Integrated Water Management Under Different Water Rights Institutions and Population Patterns: Methodology and Application

Abstract

While numerous studies have investigated demand management policies as a means of mitigating the impacts of climate change and population growth, little attention has been given to the interaction of spatial population patterns and water institutions that affect water shortages. In this article, we develop a methodology to evaluate how population location under alternative water institutions and climate scenarios impacts water demands, shortages, and derived economic values. We apply this methodology to the South Platte River Basin (SPRB) in Northeastern Colorado under three scenarios with ∼1,800 simulations. Results suggest that while water rights institutions have a negligible impact on total volumetric shortages relative to climate change, they have substantial distributional and economic implications. Results also suggest that continuous population growth in upstream cities yields the lowest water shortages if per capita use decreases with urbanization. However, if we assume that per capita demands do not decrease with population density, an equal distribution of population to upstream and downstream regions yields the lowest water shortage and highest economic value. These findings indicate the need that planning efforts must account for return flows and development patterns throughout a watershed in order to reduce water shortages and promote economic prosperity.

Full text

Integrated Water Management Under Different Water
Rights Institutions and Population Patterns: Methodology
and Application
Ahmed A. Gharib
1,2
, Mazdak Arabi
1
, Christopher Goemans
3
, Dale T. Manning
3
, and
Alexander Maas
4
1
Civil and Environmental Engineering Department, Colorado State University, Fort Collins, CO, USA,
2
Drainage Research
Institute, National Water Research Center, Cairo, Egypt,
3
Agricultural and Resource Economics Department, Colorado
State University, Fort Collins, CO, USA,
4
Agricultural Economics and Rural Sociology, University of Idaho, Moscow,
ID, USA
Abstract While numerous studies have investigated demand management policies as a means of mitigating
the impacts of climate change and population growth, little attention has been given to the interaction of spatial
population patterns and water institutions that affect water shortages. In this article, we develop a methodology
to evaluate how population location under alternative water institutions and climate scenarios impacts water
demands, shortages, and derived economic values. We apply this methodology to the South Platte River Basin
(SPRB) in Northeastern Colorado under three scenarios with ∼1,800 simulations. Results suggest that while
water rights institutions have a negligible impact on total volumetric shortages relative to climate change, they
have substantial distributional and economic implications. Results also suggest that continuous population
growth in upstream cities yields the lowest water shortages if per capita use decreases with urbanization.
However, if we assume that per capita demands do not decrease with population density, an equal distribution of
population to upstream and downstream regions yields the lowest water shortage and highest economic value.
These findings indicate the need that planning efforts must account for return flows and development patterns
throughout a watershed in order to reduce water shortages and promote economic prosperity.
1. Introduction
Sufficient freshwater supplies are crucial for food production, economic prosperity, and ecosystem functions.
While the total amount of water present on Earth remains substantively constant from year to year, its temporal
and spatial location has shifted over the past half‐century (IPCC, 2022). These changes in hydrologic regimes
over time and space have exacerbated water shortages in many basins (Degefu et al., 2018; Liu et al., 2018).
Simultaneously, increasing demands driven by population growth, industrial expansion, and environmental
considerations have intensified the competition for limited water resources, particularly in arid western US states
(Brewer et al., 2008; Brown, 2006; Tidwell et al., 2014). Water managers are now working to find novel solutions
that better balance water supply with demand (e.g., Golfam et al., 2021; Kolokytha & Malamataris, 2020; Sun
et al., 2017; H. Wang et al., 2020). Academics and practitioners have long argued for updating water rights in-
stitutions (water institutions) as a means of dealing with increased water scarcity (Grafton et al., 2013). However,
modifying existing water allocation institutions is not the only way to address water scarcity. Urban planning
policies that impact the density and location of population, also play an important role in determining water
demand patterns (A. Miller, 2023; Richter, 2023; Ty et al., 2012).
While water supply and demand management strategies have traditionally been options to address water short-
ages, these methods have diminishing returns since the “low‐hanging fruit” has already been picked (Barnett
et al., 2008; Brown et al., 2019; Gutzler & Robbins, 2011; Seager et al., 2013). For example, most high‐quality
dam sites have already been developed; where options do exist, environmental objections to dams and reservoirs
often preclude their construction (Glennon, 2005). Water conservation technologies, such as center pivot irri-
gation or low‐flow toilets, have seen mass adoption in recent decades such that additional demand‐side con-
servation is likely to require substantial behavioral and technological change (Fleck, 2016; Gilligan et al., 2018;
Gleick, 2002; Sankarasubramanian et al., 2017). The diminishing returns to these strategies have led some to
argue for more systemic change.
RESEARCH ARTICLE
10.1029/2024WR037196
Key Points:
•Water institutions have little effect on
basin‐wide water shortages, but clearly
determine who experiences shortages
•The location and density of population
have significant effects on water
shortages and economic value
•Even distribution of population
between regions in a basin provides
lower shortages and higher values
assuming constant per capita demand
Supporting Information:
Supporting Information may be found in
the online version of this article.
Correspondence to:
A. A. Gharib,
ahmed.gharib24@alumni.colostate.edu
Citation:
Gharib, A. A., Arabi, M., Goemans, C.,
Manning, D. T., & Maas, A. (2024).
Integrated water management under
different water rights institutions and
population patterns: Methodology and
application. Water Resources Research,
60, e2024WR037196. https://doi.org/10.
1029/2024WR037196
Received 2 APR 2024
Accepted 3 OCT 2024
Author Contributions:
Conceptualization: Ahmed A. Gharib,
Mazdak Arabi, Christopher Goemans,
Dale T. Manning
Formal analysis: Ahmed A. Gharib
Funding acquisition:
Christopher Goemans, Dale T. Manning
Methodology: Ahmed A. Gharib,
Christopher Goemans
Resources: Mazdak Arabi,
Christopher Goemans, Dale T. Manning,
Alexander Maas
Supervision: Mazdak Arabi,
Christopher Goemans
Validation: Mazdak Arabi,
Christopher Goemans, Dale T. Manning,
Alexander Maas
© 2024. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution‐NonCommercial‐NoDerivs
License, which permits use and
distribution in any medium, provided the
original work is properly cited, the use is
non‐commercial and no modifications or
adaptations are made.
GHARIB ET AL. 1 of 19

Current water allocation institutions may be insufficient to mitigate extreme water shortages and economic losses
under a changing climate (K. A. Miller et al., 1997). Currently, most states throughout the western US allocate
water according to the Doctrine of Prior Appropriation (PA), which allocates water based on the seniority of the
water rights. Greater utilization of water rights transfers within the Doctrine of PA provides one example of an
institutional change that has been proposed to minimize the impacts of future shortages, because this flexibility
can reallocate water efficiently among new and competing uses (Garrick et al., 2013). However, the effectiveness
of water rights transfers in the western United States has been limited by high transaction costs and legal barriers
imposed by the region's water laws (Womble & Hanemann, 2020). Historically, water trades that have occurred
predominantly involve transfers from agriculture to urban areas (Payne et al., 2014) and have been controversial
due to the negative impacts on agriculturally dependent rural communities. An alternative to allowing flexibility
in the reallocation of water rights under PA would be to utilize a more “equitable” allocation institution. For
example, some participants in the ongoing Colorado River Basin negations have argued that—similar to the
original approach used to allocate water between the upper and lower states—future shortages should be allocated
equally among all users (Estabrook & Wertz, 2024).
Concurrent with concerns over water supplies, there is an ongoing debate over future development and zoning
policies throughout the western US. In response, numerous states have adopted legislation designed to promote a
more wholistic, state‐level view of land use planning. Examples of these efforts include new legislation in
Colorado—HB 1313—aimed at increasing high‐density residential development in transit‐oriented communities
(House Bill, 2024b) and—HB 1007—banning local residential occupancy limits (House Bill, 2024a), as well as
recent legislation in Arizona—HB 2570—that would allow the state to override local zoning laws (House
Bill, 2024c). Although not necessarily driven by concerns about future water shortages, land use planning efforts
that impact density and location of population centers throughout a basin, undoubtedly impact the availability of
water throughout a basin (A. Miller, 2023; Richter, 2023; Ty et al., 2012).
Currently, there is a limited understanding of how primary drivers of water scarcity—population location,
population density, water allocation institutions, and climate conditions—interact with each other at a basin level
to cause water shortages. Understanding how the location and density of population impact water demand and
supplies throughout a basin is key to developing water management policies aimed at mitigating the impacts of
climate change and rapid population growth.
In previous research, Räsänen et al. (2018) reported that water and land use policies need tighter integration to
minimize water‐related risks (e.g., floods, droughts, and poor water quality). Wang (2020), as well as numerous
technical papers (Belete & Gezie, 2017; Chhipi‐Shrestha et al., 2017; Shandas & Parandvash, 2010; Stoker
et al., 2019), suggest densifying the population through zoning and land use regulations as an effective tool for
improving water use efficiency and reducing per capita water demand. Despite this previous work, to our
knowledge, no existing study has examined how the distribution and density of populations interact with allo-
cation institutions and hydrologic conditions to impact the frequency and magnitude of water shortages
throughout a river basin, or the economic implications of such shortages.
While the importance of integrating land use and water management has been identified by researchers and
policymakers, as an important next step, its implementation is still limited. Stoker et al. (2022) published a
literature review on the integration of land use planning and water management and highlighted calls for better
integration (Angelo, 2001; Carter et al., 2005; Lucero & Dan Tarlock, 2003; Mitchell, 2005; Plummer et al., 2011;
Shandas et al., 2015; Stoker et al., 2022; X. Wang, 2001). Similarly, Colorado's Governor has acknowledged the
need for intentional land use/housing density policy given its clear implications for, inter alia, water use and
continued economic prosperity (A. Miller, 2023).
This study builds on the modeling framework by Gharib et al. (2023) and provides a new method for evaluating
integrated water and urban land use management strategies under alternative climate and institutional settings.
First, the methodology is presented; then it is applied to a representative watershed, the South Platte River Basin
(SPRB) in Colorado. Specifically, we consider three water institutions, update Gharib et al.'s (2023) urban de-
mand modeling to account for population density, and explore varying population patterns as a part of urban land
use planning. Lastly, we characterize the distribution of population patterns within the water basin that are most
likely to maximize economic values or minimize water shortages based on projected climate conditions and water
institutions.
Visualization: Ahmed A. Gharib
Writing – original draft: Ahmed
A. Gharib
Writing – review & editing: Ahmed
A. Gharib, Mazdak Arabi,
Christopher Goemans, Dale T. Manning,
Alexander Maas
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2. Methodology
This section outlines novel methods for evaluating integrated water management and urban land use planning,
presented by population location and density. The next section discusses the application of this method by
parameterizing and calibrating the models used for simulations. Figure 1provides an overview of the model
framework developed for this analysis. Model drivers (in gray) include irrigated area, climate, urban land use,
population density, and water institutions. These are used to generate model inputs (in green) that include water
supply, agricultural demands, and urban demands. Based on this information, the water allocation model gen-
erates half‐monthly water deliveries and calculates water shortages (yellow) for each user throughout the basin.
Simulated water deliveries are then input into an economic model to estimate the generated economic value (also
in yellow) from water across different runs.
In the context of this paper, and as further described below, each region consists of multiple demand “nodes”
corresponding to different uses of water. The demand for each node is calculated by aggregating the water use of
individuals within that region for that specific type of water use. For example, the indoor water use for an in-
dividual homeowner located within region 1a is aggregated, along with the indoor water use for all other in-
dividuals within region 1a, into a single node that reflects the indoor water demands for all water users within that
region. We use the terms “users” and “sector” synonymously to refer to these demand nodes.
For water rights institution θand climate scenario δ, the objective of this framework is to provide the shares of
population (x
r
) in each region, r, within a basin that yields the lowest basin‐wide volumetric water shortage (Z|θ,δ)
or that generates the maximum basin‐wide economic value (P|θ,δ) under dynamic modeling of water demand and
shortage. Both objective functions are solved independently, and optimal solutions may differ. The objective
functions are:
Minimize x(Z|θ,δ)=E[∑
i∑
r∑
t2
t1
Di,r,t(xr,θ,δ)Yi,r,t(xr,θ,δ)]Water shortage objective function (1)
Maximize x(P|θ,δ)=E[∑
i∑
r∑
t2
t1
Vi,r,t(xr,θ,δ)]Economic value objective function
Figure 1. Integrated urban land use planning and water management Framework. Model Drivers in gray, modeling tools in
green, outputs in yellow, and the integrated assessment solver in blue.
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Subject to:
∑
r
xr=1 Population shares constraints
Z|θ,δ≥0 Shortage constraints
Yi,r,t(xr,θ,δ)≤Di,r,t(xr,θ,δ)Water delivery constraint
∑
i∑
r
Yi,r,t(xr,θ,δ)≤Wt(δ)Water balance constraint
Where E[.] denotes the expected values of a response, Z|θ,δis the expected value of the annual total shortage
between years t
1
and t
2
for all users iin all regions rconditional on the water rights institution θand the climate
scenario δ, P|θ,δis the expected value of the annual total economic value between years t
2
and t
1
for all users iin all
regions rsimulated under the water rights institution θand the climate scenario δ,xis a vector of shares of basin
population in all regions, x
r
is the share of basin population in region r,D
i,r,t
is the water demand for user iin region r
in year t,Y
i,r,t
is the water delivered for user iin region rin year t, solved through a water allocation model, W
t
is the
water supply available for delivery in year tunder climate scenario δ, and V
i,r,t
is the value generated for user iin
region rin year t, solved through a model of economic value. Specifically, V
i,r,t
is the integral of the marginal
willingness to pay for water, p
i,r,t
, equal to the inverse demand function for water as presented by Maas et al. (2016):
pi,r,t=⎧⎪
⎨
⎪
⎩(Yi,r,t(xr,θ,δ)ηir
ci,r)1
ϵiif Yi,r,t(xr,θ,δ)≥˜
Yi,r,t
pmax
iOtherwise
(2)
where Y
i,j,t
is the quantity of water delivered to aggregate user iin region rat time t,c
i,r
is a calibrated constant,
p
i,r,t
is the marginal value of water, ε
i
is the price elasticity of demand for water, and η
i
represents water use
efficiency. Determination of a maximum marginal value is necessary for this model specification; otherwise, the
inverse demand function (p) in Equation 2goes to infinity as water delivery goes to zero. Therefore, we define a
parameter, pmax
i, as the maximum marginal willingness‐to‐pay (mWTP) for each user ithat represents the mar-
ginal value of water when water deliveries fall below a threshold level,
˜
Yi,r,t. In reality, the mWTP for water would
not go to infinity, particularly for agricultural water users who would face negative profits at high water prices.
Non‐agricultural users would have opportunities to use alternative sources, implying that the benefits of water are
finite.
The urban demand D
i=urban,r,t
is calculated by multiplying the population φ
r,t
in each region rby the per capita
demand in urban use j∈{indoor, outdoor}, U
j,r,t
. U
j,r,t
is a function of population density, S
j,r,t
such that:
Di=urban,r,t=∑
j
φr,tUj,r,t=∑
j
φr,t[αjSj,r,tβj](3)
where D
i,r,t
is the demand for user i∈{urban} in region rand year t,φ
r,t
is the total population of region rin year t,
U
j,r,t
is the per capita demand for urban use jin region rin year t,S
j,r,t
is population density per 10,000 m
2
,α
j
and β
j
are calibrated model parameters for sub‐users j. Total population φ
r,t
in each region rin year tis calculated by one
of the following equations:
φr,t=⎧⎨
⎩φH
r,to+xrφG
tif reallocating only population growth
xrφH
to+φG
t)if reallocating the total population
(4)
where φ
r,t
is the total population of region rin year t,x
r
is the share of population in region r,φH
r,tois the historical
population in region rat the baseline year t
o
,φG
tis the basin‐wide population growth from the baseline year t
o
to
year t, and φH
tois the basin‐wide historical population the baseline year t
o
.
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Finally, the statistically coherent probabilistic Dirichlet Distribution (Frigyik et al., 2010; Wong, 1998), a
common probability distribution in Bayesian statistics, is selected to generate random samples xof the population
shares across the model regions. The Dirichlet Distribution is specifically chosen as it ensures that the compo-
nents of the sample vector xare non‐negative and sum to one, which is essential since the elements of xrepresents
shares of total population (or population growth). It takes the form:
f(x;γ)=
Γ(∑
r
k=1
γk)
∏
r
k=1
Γγk)∏
r
k=1
xγk1
k(5)
where γis the shape parameter, fis the probability mass function, and xis the vector of population shares in each
region. The concentration of the distribution varies based on a shape parameter, γ. When γis greater than 1, the
density concentrates in the center of the probability simplex, defined as the set of all non‐negative vectors whose
components sum to one (Frigyik et al., 2010; Legaria et al., 2023). If γis between 0 and 1, the concentration shifts
to the vertices of the simplex (Frigyik et al., 2010). The distribution becomes uniform when γequals 1 (Frigyik
et al., 2010). Equations 1–5 present the mathematical formulation of the framework and the newly developed
methods. In the next section, we introduce the study area and methods for parameterizing the model.
3. Application
3.1. Study Area
The methodology is applied to the SPRB in Colorado, USA, which is in the Northeastern portion of the state and is
a critical water source for irrigation, municipal use, and recreation. Colorado is a state with well‐developed water
laws and active water markets (WM) (Brewer et al., 2008; Womble & Hanemann, 2020), which makes it an ideal
venue for this study. We chose SPRB as a case study because it represents many basins throughout the western US
that are facing water shortage challenges largely driven by rapid population growth and climate change. It is semi‐
arid and snow‐dominant with no upstream basins, relies partly on inter‐basin transfers, has an active water market,
and has mixed agricultural and urban communities. Around 20% of the basin water supply comes from inter‐basin
transfers from the Colorado River Basin, which is experiencing a 23‐year‐long severe drought (Wheeler
et al., 2022). The SPRB contains 71% of the state's population.
3.2. Data and Model Parameters
A calibrated water allocation model for the SPRB was developed by Gharib et al. (2023) using the Water
Evaluation and Planning (WEAP) Model (Yates et al., 2005), referred to as WEAP‐SP. WEAP attempts to
maximize deliveries to users throughout the basin using linear programming iteratively for each priority in each
timestep. In simple terms, WEAP allocates water to those nodes with the highest priorities first. Available water
supplies are then re‐calculated, including return flows, based on initial diversions. Subject to availability, water is
then allocated to the next highest priority user, after which streamflow conditions are recalculated once again.
WEAP iterates for each demand priority in each timestep without foresight until all demands are met, or water is
fully allocated (denoting a shortage).
Figure 2a illustrates the SPRB spatial layout and Figure 2b shows a schematic for the five SPRB demand regions
along the major water stream. WEAP‐SP runs from 1980 to 2099 on a half‐monthly time step basis. The water
supply to WEAP‐SP comes from 14 HUC8 catchments within the basin and six inter‐basin transfer projects that
provide water to agricultural and urban demands across the five demand regions. Urban demands are split into
indoor and outdoor demand nodes representing commercial, institutional, and industrial (CII), and residential
water demands. Sixty agricultural demand nodes are modeled to reflect the main crop types in the SPRB under
flood and sprinkler irrigation, represented separately. The coming section introduces the newly developed data for
WEAP‐SP upgrades with a brief description of the existing data in the model. Readers are referred to Gharib
et al. (2023) and the Supporting Information S1 for more details about the WEAP model and how it has been
calibrated for SPRB.
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3.2.1. Water Rights Institutions
Colorado, like 17 other western states, allocates water under the Doctrine of PA (Brown, 2006; Leonard &
Libecap, 2019). Under this doctrine, individuals and entities who first diverted water for “beneficial use” are
granted “seniority.” In times of shortage, if senior water users are unable to receive their total allotment due to
diminished flows, they can “call” junior water rights holders, forcing them to cease diversions until the senior
users' full allotments are met. In practice, this generally results in a seniority date, below which junior users must
reduce or pause withdrawals (Womble & Hanemann, 2020). PA does not broadly include any determination of the
economic value of water use when allocating flows during times of shortage (Burness & Quirk, 1979). Most PA
rights were established between 1850 and 1920 when water was valued primarily as an input to irrigated agri-
culture (Brewer et al., 2008). As such, it is feasible—and indeed frequent—that low‐value users have senior water
rights (Howe et al., 1982), though water rights sales from agriculture to urban users have occurred (Payne
et al., 2014; Womble & Hanemann, 2020).
For this analysis, we consider three simplified alternative water rights institutions (θ) including PA with fixed
water rights (PA), PA with reallocation consistent with functioning WM, and an institution that shares shortages
equally across all uses (ES). In reality, the PA and WM institutions share the same core underlying allocation
principles (e.g., water is allocated based on priority) but differ in how water rights are allocated in response to new
population growth. Under PA, we assume that the current allocation of water rights across sectors/regions re-
mains the same without the ability to reallocate water rights between users. Specifically, in the model, each
(aggregated) user's priority was assigned based on the weighted mean of the appropriation dates and the decreed
flow rate for the portfolio of water rights held by the respective user, as reported by the Colorado Decision
Support System database up to the year of 2015. This setup of PA institution not only helps us better understand
the role of transfers in meeting future demand challenges, but it also provides important information regarding
what the future would look like if transfers were no longer allowed.
Figure 2. (a) The South Platte River, South Platte River Basin, and the model regions. (b) Simplified WEAP‐SP schematic.
Water flows Northeast from regions 1a and 1b, ultimately leaving the basin once past region 4. Region 1a presents Boulder,
Broomfield, and Larimer Counties. Region 1b presents Douglas, Elbert, and Park Counties. Region 2b presents Adams,
Arapahoe, Clear Creek, Denver, Gilpin, and Jefferson Counties. Region 3 presents Weld County. Region 4 presents Logan,
Morgan, Sedgwick, and Washington Counties. Refer to Figure S1 in Supporting Information S1 for more details about
WEAP‐SP links and nodes.
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The WM institution simulates the outcome of PA when fully functioning WM exist; that is, when water rights are
allowed to be reallocated from agricultural to urban users to meet the demands associated with new population
growth. The primary difference between the two institutional settings is how water rights are assigned to new
demands. Under PA, water demands associated with new population growth are assigned to new nodes and
assumed to have a lower priority than all other existing demand nodes. Under WM, urban nodes associated with
population growth are assigned higher priority than agriculture users within each region, the assumption being
that urban communities will acquire senior water rights given the existence of a well‐functioning water market.
This assumption is consistent with how WM have functioned historically throughout the West previous water
market activity (Brown, 2006) and is in part a result of utility policies (and some state laws) throughout much of
the Southwest that require new developments to secure reliable water.
The ES institution represents a proportional allocation of shortages. The ES institution represents a proportional
allocation of shortages, where all nodes in the basin have the same priority. WEAP then allocates an equal
percentage of delivered water to each node based on its marginal demand. To implement this scenario within the
WEAP modeling framework all nodes in the basin are assigned the same priority. When multiple nodes share the
same priority and there are insufficient flows to meet all demands, WEAP then attempts to spread the shortages
equally across all nodes proportion to each node's demand. Collectively, these three institutions capture a wide
range of allocation scenarios: one which allocates shortages based on which use first diverted the water, one that
allocates shortages based on economic value, and one that allocates shortages equally across all uses regardless of
economic value or date of first use. Given concerns surrounding the distributional impacts of WM, the ES
institution is simulated as an alternative water institution that aligns with recent calls for a more equitable
allocation of water and water shortages. Table S1 in Supporting Information S1 summarizes all priority numbers
assigned to each demand node under all the water institutions; lower numbers mean higher priorities.
3.2.2. Climate, Water Supply, and Agricultural Water Demand
In this study, no changes are applied to the presented water supply, agricultural water demand, or climate sce-
narios in the calibrated WEAP‐SP from Gharib et al. (2023). Historical climate data from 1980 to 2015 are
sourced from Naz et al. (2016). Future climate projections through the end of the century come from Abatzoglou
and Brown (2012), who used Multivariate Adaptive Constructed Analogs (MACA) to downscale Global Climate
Models (GCMs) of the Coupled Model Inter‐Comparison Project Phase 5 (CMIP5) to high spatial resolution.
Four climate models are selected based on Joyce & Coulson's (2020) definitions of the hottest (HadGEM2‐
ES365), driest (IPSL‐CM5A‐MR), wettest (CNRM‐CM5), and warmest (MRI‐CGCM3) average over the US.
These definitions are based on precipitation and temperature changes over time as described by Joyce and
Coulson (2020). Also, two Representative Concentration Pathways (RCPs), 4.5 and 8.5, are considered for each
climate model, resulting in eight total climate scenarios, δ={hottest 8.5, hottest 4.5, driest 8.5, driest 4.5, wettest
8.5, wettest 4.5, warmest 8.5, warmest 4.5}.
The water supply, W
t
(δ), represents the summation of the water yield and the inter‐basin transfers to the basin
from neighboring basins. Water yield, from Heidari et al. (2020), refers to the contribution to renewable water
supply from recent precipitation, simulated under the above‐mentioned climate scenarios. It equals the sum of
surface runoff and base flow estimated by the Variable Infiltration Capacity (VIC) model (Liang et al., 1994). VIC
is a semi‐distributed macroscale scale model that solves full water and energy balances to simulate land‐
atmosphere fluxes and flow routing (Liang et al., 1994).
Historical and future agricultural water demands, D
i=Ag,r,t
, come from Gharib et al. (2023), where 6 crops (corn,
alfalfa, grass pasture, wheat & small grains, sugar beets, and dry beans) and two irrigation technologies (flood and
sprinkler), under both historical and the 8 future climate scenarios were simulated (Gharib et al., 2023). Gharib
et al. (2023) simulated the irrigation water requirements of each of the 5 regions in SPRB using the DayCENT
model (Del Grosso et al., 2000). DayCent is a daily timestep version of the CENTURY model, which is used
widely in agroecosystem studies to simulate crops, grasslands, forests, and savannas (Del Grosso et al., 2000).
Similar to Gharib et al. (2023), irrigated crops and irrigation technology —flood or sprinkler irrigation— are
assumed to remain constant in all future scenarios. Although this assumption may not entirely reflect reality, it
allows us to isolate the role of climate and institutions.
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3.2.3. Urban Water Demand
Historical urban water demands, D
i=Urban,r,t
, also come from Gharib et al. (2023), who used the Integrated Urban
Water Model (IUWM) (Sharvelle et al., 2017). The main inputs of the model are population, climate, and land
use. IUWM simulates residential indoor, CII indoor, and total outdoor demands. We aggregate them into indoor
and outdoor urban water demand for each region. Using the IUWM results from Gharib et al. (2023), we estimate
the historical indoor and outdoor per capita demands, U
j,r,t
, in each of the model regions.
To parameterize Equation 3, and calculate future per capita demand U
j,r,t
, we analyze monthly data on the total
billed residential and CII water from the Denver, Fort Collins, and Pueblo municipalities from 2010 to 2017
(Figure S3 in Supporting Information S1). These data were obtained from Chinnasamy et al. (2021) who analyzed
water data from 157 municipalities across the United States (Chinnasamy et al., 2021). Utilizing this data we first
estimate monthly indoor and outdoor per capita use. Average data for the months of December to March are used
to represent the indoor per capita demand U
j=indoor,t
in liters per capita per day (lpcd) for the entire year. Outdoor
per capita water demand U
j=outdoor,t
is calculated by subtracting the annual indoor per capita water demand from
municipalities' total annual per capita demand. The monthly outdoor demand patterns come from the historical
monthly average of the years 2010–2014 for each region of the IUWM simulations.
The population density, S
j,r,t
, is calculated as the total population divided by each city area and expressed in
population per 10,000 m
2
. These values were used to calibrate the power function in Equation 3for the indoor and
outdoor per capita water demand, U
j,t
. The calibrated parameters are α
indoor
=748.93, β
indoor
=  0.348,
α
outdoor
=4008.3, and β
outdoor
=  1.25 (Figure S3 in Supporting Information S1). Both βparameters are negative
meaning that as population density increases, the per capita demand decreases, with the outdoor declining more
rapidly. The R‐squared values and the Nash Sutcliffe Efficiency (NSE) for both equations are above 0.85 with less
than 3% Bias and above 0.82 Kling‐Gupta Efficiency (KGE), which indicates very good model performance
(Knoben et al., 2019; Moriasi et al., 2015, Table S1 in Supporting Information S1).
The future population projections, φG
r,t, were accessed from the Integrated Climate and Land Use Scenarios
(ICLUS) tool. ICLUS provides population projections from 2020 to 2100 for all US counties (EPA, 2017). The
SSP5 scenario is selected from the ICLUS V2.1.1 (EPA, 2020) to present the highest expected growth. As
described in Equation 3, the population φG
r,tis multiplied by the per capita demand U
j,t
to get the indoor and
outdoor total urban demand D
i=urban,r,t
.
Finally, water use efficiencies and losses were estimated during the calibration of the water allocation model by
Gharib et al. (2023) to calculate the required diversions. Required diversion is the consumptive plus return flow
and losses. For simplicity, required diversions will be referred to hereafter as water demand. In 2014, agricultural
demands represented 75% of the total demands with over half in Region 1a and 38% in the downstream regions
(Figure S2 in Supporting Information S1). Urban demand was 69% in Branch B and 20% in Branch A, leaving
11% of urban demand in the downstream regions (Figure S2 in Supporting Information S1).
3.2.4. Economic Model Parameter
Stylized demand curves, as presented in Equation 2, are developed for agricultural and urban users in each
region following Maas et al. (2016). The goal of this analysis is to capture the non‐constant marginal benefit of
water use in each of the sectors modeled. For agricultural users, we aggregate the agricultural users in each
region by irrigation type as Ag Flood and Ag Sprinkler. Similarly, indoor and outdoor urban users are com-
bined and then disaggregated by season into Urban Winter and Urban Summer. The maximum mWTP, pmax
ifor
urban and agricultural nodes are assumed as $405/1,000 and $81/1,000 m
3
, respectively. Ag elasticities,
ε
i∈{AgFlood,AgSprinkler}
, are estimated from the literature at 0.6 for Ag (Maas et al., 2016; Scheierling
et al., 2006; Schoengold et al., 2006). Urban elasticities ε
i∈{UrbanSummer,UrbanWinter}
, are assumed to be 0.7 and
0.2 for summer and winter periods, respectively (Dalhuisen et al., 2003; Espey et al., 1997; Olmstead
et al., 2007). Efficiencies, η
m
, are assumed as 0.5, 0.8, and 0.9 for Ag flood, Ag sprinkler, and both urban users
based on SPRB WEAP assumptions.
The demand curve for each user (i) (flood‐irrigated agriculture, sprinkler‐irrigated agriculture, summer‐time
urban, and winter‐time urban) has a unique kink point,
˜
Yi,r,t, when the demand function reaches pmax
i, calcu-
lated through the calibration of the demand curve, Figure 3). To calibrate the demand curves (Equation 2) and
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calculate c
i,r
, the initial price, p
i,r,t
is set to the lease price of $33.25/1000 m
3
based on historical climate and
hydrologic averages, suggested by Maas et al. (2016) relevant to SPRB. All dollar amounts are in 2016 nominal
values. The calibration constant c
i,r
is then calculated separately for each region under each simulation to get the
kink point
˜
Yi,r,t. The baseline demand curves of the baseline year 2014, the last year of the historical water
allocation model simulations, are presented in Figure 3. Finally, the generated economic value from water V
i,r,t
is
calculated by integrating the demand curves from zero to the water delivery Y
i,r,t
for each user and region and
normalized by the generated values in the baseline year of 2014. Qualitative results are consistent but exact
monetary values are sensitive to the choice of pmax
i. It is important to note that the generated values do not reflect
payments from buyers to sellers that would be associated with water market transactions. Instead, changes in
values captured by movement along the demand curves reflect the change in use value associated with receiving
more or less water in that sector.
3.3. Alternative Water Institutions and Population Patterns Scenarios
This section outlines the three key modeling scenarios applying the framework developed here (Table 1) to get
approximate solutions to the water shortage and economic value objective functions. Thousands of simulations
are implemented under these three scenarios to isolate the effects of changing climate, population location,
population density, and water institutions on water shortages and economic value using the water allocation
model, WEAP. The first scenario compares the effect of water institutions and climate on the water shortages and
generated values from water based on projected population growth locations and densities. The second scenario
tests the effects of population growth reallocation in SPRB by considering alternative spatial distributions of new
population in the SPRB, allowing density to differ based on location. The last scenario is intended to isolate the
effect of population location from the effect of the population density, by holding the population density constant
across space and testing the significance of only varying population locations within the basin. In this third
scenario, we consider moving total population around the basin not only population growth to get more gener-
alizable results. These scenarios are not designed to provide explicit policies to move current cities but to provide
better options for future urban land use and housing policies.
Figure 3. Demand functions for each water demand sector in Region 1a —largest Ag user— and Region 2b —largest Urban
user— calibrated to the year 2014. (Refer to Figure S4 in Supporting Information S1 for the functions of the five regions).
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A few key modeling assumptions are applied consistently across scenarios. Irrigated crop areas, crop types, and
irrigation technologies are held constant throughout the future time horizon as simulated by Gharib et al. (2023).
These assumptions control for agricultural demands so that the scenarios focus specifically on the effects of
changing climate and population patterns. The three alternative water institutions—prior appropriation, water
market, and ES—are applied to all simulations.
The first scenario provides an initial reference point to compare the three institutions and eight climate scenarios
before manipulating population densities and locations. We first assume that the projected locations of the
population come directly from the ICLUS dataset without any changes to their locations. Second, the urban per
capita demands U
j,r,t
for regions 3 and 4, with predominantly agricultural water use, are assumed to be constant
into the future, equal to their historical values. This is mainly due to their low‐density patterns in cities. Third, the
urban per capita demands U
j,r,t
for the upstream regions 1a, 1b, and 2b are predicted based on population density
using the power function presented in Equation 3. These regions are more urbanized areas and are assumed to
experience increased housing density that decreases the urban per capita demand.
The target of the second scenario is to test how the population density and location affect water shortages, and the
economic value generated. We assume that urban per capita demands U
j,r,t
hold as described in the previous
scenario; the downstream regions grow with historical per capita demand, and the upstream regions grow with
declining per capita demand. However, we vary the locations of the population growth across the regions rather
than relying on the values reported by ICLUS in each region. We employ two shape parameters in the Dirichlet
Distribution (Equation 5), γ∈{0.1, 0.7}, to generate two‐150 random variable sets xusing the gtools R package
(Bolker et al., 2022). The generated total of 300 samples covers a broad range of population combinations across
the regions, as demonstrated in the results section. Equations 3and 4are then applied to calculate the total
population φ
r,t
in each region and its urban water demand D
i=urban,r,t
for each population shares sample x. These
simulations are carried out under the driest 4.5 climate scenario and three different water institutions, with a total
of 900 simulations.
The last scenario focuses on the effects of population location within the basin while assuming constant future per
capita demand across all regions and future years to highlight the effect of population locations on water allo-
cation and economic value calculation. We assume all regions in the future have the same per capita urban de-
mand, similar to Region 2b's historical per capita demand. Region 2b is selected as the majority of the population
resides in it, and it has the highest efficiency of current water use. This approach allows us to isolate the impact of
population location on water allocation and the importance of their return flow while holding other factors
constant. Using this approach, we test how redistributing total population (including existing plus new
Table 1
Alternative Water Rights and Land Use Policies Scenarios
Scenario 1 Scenario 2 Scenario 3
Comparing the effects of water institutions and
climate scenarios
Population growth reallocation under SPRB land
use patterns
Effects of population locations to the water
allocation under constant per capita demand
Objective How do water institutions and climate scenarios
affect water shortages and economic values?
How does the incorporation of urban land use
intensification influence water shortages and
economic values in SPRB?
What is the preferred spatial pattern of
population within a basin assuming constant
population density across the basin?
Water
Institutions
3 3 3
Climate
Scenarios
8 1 1
Population
Locations
As Projected by ICLUS. 300 reallocation scenarios of the population
growth
300 reallocation scenarios of the total population
Population
Density
‐ Increases in upstream regions
‐ Constant in the downstream regions; urban per
capita demand is like the region's historical
values
‐ Increases in upstream regions
‐ Constant in the downstream regions; urban per
capita demand is like the region's historical
values
‐ Constant in all regions; urban per capita de-
mand is the same across all the regions
Number of
Simulations
24 900 900
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population) affects the water shortages and economic value. The same distribution (Equation 5) with the same
parameters as the second scenario is used to generate the sample vectors xof the population shares in each region.
4. Results and Discussions
In this section, the results of each scenario are presented separately. To simplify presentation, the five regions are
aggregated into two main regions: downstream regions (DS) representing Regions 3 and 4, and upstream regions
(US) representing the other three regions (see Figure 2). The results are presented for the mean of the far future
period from 2090 to 2099 to give average conditions not related to specific 1‐year climate data. Two key metrics
are used to assess scenario performance: the mean annual shortage ratio (annual shortage divided by annual
demand) and the mean annual generated economic value (generated economic value from mean annual water
delivery divided by the total generated value of the year 2014). These represent the values of the objective
functions described in Equation 1. Comparison of objective function values at all randomly drawn values of x
reveals approximate solutions to the optimization problems.
4.1. Comparison of Climate Scenarios and Water Institutions Under Baseline Population Growth and
Land Use Policies
Overall, water institutions do not appear to have a substantial effect on total shortages at the river basin level
compared to climate scenarios, but they influence the distribution of shortages across users and the total economic
value generated (Figure 4). This section presents the results of the first scenario (Table 1) which focuses on
investigating the effects of climate scenarios and water institutions on water shortages and economic value under
baseline population growth and land use projections in the SPRB for the far future period. Figure 4illustrates the
mean annual far future shortage ratios and generated economic values relative to the baseline year of 2014 (both
total and by sector) across each water institution and climate scenario. First, total shortage amounts vary little
across water institutions (maximum of 2% points), in contrast to the significant variations observed across climate
scenarios (above 35% points, Figure 4a). Second, while institutional changes have a relatively minor impact on
total shortage amounts, they have a significant effect on who gets shorted (Figures 4a and 4b).
The total economic value increases in the wet and warm climate scenarios regardless of the water institution
(Figure 4c), driven by population growth, as the average annual shortages are less than 4% (Figure 4c). For the dry
and hot climate scenarios, the generated value decreases in all except for Dry4.5 and Hot8.5 under WM institution
(Figure 4c), where water is allocated to urban users that have higher marginal value. Despite ES resulting in the
highest total shortage under each climate scenario (Figure 4a), it exhibits two positive aspects: it efficiently
distributes shortages between agriculture and urban sectors (Figure 4b) and generates higher total economic
values than PA by allocating water from low‐value users (e.g., flood irrigators) to high‐value users (e.g., urban)”
(Figure 4c).
As expected, the agricultural sector faces lower shortages and generates higher agricultural value under the PA
institution compared to the other two institutions (Figures 4b–4d). On the other hand, the urban sector faces lower
shortages and generates higher value under the WM institution compared to the other two institutions
(Figures 4b–4d). Figure 4d also reveals that all urban users under the WM institution generate more economic
value compared to 2014, irrespective of the climate scenario. These results collectively imply that altering water
institutions can influence which sectors experience water shortages and generate more value, but the overall
shortage and magnitude of value generated are primarily determined by climate changes, which are inherently
uncertain and not controlled by local policymakers.
4.2. Population Growth Reallocation Under SPRB Land Use Patterns
In SPRB, the lowest water shortage is observed as more population growth joins the upstream regions, which
reduces the total water demand because of the densification effect on urban water demand. As illustrated in
Figure 4, climate plays a pivotal role in determining water availability, serving as the primary driver of total
shortages, while other policies influence who experiences shortages and the extent of those shortages. Hence, to
facilitate interpretation of the effects of population growth location, we present results for the Dry 4.5 climate
scenario, which is the middle range of the simulated shortage and economic values (Figures 4a–4c). The results of
the second scenario (refer to Table 1) of reallocating the population growth with different patterns of per capita
demands are summarized in Figure 5, with the downstream share of population growth on the x‐axes. In each plot,
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900 points are presented for each simulation under different population growth distributions and water rights with
lines for the fitted second‐degree polynomial.
The mean total annual shortage for the far future period increases as the downstream share of population growth
increases (Figure 5a). This is mainly due to the constant (and relatively high) per capita urban demand assumed in
downstream regions, and the limited ability to reuse their return flows. On the other side, as more population joins
the upstream regions, the urban per capita demand decreases as population density increases (Figure 5c), which
decreases the shortage ratio (Figure 5a). Interestingly, the same trend applies across all water institutions, with ES
providing the highest shortage, similar to the results of the first scenario (Figures 4a and 5a). Prior Appropriation
tends to provide lower shortages compared to the water market institution as more population joins the down-
stream regions as seen by the increasing distance between the green and orange curves in Figure 5a.
According to the current distribution of population in SPRB, only 9% live in the downstream regions (Regions 3
and 4 in Figure 2b), and 63% reside in Region 2b, around Denver (Figure 2b). Although the total population of the
basin is projected to double by the end of the century, only 11.2% of the population growth is expected to occur in
the downstream regions (CWCB, 2019), reinforcing current population concentrations in upstream regions. This
suggests that projected growth is likely to lead to a relatively low overall shortage based on this scenario's
assumptions.
The mean annual value generated in the far future shows a different story, highlighting the importance of
including both metrics in water management studies (Figure 5b). The economic model generates more value as
Figure 4. Baseline Mean Annual Shortage Ratio and Mean Annual Value Generated (relative to the baseline year of 2014) for
the far future period 2090 to 2099. (a) Mean Annual Total Shortage Ratio. (b) Ag and Urban Mean Annual Shortage.
(c) Mean Annual Total Value Generated. (d) Ag and Urban Mean Annual Value Generated.
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more water is delivered to the sectors with high marginal WTP for water, specifically, to the urban sector.
Figure 5b shows that as the population growth share in downstream regions increases, more value is generated,
mainly because of increased water deliveries for the urban users that derive relatively large benefits from using
water. The total urban water demand is almost double when 100% of population growth is located downstream
compared to 100% located upstream (Figure S5 in Supporting Information S1). Urban demand has lower
consumptive use compared to agricultural demand which generates more return flow that can be used more than
once allowing for an increased amount of overall water delivery (Figure 5c, Figure S5 in Supporting Informa-
tion S1). This result occurs because downstream households have larger lawns and other outdoor water uses for
water that have high value. On the other side, densifying people in upstream regions reduces the urban marginal
WTP for water as people have smaller lawns and fewer outdoor water uses. This lowers the total economic
benefits from water used by urban households (Figure 5b).
Figure 5d shows the tradeoffs between the shortage ratio and the economic value generated across the population
growth reallocation scenarios. While denser urban development may lower total economic benefits from water
use due to reduced outdoor demand, this analysis does not imply that sprawling growth is preferable. Instead, it
emphasizes the importance of considering both economic and non‐economic factors, such as sustainability and
water efficiency, in guiding decisions about urban growth and water allocation.
Figure 5. Far future mean annual results for the second scenario which reallocates population growth in South Platte River
Basin with constant urban per capita demand for the downstream regions and declining per capita demand for the upstream
regions under the dry4.5 climate scenario (a) total shortage ratio, (b) total generated economic value relative to 2014, (c) total
delivered volume, and (d) total shortage ratio and generated economic value relative to 2014. Each dot represents one of the
900 simulations, and the lines show second‐degree polynomial fit.
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4.3. Effects of Population Locations to the Water Allocation Under Constant per Capita Demand
If all cities in the basin grow with the same urban water demand pattern, an even distribution of population
between upstream and downstream regions provides the lowest shortage and the highest economic value. For
more generalizable results that are not specific to the growth conditions in the SPRB, this third scenario (refer to
Table 1) assumes a constant per capita urban demand across all the regions in the basin and highlights the effects
of only varying the location of the population within the basin. Figure 6shows the results if all population –
including current population– is reallocated across the basin holding the per capita demand constant. It is
important to highlight that these results are conditioned on the locations of agricultural demands across the basin
(Figure S2 in Supporting Information S1).
Figures 6a and 6b display the result of the total population reallocation scenario with constant per capita demand
to eliminate the effect of the distribution of the current population of SPRB. It is apparent that the most favorable
outcomes, characterized by the lowest water shortages and highest economic values, emerge when populations
are distributed more evenly across both upstream and downstream regions under all institutions, assuming all
cities have the same water use pattern (Figures 6a and 6b). This finding emphasizes the importance of spatially
distributing populations within a basin to effectively manage water resources, taking into account the competing
demands for local water resources and return flows associated with each use.
Total shortages decrease and then increase as the downstream share of total population increases (Figure 6a). At
the same time, total value increases and then decreases (Figure 6b). These qualitative results hold under all water
institutions. Across the 300 model runs for each institution, the total shortage ratio spans from 15.5% to 28.9%
(Figure 6a). The range of economic values relative to the values of the year 2014 across all simulations is from
1.16 to 1.6 which reflects that economic value increases as more population exists regardless of the institutions
(Figure 6c). The water market institutions yield the highest values, followed by ES and finally PA. The lowest
shortage and the highest economic value take place when around 50%–70% of the total population is located in the
downstream regions (Figures 6a and 6b).
This finding emerges because urban water users typically have relatively low consumptive use rates, resulting in a
large return flow that can benefit downstream users. The advantage (from a water shortage perspective) of
distributing the total population between downstream and upstream regions is that the upstream population
generates high return flows that become available to the downstream populations. If all population is upstream,
this leads to high return flows but low downstream demand, diminishing the benefits from the return flows.
Similarly, if the population is concentrated downstream, no users in the basin could benefit from the generated
return flows. Further, concentrating the population downstream or upstream has other drawbacks, such as
intensifying competition for local water resources and increasing vulnerability to climate extremes. One
advantage of downstream population allocation is their ability to use all water infrastructure (e.g., reservoirs) and
Figure 6. Mean annual total shortage ratios (a) and mean annual total economic value generated relative to 2014 (b) for the far
future period 2090 to 2099 under Prior Appropriation, equal sharing, and water markets institutions and the dry4.5 climate
scenario. Each point represents one of the 900 simulations under the third scenario, which total population of South Platte
River Basin with constant urban per capita demand for all regions. The lines show second‐degree polynomial fit.
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access more of the water inflows into the basin. This reduces their vulnerability to climate extremes, similar to
California in the Colorado River Basin. The introduction of new land use policies governing where and how
populations grow emerges as a possible strategy for impacting water shortages and value, highlighting the sig-
nificant impact of population locations and their per capita use on water shortages and economic values.
5. Conclusions
This study develops an integrated assessment framework to evaluate the interactions of water allocation in-
stitutions, population patterns, and climatic conditions. The framework is then applied to the SPRB under three
main scenarios that provide insights into factors influencing water shortages and their associated economic
values. The first scenario involves the impact of climate scenarios and water institutions on water shortages and
economic value under baseline population growth assumptions in the SPRB. The second scenario explores the
effects of population growth location and density on water demand, water shortage, and the generated economic
value under varying water institutions. The last scenario isolates the effects of current and future population
locations on water shortages and the economic value generated.
Results from the first scenario reveal that while water institutional changes influence the distribution of shortages
among sectors, climate (together with population growth) remains the primary driver of total shortage. Despite
notable increases in shortages under some climate scenarios, the total economic value increases, as the urban
sector has increasing demands and willingness to pay for water, leading to higher economic values. While these
results are intuitive—more people demanding water leads to a higher marginal and total value for water—,
welfare implications should be interpreted with caution since future per capita water use is still lower than current
use. Notably, WM and ES institutions exhibit higher value generation due to the reallocation of water from
agriculture to urban users where the marginal value of water is higher. Population growth is identified as a factor
likely to amplify the economic value generated, particularly in the context of WM. In the SPRB, the lowest water
shortage is observed as more population growth occurs in the upstream regions, which reduces the total water
demand because of the densification effect on urban water demand.
Assuming the current urban land use of SPRB continues, the second scenario suggests that as more population
growth occurs in upstream regions, water shortages decrease, but the generated economic value also decreases.
While this result initially seems counterintuitive, it manifests largely because less dense communities have equal
or higher marginal values for a given level of water use. For example, a residential water user in downtown
Denver gets very little value from additional units of water beyond what is needed for domestic purposes, whereas
a user in a more rural community can use additional water for lawn irrigation or to fill pools. In this case,
allocating people to the upstream denser communities is better from the perspective of reducing water shortages.
The third scenario examines population reallocation under constant per capita demand, emphasizing the sig-
nificant influence of population location on total and sector‐specific shortages and economic values. Minimum
shortage and maximum economic value occur when population is distributed evenly between upstream and
downstream regions, representing a favorable strategy for minimizing water shortages while maximizing value.
Furthermore, the downstream population has advantages in terms of return flow availability, infrastructure uti-
lization, and climate resilience.
The presented scenarios highlight tradeoffs between water allocation institutions. The ES institution causes the
highest total shortage but allocates water more evenly between agricultural and urban users, which yields a
moderate economic value. The water market institution, on the other hand, generates the highest value as water is
allocated first to urban uses that have higher marginal values and higher return flows, but it also creates moderate
volumetric shortages. Lastly, the PA institution yields the lowest water shortage under most conditions but also
generates the lowest economic value.
Ultimately, this study demonstrates the importance of land use policies and the location of urban development as
tools to address water scarcity, irrespective of climate uncertainties or challenges associated with water rights
institutions. It highlights that both how and where communities grow matter in water management and assess-
ment. As policymakers seek reliable solutions to water resource challenges, the insights from this study offer
valuable guidance toward achieving sustainable water management through strategic land use planning.
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Notation
CII commercial, institutional, and industrial
Ag Agriculture
E[Z|θ,δ] expected value of the annual total shortage between years t
2
and t
1
for all users i∈{Agriculture,
Urban} in all regions rsimulated under the water rights institution θand the climate scenario δ
E[P|θ,δ] expected value of the annual total generated value between years t
2
and t
1
for all users iin all
regions rsimulated under the water rights institution θand the climate scenario δ
D
i,r,t
(x
r
) water demand for user iin region rat year t,
Y
i,r,t
(x
r
,θ,δ) water delivered for user iin region rat year tsolved through the water allocation model
V
i,r,t
(x
r
,θ,δ) value generated for user iin region rat year tsolved through the economic value model
xratio of the basin wide population in region r
x
r
vector of the ratios of the basin's population in each region r
W
t
(δ) water supply available for delivery at year tunder climate scenario δ
θWater institution
δClimate scenario
iDemand users i
rModel regions
tTime step or year
pmarginal value of water
mWTP marginal willingness‐to‐pay
pmax
imaximum marginal willingness‐to‐pay
ε
i
price elasticity
c
i,r
calibrated constant
η
i
Water use efficiency
Y
i,r,t
(x
r
,θ,δ) the quantity of water delivered user i
˜
Yi,r,tthreshold water delivery level
φ
r,t
total population of region rat time t
U
j,r,t
per capita demand for urban sub‐uses j∈{indoor, outdoor} in region rat year t
S
j,r,t
population density per 10,000 m
2
α
j
Calibrated parameter
β
j
Calibrated parameter
φH
r,tohistorical population in region rat the baseline year t
o
,
φG
r,tpopulation growth of region rfrom the baseline year t
o
to year t
γshape parameter of the Dirichlet Distribution
fprobability mass function of the Dirichlet Distribution
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Data Availability Statement
The data used in this model can be found at Gharib et al. (2024) (https://doi.org/10.4211/hs.cdeba87d39d94
8f6bdc91aefec6d1a1a).
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