwater recharge in dry season decreases. Streams under existing stressors will
experience an exacerbated low flow with increasing groundwater extraction.

2.5: Baseflow Recession in the Deschutes
2.5.1: What is Baseflow Recession?
The role of baseflow connecting the two water systems—surface water and
groundwater system—is especially vital during low flow periods due to prolonged dry
spell. The deterioration of baseflow, “baseflow recession”, is detrimental in a low flow
period when a surface stream is most dependent on baseflow from groundwater.
Groundwater pumping is an anthropogenic impact that converts the river from a
balanced flow to a predominantly losing stream (Fleckenstein et al. 2004). “Losing
stream” occurs when the uppermost level of groundwater, or “water table”, is lowered to
a level that groundwater no longer reaches to the surface streamflow (Fig. 11). When
15

Skagit River basin (Johnson & Savoca, 2011) and Chambers-Clover Creek watershed (Johnson et al.,
2011) show a 20% reduction in annual groundwater recharge to climate change effects.

24

groundwater is overly consumed by excessive pumping, the water table drops, and
groundwater is likely to disconnect from the surface flow system (Panza et al., 2015). In
that case, baseflow is no longer hydraulically connected nor contributing to the surface
flow, resulting in streamflow depletion (Barlow & Leake, 2012).
Figure 11
Schematic effects of pumping on a water movement. Barlow & Leake, 2012.

Note. (10-A) Under natural conditions, recharge at the water table is equal to discharge
(i.e., baseflow) at the stream. (10-B) Soon after pumping begins, all the water pumped by
the well is derived from groundwater storage. (10-C) As the cone of depression (red)
expands, the well begins to capture groundwater that would otherwise have discharged to
the stream. (10-D) The pumping rate of the well may be large enough to cause water to
flow from the stream to the aquifer, a process called “induced infiltration” of streamflow.
The stream then transforms into a “losing stream” (Barlow & Leake, 2012).
25

2.5.2: Baseflow Recession in the Deschutes River
Baseflow is a proxy for groundwater discharge (𝑄). Depending on the destination
of groundwater outflow, the groundwater discharge (𝑄) may take a form of “baseflow”
when discharged to surface stream or of “submarine groundwater discharge” when
discharged to sea water (Stieglitz, 2011). In this study, groundwater discharge (𝑄) is
used interchangeably with baseflow. The “baseflow recession period” refers to the
period of baseflow reduction. The highest point of recession (𝑄 ) is when the baseflow
starts to decline; the lowest point of recession (𝑄 ) is the baseflow right before when the
it starts to increase after continuous recession. The time of each recession event (𝑡)
varies with the length of each recession on the baseflow hydrograph (Fig. 12).
Figure 12
Components of baseflow. Streamflow data from NWIS; Precipitation data from NOAA.

180
160
140
120
100
80
60
40
20
0

𝑸𝟎

Recession
period

𝑸𝒕

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0

precipitation (in)

flow (cfs)

Surface flow and Baseflow (Q)

Time (days)

Note. Surface flow (green) is restored by base flow (blue) while there is no precipitation
(orange). The lowest point (𝑄 ) refers to the least amount of baseflow contribution,
indicating depletion in the groundwater storage or dry year.

26

Thurston County (2002: Thurston County, 2012) and Department of Ecology
(2007: Sinclair & Bilhimer, 2017) monitored the baseflow recession of streams in
Washington. The baseflow recession period (t) varies each year, depending on the
amount of precipitation and groundwater storage. The lowest point of baseflow (𝑄 ), the
least amount of baseflow contribution, in the Deschutes River showed a decline from
1945 to 2019 (Fig. 13). The declining trend of the 𝑄 during the recession period
indicates that the capacity of groundwater contribution has weakened or decreased.
Figure 13
Lowest Baseflow in the Deschutes. Streamflow data from NWIS. Baseflow separated
using WHAT.

Lowest flow trend (1945-2019)
180.0

y = -0.0439x + 83.004

160.0

baseflow (cfs)

140.0
120.0
100.0
80.0
60.0
40.0
20.0
1945
1947
1951
1953
1957
1959
1961
1964
1969
1974
1979
1984
1989
1993
1996
1998
2002
2005
2008
2010
2013
2016
2019

0.0

Time (years)

Note. The linear regression (dotted line) of the decline has a gradual negative coefficient
of -0.0439. This implies the future points of lowest baseflow (Q ) are likely to show
declining trend.
The mean baseflow of this set of streams declined from 293 cubic feet per second
(cfs) of the earlier period (1949-1963) to 258 cfs of the later period (1991-1997) (Sinclair
& Pitz, 1999). Between 1956 and 1994 there was a decrease in baseflow of 35cfs or 450
27

gallons per minute (gpm). The decreased baseflow represents the “lost” flow rate that
would have been available as baseflow discharge from the underground aquifer to the
surface flow. Such a baseflow recession trend explains groundwater storage depletion,
which may be attributed to climate change and human groundwater withdrawals.
Groundwater pumping is detrimental in stream ecology during low flow as it intercepts
the groundwater storage and causes baseflow recession (Barlow & Leake, 2012).
2.5.3: Groundwater demand
2.5.3.1: Reliance on Groundwater in the US
Groundwater is used for various purposes (Table 2). Among the different
purposes for groundwater withdrawals, public water supply and general domestic uses in
metropolitan and greater city areas have soared due to population growth (Konikow &
Kendy, 2005; Jakeman et al., 2016). In 2015, one-third of the US population (about 115
million people) relied on publicly or privately supplied groundwater (USGS, 2015).
Some major cities such as San Antonio, Texas, rely solely on groundwater for all their
public and privately supplied water consumption (USGS, n.d.). The interdependence of
groundwater and population has grown as the groundwater supplies both public wells
inside city water limits and outside in suburban or rural areas (Fienen & Arshad, 2016).
Table 2
Purposes of wells. Dieter et al., 2018.
Category
Public Supply Group
A
(Chapter 246-290
WAC)

28

Purposes
Water withdrawn by public and private water suppliers that provide
water to at least 25 people or minimum of 15 connections. Supplied
for domestic, commercial, industrial, thermoelectric-power, and public
water use (firefighting, street washing, flushing of water lines, and
maintaining municipal parks and swimming pools).

Irrigation
Commercial
Industrial
Livestock

Domestic General
Public Supply Group
B
(Chapter 246-291
WAC)

Water to assist crop and pasture growth, or to maintain vegetation on
recreational lands such as parks and golf courses.
Water for motels, hotels, restaurants, office buildings, other
commercial facilities, and military and nonmilitary institutions.
Water for fabrication, processing, and cooling in industries, such as
chemical and allied products, food, mining, paper, petroleum refining,
and steel.
Water used for livestock watering, feedlot, dairy operations, and other
on-farm needs.
Water used for indoor household purposes such as drinking, food,
preparation, bathing, washing clothes and dishes, flushing toilets, and
outdoor purposes such as watering lawns and gardens. Domestic
water use includes public supply water (A and B) and self-supplied
water.
Water serving fewer than 15 connections or 25 people per day. Most
Group B water systems use the groundwater permit exemption (RCW
90.44.050) (DoH, 2018).

Population growth has become the second-largest factor reducing groundwater,
after the agricultural purpose (Groundwater Facts, n.d.). The groundwater withdrawal
rate for agriculture has comparably slowed down while the withdrawal rate for the
urbanization and population growth has grown faster in recent years (Rosegrant & Cai,
2009). “Domestic use” categorizes the groundwater demand to meet growing population
and urbanization, and it comprises about 87% of the groundwater withdrawals for the
public supply (public supply A and public supply B, from Table 2; Dieter et al., 2018).
Self-supplied domestic water use is typically withdrawn from private sources, such as a
well, or captured as rainwater in a cistern (Dieter et al., 2018). Public and domestic water
use has comprised much of the total groundwater withdrawals in the past 20 years
(between 58% to 73%; Dieter et al., 2018). This may threaten the depleting groundwater

29

resources with projected increases in withdrawals or freshwater delivery from other
watersheds16.
2.5.3.2: Groundwater demand in Thurston County
With the third-fastest growing population in the nation (US Census Bureau,
2019), Washington State’s reliance on groundwater for domestic use through public
supply water and self-supplied wells increased between 1985 to 2010 (Lane & Welch,
2015). The domestic water use via public supply in Thurston County has increased at a
fast pace compared to other 19 Western Washington counties17.
Groundwater is the major source of freshwater use in the Thurston County
(85%)18. Most groundwater withdrawal is associated with domestic water use through
public supply and self-supplied wells. The public supply (blue) and general domestic
water use (orange) has consistently accounted for most of withdrawals (Fig. 14): 69% in
1985, 71% in 1990, 72% in 1995, 65% in 2000, 60% in 2005, 58% in 2010, and 73% in
2015. The groundwater withdrawal data below collected by USGS includes uncertainties
for wells exempted from recording withdrawal amounts (see section 2.5.4.2).

16

E.g., City of Bellevue purchases water from Seattle, delivering it for public supply from Cedar River and
Tolt River watersheds through water pipes (City of Bellevue Utilities, n.d.).
17
The rate of groundwater appropriation for Thurston County in 2010 was ranked as the 5 th highest in the
nation (Lane & Welch, 2015).
18
Thurston County’s total water withdrawals is estimated for 52.3 Mgal/day; the water source composites
groundwater with 44.2 Mgal/day (84.51%) and surface water with 8.16 Mgal/day (15.60%).

30

Figure 14
Groundwater withdrawal purposes in Thurston County (1985-2015). Withdrawal data
from USGS, 2018.

Time (years)

Groundwater Withdrawal Purposes of Thurston
County
2015
2005
1995
1985
0

10

20

30

40

50

60

70

80

90

100

Percent of withdrawals (%)
Public supply

General Domestic

Irrigation

Industrial

Aquaculture

Commercial

Livestock

Golf Courses

Mining

2.5.3.3: Growing demands in Thurston County
Population increase positively associates with the amount of groundwater demand
(Dieter, 2018). Thurston Regional Planning Council projected that the total population in
Thurston County will grow by over 25% by 2045 compared to the population in 2012
(TRPC, 2019)19 while some major cities, such as Olympia-Tumwater-Lacey urban areas,
are projected to have almost double the population of 1995 in 2045 (Fig. 15).

19

Population projection information in Appendix B.

31

Figure 15
Population trend and projection in Olympia-Tumwater-Lacey urban area. TRPC, 2019.

Olympia and Yelm have greater growth rates for their urban growth area (UGA)
of 1.2% and 4.0% when projected from 2017 to 2045, respectively, than within their city
limits (TRPC, 2019). This suggests the possibility that: 1) the groundwater pumping rate
will increase to supply water to the expanding cities; 2) individual wells for domestic
uses may increase in urban growth areas (UGAs), intercepting more groundwater via
pumping. UGAs are outside urban centers and designated to be "annexed into city limits
over 20 years" to accommodate urban growth (TRPC, 2019). As City limits expand to
meet projected population increases, resultant freshwater demands may depend
proportionally more on self-supplied domestic wells than public supply water. This is
concerning as self-supplied domestic wells are mostly exempted wells that are not
regulated for their withdrawals.
Lacey, Tenino, and Tumwater city project greater population growth in UGA of
1.8%, 3.5%, and 3.8%, respectively (Appendix B) that the population growth will mostly
32

occur within UGAs (TRPC, 2019). The number of dwelling units (Appendix C) projects
an increase in all parts of Thurston County that new development relying on self-supplied
domestic wells in rural areas is expected 20. This may result in more frequent interception
of groundwater through pumping in rural areas, which are not regulated for the
withdrawals under groundwater permit exemption (Chapter 90.44.050 RCW, 1945). The
unregulated wells’ withdrawals are not monitored or reported so that their hydrological
impact on lowering groundwater and surface water is difficult to identify. The issue of
sprawling unregulated wells and their effect of lowered streamflow elicited Hirst
Decision (2016), which enforced permit-exempt wells and monitoring rural development
(see 2.5.4.3).
2.5.4: Hydrological Impact of Wells in Deschutes River
2.5.4.1: Instream Flow
Baseflow input to the surface water system has hydrological and ecological
impacts on low flow during dry seasons. The Department of Ecology established
minimum water flows or levels for streams required to protect the resource 21 or preserve
water quality, referred to as “instream flows” (RCW 90.22.010) 22. The instream flows
intend to protect the river flows and limit new development or withdrawals that could
harm ecological streamflow. Also, the instream flows protect senior water rights that
were established prior to the instream flow (1980 for WRIA 13 Deschutes River Basin).
20

The number of dwelling units is in Appendix C
Instream values or merits for a healthy riverine ecosystem include fish, wildlife, recreation, aesthetics,
water quality, and navigation.
22
Instream flows for 26 watersheds in the Washington State differ from individual watersheds (or
Watershed Resource Inventory Areas, WRIA) and were established at different times. The instream flow
of the Deschutes River Basin (WRIA 13) was established in 1980 under the authority of Chapter 90.54
RCW (Water Resources Act of 1971), Chapter 90.22 RCW (Minimum Water Flows and Levels), and Chapter
173-500 WAC (later Resources Management Program) (Washington, 1980)
21

33

According to the “prior appropriation doctrine”, the senior water rights (i.e., pre-existing
water rights) are guaranteed before junior water rights do (“first-in-time, first-in-right”).
The instream flow protects senior water rights, such as Native Tribes’ sovereign water
rights, for their priority, as it restricts excessive groundwater pumping (Osborn, 2013).
The instream flows during low flow periods in the Deschutes River show the need
to protect water quantity. The instream flow is “closed” for additional uses from April
15th to October 31st (Fig. 16) to restrict further consumptive appropriations that would
harmfully impact instream values (Chapter 173-513 WAC, 1988), based on the basin
hydrology and surveys of fish production capabilities (Kavanaugh, 1980).
Figure 16
Instream flow of the Deschutes River Basin 23. Chapter 173-513 WAC, 1988.

Note. “Closed” denotes the period when all consumptive uses are restricted 24.
23

Chapter 90.22 and 90.54 RCW. 80-08-019 (Order DE 80-11), § 173-513-030, filed 6/24/1980.
“Water use” can take two forms, consumptive or withdrawal. Withdrawal water use refers to “water
diverted or withdrawn from a surface water or groundwater source”. Consumptive water use refers to
24

34

The low flow trend of the Deschutes has shown that the flow during the closed
period violates and falls below the instream flow levels (Fig. 17). The minimum required
instream flows during closed periods was set around 100 cubic feet per second (cfs)
(Kavanaugh, 1980). The surface flow shows that the lowest flows were near or lower
than 100 cfs, reaching as low as 40 cfs (for example, around 2003 and 2006 in Fig. 17).
This denotes that the low flow status during a closed period is questionable whether it can
sustain ecological streamflow and can preserve the instream values.
Figure 17
Trend of surface flow of the lower Deschutes River (1991-2019). Modified from
streamflow data from NWIS.

400

Note. The daily surface flow, or discharge, shows the average daily streamflow (blue
line). The median daily surface flow in the past 44 years shows a historical trend of
surface flow change (yellow line). The approved surface flow data (green line) and
provisional data (purple line) indicate an official period of surface flow record. Daily
surface flow (blue line) has exceeded and violated the wet and dry period instream flow
(denoted in red) since 1999.
“water use that permanently withdraws water from its source that water is no longer available and
removed from the immediate water environment (Water footprint calculator, 2018).

35

2.5.4.2: Permit-exempt Wells and Instream Flows
To protect the minimum instream flow in the Deschutes, consumptive water use
has been restricted. However, there are some exemptions to the instream flow rule. The
effect of additional consumptive water uses through exempted withdrawals has not been
clarified; however, they are still in use. Types of withdrawals that are exempt from
surface stream closure include domestic use wells for single residence and stock
watering, except for feedlot (Chapter 173-513 WAC, 1988). These domestic wells are
typically "permit-exempt" wells that do not require a procedural obligation to obtain
water use permits; however, they are still subject to the prior appropriation rule that their
use cannot hypothetically interrupt senior water rights. Most importantly, new permitexempt wells have been allowed in rural areas even though their groundwater extraction
has not been analyzed for a potential effect of reducing groundwater and surface water to
an unsustainable level (AGO, 1997). The continued withdrawal via permit-exempt wells
is a regulatory and ecological interruption of the senior instream flow, which has often
been violated (Fig. 17). Therefore, the potential impact of permit-exempt wells on the
low flow hydrology should be analyzed from a more precautionary respective.
2.5.4.3: Permit-exempt Wells’ Effects on Baseflow
While permit-exempt wells are intended for “small withdrawals”, the hydrological
impact of permit-exempt wells on the extent of groundwater reduction and baseflow
decrease has not been analyzed in the Deschutes River. Therefore, we should pay close
attention to some uncertainties regarding permit-exempt withdrawals as their impact is
not identified. Three considerations include 1) the possible increase in permit-exempt
wells in rural areas, 2) disparity of allowed withdrawals through permit-exempt wells and
36

public water use permit-exempt wells, and 3) the importance to understand the impact of
withdrawals—rather than consumptive uses—on the groundwater storage and baseflow.
First, permit-exempt uses may increase with projected population growth; their
withdrawals are not monitored and may reduce groundwater storage. As discussed, the
population increase in urban growth areas (UGA) in Thurston County (see section
2.5.3.3) may result in increased permit-exempt well constructions. Increasing permitexempt wells will result in uncertainties in groundwater management because of permitexempt wells not being monitored or restricted for their uses. Because the actual
withdrawals from individual permit-exempt wells are unknown, municipalities rely on
averaged withdrawal rates estimated from septic system use (Hansen, 2018). The
withdrawals via unregulated permit-exempt wells remain uncertain to estimate the precise
impact on the groundwater storage.
Second, recently established regulations on withdrawal allowances may not help
to solve groundwater depletion and baseflow recession during low flow. The Hirst
Decision25 directed counties to develop watershed plans that offset impacts from new
domestic permit-exempt wells. This includes setting a new withdrawable groundwater
amount depending on the individual watershed situation. Before the Hirst Decision, the
groundwater withdrawal per well was limited to a maximum annual average of 5,000
gallons per day (gpd). After the Hirst Decision, this maximum withdrawal amount
changed to 950 gpd, which may be curtailed to 350 gpd under declaration of a drought
(TCCP, 2018). The 950 gpd withdrawal applies to the small withdrawals for domestic,

25

Whatcom Cty. v. Hirst, 186 Wash, 2016.

37

industrial, and commercial uses; stock water is allowed for unlimited withdrawals. As
permit-exempt wells are generally not monitored, their future withdrawals remain as
uncertain as their current withdrawals.
The newly established withdrawal amount after the Hirst Decision, however, may
still overestimate the practical domestic water use and set the bar higher than our typical
consumption. Daily water consumption in the US estimated in 2010 was on average 79
gpd per person (Bracken, 2010). Equivalently, the withdrawal per dwelling was
estimated with 205 gpd with an assumption that 2.95 people live in a dwelling (Golder
Associates, 2015), sharing one permit-exempt well. Another study conducted in 2014
showed that the daily average was 111 gpd per person (The Associated Press, 2014), or
327 gpd from the same assumption of 2.95 people sharing a well. These daily average
water consumption per well (205 or 327 gpd) is much lower than the regulated maximum
withdrawals of 950 gpd (or 350 gpd under a drought scenario). Other uses, such as
irrigations or stock-water, may require extractions near 950 gpd or even 5,000 gpd, which
was the previous limitations on permit-exempt well withdrawals prior to the Hirst
Decision. On top of this, the stock-watering is allowed for an unlimited amount; these
curtails of 950 gpd (or 350 gpd) are not quite restrictive to permit-exempt well uses,
which was originally purposed for “small withdrawals” (RCW 90.44.050).
Third, the permit-exempt wells’ impact on the baseflow recession accounts for
their total withdrawal amount, rather than their consumptive use. Typically, when
quantifying the impact of withdrawals on the surface flow, consumptive use represents

38

the “impact” or the “lost” flow26. The consumptive use27 refers to the amount that is
completely used or lost from the surface system:
𝐶𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑣𝑒 𝑢𝑠𝑒 = (𝑊𝑖𝑡ℎ𝑑𝑟𝑎𝑤𝑎𝑙 𝑎𝑚𝑜𝑢𝑛𝑡) − (𝑅𝑒𝑡𝑢𝑟𝑛 𝑡𝑜 𝑔𝑟𝑜𝑢𝑛𝑑𝑤𝑎𝑡𝑒𝑟)
Consumptive use does not fully describe the impact of pumping on groundwater
loss; instead, total withdrawal amount associates with a direct reduction of baseflow and
affects baseflow recession. This is because the baseflow is a proxy of groundwater
storage that discharges to the surface water system (EPA, 2018). Therefore, the total
withdrawal amount of groundwater pumping wells will be a better index than
consumptive use to estimate the impact of groundwater withdrawals on the streamflow.
2.5.5: Consequences of Baseflow Recession
Baseflow recession refers to the phenomenon when the amount of baseflow
contributing to the surface flow reduces or recedes (see section 2.6.1). The baseflow
recession impacts the water quality as it associates with some water quality indices, such
as water temperature, dissolved oxygen, pH, and pathogen. Such an impact on surface
water quality affects the surface water—groundwater interaction within the hyporheic
zone, which serves as a desirable habitat environment for salmon and other anadromous
species.
2.5.5.1: Baseflow Function on Water Quality
Summer low flows affect rivers’ ecological functions on biotic and abiotic
conditions and aquatic species dependent on the flow. Potential negative impacts of low

26

Technical reports aiming to discern the impact of groundwater withdrawals on the surface flow utilize
the consumptive use instead of withdrawal amount as their subject (e.g., Golder Associates, 2015).
27
Return to groundwater can come from septic systems or irrigation through land or surface flow.

39

summer flows include higher water temperatures, low dissolved oxygen, and more
frequent diseases (Essington et al., 2010). Ecological functions during low flow largely
rely on baseflow contributions. Baseflow adds refreshing cold groundwater to summer
low streamflow (DoE, 2012). In reverse, baseflow recession can have devastating
ramifications on the river’s ecological functions including degraded water quality or
undesirable habitat environments.
A longitudinal survey on total maximum daily load (TMDL) shows the surface
water quality in the Deschutes River since 2003 (DoE, 2015). TMDL refers to the
“highest pollutant loads a surface water body can receive and still meet water quality
standard” (DoE, 2015). The mainstem Deschutes River is impaired by high water
temperature and low dissolved oxygen (DO), which affects the physiology and behavior
of fish and other aquatic life (DoE, 2015). The warmer stream provides less capacity to
hold oxygen within water molecules, entailing deficient oxygen and unbalanced organic
matters (e.g., high phosphorous or nitrogen 28) within the stream. High temperature
generates to degraded pH, which can impair the ecological function of the river. In the
following sections, we will discuss the reduced baseflow function on water quality.
2.5.5.1.1: Function 1. Lowering Stream Temperature
Low stream temperature is essential for aquatic species, especially anadromous
fish, such as salmon. Warm streams result in deteriorated water quality as it reduces the
stream’s capacity for dissolved oxygen level and other water quality standards, such as

28

Walczyńska & Sobczyk, 2017

40

pH or pathogen. During low flow in the summertime, the temperature in the stream
increases, and the baseflow contribution can positively lower the stream temperature.
Stream temperatures in the upper and lower Deschutes River are at a threatening
level to sustain healthy salmon habitats (Fig. 18). The mean stream temperature at the
upstream Deschutes River (near Rainier) was 10.56 °C (wet season 7.92 °C; dry season
15.83 °C). At the downstream Deschutes River (near Tumwater), the mean stream
temperature was significantly higher, at 11.71 °C (wet season 9.00 °C; dry season
17.14 °C). Compared to the standard stream temperature desirable to protect fish and
their habitats29, the stream temperatures during dry seasons in the lower Deschutes River
exceed the core summer salmon habitat standards (16 °C); if not, the maximum
temperature for salmonid spawning, rearing, and migrating (17.5 °C). However, the
difference between the lower stream temperature in the dry season, and the standard is
0.36 °C, which is a marginal gap that can be exceeded by increasing dry season stream
temperature.

29

The standards were estimated with 7-DADMax; a 7-day average of daily maximum temperatures should
not be exceeded more than once every 10 years on average.

41

Figure 18
Stream Temperatures and salmon habitat standard temperatures. Data from DoE, 2015.

Stream Temperatures in Deschutes River
(2017-2018)
20

17.5
1…

18

Temperature (°C)

16

14 Mean Stream Temp
12

(near Rainier, green),
10.56 °C

Mean Stream Temp
(near Tumwater, blue),
11.71 °C

10
8

Stream Temperature
(Deschutes River near
Rainier)
Stream Temperature
(Deschutes River near
Tumwater)
Max Temperature for Core
Summer Salmonid Habitat

6
4
2
0
wet season

dry season

Seasons

Max Temperature for
Salmonid Spawning,
rearing, and migration

Currently, the water quality of the Deschutes River is deteriorated below TMDL
standards. The stream temperature of the Deschutes River has exceeded the TMDL
standard, which deteriorated other water quality standards—dissolved oxygen (DO), pH,
fecal coliform bacteria, and fine sediment 30 (DoE, 2012; Wagner & Bilhimer, 2015).
Warm stream reduces the amount of soluble oxygen in the water and degrades ecological
conditions for riverine species and their habitats (Rounds et al., 2013). Enhancing
baseflow contribution during a low flow period was one suggested TMDL management
strategy (DoE, 2012; DoE, 2015). Improving baseflow from 20% to 40% has a potential
to decrease stream temperature by 0.3°C (Table 3), based on a scenario which evaluated

30

Clean Water Act 303(d)

42

the changes in baseflow due to anthropogenic influences (domestic exempt wells
construction) and climate change (DoE, 2015) (Table 3).
Table 3
Management action scenarios to reduce stream temperature of the Deschutes River.
Data from DoE, 2015.

Streamflow
temperature
reduction related to
Management
actions

Management actions
Restoring mature vegetation
Reducing Channel Width
Improving microclimate
Reducing headwater and tributary
temperature
Increasing Baseflow

Expected Temperature Change
- 4.5°C
- 1.3°C
- 0.7°C
- 0.4°C
- 0.3°C

The effect of increasing base flow is seen as a less powerful management action
than, for example, restoring vegetation, which is projected to reduce the stream
temperature by 4.5°C (Table 3). However, a report on recovering Coho salmon migration
on the Deschutes specified that the effect of the baseflow improvement should not be
treated as a single variable but with other variables (Cherry Shane Consultant, 2015).
This is because the enhanced baseflow contribution has a chain-effect that positively
affects other variables in the scenario (Table 3), such as improved microclimate or
lowered stream temperature (Cherry Shane Consultant, 2015). The improved base flow
yields cooler groundwater while flowing into the surface water system, which benefits
fish habitat sites or cool water refugia (Watershed science, 2004; Cherry Shane
Consultant, 2015).
2.5.5.1.2: Function 2: Hyporheic Zone, Salmon Habitat
Deteriorated water quality in the Deschutes streamflow has degraded habitat
environments for fish. The Deschutes River supports anadromous species, such as sea43

run cutthroat trout, coho, fall Chinook salmon, sea-run and winter steelhead 31
(Conservation & Lead, 2004; Cherry Shane Consultant, 2015). The coho salmon return
was once prosperous, however, it has markedly reduced since the 1980s in the mainstem
of the Deschutes River; two of the three coho brood lines in the Deschutes have
experienced a severe reduction or are “virtually extinct” in the past two decades
(Zimmerman, 2010).
Improved baseflow enhances hyporheic exchanges in subsurface water where
surface water and groundwater intermix (Wagner & Bilhimer, 2015). Hyporheic
exchange is the intermixed flow of groundwater and surface water, where cold
groundwater seeps into the surface water system and alleviates stream temperature and
improves oxygen exchange (Hayashi & Rosenberry, 2002). The baseflow movement
contributes to expanding and activating the hyporheic exchange and the zone. The
hyporheic zone (Fig. 19), where the hyporheic exchange occurs, is the “buffer” in the
subsurface water in shallow sediments and creates a desirable fish habitat with lower
stream temperature and abundant dissolved oxygen (DO) 32.

31

Anadromous species describes fish “born in freshwater who spend most of their lives in saltwater and
return to freshwater to spawn, such as salmon and some species of sturgeon” (NOAA, n.d.).
32
id

44

Figure 19
Hyporheic zone. Winter et al., 1998.

Note. The arrows denote groundwater flow between the underground aquifer, hyporheic
zone, and surface stream. The upward arrow denotes baseflow, which contributes from
the groundwater to the surface flow.
Under low flow circumstances, baseflow movement is critical in forming
hyporheic zones for fish habitats (WRIA 13, 2019). The volume of the hyporheic zone is
controlled by ambient groundwater flow (Singh et al., 2018), which is represented as
baseflow. The hyporheic exchange contributes to lower the stream temperature as cooler
baseflow enters into the surface water system. For example, Roberts et al (2008)
concluded that the existing depth of the hyporheic zone was projected to lower the
summer stream temperature by 5ºC in Black Lake Ditch and 7 ºC in Percival Creek above
the confluence with Black Lake Ditch (Roberts et al., 2008). In the Deschutes River
mainstem, doubling the baseflow is projected to lower the stream temperature by 0.9 ºC
(Roberts et al., 2008). In contrast, halving the baseflow is projected to increase peak
temperatures as much as 0.8 ºC (Roberts et al., 2008). These simulated TMDL
managements for the baseflow and hyporheic zone alterations indicate the baseflow is
45

positively related to lower and healthier surface streamflow, which facilitates better
habitat conditions (Roberts et al., 2012; TRPC, 2015).
The baseflow contribution is strongly related to improving water quality (e.g., low
stream temperature) and ecological functions (e.g., hyporheic zone formation, healthy
fish habitat). Groundwater pumping should be carefully modeled and monitored as the
withdrawal reduces groundwater storage, decreases flow and frequency of hyporheic
exchange, and degrades potential water quality.

2.6: Well Pumping Mechanism
2.6.1: Cone of Depression
A pumping well affects a stream by reducing groundwater levels and baseflow
input (Fig. 20). When groundwater is pumped, the tip of a well can create a gradient,
which intercepts surrounding groundwater flow that would have otherwise discharged as
baseflow to the surface water. When pumping rates are sufficiently high, declining
groundwater induces a ‘reverse’ flow from the surface water to the aquifer via
infiltration. This leads to streamflow depletion as water demand increases (Sophocleous,
2002), particularly during dry periods (Douglas, 2006).
Groundwater pumping generates storage reduction as well as groundwater flow
diversion. First, the pumping draws stored groundwater into the head of the well, which
results in the formation of a “cone of depression” (Fig. 20-a) (Heath, 1983). The water
level around the well begins to decline as the pumping continues, lowering the overall
water table and forming a new equilibrium (see section 2.6.2.1). The void space above
46

the water table is where surface water infiltrates and recharges; however, the complete
recharge is not available when withdrawals occur faster than natural recharges. Second,
the usual groundwater discharge through baseflow is reduced by well pumping, diverting
the groundwater flow, or induced infiltration (Fig. 20-b). In the initial phase, pumping
depletes the stored groundwater. As pumping continues and the water table lowers, the
groundwater discharge to the surface stream (baseflow) is drawn back toward the head of
well and begins to supply the withdrawal. Such continued supply from baseflow causes
“baseflow recession”, reducing the groundwater that otherwise would have flowed to the
surface stream and supplying further withdrawals (Barlow & Leake, 2012).
Figure 20
Cone of depression. Gleeson & Richter, 2018.

Note. Pumping lowers the water table (dashed line), forming a cone of depression (red
line), and induces infiltrating surface water back to the groundwater system.

47

2.6.2: Residual Depletion and Lag Effect
2.6.2.1: Renewed Equilibrium
The status of hydrologic equilibrium refers to the groundwater storage pursuing a
balance between recharge and storage (Theis, 1938). The lower water level throughout
the aquifer requires increased recharge to an extent equal to the amount withdrawn by the
well, leading to a renewed level of equilibrium in storage (Theis, 1938). Groundwater
budget theory provides a quantitative view on groundwater storage in balance (net
storage change=0): 𝑄 = 𝑑𝑆, where 𝑄 is groundwater discharge, 𝑑𝑆 is the change in
groundwater storage. This means that the groundwater reduction leads to a new and
lower equilibrium level.
2.6.2.2: Lowered Groundwater Table and Disconnection from Surface Water
The combined effect of reduced storage impacts the aquifer, both at the time of
pumping as well as after the pumping stops due to a “residual effect” (Healy, 1983).
When the amount of discharged groundwater due to the pumping effect is greater than the
recharged amount, the total groundwater storage reduces and forms the storage in
equilibrium. Ultimately, reduced groundwater storage affects the amount of baseflow
discharge, which consequently reduces the streamflow. This cycle of continuous
withdrawal, groundwater flowing back to aquifer, baseflow recession, and streamflow
depletion continue even after pumping ceases.
Depending on the depth and amount of pumping, location of wells, and current
groundwater storage condition, the magnitude of residual depletion varies. The bigger
the residual effect is, the longer the aquifer will take to recover from the loss even when
pumping ceases (Obergfell et al., 2019). This indicates that the effect of pumping does
48

not stop at the time when pumping ceases; rather, the lagging effect of pumping causes
continuous baseflow recession and surface streamflow depletion after pumping stops for
additional hours to years (Schneider, 2010). Thus, the groundwater availability should be
estimated in advance to when the streamflow depletion occurs.
2.6.3: Losing and Gaining streamflow
Losing surface flow is a final stage that occurs from groundwater pumping.
Groundwater depletion causes streams to transform into intermittently or persistently dry
streams33 (Fig. 21-B). Such transformation depends on whether the hydraulic connection
between surface water and the groundwater system remains (Barlow & Leake, 2012).
Figure 21
Groundwater depletion and losing surface flow. Barlow & Leake, 2012.

Note. (21-A) Losing stream: Streamflow has become a source of recharge to the
underlying groundwater system.
(21-B) Ephemeral stream: Low water table is disconnected from the surface flow so that
groundwater does not contribute baseflow to the surface water system.
33

Ephemeral streams are features that carry “only stormwater in direct response to precipitation with
water flowing only during and shortly after larger precipitation events” (Dorney & Russell, 2018).

49

2.7: Baseflow recession analysis
The recession curve (Fig. 22) explains a theoretical relationship between aquifer
structure (i.e., groundwater storage) and groundwater discharge (Thomas et al., 2013).
Baseflow recession analyses began with studies by Boussinesq (1877) and Maillet
(1950), who developed a theoretical quantification of recession slopes to understand the
physical groundwater flow mechanism (Thomas et al., 2013). The groundwater flow
involves the behavior of groundwater storage and discharge, and baseflow is a proxy for
groundwater discharge to streams (Rumsey et al., 2017). In this study, baseflow indicates
groundwater discharge in hydrograph recession analysis as most groundwater discharges
to the surface stream under a natural setting.
Figure 22
Recession Curve, period, and segment. Tallaksen, 1995.

2.7.1: Baseflow Recession Analysis Methods
For an aquifer with no external transfers (Thomas et al., 2013), the groundwater
budget theory describes the changing volume of storage (𝑆) over time (𝑡) with the inflow
50

and outflow of the groundwater system (Theis 1938):
𝑑𝑆/𝑑𝑡 = 𝐼(𝑡) − 𝑄(𝑡) − 𝑊(𝑡) − 𝐸𝑇(𝑡)

(1)

where 𝐼(𝑡) is recharge to groundwater (normally via precipitation), 𝑊(𝑡) is groundwater
withdrawal, 𝑄(𝑡) is baseflow, and 𝐸𝑇(𝑡) is evapotranspiration from the groundwater
table and stream (from plants). We assume that 𝐼(𝑡) = 0 during the dry summer days of
our recession periods. Also, we assume that 𝐸𝑇(𝑡) has a negligible impact on the
groundwater system during the baseflow recession period (𝑡) (Thomas et al., 2013).
Groundwater withdrawals, 𝑊(𝑡), describe the impact of groundwater pumping via wells
(see section 3.3.2.4.2).
Brutsaert and Nieber (1977) describe the change in storage (𝑆) over time due to
baseflow (𝑄) lost from the groundwater system (see Fig. 2).
𝑑𝑆/𝑑𝑡 = −𝑄 (2)
where 𝑑𝑆 is the change of groundwater storage (𝑆), 𝑑𝑡 is the change of time (𝑡), and 𝑄 is
discharge or baseflow in the research. Previous studies to characterize the groundwater
storage and discharge behaviors assumed a power-law relationship between baseflow, 𝑄,
and groundwater storage, 𝑆 (Boussinesq, 1904; Brutsaert & Nieber, 1977; Thomas,
2013):
𝑄 = 𝛼𝑆

(3)

where 𝑆 (𝑚 ) is groundwater storage within an aquifer volume, 𝑄 (𝑚 𝑑

, 𝑑 = 𝑑𝑎𝑦) is

groundwater discharge (or baseflow) to surface water, and α has units of inverse time
(𝑡

) and 𝑛 (dimensionless) are constants (Gan & Luo, 2013; Thomas et al., 2013).
51

Combining (2) and (3) and solving for 𝑑𝑄/𝑑𝑡 𝑜𝑟 𝑄(𝑡) leads to
= −𝑎𝑄

(4)

where 𝑑𝑄 is the change of baseflow (𝑄), 𝑑𝑡 is the change of time (𝑡), and 𝑎 and 𝑏 are
constant values to determine the degree of baseflow recession: 𝑏 = (2𝑛 − 1)/𝑛 and 𝑎 =
𝑛𝛼

/

(Thomas et al., 2013). The equation (4) replaces 𝑆 with 𝑄 by substituting equation

(3) into equation (2) (Brutsaert & Nieber, 1977; Eng&Milly, 2007; Thomas et al., 2013).
Possible solutions to (3) assume that 𝑄 is either a linear or a nonlinear function of
𝑆. When 𝑛 = 1, there is a linear relationship between 𝑆 and 𝑄 (𝑏 = 1); nonlinear case is
when 𝑛 is not 1 (𝑏 ≠ 1). Neither a linear or a nonlinear relationship can be generalized
in all aquifers because of the unique characteristics of aquifers and geologic traits. The
different aspects of an aquifer that affect the groundwater storage-discharge behavior
include watersheds that are glacier-dominant or rain-dominant, effects of climate change,
and heavy anthropogenic interruption via excessive pumping (Gan & Luo, 2013).
Therefore, understanding whether a watershed shows either linear or nonlinear behavior
between groundwater storage and discharge should occur prior to a baseflow recession
analysis. The linear or nonlinear models of the groundwater storage-discharge
relationship are compared and we choose the model that fits better to the natural baseflow
status, using linear regression analysis (Gan & Luo, 2013).
2.7.2: Linear or Nonlinear Relationship
We should understand how a given aquifer storage (𝑆) reacts to the baseflow (𝑄)
before identifying the impact of groundwater pumping (𝑊). The linear relationship (𝑛 =
1, 𝑏 = 1) between groundwater storage and discharge (or, baseflow, see Fig. 2) has been
52

widely used for numerous baseflow analyses (e.g., Brutsaert & Nieber, 1977; Thomas et
al., 2013). This assumes that the storage reacts in direct proportion to the discharge.
Vogel and Kroll (1992) studied 23 watersheds under a low flow status and determined
that groundwater showed a linear behavior (Vogel & Kroll, 1992). On the other hand, a
nonlinear model has gained attention as there has been significant human interruption on
hydrograph in recent years. Thomas et al. (2015) addressed the significance of applying
nonlinear equation while current streamflow and aquifer storage is substantially affected
by the pumping. These findings deny the traditional applications of linear equations and
imply the necessity to assess the aquifer system before applying the linear or nonlinear
analysis method.
2.7.3: Recession Constant (𝑲 𝒐𝒓 𝒂)
The recession analysis is a widely recognized method to estimate the baseflow
component to the stream hydrograph (Yang et al., 2018). Baseflow “recession constant”,
is a representative value of the recession analysis, which characterizes the interaction of
groundwater and surface water systems (Thomas et al., 2013). The recession constant
explains the rate at which baseflow recession (decreasing hydrograph) occurs in each
recession period. If the recession constant is bigger, the greater the degree by which
baseflow recedes.
A precedent study by Dupuit (1863) and Boussinesq (1877) found solutions for
linear and nonlinear groundwater discharge and aquifer storage relationships. The
Dupuit-Boussinesq equations (1904) describe groundwater flow in differential equations
governing flow in an aquifer, depending on how the aquifer behaves in response to
discharge-storage:
53

When 𝑏 = 1, the linear equation

= −𝑎𝑄 is solved by:
(5-1)

𝑄 =𝑄 𝑒
When 𝑏 ≠ 1, the linear equation

= −𝑎𝑄 is solved by:

𝑄 = 𝑄 (1 +

(

)

(5-2)

𝑡)

where 𝑄 is groundwater discharge at the time t, 𝑄 is the baseflow at the time of initial
recession occurrence (Fig. 23), 𝑡 is the time taken between 𝑄 and 𝑄 , and 𝑐 (5-1) and 𝑎,
𝑏 (5-2) are constants34. For convenience, the constant 𝑐 the is substituted for a
nondimensional constant, 𝐾 = 𝑒 , which may be used in place of c:
𝑄 =𝑄 𝑒

=𝑄 𝐾

Figure 23
Recession Curve, period and segment. Modified from Tallaksen, 1995.

𝑄

𝑄

Note. Discharge (y-axis) = 𝑄, Time = 𝑡.
34

Appendix D explains the nonlinear baseflow recession constants.

54

2.7.3.1: Nonlinear Recession Constant (𝒂)
The nonlinear recession equation (5-2) has two constants: 𝑎 (𝑚𝑚

𝑑 ) and 𝑏

(dimensionless). The nonlinear recession constant, “𝑎” in equation (5-2) depends on the
“physical dimensions and hydraulic properties of the aquifer” (Brutsaert & Nieber, 1977,
cited in Rupp & Selker, 2006). To solve the equation for the constant 𝑎, the value for 𝑏
is must be chosen. Numerous studies showed various values for 𝑏: Clark et al (2008)
found the relationship between storage and discharge during the recession is
approximately consistent, 𝑏 = 1; Gan & Luo (2013) argued 𝑏 = 0.25 with glacier- and
snowmelt-dominated basins (Gan & Luo, 2013); Tague and Grant (2004) showed a
negative value of 𝑏, which implies a hyperbolic storage-discharge relationship (Kirchner,
2009); Rupp and Selker (2006) found 𝑏 = −1 for early stages of recession and 𝑏 = 0 for
later stages (Rupp & Selker, 2006). Finally, Wittenberg (1999) analyzed the recession
curves of more than 80 streamflow gauge stations of an unconfined aquifer with an entire
watershed and found the mean value of 𝑏 as 0.49 (Wittenberg, 1999, cited in Wang &
Cai, 2009). We use 𝑏 = 0.5, following Wittenberg (1999), under the assumption that the
Deschutes River basin possesses the same hillslope (Harman et al., 2009). This is based
on the assumption that the groundwater storage deviates in a relatively negligible degree
within the same slope. With these assumptions, the nonlinear recession becomes
1+

.

𝑡

or, equivalently, −2 𝑙𝑛 1 +

𝑄

.

=

(Appendix D).

2.7.4: Baseflow Separation Method
As discussed earlier, baseflow contributes to streamflow along with direct runoff
(see section 2.3.2). We can directly measure the surface streamflow (e.g., USGS
55

streamflow gauge stations). In contrast, we can only estimate the baseflow through
separating the streamflow into “direct runoff” and “baseflow” via a separation method.
This is because groundwater seepage to the surface stream is invisible and highly
dependent on the geologic trait of aquifers, which determines the capacity of groundwater
interaction with the surface water.
There are two main baseflow separation methods. The graphical method focuses
on identifying “the points where baseflow intersects the rising and falling” surface stream
hydrograph (Fig. 24; Brodie, 2005). The filtering method focuses on the entire stream
hydrograph data to derive baseflow changes (Brodie, 2005). This filtering method
provides a reliable baseflow separation analysis in cases of a long period of record over
50 years (Brodie, 2005).
Figure 24
Components of a typical flood hydrograph. Brodie, 2005.

The web-based hydrograph analysis tool (WHAT) is a user-friendly tool to
separate baseflow from the streamflow, using two digital filters, BFLOW, and Eckhardt
filters (Lim et al., 2005). Here, both BFLOW and Eckhardt filters utilize a maximum
56

baseflow index (𝐵𝐹𝐼𝒎𝒂𝒙 ), which is the maximum value of long-term ratio of baseflow to
total streamflow (Lim et al., 2005). First, WHAT is an accessible public domain that
separates baseflow from USGS streamflow measurement data by using automated
hydrograph filters. Conceptually, the baseflow is an estimated portion of the surface flow
without direct runoff. On a hydrograph, the start and end point of the direct runoff
determines the portion of streamflow that is directly generated from the excess rainfall.
In contrast, a widely common baseflow separation program from USGS, HYSEP,
requires a great deal of “user intervention to prepare input data and run the program”
(Lim et al., 2005). In WHAT, the separated baseflow using a combined digital filter of
BFLOW and Eckhardt filters generates a high coefficient of determination (𝑅 )
compared with the manual separation of baseflow from streamflow. Lim, et al. (2005)
experimented and the filtered baseflow using BFLOW and Eckhardt filters showed a
comparable coefficient of determination of 0.83 and 0.9, respectively (Lim et al., 2005).
This indicates that the separated baseflow will simulate the natural baseflow if measured.
Lastly, I used a recursive digital filter to represent perennial streams with porous
aquifers (WHAT). A recursive digital filtering is a type of digital filter which assumes
that the outflow (𝑄) is linearly proportional to its storage (𝑆). This parameter is chosen
for the Deschutes River Basin as the study site is comprised of porous aquifers, rather
than other aquifer characteristics: a perennial hard rock aquifer or an ephemeral stream
with a porous aquifer. The Deschutes is not an ephemeral stream but is rather perennial.

57

2.8: Frequency Analysis
Frequency analysis can be used to understand the flow variability over time. The
frequency analysis explains how fast current streamflow status reaches a certain flow
standard. This differs from baseflow recession analysis in that the amount of recession is
identified through ‘time’, rather than streamflow reduction (e.g., baseflow recession
analysis). This temporal approach provides a different view to understand the impact of
groundwater withdrawals on the baseflow recession of the Deschutes River.
2.8.1: Low Flow Parameters in the Deschutes
The low flow characteristics of streamflow emphasize the ecological function of
the riverine environment from a perspective of quantitative hydrology. In Washington
state, the instream flow (see section 2.5.4.1) indicates the ecological function of
streamflow. The instream flow in Washington State is determined by different low flow
frequency parameter (i.e., 7-day, 10-years flow measurement, or 𝑄

,

. See section 2.8.2)

and the instream flow incremental methodology (IFIM) regarding available fish habitats
(DoE, 2010). As noted earlier, instream flow in the Deschutes River Basin provides
regulatory standards (i.e., “closure” of consumptive use). However, the instream flow
during a “closed” period does not provide a numeric guidance to compare the baseflow
recession under external impacts, such as climate change or groundwater withdrawals.
Therefore, this state regulation should include quantitative minimum streamflow during a
low flow period to parametrize streamflow, which is subject to various anthropogenic
impacts.

58

2.8.2: A Different Frequency Analysis in Washington State
One low flow analysis parameter, the 7-day, 10-year flow (𝑄

,

), monitors and

assesses whether streams in Washington State maintain minimally required streamflow
for stream ecology. A widely used low flow metric, 𝑄

,

, is defined as the lowest

average streamflow that recurs once every 10 years (Curran et al., 2012). Even though
the 𝑄

,

metric is a commonly used frequency parameter for the low flow analysis, it is

not very applicable to the purpose of this study to analyze past data and predict the future
baseflow recession patterns. An empirical study of statistical analysis on 7-day, 10-year
indices showed that the 𝑄

,

has weak predictability for future flow prediction (Stuckey,

2006); it had a higher standard error of prediction, which indicates that 𝑄

,

has a larger

deviation against the observed streamflow measurement. To predict the future baseflow
recession, a different frequency parameter, 𝑄90, is used (Gleeson & Richter, 2017).
The 𝑄90 refers to a 90% exceedance probability of a set of flows. The value of
𝑄90 is the flow rate which is exceeded for more than 90% of time during a certain
period. For example, the flow rate that is exceeded more than 9 years among 10 years of
time (90% of time) becomes the value for 𝑄90. The exceedance probability is a metric to
assess the frequency of streamflow against a certain standard. Depending on purposes,
the exceedance probability of streamflow can take different measurements other than
90%. In many practices, 𝑄90 is used to assess the low flow status as an ecological
parameter (e.g., presumptive standards, Gleeson & Richter, 2018).
2.8.3: Environmentally Critical Streamflow
De Graaf et al (2019) conceptualized the minimum streamflow as “Environmental
Critical Streamflow (ECS)”, which is required to maintain healthy ecosystems (Graaf et
59

al., 2019). The concept of ECS was derived from a groundwater “presumptive standard”
(Gleeson & Richter, 2017). The presumptive standard proposes a percentage-based range
around natural flow variability to assess the relationships between hydrologic alterations
and ecological responses (Gleeson & Richter, 2017).
The streamflow is at ‘risk’ that longer supports ecological functions when it
reaches or exceeds the ECS (red lines in Fig. 25). With continuous pumping,
groundwater and baseflow reduce and lower the surface streamflow during the dry
period. The streamflow transforms into a losing stream from a gaining stream when
withdrawals reduce the direct runoff of streamflow, which is recharged by rainfall. The
losing stream occurs when the depleted groundwater system is no longer connected with
the surface flow while the groundwater is being extracted (Fig. 25-B) Groundwater
reduction ultimately reduces streamflow, which will reach the environmental flow limit
(ECS) at a certain point. The time at which the ECS is reached differs depending on the
severity of low flow and the amount of groundwater withdrawals 35.

35

In Fig. 25, the red lines on the right diagrams indicate the time of when streams meet the
environmentally critical flow level, which indicates the stream is at risk of ecological unsustainability.

60

Figure 25
Continuous pumping and Streamflow reaching the environmental flow limit. Graaf et al.,
2019.

A

B

Note. (25-A) After pumping started at a moderate level (𝑞 starting at black dashed lines
on both graphs), the groundwater discharge (i.e., baseflow) starts to reduce. The
streamflow, however, stays as a gaining stream that groundwater storage can still support
the withdrawals.
(25-B) With higher groundwater withdrawals (𝑞 ), the time at which reduced streamflow
meets the environmental flow limit (ECS) is earlier than with a moderate withdrawal case
(25-A). The streamflow transforms into a losing stream with the pumping now intercepts
recharged streamflow as groundwater storage is limited.
2.8.3.1: Choice of the Time at which ECS is Impaired
The environmentally critical streamflow (ECS) is a time-sensitive value; the flow
which is exceeded 90% of the period of research. De Graaf et al (2019) estimated the
ECS as the 𝑄90 of monthly baseflow in major rivers in the globe over the past five-year
period (i.e., the flow at which is exceeded more than 54 months out of 60 months). Since
hydrographic changes occur over five to ten years (e.g., Pacific Decadal Oscillation has
61

10 years of recurrence), any shorter period than five years may not reflect significant
differences in low flow. I adopt this method for the ECB of the Deschutes River since
the total study period is similar and long enough: 1954-2069, 116 years.
The ECS is used to assess the impact of groundwater withdrawals of wells (𝑊) by
comparing when the ECS is lowered to a certain degree by pumping. The natural ECS is
the 𝑄90 value of a five-year period. The impacted ECS is calculated from a baseflow
recession analysis which incorporated the impact of withdrawal (𝑊). The two predicted
ECS (natural versus impacted) scenarios are compared to see if the ECS from the
impacted baseflow comprises more than 90% of the natural ECS. The 90% composition
is derived from the “method of a presumptive standard” (Gleeson & Richter, 2017):
“High levels of environmental protection will be provided if groundwater pumping
decreases monthly natural baseflow by less than 10% through time” (Gleeson & Richter,
2017). In other words, the withdrawal impact should comprise less than 10% of the
natural Q90 to be ecologically sustainable baseflow.
“Localized baseflow recession analysis” can determine the time when the
impacted ECS baseflow exceeds 10% of the natural ECS value. Even if the impact
exceeds more than 10% of the baseflow, it must continue for some time to cause
“unsustainable” or “impaired” baseflow. To calculate the standard duration of prolonged
impaired baseflow, I developed a simple statistical calculation using composition
function (𝐶):
𝑥∁𝑦 = 0.01

62

(6)

where 𝑥 is the average days of recession, 𝑦 is the number of consecutive days determined
to assess the impact exceeded the natural 𝑄90, and ∁ is a function for combination, a
selection of items from a collection when the order of selection does not matter (Mazur,
2010). Here, the value for 𝑥 can be found from baseflow recession data. The value 0.01
indicates a 1% probability for 𝑦 number of successive days occurs to have lower value
(here, streamflow) than the 𝑄90 value (Graaf et al., 2019). The dependent variable (𝑦)
will then assess the ECS of impacted baseflow from withdrawals in the Deschutes River.
2.8.3.2: Environmentally critical baseflow (ECB)
Environmentally critical streamflow (ECS) conceptualizes the minimum
streamflow during low flow, addressing the ecological requirement in quantitative
streamflow. For the Deschutes River where baseflow dominates the low flow (see
section 2.3.3), the minimum streamflow should account for the baseflow contribution as
the main criterion. In this case, the ECS for this study transforms into ECB, or
“environmentally critical baseflow”. The ECB will enable an analysis of baseflow trends
and recessions since it accounts for the baseflow as the analysis subject.

2.9: Conclusion
Attention toward the relationship between increased groundwater withdrawals
(𝑊) and hydrologic impact on surface streamflow (see section 2.7.1) has soared in recent
decades (Wang & Cai, 2009; Thomas et al., 2013; Gleeson & Richter, 2018; Graaf et al.,
2019). The impact on groundwater reduction via pumping and consequently lower
surface streams is more deleterious during dry seasons when streams are already under

63

low flow stress. Many global streams have already lost their ecological functions and
instream values due to severely lowered streamflow (Graaf et al, 2019). In the ‘wet’
PNW, many streams have experienced continuously lowered streamflow in low flow
periods despite ample precipitations in wet seasons (Georgiadis, 2018). Low flows in
PNW are associated with climate changes and groundwater withdrawals, both of which
exacerbate reduced baseflow (𝑄) inflow to the surface water system during dry seasons.
Less baseflow inflow, or baseflow recession, is closely related to lowered groundwater
storage (𝑆), lower surface flow, degraded water quality, and unsustainable fish habitat
environments.
The baseflow recession analyzes low flow characteristics and trends of a stream
during dry periods. The baseflow contribution (𝑄) largely depends on the groundwater
storage (𝑆), which implies that groundwater storage status can be analyzed through
baseflow recession trends and patterns. Many empirical studies have started to
incorporate the impact of groundwater withdrawals on the baseflow recession; the
withdrawal (𝑊) is now an essential variable in the differential equation (e.g., equation 1).
The baseflow recession slope, or the recession constant 𝐾 for a linear, or 𝑎 for a
nonlinear aquifer), represents the impact of groundwater withdrawals on the baseflow
recession. The baseflow recession constant analysis enables us to predict future trends of
baseflow during a low flow period. This is useful in many streams in the PNW which
depend largely on the baseflow contribution in dry seasons.
A frequency analysis explains how often streamflow falls below a certain
streamflow standard (e.g., environmental flow limit, 𝑄

,

) within a certain period. The

frequency analysis of low flow is a different tool to understand the baseflow recession
64

from a perspective of time36. While baseflow recession analysis provides how much
baseflow will be lost out of the system, the frequency analysis explains how early (in
time) the streamflow will reach a hydraulic threshold. The “environmentally critical
streamflow” (ECS, or environmentally critical baseflow, ECB) describes how streams
with perpetuated groundwater withdrawals will inevitably reach thresholds that will harm
the ecological functions of streams.
Using baseflow recession analysis and frequency analysis, I will analyze low flow
characteristics and trends of a stream in the PNW, the Deschutes River. A focused study
on the relationship between anthropogenic groundwater exploitation and baseflow
recession will guide a sustainable groundwater resource management in Washington
State for future generations.

36

E.g., reduced groundwater storage, lowered surface flow, reduced baseflow contribution to the surface
water system

65

Chapter 3: Methods

3.1: Roadmap
The Methods part has two sections: Data description and Formula development.
The ‘Data description’ section describes methods to obtain and analyze 1) streamflow, 2)
baseflow separation and selection, and 3) well data. The ‘Formula development’ section
has three sequential steps to analyze the baseflow recession. The first step will analyze
baseflow recession and generate recession constants to describe relationships between the
starting and ending points of baseflow recession periods. The second step will predict
future baseflow contributions to the surface streamflow using the baseflow recession
constants derived from the first step. The third step will identify the impact of wells’
groundwater withdrawals by finding the time at which the baseflow recession reaches
environmentally critical streamflow (ECS). The difference in time of ‘natural’ baseflow
and ‘impacted’ baseflow (due to withdrawals) represents how much groundwater
pumping has an impact on baseflow recession.

3.2: Data Description
3.2.1: Basic Concept of Data Analysis
The goal of our study is to understand the impact of groundwater pumping on the
reduced groundwater contribution to the surface water, or baseflow, of the Deschutes
River (Fig. 26). Under natural conditions, groundwater flows into the surface stream and
maintains minimum flow when there is no rainfall to recharge the stream. This
groundwater inflow can be intercepted by groundwater withdrawals through water
66

pumping wells. The interactive relationship between groundwater and surface water via
baseflow will allow us to assess whether current groundwater management is sustainable
and ecological.
Figure 26
Groundwater withdrawals and baseflow. Modified from Grannemann et al., 2000.

baseflow

Withdrawal(W)
baseflow

Note. This diagram shows a baseflow contribution from groundwater to surface water
under ‘natural circumstances’ (26-A) and under an ‘impacted’ condition (26-B). The
blue arrows denote the groundwater contribution. The size of the blue arrows signifies
different amounts of groundwater contribution to the surface flow. The volume of
baseflow into a stream varies depending on the amount of groundwater contribution. The
red arrow denotes the groundwater withdrawal through pumping.
3.2.2: Selecting a Streamflow Gauge Station
Streamflow data on the main stem of the Deschutes River was obtained from
“USGS Current Water Data for Nation” (USGS, n.d.). In the Deschutes River Basin, two
67

USGS streamflow gauge stations record continuous streamflow: one near E street in
Tumwater (USGS 12080010) and one near the city of Rainier (USGS 12790000). The
Tumwater Falls gauge station is in the lower stem of the Deschutes River (river mile,
RM, 2.4). This lower gauge station in Tumwater represents the impact of groundwater
withdrawals via wells better than the upper station (RM 25.9 near Rainier) (Kimbrough et
al., 2005). Located at a lower elevation, the lower gauge station can catch the hydraulic
impact of groundwater withdrawals from higher elevations. For this reason, I selected
the Tumwater Falls gauge station to represent the baseflow change under natural and
impacted conditions37.
3.2.3: Baseflow Separation and Selection
‘Baseflow’ and ‘direct runoff’ constitute total surface flow (Fig. 27; baseflow +
direct runoff = surface flow). I separated baseflow from the surface flow using “Webbased hydrograph analysis tool (WHAT)” (see section 2.7.4). A hydrograph shows
change in the hydrologic variables (e.g., streamflow, baseflow) over time.

37

The Tumwater gauge station (USGS 12080100) measured streamflow from 1945 to 2019. The data is
not continuous that there are missing periods: from 1955 to 1956 (2 years) and from 1964 to 1990 (27
years). The streamflow data during these missing periods are predicted using Interpolation in order to
treat the data of the whole period as continuous.

68

Figure 27
Surface Streamflow Components.
Streamflow data from NWIS streamflow gauge station USGS 1280010 near Tumwater.

Streamflow and Baseflow (lower Deschutes River, 2018)
2500

Flow (cfs)

2000
1500
1000
500
0

Time (days)
streamflow (cfs)

base flow (cfs)

Note. This chart displays a hydrograph of streamflow (blue) and baseflow (orange)
between January 1st, 2018 to December 31st, 201838. The streamflow hydrograph
encompasses the baseflow part (orange) along with direct runoff (blue area without the
orange area).
Only selected periods of baseflow data were utilized for the baseflow recession
analysis. First, I selected a dry season, from June to October, when the lowest
streamflow occurs and baseflow constitutes most of the surface flow. Second, only the
dates that show declining “three-day average moving streamflow” were selected to
highlight the baseflow recession (Vogel and Kroll, 1996). The three-day average
baseflow movement is the averaged flow rate of three days, which was calculated for
each day39. Then, I selected sets that had a minimum of 10 days of recession (Fig. 28)

38
39

Streamflow data obtained from USGS Current Streamflow database Water Watch (USGS, n.d.)
Example of three-day average moving streamflow in Appendix E

69

(Kirchner, 2009). This enabled more substantial analysis with data that showed recession
trends because I eliminated some days with the increasing flow in the hydrograph during
selected dry months. The data used for the recession analysis incorporated these
conditions (three-day average decline, minimum 10 days recession).
Figure 28
Baseflow data description and selection. Streamflow data from NWIS.

Baseflow Data Selection
140.00
120.00

Recession period

1.5

Recession period

100.00Recession period

1.3
1.1
0.9

80.00

0.7

60.00

0.5

40.00

0.3

20.00

0.1

0.00

-0.1

Precipitation (in)

3day average baseflow (cfs)

160.00

Date

Note. This hydrograph shows selected baseflow recession data during the summer of
2004 in the Lower Deschutes River. Three-day average baseflow movement (cfs, cubic
feet per second): blue marker and blue line. Precipitation (in, inch): orange column.
Recession periods: black arrows. Each recession period is more than 10 days.
3.2.4: Well Data
3.2.4.1: Location
Well data is required to estimate the impact of groundwater withdrawals on the
reduced baseflow. The amount of well pumping is the ‘impact’, which is the lost amount
of groundwater storage from an aquifer. Lost groundwater storage means less baseflow
inflow from the groundwater to the surface stream. The impact of groundwater
70

withdrawals is more pronounced during a low flow period when there is little to no
precipitation to recharge the surface flow system.
The secondary well data was collected from the Thurston County Water Planning
department (Thurston County Water Planning, 2019). The data included some
groundwater pumping wells and their withdrawal amounts in Thurston County, which
had hydraulic connectivity to the surface flow of the Deschutes River (Hansen, 2018). I
separated wells based on through which aquifers the wells pump groundwater: either
unconsolidated or consolidated rocks of the Puget Sound aquifer 40 (Wallace & Molenaar,
1961) (Table 4). The wells located where unconsolidated rocks are revealed on the
surface have a direct hydraulic connection to the surface stream of the Deschutes River.
Using the ArcGIS Online program (AGOL), I selected wells that were located on
unconsolidated aquifer layers (Qa, Qad, Qgd in Table 4) in order to understand their
impact on lowering baseflow and surface streamflow (Fig. 29). On the other hand, wells
located on consolidated aquifer layers (Tm, Tv(c), Tn in Table 4) were excluded from the
analysis as I assumed these wells pumped groundwater from confined aquifers, which
were not hydraulically connected with the surface flow of the Deschutes River.

40

Unconsolidated sand and gravel aquifers have intergranular porosity, which enables groundwater flow.
Glacial deposits of coarse gravel and sand are permeable medium. The consolidated layer includes high
volume of clay and silt along with some sand, pebbles, cobbles, and boulders. High density in clay and silt
generates the aquifer to be confined and impermeable that groundwater flow is limited within the
consolidated aquifers.

71

Table 4
Aquifer layers in Deschutes River Watershed. Schuster, 2015.
Geolog
ic code

Included

Excluded

72

Geologic unit

Geologic Description
Moderately sorted deposits of cobble gravel,
pebbly sand, and sandy silt along rivers and
streams. Also includes alluvial fans, common
particularly where streams reach the coastline.
Surfaces generally unvegetated.
Till and outwash clay, silt, sand, gravel, cobbles,
and boulders deposited by or originating from
continental glaciers; locally includes peat,
nonglacial sediments, modified land, and artificial
fill

Qa

Quaternary
alluvium

Qgd

Pleistocene
continental glacial
drift

Qad

Pleistocene alpine
glacial drift

Till, outwash, and glaciolacustrine sediments;
locally includes loess, talus, and lacustrine
deposits

Tv(c)

Tertiary volcanic
rocks, Crescent
Formation

Siltstone, sandstone, and conglomerate;
fossiliferous, concretionary, and carbonaceous

Tm

Tertiary marine
sedimentary rocks

Tn

Tertiary nearshore
sedimentary rocks

Lithofeldspathic or feldspatholithic sandstone and
siltstone; common claystone, shale, and mudstone;
minor conglomerate and breccia; locally
tuffaceous; local basaltic sandstone and poorly
sorted basal conglomerate.
Siltstone, sandstone, and conglomerate;
fossiliferous, concretionary, and carbonaceous

Figure 29
Aquifer layers in Deschutes River Watershed – Included or Excluded.
Map created using ArcGIS Online. ESRI ArcGIS Online Layer sources: WSDOT, 2012;
Bilhimer, 2014; City of Tacoma GIS, 2019.

Note. The “Included geologic layers” (Qa, Qad, Qgd) represent the geologic scope of the
Deschutes Watershed that incorporates wells that overlie these layers. The “Excluded
geologic layers” (Tm, Tv(c), Tn) represent the geologic scope where wells overlying on
these layers are excluded from the study area.
3.2.4.2: Calculating Withdrawals
In order to calculate the annual withdrawal amounts, I used three steps to sort the
wells, add all wells’ withdrawal by each year, and multiply the annual withdrawals by the
wells’ lifetime to obtain the cumulative withdrawal amount.

73

3.2.4.2.1: Yearly Withdrawal Amounts
First, the wells and withdrawal amount were sorted by years to understand the
yearly trend of the groundwater pumping amount. This applies to all permitted wells that
had known withdrawal rates.
I calculated the total withdrawal amount as of a given year by multiplying the
rates by the well’s lifetime. The cumulative withdrawal at any (𝑦 ) is then the sum of
withdrawals (𝑥 ) in previous years (𝑖) up to the year of interest (year 𝑘):

𝑦 =

𝑥

The starting year of the analysis was fixed at 1945 (the starting year of the baseflow data
record). The result of this cumulative sum solved for 𝑦 will be the total withdrawal up
to year 𝑦s, for example:
𝑦 = 𝑥 , 𝑦 = 𝑥 +𝑥 , 𝑦 = 𝑥 +𝑥 +𝑥 , … , 𝑦 = 𝑥 +𝑥 +𝑥 +⋯+ 𝑥
The well withdrawal data included wells from 1860 to 2019. I used Thurston
County’s well withdrawal data as a variable (𝑊) in my baseflow recession analysis,
which is 𝑥 from above. The baseflow data existed from 1945 and the starting point of
the withdrawal data should align with the same starting year (1945). In order to include
the total impact from all wells, the withdrawal data preceding 1945 (1860-1944) was
included as a ‘base’ withdrawal; the base withdrawal was included in the following
year’s withdrawal amount; for example:
𝑦

74

= (𝑥

+𝑥

+⋯+ 𝑥

)+𝑥

where the withdrawal amount for the year 1945 involves all the preceding withdrawals.
3.2.4.2.2: Permit-exempt Wells Withdrawal
Second, the withdrawal amount was calculated for the wells that had measured
pumping rates or estimated for the other wells that do not have recorded withdrawal rates.
All wells were categorized into two groups: permitted or exempted wells, depending on
whether the withdrawal rates were known or unknown, respectively. Permitted wells are
the wells that acquired groundwater permits to pump groundwater from the Department
of Ecology; exempted wells (hereafter “permit-exempt”) did not require permits as their
withdrawals were expected to be “small” and considered to have an insignificant impact
on surface water (DoE, 2015). From earlier sections, recall that exempt wells, however,
may pump up to 5,000 gallons per day.
A majority of groundwater withdrawal in the study area of the Thurston County
was attributed to domestic and public supply purposes. The public supply wells were
divided into group A and B depending on the septic connection system (DoH, 2018);
Group A wells were permitted while group B wells were mostly permit-exempt wells.
Also, domestic wells, referring to the water supplies to single or group homes, were
exempted and included in the permit-exempt well. Over half of total the withdrawals
were comprised of permit-exempt wells, which were mainly domestic and public supply
group B wells (Fig. 30).

75

Figure 30
Purposes of groundwater withdrawals in Thurston County.
Well withdrawal data from Thurston County Water Planning.

Livestock,
3 Mgpd
Fish propagation,
11 Mgpd

Groundwater Withdrawals (2019)
Industrial,
2 Mgpd

Commercial,
1 Mgpd
Wildlife+Rail+Recreation,
< 0 Mgpd

Irrigation,
24 Mgpd
Public Supply A,
37 Mgpd

Domestic+Public Supply B,
87 Mgpd

Note. Mgpd: million gallons per day (Mgpd).
3.2.4.2.3: Yearly Cumulative Withdrawal
Third, I added the yearly estimated withdrawal amount by multiplying the
withdrawal rates to the well’s lifetime, which produced the ‘impact’ of wells. The impact
of wells is the lost amount of groundwater that would have been a potential baseflow
contribution to the surface stream. The total withdrawal amount of a certain year was the
cumulative withdrawal sums of the years in the past and the withdrawal amount of the
very year; for example, the withdrawals in 1946 were the summation of withdrawals of
1945 and 1946. This assumed that all wells from the well data were “active” wells that
had been pumping groundwater since the year they were constructed (Hansen, 2018).
After calculating the total withdrawal amount of all wells in the study area of
Thurston County, I will next use this as the withdrawal impact to calculate the baseflow
76

recession of the lower Deschutes River. The future withdrawal amount was projected to
increase in Thurston County41 (TRPC, n.d.). The estimated future withdrawals are
expected to increase with population growth 42. The estimated future withdrawals will
then be used to 1) test baseflow recession models (see section 3.3.2.4) and 2) assess
future baseflow recession against the environmentally critical streamflow threshold (see
section 3.3.3.1).

3.3: Formula Development
3.3.1: Step 1. Baseflow Recession Analysis
Baseflow describes interconnected hydrology between groundwater and surface
water systems. A baseflow analysis is useful to understand the low flow period of a
stream when groundwater contribution (i.e., baseflow) dominates the surface flow. Low
flow, again, refers to the period when groundwater contribution governs the surface
streamflow as there is little to no precipitation input on the stream (Stuckey, 2006). The
change in the quantity of baseflow should be carefully analyzed during the low flow
period since surface flow relies mostly on baseflow to maintain ecological flow for
aquatic species and other ecosystem functions. The reduction in baseflow, referred to as
“baseflow recession”, delineates the decreasing patterns of groundwater discharge
(baseflow) and groundwater storage (groundwater in aquifers) in a metric relationship.

41

Population changing rate = (Population projection in 2025)/(Population in 2015)
Estimated future withdrawals = (Population changing rate 6) * (Cumulative Withdrawal Total of the
withdrawals from the closest year)
42

77

To characterize the baseflow recession pattern, I employed the Boussinesq-Dupuit
equation (1904, cited in Hall, 1968). Reviews by Hall (1968) and Tallaksen (1995)
explained how the Boussinesq-Dupuit equation was developed through model
experiments and case studies. The baseflow recession assumed a power-law relationship
between baseflow (𝑄) and groundwater storage (𝑆) (Brutsaert & Nieber, 1977) 43. The
baseflow recession patterns were categorized into two groups: linear or nonlinear
relationships (Tallaksen, 1995). The linear relationship assumed that the groundwater
storage (𝑆) changes in proportion to the baseflow (𝑄). The nonlinear relationship
assumed that the groundwater storage (𝑆) changes proportional to the power of the
baseflow (𝑄).
3.3.1.1: Model Development
To characterize the relationship between the groundwater storage (𝑆) and
baseflow (𝑄), I adopted the simple decay model (Hall, 1968; Brutsaert & Nieber, 1977,
cited in Thomas et al., 2013), which compared the flow rate at the beginning of the
baseflow recession (𝑄 ) to that at the end of the baseflow recession (𝑄 ) after a certain
period of time (𝑡) passed. The 𝑄 and 𝑄 represent the groundwater discharges at
different times, either at the beginning or end of recession periods. This will either be
linear or nonlinear, such as the relationship between the groundwater storage and
discharge. Using 𝑄 and 𝑄 , we can predict the pattern of groundwater discharge patterns

43

In literature, 𝑄 is “groundwater discharge”, which refers to the amount of groundwater released or lost
from the groundwater system. In this study, 𝑄 represents “baseflow” as it means the amount of
groundwater contributed or “lost” to the surface water system. This study focuses on the low flow period
when there is hardly other components in the streamflow or groundwater discharge than baseflow. I can
estimate the baseflow through observed streamflow separation that baseflow provides a physical value to
the concept of groundwater discharge.

78

without having to calculate total groundwater storage, which is nearly impossible without
a precise groundwater modeling (Thomas et al., 2013).
I assume that the selected recession periods have no external input from
precipitation (𝐼) and negligible evapotranspiration (𝐸𝑇) (see section 2.7.1). Brutsaert and
Nieber (1977) defined the relationship between the change in storage (𝑆) over time as the
amount of baseflow (𝑄) in a negative form, which indicated the direction of groundwater
being lost from the groundwater system. Both linear and nonlinear relationships between
𝑆 and 𝑄 assume a simple differential equation for baseflow (𝑄), when 𝐼 = 0, 𝐸𝑇 = 0, and
𝑊 = 0 (see section 2.7.1):
(4)

= −𝑎𝑄

3.3.1.1.1: Linear Baseflow Recession Model
The linear relationship between groundwater storage-baseflow is the case with
𝑏 = 1. The solution is a simple exponential decay (Boussinesq, 1877; Hall, 1968):
𝑄 =𝑄 𝑒

/

(7)44
(8)

𝑄 =𝑄 𝐾
where 𝑄 (𝑚 𝑑 ) is baseflow at time 𝑡, 𝑄 (𝑚 𝑑

) is the value when baseflow starts to

show a decline on hydrograph, and 𝑐 is a baseflow constant with the dimension of time.
The equation (8) defines (7), the recession constant 𝐾 = 𝑒

/

. The baseflow recession

constant (𝐾) indicates the groundwater storage (𝑆) behavior against the baseflow (𝑄). In
other words, this form of solution for 𝑄 assumes that the baseflow consistently decreases

44

The equation (5-1) (see section: 2.7.3) and the equation (7) are identical but explained in section 2.7.3.

79

at a constant rate (𝐾) during the recession period (Yang et al., 2018). The estimation of
𝐾 is required for many hydrologic models as it describes the interconnectivity between
groundwater and surface water system (Thomas et al., 2013). In sum, the equation (7)
and (8) describes the exponential decay of 𝑄 assuming a linear relationship between 𝑄
assuming a linear relationship between 𝑄 and 𝑆.
3.3.1.1.2: Nonlinear Baseflow Recession Model
Followed by the equation (4) with a case when b is not 1 (𝑏 ≠ 1) leads to a
nonlinear baseflow recession; groundwater storage (𝑆) changes in a nonproportional way
against the discharge (𝑄) (Wittenberg, 1999, Gan & Luo, 2013). If we assume a linear
power-law relationship between 𝑄 and 𝑆 (𝑏 ≠ 1), the solution for 𝑄 takes the form:

𝑄 = 𝑄 (1 +
where 𝑎 is a constant (𝑚𝑚

(

)

𝑡)

(9)45

𝑑 ) and 𝑏 is a constant (dimensionless) which describes

the power-law relationship between 𝑄 and 𝑆. In a nonlinear groundwater storagedischarge relationship, the degree of baseflow recession cannot be represented with a
single constant value. In this case, the hydrograph curve is not a straight line that there
cannot be a single value of slope (it is not a straight line for the exponential decay, either,
unless we take the logarithm form). Therefore, nonlinear constant values (‘𝑎’ and ‘𝑏’)
represent the storage property, which describe to which degree the baseflow (𝑄) reduces
over time (Rupp & Selker, 2006).

45

The equation (5-2) (see section: 2.7.3) and the equation (9) are identical but explained in section 2.7.3.

80

Many studies explore the values for the constant 𝑏, or the slope of baseflow
recession (see section 2.7.3.1). Wittenberg (1995) found 𝑏 = 0.5 in 23 unconfined
watersheds (Wittenberg, 1999). Fixing 𝑏 enables us to find the constant value for ‘𝑎’,
when the baseflow at the beginning (𝑄 ) and the ending (𝑄 ) are known (Equation 10).
The form of the solution for the nonlinear case with b = 0.5 is (Appendix D):
.

𝑄 = 𝑄 (1 +

(10)

𝑡)

I will calculate the baseflow constant ‘𝑎’ each year from 1945 to 2019 by solving
equation (9) for ‘𝑎’. We can find the ratio of 𝑄 /𝑄 for the special case of b = 0.5 (11-1,
11-2) (Wittenberg, 1995):
= (1 +

ln
where 𝑎 is a constant (𝑚𝑚

.

(11-1)

𝑡)

= −2 ln (

.

)

(11-2)

𝑑 ).

3.3.1.2: Use of Baseflow Recession Constants
Baseflow recession constants indicate how fast baseflow decreases. The decay
rate is 𝐾 for the linear model and 𝑎 for the nonlinear model. I can use the recession
constants to predict future baseflow values at the ending point of the recession
hydrograph (𝑄 ). First, I substitute data for the beginning (𝑄 ) and the ending (𝑄 )
recession points into the linear and nonlinear equations to obtain recession constants (𝐾
for the linear and 𝑎 for the nonlinear equation)46. Next, I plot a set of recession constants

46

Existing baseflow recession data from 1945 to 2019

81

against time to get the trend of changing recession constants (𝐾 and 𝑎). The recession
constant trends 1) determine how the degree of baseflow recession changed and 2) are
used to extrapolate future baseflow recession constants 47. Finally, using the predicted
future recession constants, the future baseflow values will be estimated. This future
baseflow will ultimately assess the low flow status in the Deschutes River surface stream
against ecological threshold called, environmentally critical baseflow (ECB, discussed in
“Environmentally Critical Baseflow”).
3.3.2: Step 2. Data Preparation and Prediction
Prior to linear and nonlinear baseflow recession analyses, the primary baseflow
data and recession constants should be prepared to predict future baseflow recession data.
First, the primary baseflow is the baseflow data separated from the measured USGS
streamflow data through the WHAT (1945-2019). Next, three different methods
estimated values for the future independent variables. The future independent variables
from the most reliable method estimates produce the future dependent variable, the
minimum baseflow (𝑄 ). Finally, the most reliable set of independent variable and
resultant dependent variable is determined by statistical testing (e.g., low p-value and
high coefficient of determination, 𝑅 ).
3.3.2.1: Variables
The trend of recession constants enables us to predict future recession constant
values. The dependent variable is then 𝑄 while the independent variables were the
estimated recession constants (𝐾 for linear and 𝑎 for nonlinear), time (𝑡), and the

47

Prediction for recession constants made from 2020 to 2069

82

baseflow value at the start of recession periods (𝑄 ) 48. Here, the future dependent
variable (𝑄 between 2020-2069) was predicted using a ‘forecast’ function 49; the
independent variables (𝑄 and 𝑡) were predicted using three different methods: average,
forecast function, and trendline (section 3.3.2.2.2; Table 5). Linear regression analysis
determines which set of 𝑄 and 𝑡 predicts future minimum baseflow (𝑄 ) that fits most to
the ‘forecasted future 𝑄 ’.
3.3.2.2: Data Prediction
3.3.2.2.1: Missing Data Treatment
The existing data (1945-2019) should be continuous to generate future (20202069) 𝑄 and 𝑄 . However, the baseflow data (separated from streamflow measurement,
USGS streamflow gauge station 12080010) had missing data sets 50. I used a “linear
interpolation” to estimate these missing data. Linear interpolation assumed that a trend of
two distant data points is proportionally estimated (Bayen & Siauw, 2015):
𝑛 (𝑦𝑒𝑎𝑟𝑠) = 1957 − 1954 = 3, 𝑄

48

𝑄

,

=𝑄

,

+

𝑄

,

=𝑄

,

+

𝑄,

−𝑄
𝑛

𝑄,

−𝑄
𝑛

,

= 80, 𝑄

110 − 80
3

,

= 80 +

,

∗ 2 = 80 +

Linear model (𝑄 = 𝑄 𝐾 ), Nonlinear model (𝑄 = 𝑄 (1 +
49
See section 3.3.2.2.2
50
Missing data between 1955-1956, 1964-1990.

(

= 110

,

)

110 − 80
∗2
3

𝑡)

)

83

3.3.2.2.2: Predicting Future Data
I used a continuous data set between 1945 to 2019 to predict future independent
and dependent variables between 2020 to 2069. I used three combinations of a method to
determine the future independent variables, 𝑄 𝑎𝑛𝑑 𝑡: averages, forecast function, and a
trendline. After that, I used linear regression to decide which set of the 𝑄 𝑎𝑛𝑑 𝑡
calculates minimum future baseflow (𝑄 ) that has the highest correlation with the
dependent variable (𝑄 ).
First, I used the ‘average’ of past data of the independent variables (𝑄 𝑎𝑛𝑑 𝑡) to
represent the future estimation.
Second, I used the ‘forecasted’ past data using a ‘forecast’ function to represent
the future independent variables estimation. This function uses a linear equation between
independent (x) and dependent (y) variables to predict future trends, y = ax + b, where a
is a cross-correlation constant:

a=

∑(𝑥 − 𝑥̅ )(𝑦 − 𝑦)
∑(𝑥 − 𝑥̅ )

and b is calculated from averages of existing data:
b = 𝑦 − 𝑎𝑥̅
where 𝑥̅ = average of existing 𝑥 values and 𝑦 = average of existing 𝑦 values. The
predicted future value (y) is a continuation of the historical values of a specified period of
time, which should be a continuation of the timeline (Microsoft, n.d.).
Third, the ‘trend’ of past data (𝑄 𝑎𝑛𝑑 𝑡) was used to estimate the future
independent variables (𝑄 𝑎𝑛𝑑 𝑡).
84

3.3.2.3: Model Fitness: Linear vs Nonlinear
The linear and nonlinear baseflow recession models were tested for their fitness to
the ‘forecasted future 𝑄 ’ data (2020-2069). Here, a ‘forecast’ function of Microsoft
Excel generated the ‘forecasted future minimum baseflow (𝑄 )’. This ‘forecasted future
𝑄 ’ functions as a ‘control’ case, which we use to compare the 𝑄 values calculated from
linear and nonlinear models. By comparing them against the future forecasted 𝑄 , using
linear regression analysis, we can determine which model is more reliable to predict
future 𝑄 . For example, each case of the calculated 𝑄 is an independent variable (x-axis)
and the ‘forecasted future 𝑄 ’ is a dependent variable (y-axis) on a linear regression plot
(Fig. 31). The model with a higher coefficient of determination (𝑅 ) has a higher
goodness-of-fit and was chosen to further the baseflow analysis under the impact of
groundwater withdrawal effect (see section 3.3.2.4).
Figure 31
Model fitness through linear regression. Gan & Luo, 2013.

Note. Comparison of the simulated and observed recession data: (left) using the linear
aquifer storage-discharge relation model; (right) using a nonlinear aquifer storagedischarge model (Gan & Luo, 2013).

85

In sum, the three methods to estimate future 𝑄 and 𝑡, two recession models
(linear and nonlinear) to test more fitted model, and forecasted baseflow recession
constants (𝐾 or 𝑎) generate six different cases of potential future minimum baseflow (𝑄 )
(Table 5). The six cases of 𝑄 will be compared and statistically analyzed (two-sample
Student’s t-test)
Table 5
Six cases of modeled future minimum baseflow (Qt)
𝑄 and 𝑡
Estimating
Methods
Averages

Baseflow
Recession
Models
Linear

Forecast
function
Trendline

Nonlinear

Baseflow
Recession
Constants (𝐾 or
𝑎)
Estimated from
the Forecast
Function
(compared
against
Trendline)

Cases
1.
2.
3.
4.
5.
6.

Averaged 𝑄 and 𝑡, Linear Model
Averaged 𝑄 and 𝑡, Nonlinear Model
Forecasted 𝑄 and 𝑡, Linear Model
Forecasted 𝑄 and 𝑡, Nonlinear Model
𝑄 and 𝑡 from Trendline, Linear Model
𝑄 and 𝑡 from Trendline, Nonlinear Model

3.3.2.4: Natural vs Impacted
3.3.2.4.1: A Different Perspective
After evaluating the model fitness, we will choose either a linear or nonlinear
model to predict future minimum baseflow (𝑄 ). Now we add the impact of groundwater
withdrawal51 (𝑊) into the future 𝑄 in order to assess the impact of pumping on the
baseflow recession. Typically, we subtract 𝑊 from the modeled 𝑄 to generate the
‘impacted’ 𝑄 values (𝑊 ≠ 0, 𝑊 > 0). However, I will use an inverted approach to the
conventional way of subtracting withdrawals from the 𝑄 for convenience in the

51

Section 2.7.1 equation 1

86

calculation. This means that I will leave the modeled 𝑄 to represent the ‘impacted’ case
while I will add the 𝑊 to the modeled 𝑄 to represent the ‘unimpacted’ or ‘natural’ case.
The predicted future baseflow was categorized into two groups, one with a
‘natural’ flow and the other with groundwater withdrawal ‘impact’ from wells. First, I
assumed the ‘natural’ flow was without groundwater pumping effects (𝑊 = 0). The
natural flow theoretically represented a scenario when groundwater withdrawals did not
occur. The withdrawals (𝑊) were constant values (see section 3.2.4.2), estimated from
the annual average withdrawal amount assuming the withdrawal rate per unit time has not
changed. By contrast, the ‘impacted’ flow represented the baseflow values from the
existing streamflow (𝑊 ≠ 0). This was because the existing streamflow measured from
the USGS gauge station already includes the impact of groundwater withdrawals (𝑊).
Adding the withdrawal impacts to the virtual case of naturally flowing baseflow
without pumping effect (𝑄 + 𝑊 = 𝑄

,

) is a different approach from previous

literature. This method is useful to calculate the baseflow as the impact (𝑊) is added as a
positive value than to subtract the impact (𝑊) from the baseflow (𝑄 ). It ensures the
baseflow result with the impact (𝑊 ≠ 0) does not become a negative value that
calculation becomes easier (e.g., taking negative value in a logarithm is not possible).
This is useful when the withdrawal is larger than the baseflow amount (𝑄 < 𝑊). Also,
the impacted baseflow (𝑄

,

) represented the existing streamflow and baseflow

that were under pumping effects. This informed how current groundwater pumping
practices would result in the future baseflow (𝑄

,

) with the existing baseflow

trends. Thus, the existing method in the literature to add the withdrawals (𝑊) to the

87

impacted scenario ultimately resulted in subtracting the impact of withdrawals (𝑊) twice
as the streamflow already incorporated the impact of withdrawals (𝑊). Therefore, the
new perspective to represent the natural flow as a virtual scenario without pumping effect
would represent the baseflow recession trends more realistically.
3.3.2.4.2: 𝑸𝒕,𝒏𝒂𝒕𝒖𝒓𝒂𝒍 and 𝑸𝒕,𝒊𝒎𝒑𝒂𝒄𝒕𝒆𝒅
The natural baseflow (𝑄

) included the groundwater withdrawals to

,

represent the scenario when there was no groundwater withdrawal existed. On the other
hand, the impacted baseflow (𝑄

) was derived from the existing baseflow data

,

which already incorporated the groundwater pumping via wells. To specify the impact of
groundwater withdrawal impact on the baseflow, I adopted Wang and Cai’s method
(2009). Thomas et al (2013) estimated the baseflow recession constant under the impact
of withdrawals, which deplete aquifer storage:
= −𝑄 − 𝑊

(12)

where 𝑊 is withdrawal rate at the same period of the occurrence of 𝑄 , baseflow.
Combining equation (3) and (11) using 𝑘 = 1 𝛼 ,
(

)

= −𝑄 − 𝑊

(13)

Here the groundwater withdrawals were constant during each individual recession
hydrograph (Thomas et al., 2013); the secondary withdrawal data involved a fixed

88

pumping rate as an averaged per-day withdrawals (Hansen, 2019). The equation was
linearized52 in a logarithmic form
ln(𝑄 + 𝑊) = ln(𝑄 + 𝑊) + 𝑡𝑙𝑛(𝐾)

(14)

The equation (14) is a linear model with a dependent variable ln(𝑄 + 𝑊),
independent variable time 𝑡, intercept ln(𝑄 + 𝑊), and slope 𝑙𝑛(𝐾) (Thomas et al.,
2013). Ultimately, the exponential form of the (13), (𝑄 + 𝑊) = (𝑄 + 𝑊)𝑒
equated the form of precedent Boussinesq equation of 𝑄 = 𝑄 𝑒

,

, or 𝑄 = 𝑄 𝑘 with

𝑘=− .
Under the assumption the groundwater storage-discharge showed a linear
behavior, the baseflow at the lowest point was categorized into natural (𝑄 ,
impacted (𝑄

52

=𝑄,

) flow scenarios (Table 6).

Multiplying the integration factor 𝑒

integration leads to 𝑄 =

) or

/

leads to 𝑘𝑒

+ 𝑒 𝑄 = −𝑒 𝑊. Using the chain rule and

= −𝑊(1 − 𝐾 ) + 𝑄 𝐾 , where 𝑄 (ft s ) is the lowest

baseflow and 𝑄 (ft s ) is the highest baseflow, 𝑘 (unit of time) is the baseflow recession constant, and
𝑊 is the rate of withdrawal (ft s ).

89

Table 6
Baseflow recession analysis equations under Natural or Impacted scenarios and Linear
and Nonlinear models
Equations derived and modified from Boussinesq-Dupuit (1903) and Thomas et al.
(2013).
Natural flow (𝑄 )
Linear
model (𝑄 , )
Nonlinear
model
(𝑄 , )

𝑄

,

+ 𝑊 = (𝑄
𝑄(

(𝑄(

) )(1

+

Withdrawal impacted (𝑄 )
(15-1)

+ 𝑊) 𝐾
)

,
. ( (

,

.

𝑡)

(15-2)

𝑄

,

(8)

= (𝑄 )𝐾

=
))

.

𝑄

= 𝑄 (1 +

.

.
.

𝑡)

(10)

Note. Equations used for Natural and Impacted baseflow with linear or nonlinear
assumptions on aquifer behavior. Q , , Q , (ft s ): i is baseflow under natural (Q ) or
impacted (Q ) models, L is linear model, N is nonlinear model with a special case when
𝑏 = 1 2. 𝐾 : coefficient of linear model under natural flow. 𝐾 : coefficient of the
linear model under wells’ withdrawal impacts. a : constant of the linear model under
natural flow. a : constant of the nonlinear model under wells’ withdrawal impacts. 𝑊 is
a withdrawal amount from well pumping activity (ft s ).

3.3.2.5: Statistical Testing
The difference between 𝑄 ,

and 𝑄

,

will be statistically tested.

The simulated baseflow calculated from a chosen model at the lowest point (𝑄 ) on a
hydrograph were tested using two-sample Student’s t-test. I hypothesized the difference
between current and future 𝑄

and 𝑄 ,

,

show the significant differences

due to the effect of groundwater withdrawals (𝑊). The null hypothesis was that there
was no difference in mean values (μ) in the natural verses impacted baseflow (𝑄 )with
the confidence interval of 95%:
μ

90

=μ

3.3.3: Step 3. Withdrawal Impact on Ecological Functions of a River
Baseflow contribution to the surface flow sustains an ecological function of a
river during a low flow period. Previous baseflow recession analyses focused on the
assessing methods (e.g., linear or nonlinear groundwater storage-discharge relationship,
Thomas et al., 2013) or quantifying the human’s withdrawal impact on baseflow
recession (Wang & Cai, 2010). In detail, the impact of groundwater withdrawal is
usually expressed in the flow rate that is “lost” from the baseflow or surface streamflow.
This study extended the baseflow recession analysis to future baseflow recession
prediction between 2020 and 2069. Ultimately, the predicted future baseflow provided a
different interpretation of the baseflow recession phenomenon, in relation to the stream’s
ecological function.
The ecological function of streamflow during low flow was assessed by
comparing the predicted future baseflow contribution on the streamflow to a
parameterized threshold that was required to sustain the ecological river function. The
former was derived from the baseflow recession analysis. The latter was derived from
conceptualized minimum streamflow standards, which were “Ecologically critical
streamflow (ECS)” (de Graaf et al., 2019) and “Presumptive standards” (Gleeson &
Richter, 2018), from which ECS derived. Ultimately, the ECS is the threshold that is
required for streamflow to maintain its ecological function and can serve as a standard
whether future predicted baseflow recession reaches this threshold. The time when the
baseflow recession reaches the required threshold (ECS) in the future will be when
baseflow contribution no longer supports the environmentally sustainable streamflow
under low flow.
91

3.3.3.1: Environmentally Critical Baseflow (ECB)
3.3.3.1.1: What and Why?
Environmentally Critical Baseflow (ECB) is a threshold baseflow contribution
level to the surface flow which sustains streams’ ecological function during the low-flow
period. The ECB is an altered concept adopted from “Environmentally critical
streamflow (ECS, de Graaf et al., 2019)” for the purpose of this study focused on the
baseflow. The ECB assumes that the baseflow contribution during the low flow period in
Deschutes River Watershed dominates the surface streamflow. Therefore, ‘baseflow’ can
substitute the ‘streamflow’ during a low flow period.
The environmentally critical streamflow is derived from “Presumptive Standards
(Gleeson & Richter, 2017)”, which assessed the relationships between hydrologic
alterations (e.g., decreased baseflow) and ecological responses (e.g., eroded ecological
function) (Gleeson & Richter, 2018) as a result. While these two low flow parameters—
ECS and Presumptive Standards—focus on the surface streamflow as the assessment
objective, ECB pays attention to the baseflow recession and its reducing contribution to
the surface water system. The time at which the ‘impacted’ future baseflow meets the
ECB will be compared to the time when the ‘natural’ future baseflow meets the ECB.
Comparing the ‘time’ at which each future baseflow meets the ECB will be the ‘impact’
of the groundwater withdrawals on the baseflow recession. This provides a different
perspective to understand the degree of withdrawal impact on the baseflow recession.
Such an approach may help us communicate the adverse impact of groundwater
withdrawal to a variety of audiences.

92

3.3.3.1.2: How?
Following the recent work of de Graaf. et al on the environmentally critical
streamflow (ECS) (2019), the environmentally critical baseflow (ECB) adopted the
exceedance probability (Q) every 5 years (de Graaf et al., 2019). First, the threshold or
ECB was determined to be the value of the baseflow which is exceeded 90% of the time
for each 5 years, referred to as 𝑄90. The baseflow between the study period (1945-2069)
was sorted in descending order to calculate the 90% exceedance probability value (𝑄90).
The probability exceedance was calculated as follows:
P=100{m/(n+1))

(16)

where P=exceedance probability (%), m=rank of baseflow among 5 years of record,
n=total number of baseflow record.
Next, the 𝑄90 of natural baseflow contribution assessed whether the impacted
baseflow (baseflow with the withdrawal impact, 𝑊) was above the environmentally
critical baseflow (ECB). According the Gleeson and Richter (2018), impact of
groundwater withdrawal was identified to be environmentally harmful at a time when the
groundwater pumping decreased natural baseflow by more than 10% through time
(Gleeson & Richter, 2018). Therefore, the time when estimated baseflow under
groundwater withdrawal impact (𝑄 𝑜𝑟 𝑄 ,

, see section 3.3.2.4.2) was lower than

10% of the 𝑄90 is when the ECB was exceeded. When the ECB was exceeded, the
baseflow contribution was too low to maintain the stream’s ecological function during
low flow. To calculate this, the maximum ECB will be set as the 90% of the 𝑄90 value
(Fig. 32).

93

Figure 32
Environmentally Critical Baseflow (ECB) of the Deschutes every 5 years. Q𝟗𝟎 and ECB
calculated from streamflow data (NWIS).

baseflow (cfs)

Environmentally Critical Baseflow (ECB)
90
80
70
60
50
40
30
20
10
0

y = -0.6695x + 66.522
R² = 0.0633

5-year intervals
Q90

ECB

Linear (ECB)

Note. The ECB is 90% of the 𝑄90. The trend of ECB shows decline (linear regression
with a negative slope of -0.6695)
Also, the time of reaching the ECB was determined to be at which the yearly
baseflow falls 10% below the natural 𝑄90 for at least two consecutive years (de Graaf et
al., 2019). The two consecutive years criterion was motivated by the assumption that at
least two years are needed before water management strategies are changed (de Graaf et
al., 2019). This criterion substantiated as the baseflow recession is sensitive to time
(Thomas et al., 2013).
Lastly, the impact of groundwater withdrawal against ECB was determined to be
when the impacted baseflow reached the ECB. Likewise, the natural future baseflow
from the observed data was analyzed for when it reached the ECB. Comparing the two
times when natural and impacted future baseflow met the ECB addressed the

94

groundwater withdrawal impact in a perspective of time. I hypothesized that the ECB
will be reached by the impacted baseflow (𝑄 or 𝑄 ,
baseflow (𝑄 or 𝑄

,

) earlier than the natural

) in the future.

95

Chapter 4: Results
4.1: Roadmap
Results are organized into four sections: 1) groundwater withdrawal data analysis,
2) baseflow recession models, linear and nonlinear, 3) baseflow recession analyses with
‘impacted’ and ‘natural’ scenarios, and 4) assessing the baseflow against environmentally
critical baseflow, the threshold for the river to maintain ecological function. The first
three sections are sequentially related that each step leads to the next baseflow recession
analysis. The fourth section provides a different perspective of baseflow recession data
using frequency analysis.

4.2: Groundwater withdrawals
4.2.1: Yearly Groundwater Withdrawals
The cumulative groundwater withdrawal amount of each year has continuously
increased in Thurston County53 (Fig. 33). Yearly cumulative withdrawal of the starting
year (1945) was 7.02 cubic feet per second (cfs) and the ending year (2019) was 78.65
cfs, which is an increase of more than tenfold over the 75 years. The increase in
groundwater withdrawals tracks the increase in population of Thurston County.

53

The withdrawal amount values of each year: see Appendix F

96

Figure 33
Relationship between population and groundwater withdrawals in Thurston County.
Decadal Population Data from the U.S. Census Bureau, Withdrawal Data from Thurston
County Water Planning.

350000

90

300000

80
70

250000

60

200000

50

150000

40
30

100000

20

50000

Withdrawals (cfs)

Population (person)

Population and Groundwater Withdrawals

10
0
1944
1947
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
2004
2007
2010
2013
2016
2019

0

Time (year)
Cumulative Withdrawals (cfs)

Population

Note. The population between each decade was extrapolated by using linear regression.
Withdrawal rates of the year 1971 and 1997 showed a sharp increase. Unlike the
gradual withdrawals of the rest of the period, the increases of two years are rather abrupt,
which could be because of data issues. The year 1971 was when the Department of
Ecology (Ecology) started managing received well reports (DoE, n.d.). Ecology had
received the well reports since the 1930s but not managed them until 1971 (DoE, n.d.).
There could have been missing withdrawal data that occurred before 1971, but this
cannot be confirmed without existing well data. For the year 1997, there was no
information to explain a sharp increase in the withdrawals. This could be due to a
population growth of 61.6% in 1990-2000, which was higher than the mean annual
97

growth rate of 47% between 1870 to 2000 (U.S. Census Bureau, 2014). This is a viable
conjecture as the population growth and the groundwater withdrawal rates are positively
correlated54.
The population increase is related to the gradual increase in groundwater
withdrawals in the area. Among the groundwater withdrawals dedicated to residential
uses, water uses through “domestic uses” and “public supply” composed nearly 75% of
total withdrawals in 2019 (see section 3.2.4.2.1; Fig, 34). Residential and public water
uses differ in withdrawal amount. The “public supply group A” refers to the water
supply service for at least 25 people or a minimum of 15 connections. The “public
supply group B” serves fewer than 15 connections or 25 people; most of Group B
systems use the groundwater permit exemption (see section 2.5.3.1; Table 2). In 2019,
public supply group B (exempt wells) pumped over half of the total groundwater
withdrawal amount with 87 Million gallons per day (Mgpd) (Fig. 34). These permitexempt wells were initially for “small withdrawals” in areas where public supply is not
available (DoE, n.d.)55. Under the Groundwater Code (Chapter 90.44.050 RCW), these
permit-exempt wells are not mandated to record or report the withdrawal rates of
pumping; the pumping rates or withdrawal amount can be only estimated with averaged
water use amounts (see section 3.2.4.2). The increase of these permit-exempt wells in the
area was expected as the population in Thurston County was projected for continuous
growth (OFM, 2012). Thurston County Water Planning estimates the withdrawal rates
from permit-exempt wells by averaging public water use of the area.

54

Two-sample Student’s t-test between yearly cumulative withdrawals and the population showed a
significant difference between the two groups (p-value <2.2e-16, CI=95%).
55
In this study, permit-exempt wells include the “domestic” and “public supply group B” wells.

98

Figure 34
Groundwater Withdrawals by Water Use Purposes.
Withdrawal data from the Thurston County Water Planning.

Groundwater Withdrawals (2019)
Livestock,
3 Mgpd, 2%
Fish propagation,
11 Mgpd, 6%

Industrial,
2 Mgpd, 1%

Commercial,
1 Mgpd, 1%

Irrigation,
24 Mgpd, 15%

Public SupplyA, 37
Mgpd, 22%

Wildlife+Rail+Recrea
tion,
<0 Mgpd, 0%

Domestic+Public
SupplyB,
87 Mgpd, 53%

Note. Groundwater withdrawal portions in amount (Million gallons per day (Mgpd)) and
percentage (%).
4.2.2: Concentrated Withdrawal Locations
Groundwater withdrawals intensified in different locations. Due to rural
developments, the withdrawal from the southwest region has increased dramatically from
around 1975 (Fig. 35, Map-B). Major urban areas in Tumwater, Lacey, and Olympia in
the center to the north of the county have shown consistently increasing withdrawals, at
lower rates. The spatial extent for urban development of the three major cities
(Tumwater, Lacey, and Olympia) started around 1975 and intensified afterward,
highlighting recent development and sprawl in Lacey (Fig. 35, Map-C).

99

Additionally, the pumping effect created by wells in the mid- to lower Deschutes
River was expected to be higher than the upper river. The selected wells for this analysis
were situated on geological layers that are hydraulically interconnected with the stream
(Fig. 35, Map-D). This means the increase in groundwater withdrawals from such units
will have an adverse impact on lowering the Deschutes surface stream.
Figure 35
Groundwater withdrawal concentrations in the study area of Thurston County
Withdrawal data from Thurston County Water Planning. Heat map created using
ArcGIS Online. ESRI ArcGIS Online Layer sources: WSDOT, 2012; City of Tacoma
GIS, 2019. Withdrawal amount data source: the Thurston County Water Planning.
A. 1945

B. 1975

C. 2019

D. 2019 (over selected geological units)

Note. Maps showing locations of concentrated groundwater withdrawals (A: 1945, B:
1975, C: 2019, D: 2019 with hydraulically connected geological units). Blue tint denotes
a lower withdrawal rate; red, yellow, white shows a higher withdrawal rate. The
withdrawal rate is acre-feet per year (AFY).
100

4.3: Model fitness
I used linear and nonlinear models and calculated the baseflow recession
constants to estimate the annual future 𝑄 between 2020 and 2069. Using linear
regression, the linear- or nonlinear- modeled 𝑄 were tested for their goodness-of-fit
against the predicted ‘future forecasted 𝑄 ’, which is the future 𝑄 value forecasted from
the past 𝑄 (see section 3.3.2.3). The selected model, either linear or nonlinear, will
represent the future baseflow and recession regime in section 4.3.2.2.
4.3.1: Data preparation
Data is estimated and prepared to predict future 𝑄 under linear and nonlinear
models. For the time period 2020 to 2069, I estimated the baseflow at the beginning of
recession periods (𝑄 ), the length of recession period (𝑡), and baseflow recession
constants (𝐾 and 𝑎). I then estimated independent variables for the future, including 𝑄
and 𝑡 by 1) averages, 2) forecast function, and 3) linear trend relationship. Briefly, there
are six cases of modeled minimum baseflow (𝑄 ) that I generated, compared, and chose
for the best-fit model to the ‘forecasted future’ minimum baseflow data, 𝑄 (Table 556).

56

𝑄 and 𝑡
Estimating
Methods
Averages

Baseflow
Recession
Models
Linear

Forecast
function
Trendline

Nonlinear

Baseflow
Recession
Constants (𝐾 or
𝑎)
Estimated from
the Forecast
Function
(compared
against
Trendline)

Cases
1.
2.
3.
4.
5.
6.

Averaged 𝑄 and 𝑡, Linear Model
Averaged 𝑄 and 𝑡, Nonlinear Model
Forecasted 𝑄 and 𝑡, Linear Model
Forecasted 𝑄 and 𝑡, Nonlinear Model
𝑄 and 𝑡 from Trendline, Linear Model
𝑄 and 𝑡 from Trendline, Nonlinear Model

101

4.3.1.1: Determination of 𝑸𝟎
I obtained different future estimations of the maximum baseflow at the beginning
of baseflow recession periods57 (𝑄 ).
First, the average value of the past 𝑄 data from 1945 to 2019 is of 𝑄 = 151
(cfs). I averaged data from 1945 to 2019 to find the mean of 𝑄 :

𝑚𝑒𝑎𝑛 𝑄 𝑣𝑎𝑙𝑢𝑒 =

∑

𝑄
𝑛

where 𝑛 is the number of recession periods (𝑡).
Second, I found a linear trend of the past baseflow 𝑄 (1945-2019) between
baseflow and time: 𝑄 = 0.5935𝑡 − 1025.6 (Fig. 36, blue trendline). The positive slope
indicates that 𝑄 increases with time by 0.59 cfs per day. The trend of 𝑄 between 1945
to 2019 showed a gradual increase, as the maximum baseflow at the beginning of each
recession period grew higher in recent years. I expected that this will continue to grow in
the future (Fig. 36, orange line) because of the increasing trend of the past data.
Third, the forecast function from Microsoft Excel estimated the future 𝑄 and
showed a similar value to the averaged 𝑄 (Fig. 36, gray line). This forecast function
differs to the two methods, the average and trendline, in that it uses a “process for
measuring the similarity of one time series (i.e., past) to another time series (i.e., future)”
(Onajite, 2013). The forecast function assumes a linear relationship of the independent

57

The future maximum baseflow (𝑄 ) and recession period (t) in the future (2020-2069) were estimated
based on historic data (1945-2019) using three different methods: average, forecast function, and
trendline. The estimated future 𝑄 and t is in Appendix G.

102

(x-axis) and dependent (y-axis) variables to predict future estimations (see section
3.3.2.2.2).
Figure 36
Maximum baseflow (𝑸𝟎 ) of recession periods (1945-2019) estimated from the trendline
and forecast function.

Q0 Estimated from a Trendline
700
600

Flow (cfs)

500
400
300

y = 0.5935x - 1025.6
R² = 0.0407

y = 0.0593x + 70.022
R² = 0.0588

200
100
0
1940

y = -0.6423x + 1478
R² = 0.2729
1960

1980

2000

2020

2040

2060

Time (year)
Q0 (1945-2019)

Q0 (2020-2069) from Trendline

Q0 Forecasted (2020-2069)

Linear (Q0 (1945-2019))

Linear (Q0 (2020-2069) from Trendline)

Linear (Q0 Forecasted (2020-2069))

Note. The future prediction on 𝑄 estimated from trendline (orange line) is higher than
the 𝑄 estimated from the forecasted function (gray line). The highly scattered data
causes a low coefficient of determination (𝑅 = 0.0407). The values between 1964 to
1990 were missing and they were estimated from linear interpolation.
As a result, I will use these three different methods to predict future (2020-2069)
𝑄 and determine which one will produce the future 𝑄 that fits most to the forecasted
future 𝑄 , using a Student’s t-test (Table 7).

103

4.3.1.2: Determination of recession period (𝒕)
The three different methods described above (see section 4.3.1.1) applied to
estimate the lengths of future recession periods (𝑡) 58. The lengths of recession periods
indicated how many days the recession occurred during each low flow period.
First, the averaged recession period between 1945 and 2019 was 64 days (Fig. 37,
blue markers).
Second, the linear trend of the recession period showed a gradual increase, with a
positive rate of change of 0.075 days. The recession periods varied from 10 days
(minimum) to 122 days (maximum) with an average of 64 days. The estimated recession
period in 2020 (future) is 62 days while the estimated recession period between 2021 and
2069 is 65 days (Fig. 37, orange line). On average, the future recession period was 63.5
days (≈ 64 days) when I calculated the mean of 62 days (recession period in 2020) and 65
days (recession period between 2021 and 2069).
Third, the forecast function estimated the future recession period (the forecast
function method is described in section 3.3.2.2.2). The mean value of the forecasted
future baseflow is 64 days, which is the same as the averaged baseflow of the past days
(1945-2019). The forecasted recession periods ranged from 64 days (minimum) to 65
days (maximum) (Fig. 37, gray markers). Overall, the three methods to estimate the
future recession periods (𝑡) generated a similar result of 64 days. The similarity of the

58

The future maximum baseflow (𝑄 ) and recession period (t) in the future (2020-2069) were estimated
based on historic data (1945-2019) using three different methods: average, forecast function, and
trendline. The estimated future 𝑄 and t is in Appendix G.

104

estimated results from these two methods indicate that these are reliable tool to predict
the future recession period.
As a result, I assumed the recession period (t) will remain as 64 days in the future
prediction between 2020 and 2069. The historic data (1945-2019) of the recession period
showed a gradual increase with a positive rate of 0.1406 days (blue trendline in Fig. 37).
However, the future prediction from three methods, including averaged data, trendline,
and the forecast function produced a static or marginally increasing recession period.
One reason for the static or marginally diverting estimations in the future may be because
of the relatively short predicting period of 40 years (2020-2069). Also, the historic data
had a high variability (𝑅 = 0.01, blue trendline in Fig. 37) that finding a fluctuating
trend may be less reliable than estimating the future data with a static value of 64 days.
Therefore, a future recession period is estimated with 64 days for the 2020-2069
prediction.

105

Figure 37
Recession period (t) of the historic data (1945-2019) and future (2020-2069) estimated
from the trendline and forecast function (2020-2069).

Recession Period Estimated from a Trendline
140
120

y = 0.1406x - 214.72
R² = 0.01

Flow (cfs)

100
80
60
40
20
0
1940

1960

1980

2000

2020

2040

2060

Time (year)
Recession Period t Observed (1945-2019)
Recession Period t Trendline (2020-2069)
Recession Period t Forecasted (2020-2069)
Linear (Recession Period t Observed (1945-2019))

Note. The predicted future recession period (𝑡) estimated from the trendline (orange line)
and the forecast function (gray line) show an almost identical pattern. The historic data is
represented as ‘observed’ data (blue scatters). The values between 1964 to 1990 were
missing thus estimated from linear interpolation.
4.3.1.3: Determination of Recession Constants (𝑲 and 𝒂)
The baseflow recession constants parametrize the degree to which future
minimum baseflow (𝑄 ) changed over time. The constants, 𝐾 (dimensionless) and 𝑎
(𝑚 𝑠

106

), represent the slope of the baseflow recession in a linear model and in a

nonlinear model59. The baseflow recession constants show the hydrological property of
the groundwater-surface water interaction in a nonlinear model (Rupp & Selker, 2006),
respectively. The forecast function (see section 3.3.2.2.2) estimated the future recession
constants for the linear model (𝐾) and the nonlinear model (𝑎) (Fig. 38).
Figure 38
Trend of recession constants

Nonlinear Recession Constant (a)

1.00

7000

0.99

6000
5000

0.98

4000

0.97

a

K (dimensionless)

Linear Recession Constant (K)

3000

0.96

2000

0.95

1000

0.94
1940
y = -6E-05x + 1.1162
R² = 0.0359

1960

1980

Time (year)

2000

2020

0
1940

1960

y = -7.8683x + 18182
R² = 0.0307

1980

2000

2020

Time (year)

Both linear and nonlinear recession constants estimated from the trendline of
historic data (1945-2019) showed high variability and low predictability: low coefficient
of determination (𝑅 ≈ 0.03). This means that historic data (1945-2019) can predict
future values at about 3% of probability, which is low predictability. Then, the future
estimation of the recession constant using the trend of the past data is unreliable. As an
alternative, the recession constant is predicted from the forecast function, which “smooth
out” highly variable historic data (Fig. 39) (Microsoft Office, n.d.).

59

Linear model: 𝑄 = 𝑄 𝐾 , Nonlinear model: 𝑄 = 𝑄 (1 +
constants are 𝐾 (linear) and 𝑎 (nonlinear).

(

)

𝑡)

(see section 3.3.1.1). The

107

Figure 39
Estimated recession constants (1945-2069)

Baseflow Recession Constants
(Linear model="K", Nonlinear model="a")
7000

1.0000

6000

y = -4E-06x + 0.998
R² = 0.0004

5000

0.9900
0.9800

4000
0.9700
3000
0.9600

2000

y = -3.9285x + 10406
R² = 0.0257

1000
0
1920

1940

1960

1980

2000

2020

2040

2060

0.9500
0.9400
2080

Nonlinear Recession Constant (a)

Linear Recession Constant (K)

Linear (Nonlinear Recession Constant (a))

Linear (Linear Recession Constant (K))

Note. The future baseflow recession constants for both linear and nonlinear models were
estimated using the forecast function. For the linear recession constant (𝐾), the baseflow
decreases with -4E-06 in every time period (day). For the nonlinear recession constant
(𝑎), the baseflow decreases with -3.9285 in every time period (day). However, both
linear and nonlinear recession constant data have high variability that its predictability
and power of determination (𝑅 ) is 0.04% and 2.6%, respectively.
As a result, I chose to use Excel’s forecast function to predict the future baseflow
recession constant values. Using the forecast function, the estimated future baseflow
recession constants (linear model=𝐾, nonlinear model=𝑎) between 2020 and 2069 show a
slight decreasing trend as seen in Fig. 39 60. The reducing recession constant values
indicate the slope of recession will become greater, or the degree of recession will

60

The linear and nonlinear baseflow recession constant values estimated using the forecast function is
displayed in Appendix H.

108

increase. It means the future minimum baseflow (𝑄 ) will be reducing at a faster degree.
I will discuss the future minimum baseflow (𝑄 ) in the following section.
4.3.2: Choosing a Model
4.3.2.1: Future Estimation of Data
The goodness-of-fit of linear and nonlinear models were tested to choose which
model—linear or nonlinear—had a higher correlation to the ‘forecasted future baseflow’
𝑄 . Linear regression was used to test the fitness of the models. To do this, historic 𝑄
data (1945-2019) was not applicable as the 𝑄 from the linear model and the measured 𝑄
are the same. This is because I used the measured 𝑄 to calculate the linear recession
constant (𝐾), which then is used to estimate the 𝑄 with the linear model. Therefore, I
will use the future 𝑄 data (2020-2069) to compare and assess the most fitted model to
the forecasted future 𝑄 .
4.3.2.1.1: Future Minimum Baseflow (𝑸𝒕 )
The forecasted future baseflow at the lowest point (𝑄 ), obtained from the
forecast-functioning the past 𝑄 , showed a declining trend in the future (Fig. 40). This
indicates that the predicted minimum baseflow in the future decreases, resulting in lower
streamflow during dry seasons. The reduced minimum baseflow casts a concern over
drier streamflow, which might be exacerbated in the face of climatic and anthropogenic
impacts.

109

Figure 40
Forecasted future minimum baseflow (𝑸𝒕 ). Baseflow data separated from the streamflow
data obtained from NWIS.

Forecasted Future Minimum Baseflow (Qt)
78.5

Flow (cfs)

78.0
77.5
77.0
76.5
76.0
75.5
2068

2066

2064

2062

2060

2058

2056

2054

2052

2050

2048

2046

2044

2042

2040

2038

2036

2034

2032

2030

2028

2026

2024

2022

2020

75.0

Time (year)

Note. Future baseflow at the lowest point (𝑄 ), estimated with the forecast function.
4.3.2.2: Model Selection
4.3.2.2.1: Linear Regression Analysis
The linear regression between modeled 𝑄 (linear, nonlinear) versus forecasted 𝑄
(2020-2069) identified which model best explained and predicted the relationship
between the estimated values of 𝑄 . For each case, the null hypothesis was: The slope of
linear regression is not zero between the estimated 𝑄 from a model (response variable)
and the forecasted 𝑄 (explanatory variable); The confidence interval (CI) was 95% and
the significance level at 0.05 (p-value). Depending on the estimated maximum recession
baseflow (𝑄 ), five out of six cases showed a significant relationship between the
explanatory and response variable (Table 7).

110

As a result, we obtained our best fit to forecasted 𝑄 with the 𝑄 estimated
through a ‘linear’ baseflow regression model and ‘averaged’ 𝑄 with ‘averaged’ 𝑡 (1st
case in Table 7). The low p-value (< 2e-16) of this linear model lets us reject the null
hypothesis that the slope of the linear regression between the linear model 𝑄 and the
forecasted future 𝑄 was not zero (slope ≠ 0). This means that there is a significant
difference in two variables of the ‘forecasted future 𝑄 ’ and ‘𝑄 from a linear model’; a
high coefficient of determination (𝑅 = 0.906) showed the ‘linear model 𝑄 ’ predicts the
forecasted future 𝑄 well:
Table 7
Minimum baseflow (Qt) estimation from different methods and models
Estimating
Methods

Models

Single Linear
Regression expression

P-value

Coefficient of
Determination
(𝑅 )
Averaged 𝑄 and Linear
𝑦 = 4.3𝑥 − 248
< 2.2𝑒 − 16
0.906
𝑡
Nonlinear
𝑦 = 0.8𝑥 + 55.4
2.081𝑒 − 14
0.7075
Forecast function Linear
𝑦 = 14.8𝑥 − 1042.5
4.667𝑒 − 07
0.414
(𝑄 and 𝑡)
Nonlinear
𝑦 = 12.9𝑥 − 870.9
5.918𝑒 − 05
0.2878
Trend of
Linear
𝑦 = 4.4𝑥 − 230.4
3.625𝑒 − 12
0.6381
𝑄 and 𝑡
Nonlinear
𝑦 = −0.3𝑥 + 168
0.6507
0.0043
Note. For each single linear regression, the 𝑥 represents future 𝑄 estimated from the forecast
function; 𝑦 represents future 𝑄 calculated by plugging 𝑄 and 𝑡 (estimated by three methods:
average, forecast, or trend) into either linear or nonlinear models.

Light green denotes statistical significance to explain the model and the observed baseflow
data. Red denotes statistical insignificance between variables. Dark green signifies the
most predictable model on the observed baseflow.
4.3.2.2.2: Model Validation
Linear models showed a consistently higher 𝑅 than nonlinear models across all
six different scenarios (Table 7). While two nonlinear models (2 nd and 4th in Table 7)
showed statistical significance, these had low 𝑅 values. Therefore, the linear model
with the highest 𝑅 was chosen to be the representative model that fits best to the ‘future
111

forecasted’ baseflow. Each model is compared against the future, minimum baseflow
(𝑄 ) calculated from the forecast function. The future 𝑄 functions as a ‘control’ case as
it is simply forecasted from the historic data (1945-2019) without model processes.
Finally, the future 𝑄 compares the six modeled cases to determine which model fits
closest to it and is most predictable for future 𝑄 predictions61.
The linear regression analysis showed that the linear model predicts the future 𝑄
better than the nonlinear model. The linear regression between the forecast and the
‘linear model’ shows high relatedness (Fig. 41; Fig. 42). When different statistical
parameters (i.e., mean, median, minimum, and maximum values of data) were compared
between the ‘forecasted future’ and ‘linear or nonlinear’ models, the linear model
produced estimations of future 𝑄 that are closer to the ‘forecasted future’ case (Fig. 42).
Figure 41
Linear regression analysis of the linear and nonlinear model.

Note. The linear regression analysis assumes that one variable (y) is highly predictable to
the other variable (x) when data scatters near the projected linear regression line.
61

The estimated future minimum baseflow (Q ) depending on the linear/nonlinear model and the method
to determine the maximum baseflow (Q )—trend or average: see in Appendix I

112

Figure 42
Statistical comparisons of the 𝑸𝒕 estimations from the linear and nonlinear model

Relatedness between
Forecasted Future vs Modeled Qt
140
120

Flow (cfs)

100
80
60
40
20
0
Forecasted Future Qt

Linear Model (with averaged
Q0, t)

Nonlinear Model (with
averaged Q0, t)

Data Types
min

mean

median

max

4.3.2.2.3: Residual Analysis
The residuals analysis of the two linear regression analyses in Fig. 41 signified
which model has more consistent and predictable data. Four types of tests addressed the
fitness of models. First, the residual vs fitted plot suggested that linear and nonlinear
models were linearly positive to the forecasted future Q (Fig. 43-A). Second, the normal
probability (Q-Q) plot showed that both linear and nonlinear modeled data showed
normal distribution (Fig. 43-B). Third, the scale-location plot suggested the residuals
were spread equally during the earlier phase but sprawling in a greater degree in the later
phase (Fig. 43-C). This meant the estimated Q via both linear and nonlinear models
showed greater variability over time. Lastly, the residual vs leverage plot suggested there
was a difference in influential cases (e.g., outliers). The linear model did not show an
influential case as the major trendline did not intervene with the Cook’s distance (a red
113

dashed line). However, the nonlinear model showed the data could include some
influential cases as the trendline crossed the Cook’s distance (Fig. 43-D). This indicated
that the baseflow data estimated by a nonlinear model could potentially be less
predictable of the forecasted future baseflow (Q ). Overall, the linear model was more
reliable with data distribution and predictability. Therefore, we chose linear model for
further baseflow recession analysis with the impact of withdrawals.
Figure 43
Residuals analysis of the linear and nonlinear models.
Linear 𝐐𝒕 —Forecasted Future 𝐐𝒕
A. Residual vs Fitted

B. Normal Probability Q-Q

114

Nonlinear 𝐐𝒕 — Forecasted Future 𝐐𝒕

C. Scale-Location (√Standard residuals)

D. Residual vs Leverage

4.4: Baseflow Recession Analysis
4.4.1: Existing “Impacted” Baseflow Recession
The ‘impacted’ baseflow (𝑄 ,

) in this study refers to the baseflow that

already added the groundwater withdrawals. In other words, the baseflow portion of the
observed streamflow (via USGS gauge station at Tumwater) was measured while
groundwater pumping occurred and is the baseflow under the ‘impacted’ scenario.

115

The baseflow recession constant “𝐾” under a linear mode showed a very slightly
decreasing trend in the past and the future estimation (Fig. 44). The decreasing constant
(𝐾) derived from the reduction in the minimum baseflow (𝑄 ) data from 1945 to 2019
(Fig. 44, blue column). Consequently, the decreasing trend of recession constant (𝐾)
resulted in reducing the future 𝑄 (Fig. 44, gray column), assuming more baseflow
recession occurrences and less baseflow contribution to the future surface flow.
Figure 44
Recession constant of the linear model (K) and minimum baseflow (𝑸𝒕 ) (1945-2069).
Streamflow data from NWIS, separated using WHAT.

180.0

1.01

160.0

1.00
y = -3E-06x + 0.9906
R² = 0.0004

120.0

0.99
0.98

100.0

0.97

80.0

0.96

60.0

0.95

40.0

0.94

20.0

0.93

0.0

0.92

K (dimensionless)

140.0

1945
1948
1952
1955
1958
1961
1965
1971
1977
1983
1989
1994
1997
2001
2004
2008
2011
2015
2018
2023
2029
2035
2041
2047
2053
2059
2065

Minimum baseflow (cfs)

Recession Constant (K) and Future Minimum Baseflow (Qt)

Time (year)
Observed Qt

Linear Model Qt

Linear Recession Constant (K)

Linear (Linear Recession Constant (K))

Note. The past minimum baseflow (𝑄 , blue column) and future minimum baseflow (𝑄 ,
gray column) decrease. The trendline of the linear recession constant (𝐾, orange line) has
a negative coefficient, showing a decrease in the future baseflow. On the linear
regression equation of the trendline y = −3E − 06x + 0.9906, ‘𝑥’ is time (year) and ‘y’
is constant 𝐾 (dimensionless).

116

4.4.2: Hypothetical “Natural” Baseflow Recession
The baseflow under a ‘natural’ condition is a hypothetical setting as if there have
not been any groundwater withdrawals; we calculate this by adding withdrawals to the
baseflow (𝑄 + 𝑊 = 𝑄

,

). The null hypothesis of this section is that there is no

significant difference between minimum baseflow (𝑄 ) under the ‘impacted’ and
‘natural’ conditions. The alternative hypothesis is that there is a significant difference
between 𝑄 under the impacted and natural conditions. Here, I categorized the ‘natural’
condition into two groups with different estimations of future withdrawals: 1) In one
case, the withdrawals from 2020 to 2069 would increase in proportion to the population
growth. 2) In the other, the withdrawal would stay equivalent to that of 2019. In contrast,
the baseflow under an ‘impacted’ condition was estimated from the existing streamflow
data; the observed streamflow data and its baseflow portion was affected by the
withdrawals (𝑄

,

). The groundwater withdrawals on baseflow recession

suggested has a significant impact in baseflow with the withdrawal effects (𝑊) (Table 7).
4.4.3: Statistical Analysis on Groundwater Withdrawal Impact
4.4.3.1: Present Data Analysis (1945-2019)
The groundwater withdrawals in the study area of the Thurston County showed
the baseflow recession from 1945 to 2019 (see section 4.3.1.3). The impact of
withdrawals found from the two-sample Student’s t-test between the 𝑄
𝑄

,

,

and

showed the baseflow recession between 1945 and 2019 was significant (p-

value < 2.2e-16, CI=95%) (Table 8. 3-B in the following section 4.4.3.2). The
withdrawals comprised from 8 to 189 % of the minimum baseflow. This tells that almost
double the amount of existing baseflow (i.e., 189%) was potentially lost as an impact of
117

groundwater withdrawal (Fig. 45). The decreasing minimum baseflow (𝑄 ) represented
that baseflow contribution has lowered over time, which relates to the lack of the sole
source of surface water recharge during dry season. The depletion of baseflow due to
perpetuated groundwater withdrawal already started in the early 2000s (Fig. 45).
Figure 45
Minimum baseflow (𝑸𝒕 ) and withdrawals (W) (1945-2019).
Baseflow Data separated from the streamflow data obtained from NWIS. Withdrawal
data from Thurston County Water Planning.

Minimum Baseflow vs Withdrawals (1945-2019)
180
160

Flow (cfs)

140
120
100
80
60
40
20
1945
1947
1949
1952
1954
1957
1958
1960
1962
1965
1969
1973
1977
1981
1985
1989
1992
1995
1997
1999
2002
2004
2008
2009
2011
2013
2016
2018

0

Time (year)
Minimum baseflow (Qt)

Groundwater withdrawals

Note. The trend in past minimum baseflow contributions to the Deschutes Streamflow
(blue column). During recession periods when withdrawals (orange column) exceeded
baseflow (blue column), the baseflow was virtually eliminated from the streamflow, as
evident from comparing two columns from early 2000s 62.

62

An abrupt increase in the groundwater withdrawals (orange column) in early 1970s is most likely
attributed to the transitioning in data management (explained in section 4.2.1)

118

4.4.3.2: Entire Period Analysis (1945-2069)
The future minimum baseflow of the natural scenario (𝑄 ,
impacted scenario (𝑄

,

) versus the

) showed a substantial discrepancy in mean values in both

the past (1945-2019) and the future (2020-2069) (Fig. 46). The mean of ‘natural’
baseflow (𝑄

,

) was 125 (cubic feet per second, cfs), while the mean of ‘impacted’

baseflow (𝑄

,

) was 80 cfs. The difference of mean baseflows was more than a

half of the mean of ‘impacted’ baseflow, which implied the impact of withdrawals was as
much as half of the mean flow of the ‘impacted’ baseflow (125 − 80 = 45; 45 > (

=

40)).
Figure 46
Minimum baseflow (𝑸𝒕 ) comparisons between the Impacted versus Natural scenarios.

400
350
300
250
200
150
100
50
0
1945
1948
1952
1955
1958
1961
1965
1971
1977
1983
1989
1994
1997
2001
2004
2008
2011
2015
2018
2023
2029
2035
2041
2047
2053
2059
2065

Baseflow (cfs)

Minimum Baseflow (Qt) Comparisons (1945-2069)

Time (year)
Natural Qt (increasing W)

Natural Qt (W=2019's)

Impacted Qt

Note. The ‘impacted’ baseflow (Q ) (red line) is compared against the two hypothetical
‘natural’ baseflow (Q ) cases with increasing withdrawals (blue column) and constant
withdrawal (orange column) values in the future 63.
63

The estimated minimum baseflow under impacted, natural (with increasing withdrawal), and natural
(fixed withdrawal at 2019’s) are displayed in Appendix J.

119

The groundwater withdrawal was correlated with the present (1945-2019) and the
projected future (1945 to 2069) baseflow recession. First, a two-sample Student’s t-test
on the minimum baseflow of the natural scenario of the present groundwater withdrawals
(𝑄

,

) versus the impacted scenario without the withdrawals (𝑄 ,

) showed a

significant difference in the mean baseflow (Model B: p-value < 2.2e-16, CI=95%, Fig.
47 and Table 8). The groundwater withdrawals in the Model B includes the increasing
withdrawals that is proportional to the population growth in the past. The mean ‘natural’
baseflow (𝑄
(𝑄

,

,

, 1945-2019) was 125.2 cfs, while the mean ‘impacted’ baseflow

, 1945-2019) was 80.1 cfs. This indicates that the minimum baseflow has been

impacted over 45 cfs lost flow due to the past and present groundwater withdrawals from
1945 to 2019. This impact is over half of the mean flow of the impacted minimum
baseflow (𝑄

,

).

Second, a two-sample Student’s t-test comparing the minimum baseflow of the
future natural scenario (𝑄 ,

) to the impacted scenario (𝑄 ,

) showed a

significant difference in the mean baseflow (Model C: p-value < 2.2e-16, CI=95%, Fig.
47 and Table 8). The groundwater withdrawals in the Model C includes the increasing
withdrawals that is proportional to the projected population growth. The mean ‘natural’
baseflow (𝑄
(𝑄

,

,

, 1945-2069) was 162.4 cfs, while the mean ‘impacted’ baseflow

, 1945-2019) was 79.2 cfs. This indicates that the minimum baseflow has been

impacted by 83.2 cfs (162.4 − 79.2 = 83.2) lost flow due to the past and present
groundwater withdrawals from 1945 to 2019. The impact (83.2 cfs) is bigger than the
mean impacted minimum baseflow (𝑄

120

,

, 1945-2069), which implies that the

baseflow influx would have doubled without withdrawals. The impact was between
110% and 190% of the estimated future baseflow (Table 8. 3-C).
Third, a two-sample Student’s t-test comparing the minimum baseflow of the
future natural scenario (𝑄 ,

) to the impacted scenario (𝑄 ,

) showed a

significant difference in the mean baseflow (Model D: p-value < 2.2e-16, CI=95%, Fig.
47 and Table 8). The groundwater withdrawals in the Model C includes the same amount
of withdrawals in 2019, assuming the future groundwater withdrawal will remain the
same amount as that of in 2019. The mean ‘natural’ baseflow (𝑄
was 119.1 cfs, while the mean ‘impacted’ baseflow (𝑄

,

,

, 1945-2019)

, 1945-2019) was 79.2 cfs.

This indicates that the minimum baseflow has been impacted by almost 40 cfs lost flow
due to groundwater withdrawals from 1945 to 2019. The impact is about half of the
mean flow of the impacted minimum baseflow (𝑄

,

). A constant withdrawal rate

at 2019 levels would still be more than 100% of the estimated baseflow discharge. This
indicates that even in our more conservative case (model C), the impact could deplete the
entire baseflow to the surface water. In conclusion, the groundwater withdrawal impact
on the current and future baseflow recession from 1945 to 2069 was projected to reduce
over half of the current baseflow given the constant withdrawals, and more than double
the current baseflow given increasing withdrawals.

121

Figure 47
Two-sample Student's t-test analysis between Models
Model B: 𝑄 ,

vs 𝑄 ,

,

Model C: 𝑄 ,

vs 𝑄 ,

,

122

(

(

)

)

Model D: 𝑄

vs 𝑄

,

,

,

Table 8
Statistical comparison between the minimum baseflow (Qt) under the Impacted scenario
(model A) and Natural scenarios (model B, C, and D).
A
𝑄
(

p-value
Mean (cfs)
% of
𝑊 within
𝑄 64

B
𝑄

,

80.1
(19452019)

)

79.2
(19452069)

,

C
𝑄

,
(

)

,

D
𝑄

,
(

)

,

,
(

)

p < 2.2e-16
125.2

p < 2.2e-16
162.4

p < 2.2e-16
119.1

8 ~ 189 %
(mean 61 %)

110 ~ 191 %
(mean 147 %)

100 ~ 103 %
(mean 102 %)

Note. A: the impacted baseflow is the standard to which we compared three other models
of B, C, and D. B: hypothetical “natural” baseflow scenario between 1945 and 2019,
with increasing withdrawals proportional to population growth. C: hypothetical “natural”
baseflow scenario between 1945 and 2069 with increasing withdrawals proportional to
population growth. D: hypothetical “natural” baseflow scenario with the 2019
withdrawal rate held constant into the future (2020-2069).

64

The ratio of withdrawals to the minimum baseflow (Qt) is in Appendix K.

123

4.5: Environmentally Critical Baseflow (ECB)
4.5.1: Future Baseflow Recession and Ecological Threshold
Environmentally critical baseflow (ECB) identifies when the impact of

groundwater withdrawals finally interrupts the baseflow inflow. Once the amount of
groundwater withdrawal reaches or exceeds a certain threshold (i.e., ECB) required to
sustain riverine ecology, summer flows when the river rely on baseflow the most is
considered at risk. Determining the time at which the groundwater withdrawals will
exceed the ECB provides a temporal perspective of the impact of groundwater pumping.
This is a different approach to project the level of future baseflow recession from the
baseflow recession analysis (section 4.3; 4.4).
I projected that the impacted future baseflow trend would be exceeded by
ecological thresholds, ECB, during low flow periods. The future baseflow was estimated
by the forecast function and was compared against the 90% of the exceedance probability
that occur 90% of a given period, or Q90 65. The 90% of the Q90 indicates the minimum
threshold to sustain a healthy ecological function.
I used the analyzed baseflow estimation from Model A of the baseflow recession
analysis for the ‘future baseflow’ data (Table 8). The Model A includes baseflow
estimation with the impact of groundwater withdrawals, necessary to assess the
ecological function in the future by comparing it against the ECB.

65

The ‘Q’ symbol used here represents a low flow parameter, not the ‘baseflow’ or ‘groundwater
discharged as I used in previous sections for the baseflow recession analysis.

124

4.5.2: Different Estimation and Interpretation of ECB
To assess whether future baseflow may fall under the threshold, different
techniques to estimate the ECB were used. In method ‘median’, I used the median value
of the past ECB value (1945-2019) and used it as the ECB in the future (2020-2069). In
method ‘mode’, I used the most frequently emerging value of the past ECB (1945-2019)
as the future ECB (2020-2069). In method ‘forecast’, I used the forecast function
(Microsoft Office, n.d.) to project the future ECB (2020-2069) from the past (1945-2019)
ECB levels. These three methods will estimate the future trend of ECB that we can
determine whether the future 𝑄 will fall below the ECB.
First, with the ECB estimated by the median value of ECB levels between 1945
and 2019 (63 cfs) (method ‘median’), the future baseflow did not fall under the ECB
levels (Fig. 48, green line). Second, with the ECB estimated by the mode value of ECB
levels in the past (70 cfs) (method ‘mode’), the future baseflow did not fall below under
ECB levels (Fig. 48, orange line). Third, however, we projected that the forecasted ECB
levels would exceed the estimated baseflow (Fig. 48, yellow line). The forecasted value
of ECB levels based on the past ECB levels (method ‘forecast’) showed a slight increase
near the 2060s. This may be due to varied trend of the past ECB level on which the
future series relies and projects the future dataset. The first year when minimum
baseflow (𝑄 ) is projected to exceeded by the ECB at least for 2 years was 2061, when
baseflow will reach 77.75 cfs, which is about 2 cfs lower than the mean minimum
baseflow of 79.19 cfs. Combined with the perpetuated recession, the baseflow on 2061
will be exceeded by an ecological threshold, or ECB.

125

Figure 48
Future Impacted baseflow and ECB (mode, mean, and forecasted of the past records).

Future Impacted Baseflow Exceeded by ECB from
Mode, Median, and Forecast Function
180.00
160.00
140.00
2061, 76.58

120.00
100.00
80.00
60.00
40.00
20.00

1945
1947
1951
1953
1957
1959
1961
1964
1969
1974
1979
1984
1989
1993
1996
1998
2002
2005
2008
2010
2013
2016
2019
2024
2029
2034
2039
2044
2049
2054
2059
2064
2069

0.00

Minimum Baseflow (Qt)

ECB (90% of Q90)_Mode

ECB (90% of Q90)_Median

ECB (90% of Q90)_Forecast

Note. Future estimations on the minimum baseflow (𝑄 , blue column) from the mode
(orange line), median (green line), and forecasted (yellow line) past ECB records.
Compared to the forecasted future ECB (yellow line), the 𝑄 at 2061 is exceeded by the
ECB, falling below the ecological threshold.
Two estimations (method ‘median’ or ‘mode’) showed different results for future
baseflow falling below the ecological threshold, or ECB. Also, the pattern or trend of
future baseflow fluctuation was rather flat (less variant than the method ‘forecast’). This
can change as the baseflow trends in the past shows high variability; the future baseflow
may fall under the ECB estimations.

126

Chapter 5: Discussion, Limitations & Suggestions, Conclusion
This paper finishes with discussion, limitations and suggestions, and a conclusion.
In the Discussion section, I interpret the significance of the results and explain their
implications in relation to the theoretical framework addressed in section 2.5.2. In the
Limitations and Suggestions section I address the limitations of the study and suggest
future research to enhance the applicability and validity of this research. Finally, I
summarize and offer concluding remarks.

5.1: Discussion
This study demonstrated a correlation between groundwater withdrawals via well
pumping and the baseflow recession in the Deschutes River. Statistically, the baseflow
recession had a high correlation with the estimated groundwater withdrawals as shown in
section 4.4.2.1. The yearly groundwater withdrawal has increased more than tenfold in
the past 75 years (1945-2019), which implicated potentially reduced groundwater
storage. Such a decrease in groundwater showed lower streamflow as the deficit in
groundwater will lead to less baseflow input to the surface flow. An exponential increase
of groundwater withdrawals over time worked as a strong driver of baseflow recession, as
pumping extracts a large amount of groundwater and intercepts the groundwater flow,
lowering the groundwater table.
This study focused on the minimum baseflow of each recession period (𝑄 )
between the ‘natural’ versus ‘impacted’ scenarios (see section 3.3.2.4). I defined the
‘natural’ baseflow to be a hypothetical status with no groundwater withdrawals. In this

127

case, the withdrawal (𝑊) is added to the measured baseflow, which was separated from
the existing streamflow data via the web-based hydrograph analysis tool (WHAT). The
‘impacted’ baseflow, without added withdrawals, showed a noticeable reduction
compared to the ‘natural’ baseflow starting in the 1970s. This coincided with an abrupt
increase of recorded groundwater withdrawals in 1971 due to a shift in well-log
management (see section 4.2.1). In conclusion, the significant difference in the minimum
baseflow of the ‘impacted’ versus ‘natural’ scenario indicates that decreased baseflow
influx has reduced the minimum baseflow (𝑄 ) level over time. This raises concerns
about whether the baseflow may remain at a sustainable level to support the riverine
ecosystem of the Deschutes River stream in dry seasons, which rely heavily on
baseflow. Therefore, the decreasing minimum baseflow (𝑄 ) has an ecological
implication on the low flow period.
The overall decrease of baseflow influx during dry seasons is supported by other
indicators, including recession constant (𝐾) for each recession period (𝑡). The recession
period has increased over time between 1945 to 2019 (section 4.4.1). A longer recession
period indicates that baseflow reduction periods are longer than in the past, which
potentially addresses drier and lower flow in recent summers than in the past. The dry
months of June to October in future years are expected to become drier due to climate
change; with longer recession periods, there will be more days with less baseflow input.
The longer recession period (𝑡) indicates added stress on aquatic species relying on areas
with lower flow, higher stream temperature, and degraded water quality (section
2.5.5.1.1). Additionally, the decreasing trend of recession constant (𝐾) supports lower
baseflow and drier streams (section 4.4.1). The baseflow recession constant lets us
128

predict the amount of baseflow recession in the future. Baseflow is projected to decline,
yielding less surface streamflow during dry periods.
The maximum baseflow at the beginning of each recession period (𝑄 ) showed an
increase between 1945 and 2019 (Fig. 36). This suggests that the streamflow is higher in
recent years than the past, potentially due to extreme precipitation events and climate
change which produced higher flow in the river. The maximum baseflow (𝑄 ), at the
beginning of each recession period, has become higher than before, meaning the baseflow
after precipitation in the study period (June-October) has increased. This may be due to
the higher variability of 𝑄 values in later years (1991-2019) than in the early years
(1945-1964). Also, the precipitation pattern in early summer (April, May) and the
intermittent rainfall during dry seasons (June-October) might have positively affected the
increase in higher baseflow input at the beginning of recessions. Baseflow is highly
affected by the amount of precipitation as rainfall recharges the surface water, which then
replenishes the groundwater and increases the potential baseflow. This shows the effect
of climate change and extreme precipitation patterns on the baseflow in the Pacific
Northwest.
More importantly, the relationship between the maximum (𝑄 ) and minimum
baseflow (𝑄 ) under the impact of groundwater withdrawals (Model A) showed that
recession has increased more in recent years than in the past. The gap between 𝑄 and 𝑄
has grown greater over time, as the maximum baseflow increased while the minimum
baseflow decreased. This shows a growing gap in the actual level of the recession,
indicating less baseflow input in recent years and potentially in the future. On the other
hand, the decreasing trend of the minimum baseflow (𝑄 ) happened even though the
129

maximum baseflow (𝑄 ) showed an increasing trend. This indicates that the effect of
precipitation recharging surface water and groundwater systems might happen more
slowly, until it cannot compensate for reduced groundwater and baseflow input on the
stream. As a groundwater deficit lowers surface flow, there is a delayed impact because
groundwater in an aquifer must travel between sedimentary pores (see section 2.6.2).
The groundwater deficit can reach a level threatening significantly reduced baseflow
contribution before surface flow shows a depletion (see section 2.8.3). Therefore, the
increasing gap between the maximum (𝑄 ) and minimum baseflow (𝑄 ) in a recession
period is a salient parameter to assess the groundwater-surface water relationship.
The future baseflow recession in the Deschutes, estimated from the linear model,
is projected to reach or exceed the environmentally critical baseflow (ECB) level in 2061
(see section 4.5.2). The year in which future minimum baseflow (𝑄 ) may exceed the
ECB depends on the method of determining the ECB. The future 𝑄 fell below the
forecasted ECB in year 2061, while it was not reached when determined with either the
mode or the median of the past ECB records. Despite these differences in ECB
projections, the future minimum baseflow (𝑄 ) shows a consistent decrease and
approaches the ECB values estimated from the all three methods. Continued future
baseflow recession causes groundwater deficits due to withdrawals, and threatens the
ecological function of groundwater, which the Deschutes relies on to recharge surface
water in low flow periods. Overall, estimating the time when decreasing baseflow
exceeds the ECB offers a temporal perspective on how early the Deschutes may face the
degraded function of the baseflow recession. This has implications for management of
groundwater deficits and withdrawal practices.
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5.2: Limitations and Suggestions
There are two limitations of this study related to 1) defining the ‘impacted’ and
‘natural’ baseflow and 2) determining the level of an ecological function via the
environmentally critical baseflow (ECB). First, the past baseflow recession trend showed
a relatively gradual and small decrease compared to the extent of withdrawals. Though
there was a tenfold increase of groundwater withdrawal over 75 years, the minimum
baseflow (𝑄 ) did not decrease tenfold (Fig. 45). The difference between groundwater
withdrawals and the baseflow recession could be attributed to the difference time
between pumping and the groundwater traveling within the aquifer. For example, the
‘natural’ baseflow scenario assumes the amount of groundwater “impacted” or “lost”
would have remained in the aquifer if there was no pumping occurred . Some of this
“lost” groundwater could have discharged to the surface water in the form of baseflow
gradually travelling vertically through the aquifer. Therefore, the impact of such lost
groundwater could be more accurately calculated using the vertical hydraulic traveling
time, rather than the withdrawal amount itself. This vertical movement relates to the
concept of “hydraulic conductivity” in a permeable porous aquifer by using the hydraulic
gradient (Sinclair & Bilhimer, 2007). Therefore, the actual impact of annual groundwater
withdrawal would be more in a distributed form rather than an instant total withdrawal,
resulting in a much smaller impact of “lost” groundwater in each recession period. Even
though the total amount of impact or withdrawal may increase (as described in section
4.2.1), the hydraulic gradient and conductivity will delay the flow. I did not include the
impact of hydraulic conductivity on groundwater withdrawals (Sinclair & Bilhimer,
2007). With a further study, the yearly impact from withdrawals could be estimated with

131

the consideration of the hydraulic conductivity. To that end, the hydraulic conductivity
would adjust the withdrawal amount with the hydrogeologic consideration of
groundwater movement within the aquifer.
Second, the unique value of the environmentally critical baseflow (ECB) at which
the healthy ecological function is maintained should be assessed for the Deschutes
River. Derived from the environmentally critical streamflow (ECS), the ECB was used
to demonstrate whether the river maintained a minimum streamflow from the baseflow
contribution. While ECB could be a substitute for the ECS during the dry season, when
baseflow comprises most of the surface flow (see section 2.3.3), the ECB estimation has
not been tested for potential errors. Additionally, this research introduced the concept of
the ECB adopted from the ECS. The low flow parameter in Washington State utilizes the
7-day, 10-year (𝑄

,

) method, which is different from the 𝑄90 applied to calculate the

ECS and ECB. Therefore, further research on validating the low flow parameter to
determine the value for the ECS and ECB would clarify the standard by which the future
baseflow can be compared and assessed.

5.3: Conclusion
The impact of groundwater withdrawals on baseflow recession during low flow
periods has become a major element in streamflow changes. The two research questions
in this work assessed the impact of groundwater withdrawal on baseflow recession in the
past and the future of the Deschutes River, WA. A quantitative analysis using the
baseflow recession constant attempted to explain and predict baseflow recession trends,

132

which were then used to assess the sustainable and ecological function of the river in the
future.
The methods employed in this research explored an association between baseflow
recession and a variety of variables. The main variable, groundwater withdrawal (𝑊),
showed an impact on the baseflow recession via statistical testing (two-sample Student’s
t-test). Other variables such as recession constants (𝐾 for a linear model and 𝑎 for a
nonlinear model), maximum baseflow at the beginning of recession periods (𝑄 ), and
time (𝑡) fitted to baseflow trends. Additionally, the baseflow recession analysis from
1945 to 2019 required assessment of the ecological function of the stream using a
threshold (‘environmentally critical baseflow’, or ‘ECB’). Different methods to
determine the ECB produced different results for the time when the future baseflow
recession fall below the ecological threshold. ECB predicted from one method (forecast
function) indicated the river cannot sustain a minimum flow to sustain the riverine
ecosystem as the baseflow input weakens with less groundwater storage. Two other
methods to estimate the ECB (using the mode and the median from the past ECB trend)
showed less baseflow recession. Regardless of the different methods, future baseflow
was predicted to decline.
The method to compare and assess the groundwater withdrawals on the baseflow
recession extend the theoretical framework presented in section 3.3.2.4.1. In the
literature, the ‘impacted’ baseflow subtracts withdrawals from baseflow (𝑊 ≠ 0, 𝑊 ≤ 0)
while the ‘natural’ baseflow does not incorporate the withdrawals (𝑊 = 0). In contrast,
this research considered the ‘impacted’ baseflow as the existing baseflow from measured
streamflow (𝑊 not included in the baseflow recession equation: equation 7, 9), and
133

estimates for the ‘natural’ baseflow assumed that there were no groundwater withdrawals
(𝑊 ≥ 0: equation 14-1, 14-2). This inverted perspective facilitated our estimation of the
impact of groundwater withdrawals on the baseflow.
This research analyzed the baseflow recession phenomenon in association with
the impact of groundwater withdrawals and the ecological function of the streamflow.
The first research section (Ch 4.4) assessed the correlation between groundwater
withdrawal and baseflow recession on the lower Deschutes River streamflow. The
second research section (Ch. 4.5) revealed that perpetuated baseflow recession in the
future may threaten the ecological function to sustain the riverine ecosystem. One ECB
estimate predicted the baseflow recession would exceed baseflow discharge in the year
2061, indicating that low flow in the stream would not likely sustain ecological status.
These two findings demonstrated that current practices of groundwater pumping deserve
our attention regarding sustainable streamflow in the present and future.
In order to properly analyze the impact of groundwater withdrawal, a more
accurate baseflow model is needed. The anthropogenic impact of withdrawals should
account for the hydrogeologic characteristics of different aquifers, using the hydrologic
traveling time of withdrawals through the hydraulic conductivity of the aquifer.
Additionally, the findings of this research related to the second research question could
be improved with a more accurate estimation of the impact on the baseflow. This
highlights the need for successive research on modeling the impact of withdrawal on
baseflow in time, and the capacity to predict the impacted streamflow in the future.
The findings of this research suggest that we should be more cautious with the
quantity of water in relation to the quality of the Deschutes River stream. The
134

anthropogenic impact of groundwater withdrawals has become a major element in
groundwater depletion and streamflow alterations. This work intends to bridge the
influenced groundwater system and the streamflow on the surficial level via baseflow
recession. Future studies on groundwater management should build upon our findings to
help us further understand the impact of current groundwater appropriation on the
sustainable baseflow contribution to the surface water. This can help researchers,
groundwater resource managers, and environmentalists adapt analyses and policies to the
river’s ecological values and functions for future groundwater resource management.
That can move us closer toward intergenerational sustainability in streamflow
management to preserve the instream values of the Deschutes River for future
generations.

135

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145

Chapter 7: Appendices
Appendix A. Baseflow Composition in the Deschutes River and Washington
State. Sinclair & Pitz, 1999.
USGS
Location

gauge

Base flow composition of total annual streamflow (%)
years
Jun

July

Aug

Sep

Oct

22

92

96

97

92

74

37

81

92

91

81

57

-

86

86

77

69

station
Lower
Deschutes

12080010 E
Street in
Tumwater

Upper

12079000

Deschutes

near Rainier

Washington
State

Average of
582 gauging
stations

Appendix B. Population Projection Compared to 2012. TRPC, 2019.

Note. “Old” is the 2012 Forecast.

146

Appendix C. Total Dwelling Unit Projection in Thurston County. TRPC,
2019.

Notes.
(top) Total dwelling unit projections in
numbers. (bottom) Total dwelling unit
projections in percentages.
1. Urban Growth Area (UGA):
Unincorporated area designated to the
annexed into city limits over 20 years to
accommodate urban growth.
2. Reservations: Estimate is for Thurston
County portion of reservation only.
2. Rural Unincorporated County is the portion
of the unincorporated county that lies outside
UGA and Reservation boundaries.

147

Appendix D. Linear baseflow recession constant (K)
Appendix D-1: Linear case
As described in Sec. 2.7.1, the general differential equation for changes of baseflow 𝑄(𝑡)
with time is
= −𝑎𝑄

(4)

In the “linear case”, with 𝑏 = 1, this reduces to simple exponential decay of the
baseflow:
𝑑𝑄
= −𝑎𝑄
𝑑𝑡
In general, the solution66 takes the form 𝑄(𝑡) = 𝑄 𝑒
of (1/time).
If 𝑄(𝑡) = 𝑄 𝑒

+ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 where 𝑎 has units

+ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, then
=𝑄

𝑒

+

(𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡) = −𝑎𝑄 𝑒

+ 0 = −𝑎 𝑄(𝑡)

Substitution of 𝑎 = yields the linear baseflow recession equation:
𝑄(𝑡) = 𝑄 𝑒

/

(5-1)

where c is one form of the recession constant (with units of 1/time).
A nondimensional recession constant, 𝐾 = 𝑒
𝑄(𝑡) = 𝑄 𝑒

/

, is often used in baseflow analysis:

/

=𝑄 𝐾

In summary, the “linear” baseflow recession equation describes exponential decay of
groundwater discharge (𝑑𝑄) in a recession period (𝑑𝑡).

66

Source: E.J. Zita, 2020; Thomas et al., 2013

148

Appendix D-2: Nonlinear case
In the nonlinear case (b≠1), the differential equation for the baseflow does not have a
(

)

simple exponential decay. The general solution for 𝑄 = 𝑄 (1 +
𝑡)
is shown by Dupuit-Boussinesq (1904), where 𝑎 and 𝑏 indicate constants.

(5-2)

Appendix D-3: Nonlinear case with 𝒃 = 𝟏 𝟐
In the special case of 𝑏 = (Wittenberg, 1999), the nonlinear baseflow equation
simplifies:
𝑄 = 𝑄 (1 +

(

)

(5-2)

𝑡)

The constant 𝑏 is unitless, and the constant 𝑎 has units.
The exponent becomes:
1
1
1
=
=
= −2
𝑏 − 1 1 − 1 −1
2
2
The multiplier in the second term on the right becomes:
(1 − 𝑏) (1 − 1 2) 1 2 1
=
=𝑎 =
𝑎
𝑎𝑏
2
2 𝑎
Therefore, the solution to the nonlinear differential equation for 𝑄 takes the form
𝑄
= 1+
𝑄

(1 − 𝑏)𝑄1−𝑏
0
𝑎𝑏

1

= 1+

𝑡

𝑄0
𝑎

−2
2

𝑡

This is written in equations (10) and (11-1) as
𝑄0.5
𝑄
= 1+ 0 𝑡
𝑄
𝑎

−2

This can be rewritten using the natural logarithm, for easier graphical analysis of
recession constants:
𝑙𝑛

𝑄
𝑄

= 𝑙𝑛 1 +
𝑄
𝑙𝑛
𝑄

𝑡
𝑄
𝑎

.

= −2 𝑙𝑛 1 +

𝑎 + 𝑡𝑄
= −2 𝑙𝑛
𝑎

𝑡
𝑄
𝑎

.

.

149

Appendix E. Selection of Baseflow Recession period (t)
Date
(month_date_year)

Base flow
(cfs)

Three-day moving
average (cfs)

6_1_2004
6_2_2004
6_3_2004

141.46
148.07

138.82
140.18

151.62
152.99
153.19
153.38
154.43
154.95

147.05
150.89
152.60
153.19
153.67
154.25

154.53
154.22
153.57
152.46
151.75
152.59

154.64
154.57
154.11
153.42
152.59
152.27

152.68
151.73
150.35
148.35
145.88
143.26

152.34
152.33
151.59
150.14
148.19
145.83

140
134
130
127
124.72
122.43

143.05
139.09
134.67
130.33
127.24
124.72

119.99
117
114
111.74

122.38
119.81
117.00
114.25

6_4_2004
6_5_2004
6_6_2004
6_7_2004
6_8_2004
6_9_2004
6_10_2004
6_11_2004
6_12_2004
6_13_2004
6_14_2004
6_15_2004
6_16_2004
6_17_2004
6_18_2004
6_19_2004
6_20_2004
6_21_2004
6_22_2004
6_23_2004
6_24_2004
6_25_2004
6_26_2004
6_27_2004
6_28_2004
6_29_2004
6_30_2004

Decreasing Three-day
moving average
(included: Y, excluded: N)
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y

Notes
1. Exemplary data of selecting baseflow recession period between June and October of
2004.
2. cfs=cubic feet per second
3. Red-shaded dates are excluded while non-shaded dates are selected recession periods.
Baseflow Derived from the NWIS and Separated from the WHAT program.

150

Appendix F. Yearly Withdrawal Amount. Data from the Thurston County
Water Planning.
Year
1945
1946

Withdrawals (cfs)
7.0
7.1

1947
1948
1949
1950
1951
1952

7.3
7.8
8.1
8.6
9.2
9.9

1953
1954
1955
1956
1957
1958

10.2
10.6
10.8
10.9
11.1
11.7

1959
1960
1961
1962
1963
1964

11.9
12.0
12.2
13.2
13.3
13.6

1965
1966
1967
1968
1969
1970

13.8
14.0
14.4
14.8
15.3
15.9

1971
1972
1973
1974
1975
1976

35.4
36.1
37.4
41.1
42.0
42.1

1977
1978
1979
1980
1981
1982

46.4
48.7
50.1
51.4
52.0
52.4

1983
1984

52.5
52.6

151

1985
1986
1987

52.8
53.2
53.5

1988
1989
1990
1991
1992
1993

55.6
56.0
56.7
56.9
57.2
58.1

1994
1995
1996
1997
1998
1999

58.4
58.8
59.6
74.8
73.3
73.7

2000
2001
2002
2003
2004
2005

74.2
74.4
74.6
74.8
75.4
75.8

2006
2007
2008
2009
2010
2010

76.2
76.6
77.6
77.8
77.9
77.9

2011
2012
2013
2014
2015
2016

78.0
78.1
78.2
78.2
78.3
78.4

2017
2018
2019

78.5
78.6
78.7

Note. Unit of withdrawal amount: cfs (=cubic feet per second)

152

Appendix G. Estimated Maximum Baseflow (Q0) and Recession Period (t)
with Three Methods
Recession
Period t
Averaged
64.07

Recession
Period t
Forecasted

Recession
Period t
Trendline

Year

Q0
Averaged

2020

151.08

188.03

64.76

166.55

61.75

2021

151.08

64.07

158.09

64.75

191.75

64.68

2022

151.08

64.07

173.75

64.73

191.75

64.68

2023

151.08

64.07

207.15

64.71

191.75

64.68

2024

151.08

64.07

201.65

64.68

191.75

64.68

2025

151.08

64.07

202.37

64.18

191.75

64.68

2026

151.08

64.07

236.42

64.29

191.75

64.68

2027

151.08

64.07

168.02

64.58

191.75

64.68

2028

151.08

64.07

166.79

64.55

191.75

64.68

2029

151.08

64.07

154.06

64.51

191.75

64.68

2030

151.08

64.07

149.42

64.48

191.75

64.68

2031

151.08

64.07

162.66

64.45

191.75

64.68

2032

151.08

64.07

168.26

64.42

191.75

64.68

2033

151.08

64.07

161.51

64.40

191.75

64.68

2034

151.08

64.07

168.03

64.37

191.75

64.68

2035

151.08

64.07

164.84

64.34

191.75

64.68

2036

151.08

64.07

198.17

64.32

191.75

64.68

2037

151.08

64.07

162.17

64.30

191.75

64.68

2038

151.08

64.07

153.46

64.28

191.75

64.68

2039

151.08

64.07

163.37

64.26

191.75

64.68

2040

151.08

64.07

161.81

64.24

191.75

64.68

2041

151.08

64.07

163.65

64.22

191.75

64.68

2042

151.08

64.07

166.09

64.20

191.75

64.68

2043

151.08

64.07

180.91

64.19

191.75

64.68

2044

151.08

64.07

162.68

64.17

191.75

64.68

2045

151.08

64.07

157.44

64.16

191.75

64.68

2046

151.08

64.07

141.97

64.15

191.75

64.68

2047

151.08

64.07

153.65

64.13

191.75

64.68

2048

151.08

64.07

151.78

64.10

191.75

64.68

2049

151.08

64.07

144.61

64.09

191.75

64.68

2050

151.08

64.07

160.04

64.09

191.75

64.68

2051

151.08

64.07

163.31

64.09

191.75

64.68

2052

151.08

64.07

159.17

64.08

191.75

64.68

2053

151.08

64.07

169.81

64.08

191.75

64.68

2054

151.08

64.07

152.08

64.08

191.75

64.68

2055

151.08

64.07

156.94

64.07

191.75

64.68

2056

151.08

64.07

162.39

64.07

191.75

64.68

2057

151.08

64.07

158.23

64.07

191.75

64.68

Q0
Forecasted

Q0 from
Trendline

153

154

2058

151.08

64.07

150.39

64.06

191.75

64.68

2059

151.08

64.07

141.62

64.06

191.75

64.68

2060

151.08

64.07

152.11

64.06

191.75

64.68

2061

151.08

64.07

150.68

64.06

191.75

64.68

2062

151.08

64.07

143.68

64.06

191.75

64.68

2063

151.08

64.07

158.37

64.05

191.75

64.68

2064

151.08

64.07

162.91

64.05

191.75

64.68

2065

151.08

64.07

160.30

64.05

191.75

64.68

2066

151.08

64.07

171.79

64.05

191.75

64.68

2067

151.08

64.07

155.09

64.05

191.75

64.68

2068

151.08

64.07

161.43

64.05

191.75

64.68

2069

151.08

64.07

157.72

63.99

191.75

64.68

Appendix H. Linear and Nonlinear Baseflow Recession Constants

Year
1945
1945
1946

Linear
Recession
Constant
(K)
0.9928
0.9930
0.9892

Nonlinear
Recession
Constant
(a)
2558.9955
2351.8220
1971.0938

1946
1947
1947
1948
1949
1949

0.9959
0.9922
0.9923
0.9895
0.9935
0.9944

4290.7265
2553.9656
2215.0582
2334.5024
3035.7791
3089.1486

1950
1951
1952
1952
1953
1953

0.9931
0.9910
0.9904
0.9963
0.9724
0.9860

3156.4849
2458.2793
2172.2599
4484.2434
763.7303
1474.4337

1953
1954
1954
1955
1956
1957

0.9763
0.9896
0.9908
0.9898
0.9887
0.9904

993.7024
2218.4145
2074.7958
1975.8590
1876.6910
2313.0591

1957
1958
1958
1958
1959
1959

0.9945
0.9931
0.9931
0.9961
0.9905
0.9937

3362.4928
3237.1552
2691.9016
4240.2148
2279.8239
3241.2719

1960
1960
1961
1961
1962
1962

0.9908
0.9960
0.9913
0.9953
0.9911
0.9769

2536.6494
4937.3030
2608.7381
4074.8594
2327.7524
1049.9607

1963
1963
1964
1965
1966
1967

0.9939
0.9967
0.9956
0.9951
0.9947
0.9944

3544.4930
5955.8823
4471.3682
4061.7204
3760.3718
3530.4167

155

156

1968
1969
1970
1971

0.9940
0.9937
0.9935
0.9932

3349.9668
3205.2186
3087.0363
2989.1330

1972
1973
1974
1975
1976
1977

0.9930
0.9928
0.9927
0.9925
0.9924
0.9922

2907.0406
2837.4965
2778.0630
2726.8820
2682.5126
2643.8201

1978
1979
1980
1981
1982
1983

0.9921
0.9920
0.9919
0.9918
0.9917
0.9917

2609.8989
2580.0175
2553.5785
2530.0894
2509.1403
2490.3874

1984
1985
1986
1987
1988
1989

0.9916
0.9915
0.9915
0.9914
0.9914
0.9913

2473.5402
2458.3514
2444.6096
2432.1322
2420.7615
2410.3600

1990
1991
1992
1992
1993
1994

0.9913
0.9912
0.9945
0.9893
0.9890
0.9925

2400.8074
2391.9980
2989.5108
1439.6610
1886.4665
2536.9415

1994
1995
1995
1996
1996
1997

0.9779
0.9882
0.9868
0.9921
0.9951
0.9895

744.0308
1706.4452
1141.9587
2843.7103
3846.5794
2536.7088

1997
1997
1998
1999
2000
2001

0.9896
0.9467
0.9895
0.9921
0.9902
0.9927

2025.7319
564.2662
2025.3650
2652.6749
2259.6359
2427.5159

2002
2002
2003

0.9929
0.9968
0.9914

2613.7319
4826.2589
1856.5984

2004
2004
2004
2005

0.9851
0.9619
0.9620
0.9897

1315.0212
472.0873
543.0450
1760.8839

2006
2007
2008
2008
2008
2009

0.9864
0.9934
0.9839
0.9915
0.9970
0.9934

1272.5680
2868.9909
1404.9047
2090.3379
6170.0066
2915.3080

2009
2010
2010
2010
2011
2011

0.9938
0.9831
0.9913
0.9844
0.9877
0.9923

2771.6966
1583.5799
2568.5644
1363.5509
2186.9412
2733.4669

2012
2013
2013
2014
2015
2015

0.9906
0.9872
0.9526
0.9893
0.9909
0.9934

2422.4603
1799.7205
701.3387
1983.5954
2243.8879
2589.4065

2016
2016
2017
2018
2018
2019

0.9934
0.9948
0.9879
0.9917
0.9964
0.9954

3237.7681
3705.5930
1929.3518
2532.9231
4971.2368
4478.6727

2019
2020
2021
2022
2023
2024

0.9847
0.9925
0.9925
0.9920
0.9916
0.9922

1131.6141
2463.8251
2459.3790
2454.9940
2583.7397
2502.0069

2025
2026
2027
2028
2029
2030

0.9921
0.9921
0.9919
0.9918
0.9917
0.9917

2600.2817
2543.2892
2498.5893
2523.6186
2518.8230
2514.1397

2031
2032
2033

0.9917
0.9917
0.9917

2509.5624
2486.3633
2483.4566

157

158

2034
2035
2036
2037

0.9916
0.9916
0.9916
0.9916

2488.4642
2484.1907
2479.9944
2475.8712

2038
2039
2040
2041
2042
2043

0.9916
0.9915
0.9915
0.9915
0.9915
0.9914

2471.8173
2467.8290
2463.9031
2460.0363
2456.2258
2452.4688

2044
2045
2046
2047
2048
2049

0.9914
0.9914
0.9914
0.9913
0.9913
0.9913

2448.7627
2445.1051
2441.4936
2437.9262
2434.4007
2430.9154

2050
2051
2052
2053
2054
2055

0.9913
0.9913
0.9912
0.9912
0.9912
0.9912

2427.4683
2424.0579
2420.6825
2417.3405
2414.0306
2410.7515

2056
2057
2058
2059
2060
2061

0.9911
0.9911
0.9911
0.9911
0.9910
0.9910

2407.5018
2404.2803
2401.0859
2397.9175
2394.7741
2391.6548

2062
2063
2064
2065
2066
2067

0.9910
0.9910
0.9909
0.9909
0.9909
0.9908

2388.5585
2385.4844
2382.4317
2379.3995
2376.3872
2373.3940

2068
2069

0.9908
0.9908

2370.4193
2367.4623

Appendix I. Estimation of the Future Minimum Baseflow (𝑸𝒕 )

Year

Forecasted
Future Q
(cfs)

Q estimated from the
Averaged Q & 𝑡

Q estimated from the
Forecasted Q & 𝑡

Q estimated from the
Trendline Q & 𝑡

Linear

Nonlinear

Linear

Nonlinear

Linear

Nonlinear

2020
2021
2022
2023
2024
2025

78.3
78.3
78.1
78.0
77.9
77.8

93.5
93.4
90.2
87.7
91.2
91.1

118.0
118.0
117.9
119.1
118.3
119.2

115.8
97.3
103.2
119.7
121.2
122.0

143.3
122.6
133.5
157.9
153.1
155.1

104.9
118.1
113.9
110.8
115.3
115.1

129.8
145.9
145.8
147.4
146.4
147.5

2026
2027
2028
2029
2030
2031

77.7
77.6
77.5
77.7
77.7
77.7

91.0
90.0
89.0
88.9
88.7
88.6

118.7
118.3
118.5
118.5
118.5
118.4

142.2
99.6
97.8
90.3
87.5
95.1

177.3
130.0
129.4
120.5
117.1
126.4

115.0
113.6
112.4
112.2
112.0
111.9

146.9
146.3
146.6
146.6
146.5
146.5

2032
2033
2034
2035
2036
2037

77.6
77.5
77.5
77.4
77.4
77.3

88.5
88.4
88.2
88.1
88.0
87.9

118.2
118.2
118.2
118.2
118.1
118.1

98.3
94.2
97.9
95.9
115.2
94.1

130.1
125.4
130.0
127.7
150.7
125.8

111.7
111.6
111.4
111.3
111.1
110.9

146.2
146.2
146.2
146.2
146.1
146.1

2038
2039
2040
2041
2042
2043

77.3
77.2
77.2
77.1
77.1
77.1

87.7
87.6
87.5
87.3
87.2
87.1

118.1
118.0
118.0
118.0
117.9
117.9

89.0
94.6
93.6
94.5
95.8
104.2

119.7
126.6
125.5
126.7
128.4
138.6

110.8
110.6
110.4
110.3
110.1
110.0

146.0
146.0
145.9
145.9
145.8
145.8

2044
2045
2046
2047
2048
2049

77.0
77.0
77.0
76.9
76.9
76.9

87.0
86.8
86.7
86.6
86.4
86.3

117.9
117.8
117.8
117.8
117.7
117.7

93.6
90.4
81.4
88.0
86.8
82.6

125.9
122.3
111.3
119.5
118.2
113.1

109.8
109.6
109.5
109.3
109.1
109.0

145.7
145.7
145.6
145.6
145.5
145.5

2050
2051
2052
2053
2054
2055

76.8
76.8
76.8
76.8
76.7
76.7

86.2
86.0
85.9
85.8
85.6
85.5

117.7
117.6
117.6
117.6
117.5
117.5

91.3
93.0
90.5
96.4
86.2
88.8

123.9
126.2
123.2
130.6
118.2
121.6

108.8
108.6
108.4
108.3
108.1
107.9

145.4
145.4
145.4
145.3
145.3
145.2

2056

76.7

85.4

117.5

91.7

125.3

107.8

145.2

159

2057
2058
2059

76.7
76.6
76.6

85.2
85.1
84.9

117.4
117.4
117.4

89.3
84.7
79.6

122.4
116.9
110.7

107.6
107.4
107.2

145.2
145.1
145.1

2060
2061
2062
2063
2064
2065

76.6
76.6
76.6
76.5
76.5
76.5

84.8
84.7
84.5
84.4
84.2
84.1

117.3
117.3
117.3
117.2
117.2
117.2

85.4
84.5
80.4
88.5
90.9
89.3

118.1
117.0
112.1
122.3
125.5
123.6

107.1
106.9
106.7
106.5
106.3
106.2

145.0
145.0
144.9
144.9
144.9
144.8

2066
2067
2068
2069

76.5
76.5
76.5
76.4

84.0
83.8
83.7
83.5

117.2
117.1
117.1
117.1

95.5
86.1
89.4
87.3

131.5
119.9
124.3
121.7

106.0
105.8
105.6
105.4

144.8
144.8
144.7
144.7

Note. The unit of estimated Q : cubic feet per second (cfs), Q : cfs, t: days.

160

Appendix J. Estimated Minimum Baseflow (Qt) under Impacted and Natural
Scenarios.
Year
1945*
1945
1946*
1946
1947*
1947
1948
1949*
1949
1950
1951
1952*
1952
1953*
1953
1953
1954*
1954
1955
1956
1957*
1957
1958*
1958
1958
1959*
1959
1960*
1960
1961*
1961
1962*
1962
1963*
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974

Impact (𝑊)
yearly
withd
Populatio
rawal
n Change
s (W)
7.0
7.0
7.1
7.1
7.3
7.3
7.8
8.1
8.1
8.6
9.2
9.9
9.9
10.2
10.2
10.2
10.6
10.6
10.8
10.9
11.1
11.1
11.7
11.7
11.7
11.9
11.9
12.0
12.0
12.2
12.2
13.2
13.2
13.3
13.3
13.6
13.8
14.0
14.4
14.8
15.3
15.9
35.4
36.1
37.4
41.1

𝑊 = 0 (impacted)

𝑊 ≠ 0 (increasing)

Constant
𝐾

Estimate
dQ

Constant
𝐾

Estimate
dQ

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

64.0
59.6
79.8
72.8
68.7
68.5
89.8
73.2
72.2
88.7
81.1
75.1
60.9
81.1
88.3
125.9
88.8
83.5
88.2
93.0
97.7
75.3
118.4
66.4
66.3
84.3
101.0
96.8
86.8
92.0
87.5
72.1
124.0
95.3
88.7
87.3
86.6
85.9
85.3
84.6
83.9
83.2
82.5
81.9
81.2
80.5

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

71.1
66.6
86.9
79.9
76.1
75.8
97.6
81.4
80.4
97.3
90.3
85.0
70.8
91.4
98.6
136.2
99.3
94.1
99.0
103.9
108.8
86.4
130.1
78.1
78.0
96.2
112.9
108.7
98.7
104.1
99.6
85.3
137.2
108.6
102.0
100.9
100.4
99.9
99.7
99.4
99.2
99.1
118.0
118.0
118.5
121.6

𝑊 ≠ 0 (2015’s)
Constant
𝐾

Estimate
dQ
71.1
66.6
86.9
79.9
76.1
75.8
97.6
81.4
80.4
97.3
90.3
85.0
70.8
91.4
98.6
136.2
99.3
94.1
99.0
103.9
108.8
86.4
130.1
78.1
78.0
96.2
112.9
108.7
98.7
104.1
99.6
85.3
137.2
108.6
102.0
100.9
100.4
99.9
99.7
99.4
99.2
99.1
118.0
118.0
118.5
121.6

161

1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992*
1992
1993
1994*
1994
1995*
1995
1996*
1996
1997*
1997
1997
1998
1999
2000
2001
2002*
2002
2003
2004*
2004
2004
2005
2006
2007
2008*
2008
2008
2009*
2009
2010*
2010
2010
2011*
2011

162

42.0
42.1
46.4
48.7
50.1
51.4
52.0
52.4
52.5
52.6
52.8
53.2
53.5
55.6
56.0
56.7
56.9
57.2
57.2
58.1
58.4
58.4
58.8
58.8
59.6
59.6
72.9
72.9
74.8
73.3
73.7
74.2
74.4
74.6
74.6
74.8
75.4
75.4
75.4
75.8
76.2
76.6
77.6
77.6
77.6
77.8
77.8
77.9
77.9
77.9
78.0
78.0

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

79.8
79.2
78.5
77.8
77.1
76.4
75.8
75.1
74.4
73.7
73.0
72.4
71.7
71.0
70.3
69.7
69.0
52.5
54.2
60.5
73.1
50.8
70.2
45.3
89.1
84.9
120.2
102.4
156.5
61.9
74.8
75.7
52.4
59.0
58.6
41.6
64.4
67.0
83.2
47.9
40.4
65.2
79.0
69.1
81.6
70.6
67.2
98.3
118.0
106.5
123.6
96.4

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

121.8
121.3
124.9
126.5
127.2
127.9
127.7
127.4
126.9
126.4
125.8
125.6
125.2
126.7
126.3
126.3
125.9
109.6
111.4
118.6
131.5
109.2
129.0
104.1
148.7
144.5
193.1
175.4
231.3
135.2
148.5
149.9
126.9
133.6
133.2
116.4
139.8
142.4
158.6
123.7
116.7
141.7
156.6
146.7
159.2
148.5
145.0
176.3
195.9
184.5
201.6
174.4

121.8
121.3
124.9
126.5
127.2
127.9
127.7
127.4
126.9
126.4
125.8
125.6
125.2
126.7
126.3
126.3
125.9
109.6
111.4
118.6
131.5
109.2
129.0
104.1
148.7
144.5
193.1
175.4
231.3
135.2
148.5
149.9
126.9
133.6
133.2
116.4
139.8
142.4
158.6
123.7
116.7
141.7
156.6
146.7
159.2
148.5
145.0
176.3
195.9
184.5
201.6
174.4

2012
2013
2013
2014
2015*
2015
2016*
2016
2017
2018*
2018
2019*
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057

78.1
78.2
78.2
78.2
78.3
78.3
78.4
78.4
78.5
78.6
78.6
78.7
78.7
86.2
86.2
86.2
86.2
86.2
92.7
92.7
92.7
92.7
92.7
98.4
98.4
98.4
98.4
98.4
103.8
103.8
103.8
103.8
103.8
108.6
108.6
108.6
108.6
108.6
112.4
112.4
112.4
112.4
112.4
119.9
119.9
119.9
119.9
119.9
127.9
127.9
127.9

1.1
1.1
1.1
1.1
1.1
1.2
1.2
1.2
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

75.5
84.9
155.9
68.5
70.4
65.8
99.4
81.6
73.6
78.1
79.9
91.4
62.7
78.3
78.3
78.1
78.0
77.9
77.8
77.7
77.6
77.5
77.7
77.7
77.7
77.6
77.5
77.5
77.4
77.4
77.3
77.3
77.2
77.2
77.1
77.1
77.1
77.0
77.0
77.0
76.9
76.9
76.9
76.8
76.8
76.8
76.8
76.7
76.7
76.7
76.7

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

153.6
163.1
234.1
146.7
148.8
144.2
177.8
160.1
152.1
156.7
158.5
170.1
141.4
173.2
173.2
173.0
172.9
172.8
187.5
187.4
187.4
187.3
187.5
201.4
201.4
201.3
201.2
201.2
215.0
215.0
214.9
214.9
214.8
227.7
227.7
227.7
227.6
227.6
238.1
238.1
238.1
238.0
238.0
260.3
260.3
260.2
260.2
260.2
285.6
285.5
285.5

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

153.6
163.1
234.1
146.7
148.8
144.2
177.8
160.1
152.1
156.7
158.5
170.1
141.4
107.2
107.2
107.0
106.8
106.6
106.5
106.4
106.3
106.2
106.5
106.4
106.4
106.3
106.2
106.1
106.0
105.9
105.9
105.8
105.8
105.7
105.6
105.6
105.5
105.5
105.4
105.4
105.4
105.3
105.3
105.2
105.2
105.2
105.1
105.1
105.1
105.0
105.0

163

2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069

127.9
127.9
136.5
136.5
136.5
136.5
136.5
145.6
145.6
145.6
145.6
145.6

1.6
1.6
1.7
1.7
1.7
1.7
1.7
1.9
1.9
1.9
1.9
1.9

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

76.6
76.6
76.6
76.6
76.6
76.5
76.5
76.5
76.5
76.5
76.5
76.4

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

285.5
285.5
314.4
314.4
314.3
314.3
314.3
347.2
347.2
347.2
347.2
347.2

1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0

105.0
104.9
104.9
104.9
104.9
104.8
104.8
104.8
104.8
104.7
104.7
104.7

Notes.
1. Duplicating years (*) indicate there were multiple recession periods within the year.
2. Population change indicates the portion of increased population of a year compared
with the population of 2012.

164

Appendix K. The Ratio of Groundwater Withdrawals to the Minimum
Baseflow (𝑸𝒕 )
Year
1945*
1945
1946*
1946
1947*
1947
1948
1949*
1949
1950
1951
1952*
1952
1953*
1953
1953
1954*
1954
1955
1956
1957*
1957
1958*
1958
1958
1959*
1959
1960*
1960
1961*
1961
1962*
1962
1963*
1963
1964
1965
1966
1967
1968

Yearly Withdrawals
(𝑊, cfs)
7.0
7.0
7.1
7.1
7.3
7.3
7.8
8.1
8.1
8.6
9.2
9.9
9.9
10.2
10.2
10.2
10.6
10.6
10.8
10.9
11.1
11.1
11.7
11.7
11.7
11.9
11.9
12.0
12.0
12.2
12.2
13.2
13.2
13.3
13.3
13.6
13.8
14.0
14.4
14.8

Population Change
(against 2015)

W(=increase) / Q
(%)
9.9
10.5
8.2
8.9
10.7
10.7
8.7
11.1
11.3
9.7
11.4
13.2
16.3
12.6
11.6
8.1
11.9
12.6
12.2
11.7
11.3
14.7
9.9
17.6
17.6
14.1
11.8
12.4
13.8
13.2
13.9
18.2
10.6
14.0
15.0
15.5
15.9
16.3
16.9
17.5

W(=2015) / Q (%)

165

1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992*
1992
1993
1994*
1994
1995*
1995
1996*
1996
1997*
1997
1997
1998
1999
2000
2001
2002*
2002
2003
2004*
2004

166

15.3
15.9
35.4
36.1
37.4
41.1
42.0
42.1
46.4
48.7
50.1
51.4
52.0
52.4
52.5
52.6
52.8
53.2
53.5
55.6
56.0
56.7
56.9
57.2
57.2
58.1
58.4
58.4
58.8
58.8
59.6
59.6
72.9
72.9
74.8
73.3
73.7
74.2
74.4
74.6
74.6
74.8
75.4
75.4

18.3
19.1
42.9
44.1
46.0
51.0
52.6
53.2
59.2
62.6
64.9
67.3
68.6
69.7
70.5
71.4
72.3
73.5
74.6
78.4
79.6
81.3
82.6
108.9
105.4
96.0
80.0
115.1
83.7
129.8
66.8
70.2
60.7
71.2
47.8
118.3
98.5
98.0
141.9
126.5
127.2
179.7
117.2
112.6

2004
2005
2006
2007
2008*
2008
2008
2009*
2009
2010*
2010
2010
2011*
2011
2012
2013*
2013
2014
2015*
2015
2016*
2016
2017
2018*
2018
2019*

75.4
75.8
76.2
76.6
77.6
77.6
77.6
77.8
77.8
77.9
77.9
77.9
78.0
78.0
78.1
78.2
78.2
78.2
78.3
78.3
78.4
78.4
78.5
78.6
78.6
78.7

90.7
158.2
188.5
117.5
98.3
112.3
95.0
110.2
115.8
79.3
66.1
73.2
63.1
80.9
103.5
92.1
50.2
114.3
111.3
119.0
78.9
96.1
106.7
100.6
98.4
86.0

2019

78.7

125.4

2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036

86.2
86.2
86.2
86.2
86.2
92.7
92.7
92.7
92.7
92.7
98.4
98.4
98.4
98.4
98.4
103.8
103.8

1.1
1.1
1.1
1.1
1.1
1.2
1.2
1.2
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3

110.2
110.1
110.3
110.5
110.7
119.2
119.4
119.5
119.6
119.3
126.7
126.7
126.9
127.0
127.1
134.1
134.2

100.5
100.5
100.6
100.8
101.0
101.1
101.3
101.3
101.4
101.2
101.2
101.2
101.4
101.5
101.5
101.6
101.7

167

2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069

103.8
103.8
103.8
108.6
108.6
108.6
108.6
108.6
112.4
112.4
112.4
112.4
112.4
119.9
119.9
119.9
119.9
119.9
127.9
127.9
127.9
127.9
127.9
136.5
136.5
136.5
136.5
136.5
145.6
145.6
145.6
145.6
145.6

1.3
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.7
1.7
1.9
1.9
1.9
1.9
1.9

134.3
134.4
134.5
140.7
140.8
140.9
140.9
141.0
145.9
146.0
146.1
146.1
146.2
156.0
156.1
156.1
156.2
156.3
166.8
166.8
166.9
166.9
167.0
178.2
178.2
178.3
178.3
178.4
190.4
190.4
190.4
190.5
190.5

101.7
101.8
101.9
101.9
102.0
102.0
102.1
102.1
102.2
102.2
102.2
102.3
102.3
102.4
102.4
102.4
102.5
102.5
102.5
102.6
102.6
102.6
102.7
102.7
102.7
102.7
102.8
102.8
102.8
102.8
102.8
102.9
102.9

Notes.
1. Duplicating years (*) indicate there were multiple recession periods within the year.
2. Population change indicates the rate of increased population of a year compared with
the population of 2012.

168