Exploring the benefits of integrated energy-water management in reducing economic and environmental tradeoffs

Abstract

Integrated water-energy management is crucial for balancing socioeconomic and environmental objectives in multi-reservoir systems. Multipurpose reservoirs support clean energy production, recreation, navigation, and flood protection but also disrupt natural water flows and fish migration. As hydropower’s role evolves with grid decarbonization, managing these tradeoffs becomes increasingly complex. An integrated model combining economic and environmental factors is essential to inform how to adapt hydropower operations effectively to complement decarbonization of the electric grid. However, existing literature lacks such comprehensive models. This study introduces an integrated water-energy optimization model using the Columbia River Basin (CRB) and Mid-Columbia energy market as a case study. The model couples a simulation of operations of 47 CRB reservoirs with a unit commitment/economic dispatch model of the California and West Coast Power system. We employ Direct policy search and a multi-objective evolutionary algorithm to optimize four objectives: maximize economic benefits from energy production, minimize fossil fuel electricity generation, minimize environmental flow violations, and minimize peak flood levels. Our findings reveal that the integrated model discovers superior operational strategies compared to existing rules, with some policies outperforming current operations on all objectives simultaneously. Insights from the optimized policies include strategies for improved coordination of reservoir operations using storage and inflow data, and the strategic timing of water releases to ensure increased hydropower production leads to less fossil fuel dependence and greater revenue. These results highlight the potential of integrated models to enhance the sustainability of hydropower operations amid a transitioning energy landscape.

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Environ. Res.: Energy 1(2024) 035010 https://doi.org/10.1088/2753-3751/ad713d
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PAPER
Exploring the benets of integrated energy-water management in
reducing economic and environmental tradeoffs
Samarth Singh, Julianne Quinn∗, Jordan Kern, Rosa Cuppariand Greg Characklis
University of Virginia, Charlottesville, VA, United States of America
∗Author to whom any correspondence should be addressed.
E-mail: jdq6nn@virginia.edu
Keywords: hydropower, electricity markets, decarbonization, multi-objective optimization
Supplementary material for this article is available online
Abstract
Integrated water-energy management is crucial for balancing socioeconomic and environmental
objectives in multi-reservoir systems. Multipurpose reservoirs support clean energy production,
recreation, navigation, and flood protection but also disrupt natural water flows and fish
migration. As hydropower’s role evolves with grid decarbonization, managing these tradeoffs
becomes increasingly complex. An integrated model combining economic and environmental
factors is essential to inform how to adapt hydropower operations effectively to complement
decarbonization of the electric grid. However, existing literature lacks such comprehensive models.
This study introduces an integrated water-energy optimization model using the Columbia River
Basin (CRB) and Mid-Columbia energy market as a case study. The model couples a simulation of
operations of 47 CRB reservoirs with a unit commitment/economic dispatch model of the
California and West Coast Power system. We employ Direct policy search and a multi-objective
evolutionary algorithm to optimize four objectives: maximize economic benefits from energy
production, minimize fossil fuel electricity generation, minimize environmental flow violations,
and minimize peak flood levels. Our findings reveal that the integrated model discovers superior
operational strategies compared to existing rules, with some policies outperforming current
operations on all objectives simultaneously. Insights from the optimized policies include strategies
for improved coordination of reservoir operations using storage and inflow data, and the strategic
timing of water releases to ensure increased hydropower production leads to less fossil fuel
dependence and greater revenue. These results highlight the potential of integrated models to
enhance the sustainability of hydropower operations amid a transitioning energy landscape.
1. Introduction
The management of multi-reservoir networks is a critical aspect of water resource management (WRM),
with reservoirs serving a wide range of functions, from providing water for irrigation and clean energy to
offering flood protection and supporting recreational activities [1–3]. However, designing operations for
reservoirs is a challenging multi-objective control problem, as the need to balance competing socioeconomic
and environmental interests can lead to conflicts [4,5]. Classic tradeoffs include those between hydropower
and flood protection, or economic and environmental objectives [6–9]. However, different environmental
objectives can also conflict with one another. For example, releasing water to maximize hydropower
production and reduce fossil fuels emissions may hinder the system’s ability to meet subsequent
environmental flow requirements, thereby threatening the sustainability of fisheries that depend on natural
flows [10–12].
Improving reservoir operations to balance these objectives has been a primary research focus in WRM
for the past several decades (see reviews by [13–15]). Recent advances in model-free, closed-loop optimal
control methods like Direct Policy Search (DPS) have made it computationally tractable to optimize
operations at multiple reservoirs for conflicting objectives while implicitly capturing uncertainty in
© 2024 The Author(s). Published by IOP Publishing Ltd

Environ. Res.: Energy 1(2024) 035010 S Singh et al
stochastic weather forcing [16,17]. As a result, there have been extensive studies on operating large reservoirs
with the goal of supporting multiple needs such as renewable energy, flood control, and irrigation [18–22].
These studies span the globe’s major river basins and have led to policies that do a better job of balancing
these often competing priorities.
However, the multiple objectives considered in these studies have focused exclusively on the water system
impacts of changing reservoir operations, only considering energy impacts with respect to hydropower
generation. They have not captured the interaction of hydropower operations with energy markets, which
has proximate consequences for the calculation of both financial impacts of alternative operations on energy
distributors, and environmental impacts via fossil fuel emissions. For example, many previous studies in the
water systems literature have designed reservoir operations to maximize hydropower production under the
assumption that this will correspond to increased revenue [23–26]. However, this ignores the influence of
hydropower availability on the energy mix, electricity markets and electricity prices. In electricity markets
dominated by hydropower, energy suppliers and their customers stand to benefit from understanding how
changes in reservoir operations impact electricity prices and utility revenue. With respect to fossil fuel
generation, hydropower plays a crucial role in a sustainable energy mix by optimizing the use of water
resources to reduce reliance on fossil fuels. However, simply maximizing hydropower generation as many
studies do [27,28] will not necessarily minimize fossil fuel generation; reservoirs need to be operated
strategically to enhance grid stability and enable the integration of variable renewables like wind and solar to
minimize fossil fuel-fired power generation and their associated emissions. Yet previous water systems
models have not quantified the reduction in fossil fuel generation that can be achieved through optimized
hydropower operations [29–32].
In contrast, the energy systems literature addresses how hydropower operations influence energy markets
and fossil fuel emissions, but often omits consideration of water system objectives. For example, work in the
Brazilian hydroelectric system has jointly optimized hydropower and thermal generation utilizing stochastic
optimization to maximize net spot revenues or expected benefits of reducing thermal generation, but
neglects other priorities, such as flood control and environmental flows [33–35]. An integrated model of the
water and energy system is needed that can jointly capture all these conflicting water and energy system
objectives and design hydropower operations to balance them.
This study addresses these gaps in existing research by tightly coupling a reservoir operations model with
a power systems model and then jointly optimizing operations for multiple objectives using the integrated
model. The tight coupling of the integrated model is critical. In a hydropower system, loosely coupling a
reservoir operations model and power systems model allows one to first simulate reservoir operations and
then optimize the dispatch of other power sources conditional on those outputs. However, optimizing
reservoir operations to minimize fossil fuel emissions and maximize revenue requires a tight coupling
between these two models in which outputs from the power systems model feed back to inform the reservoir
operations model. In this case, a tight coupling is needed so that electricity prices and fossil fuels generation
from the power systems model can inform the hydropower operations in the reservoir model.
We build such an integrated model using the Bonneville Power Administration (BPA) in the U.S. Pacific
Northwest as a case study. BPA is a useful system for exploring the impacts of changing hydropower
operations on electricity markets, as half of the region’s electricity is generated by hydropower from 31 federal
dams operated by BPA [36]. BPA’s heavy dependence on hydropower exposes it to revenue fluctuations due
to weather variability which, when combined with high fixed costs and obligations to meet minimum
electricity delivery contracts, lead to financial losses. Though BPA has access to several risk mitigation tools,
this financial risk has caught the attention of credit rating agencies who have cited hydrometeorological
variability as a key factor in BPA’s creditworthiness, and also led to a 2020 downgrade of BPA’s rating by
Moody’s, a major rating company [37]. This financial risk highlights the need to assess reservoir operations
in the CRB to stabilize BPA’s revenues under variable hydrologic conditions. An integrated model of this
system could also be used in future work to inform how BPA should adapt reservoir operations as their
revenue is impacted by changes in the energy mix, climate change, and evolving regulations [38,39].
The BPA system is also an interesting case study for understanding how hydropower operations can
better complement renewables. Within the West Coast Power System, California has been rapidly expanding
solar power capacity, while the Pacific Northwest has been expanding wind power capacity [40,41]. When
production of these renewables is high, reservoirs can hold back water and store it for subsequent production
when renewable resource availability is low. Such load balancing is not restricted to the Mid-Columbia
(‘Mid-C’), market in which BPA resides, as BPA production can be exported to California as well.
Coordinating power dispatch of renewables in this way could reduce the need to use fossil fuels for load
balancing across the two regions, an environmental benefit of hydropower production that has not been
quantified in prior work.
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
In summary, this work fills two critical gaps in designing reservoir operations for conflicting social,
economic, and environmental objectives: (1) it models the impact of changing hydropower operations on
electricity prices to estimate (and ultimately, reduce) consequent impacts on revenue for power producers,
and (2) it models the integrated dispatch of electricity generators to meet system demands across two
inter-connected balancing authorities, enabling coordinated operations for minimizing fossil fuel
generation. These two objectives are included with traditional reservoir operating objectives of minimizing
flooding and environmental flows violations. While the work focuses on operations within the Columbia
River Basin (CRB), part of the Mid-C market, our approach to modeling integrated operations can be
generalized to other systems, and we find generalizable insights on how to coordinate reservoir operations
for these objectives that apply to hydropower systems around the globe.
2. Methods
2.1. California and west coast power system
This research aims to address the question of how power suppliers can adjust hydropower operations to
minimize sustainability tradeoffs between reducing fossil fuel emissions and environmental flow violations,
while maintaining or increasing hydropower revenue and flood protection. To investigate this question, we
focus on the CRB in the Pacific Northwest (PNW) as a case study (figure 1). In the CRB, there are 31 federal
dams owned by the U.S. Army Corps of Engineers (USACE) and U.S. Bureau of Reclamation, which supply a
significant portion (50%–65%) of the region’s electricity and offer 55.3 million acre-feet (AF) of storage for
flood protection [3].
The USACE establishes operating guidelines for the dams to fulfill non-power objectives like flood
control and environmental conservation. The Bonneville Power Administration (BPA) manages the dispatch
of hydropower resources within these constraints. These decisions are influenced by market forces. The CRB
dams are part of the Mid-Columbia (Mid-C) electricity market, where prices are affected not only by CRB
reservoir operations but also by activities in the California Independent System Operator (CAISO) market
[42].
Operating the CRB reservoirs within the USACE’s established constraints is becoming increasingly
challenging due to evolving political, environmental, and technological factors [43–45]. The widespread
adoption of cost-effective renewable energy sources in the Western United States has negatively impacted
BPA’s revenue [46]. Nevertheless, there are opportunities to provide valuable generation flexibility to mitigate
the variability of renewables. For instance, hydroelectric power in the CRB can be exported to California
when its energy supply is insufficient. This influences electricity prices in both regions, affecting revenue for
BPA, as well as consumer electricity costs.
However the optimal seasonality of hydropower operations can pose a threat to the survival of salmon
and other fish that rely on natural flow patterns in the CRB [47]. Flood control along the Columbia River is
another significant concern. In the CRB, this has historically been addressed by the Columbia River Treaty
(CRT) under which Canada is required to operate their reservoirs within flood risk management guidelines.
However, U.S. reservoirs may need to provide additional flood protection in the future under climate change.
These additional operational objectives for flood protection and environmental flows may limit the ability of
hydropower to serve as a renewable energy source for load balancing.
In this study, we optimize operations at four of the BPA dams shown in red in figure 2(a): Hungry Horse
(HGH), Libby (LIB), Dworshak (DWR) and Grand Coulee (GCL). While there are 31 federal dams, all but
six of them operate as run-of-river at the daily time step. Of the remaining six storage dams, we chose the
prior four for optimization based on their turbine ratio (turbine capacity/average inflow), and flood storage
capacity, measured in days of average flow. We included dams in our optimization if they have a turbine ratio
greater than 2 (GCL and HGH), or more than 250 days of flood storage (HGH, LIB, and DWR). These
thresholds were chosen to ensure that the selected reservoirs have significant capacities for either power
generation or flood mitigation. The storage and power capacities of these four reservoirs are listed in table A1.
2.2. Integrated water-energy model
In order to design better multi-objective hydropower operations at the four red dams in figures 1and 2(a),
we need an integrated, tightly-coupled energy-water systems model [48]. Figure 2(b) illustrates the
components of this integrated model and their connections. Each model component is described in more
detail within its own section.
For the reservoir system, we represent current operations in the CRB using a Python translation of the
Hydro System Seasonal Regulation (HYSSR) model, originally written in Fortran [49]. This model is
described in section 2.3. We adapt the HYSSR model by converting it from a simulation model to an
optimization model for stochastic optimization. The objectives under consideration are environmental
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Figure 1. Map of the California and West Coast Power System modeled by CAPOW. The Mid-C and CAISO markets are modeled
by separate UC/ED models, with statistically generated imports and exports between them and external markets. In this study,
reservoir operations at 47 Columbia River Basin dams are modeled according to existing rules for all but four dams, whose
operations are optimized.
Figure 2. (a) Map of the Columbia River Basin (CRB) and all modeled dams with non-zero storage. Operations at all dams in
black use existing rules, while operations at all dams in red are optimized. (b) Integrated Reservoir System Management model
(RSM), which consists of a reservoir simulation model of the CRB and an energy systems model of the California and West Coast
Power System (CAPOW).
(deviations from spills targets for salmon migration and fossil fuel generation), economic (BPA revenue),
and social (flood protection). Environmental spills violations are calculated directly from the reservoir
simulation model, while all other objectives require additional component models for their computation.
Environmental spills are calculated as the sum of squared deviations in spills simulated by HYSSR at
seven reservoirs downstream of Grand Coulee from targets informed by personal communication with
USACE ([50]; see table A2 for the list of reservoirs under the spills violations constraint). Minimum spills
during salmon migration to the Pacific Ocean allow juveniles to more easily travel downstream without going
through hydropower turbines, while maximum spills prevent dissolved gases from exceeding 110%–120%
4

Environ. Res.: Energy 1(2024) 035010 S Singh et al
saturation, levels that can give the fish gas bubble disease [51]. The flood objective is calculated using a
statistical model of the water level in Vancouver, WA as a function of discharges from the most downstream
dam (Bonneville) and other tidal components, with the goal of reducing peak levels (see section 2.4).
Estimating BPA revenue and electricity generation from fossil fuels requires an additional power dispatch
model, described in section 2.6. BPA revenue is calculated as a function of the hydropower generation
simulated by HYSSR and electricity prices. Electricity prices are computed by integrating the HYSSR model
with the California and West Coast Power System model (CAPOW). CAPOW (described further in
section 2.5) is a unit commitment and economic dispatch model for electricity markets in the Mid-Columbia
and California Independent System Operator (CAISO) regions [52]. It represents all types of generators,
including renewable and non-renewable sources, and considers interactions with other regions in the
Western Electricity Coordinating Council. From this model, we can also determine how much hydropower
generated in Mid-C in excess of its demand can be exported to CA to reduce its fossil fuel generation.
The integrated Reservoir System Management model (RSM), as depicted in figure 2(b), takes as inputs
historical or synthetic meteorological data and a reservoir control sequence (to be optimized), and provides
as outputs daily measures of renewable and non-renewable electricity generation, electricity prices, flood
levels, environmental spills, and BPA revenue.
2.3. Reservoir simulation model
For the reservoir system, we represent current operations in the CRB using the Hydro System Seasonal
Regulation (HYSSR) model, an existing operations model for the CRB developed by the U.S. Army Corps of
Engineers for planning short and long-range operations. HYSSR represents the 47 largest reservoirs in the
CRB, with a total installed hydroelectric capacity of 34 GW. These dams are shown in figures 1and 2(a), with
the exception of one non-power dam that is excluded from figure 1and 16 dams with no storage that are
excluded from figure 2(a). Nine of the 47 dams (six in the U.S. and three in Canada) impound reservoirs with
significant storage whose releases are governed by historical nonlinear rules, while the remainder are
considered run-of-river, i.e. their daily release is the same as their daily inflow. These reservoirs contain
numerous powerhouses and turbines that need to be operated in a specific order based on seasonal
requirements, including fish passage and environmental constraints.
Hydropower generation by dams is calculated using the following equation, which relates the physical
properties of the water flow to electrical power output:
P=ηρghrPH (1)
where Prepresents the electrical power generated in watts (W), ρis the density of water (1000 kg m−3), gis
the acceleration due to gravity (9.81 m s−2), his the hydraulic head (m), rPH is the flow rate through the
powerhouse in cubic meters per second (m3s−), and ηis the coefficient of efficiency, a dimensionless factor
that accounts for losses in the system.
To model oversupply events, which require a shorter time step, HYSSR has been adapted to daily
operations. This modified version includes 46 dams, categorized as storage or run-of-river projects. Storage
projects manage inflows for flood control, water supply, and power production, storing peak runoff from
spring and summer for later release. Run-of-river projects pass inflows directly through turbines (and spills,
if inflows exceed the turbine capacity).
The modified HYSSR model calculates daily storage, outflows, and power generation based on inflows,
discharge requirements, storage levels (for storage projects), and operational rule curves. These rule curves
consider projected inflows (here, using perfect forecasts), flood control, power needs, design limits, and
regulatory constraints. Using synthetic streamflow data and rule curves, the model provides daily values for
reservoir storage, outflow, and hydropower production. Generation from each of the unmodeled dams
(totaling 12.5% of system hydropower capacity) is estimated by proportionally scaling generation from the
closest modeled dam based on the ratio of their capacities [46].
Finally, in our optimization, we change the operations at four of the HYSSR dams, as described in
section 2.7.
2.4. Downstream water level model
In the CRB, the main location of concern for flood control is just above the confluence of the Columbia and
Willamette Rivers in Vancouver, WA. Water levels in Vancouver, WA are mainly influenced by releases from
the Bonneville Dam, tidal fluctuations, and backflow from the Willamette River. A statistical model was
developed to estimate the water level at the gauge in Vancouver, WA utilizing discharges from the Bonneville
Dam, periodic functions representing the tide, and prior model errors as predictors. Prior model errors
capture persistence, including in influences from the Willamette. The model is specified as follows, with the
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 3. Actual vs predicted values of Vancouver’s water level.
flood level at time t, denoted as Yt, calculated using the equation:
log(Yt) = β0+β1·log (rBON,t) + β2cos2πt
365 +β3sin2πt
365 
+β4cos2πt
14.75+β5sin 2πt
14.75+wt+ϕ1wt−1+ϕ2wt−2,
(2)
where, β0represents the intercept of the model, β1quantifies the impact of log-transformed discharge from
the Bonneville Dam on flood levels, and β2and β3capture the seasonal effects within the year, β4and β5
capture the tidal effects each month, wtare residuals distributed as wt∼ N (0,0.0942)and ϕ1and ϕ2are
moving average coefficients on the past two time steps of residuals. The term rBON,t refers to the discharge
from the most downstream dam of our network Bonneville in thousands of cubic feet per second (kcfs). The
values of the intercept and coefficients are reported in SI table S5.
Due to a limited historical record of six years of daily water level data, the model was fit to the entire
record rather than employing split training and testing. Over this period, the model exhibits strong predictive
power, with an adjusted R2value of 0.82 (figure 3). Additionally, the residuals of the model follow a normal
distribution (see SI figure S2), indicating that the model adequately captures the underlying patterns in the
data. When simulating water levels in our model, we add randomly generated noise from this distribution to
ensure we capture the full variance of downstream water levels and do not under-predict extremes.
2.5. Energy prices model: CAPOW
The California and West Coast Power System Model (CAPOW) generates synthetic data of electricity
demands and supply, and then uses a least-cost electricity dispatch model to calculate electricity prices in the
California Independent System Operator (CAISO) and the informal Mid-Columbia (Mid-C) markets [53]. It
consists of two major components, ‘Stochastic Engine’ and ‘Unit Commitment/Economic Dispatch
(UC/ED)’.
The stochastic engine uses a vector auto-regressive model to generate standardized anomalies of synthetic
hydro-meteorological data including temperature, wind speed, and irradiance, that are then un-standardized
based on monthly-varying estimates of each variable’s mean and standard deviation. Synthetic ‘modified’
streamflows are then generated from a fitted Gaussian copula, conditioned on the heating degree days from
the synthetic hydro-meteorological data. Modified streamflows refer to naturalized, i.e. unregulated flows,
minus evaporation and diversions. Thus, we do not make decisions around water supply diversions in our
optimization model, which is reasonable given the limited ability to change them through the existing water
rights system. The synthetically generated hydro-meteorological data is also used to simulate stochastic
electricity demands and supply through a number of regression models (see [52] for more details).
On the supply side, solar and wind capacity factors are simulated from multivariate regression models
applied to the stochastically generated irradiance and wind speed data, respectively. Hydropower generation
is estimated by simulating reservoir operations over the synthetically generated streamflow time series. Any
simulated generation in excess of the synthetically generated demands is assumed to be curtailed. As
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
discussed in section 2.3, dams representing over 85% of hydropower capacity in the Pacific Northwest are
modeled using a Python translation of the Hydro System Seasonal Regulation (HYSSR) model for the CRB.
Dams on the Willamette River in the Pacific Northwest are simulated by a Python translation of a
HEC-ResSim model. Finally, the Operation of Reservoirs in California model (ORCA; [54]) simulates
hydropower generation in the major dams of California, which sums up to the total hydropower supply in
the west coast [52].
In the UC/ED model, the dispatch of electric generators across the CAISO and Mid-C markets is
meticulously determined using separate least-cost mixed integer linear programs for each region, tailored to
meet the unique power demands of each system. The marginal cost of electricity from solar, wind, and
hydropower is set to 0. As such, thermal generators like natural gas and coal are dispatched last. The market
price is set by the cost of the most expensive electricity source once cheaper options are exhausted. The
UC/ED model includes interconnections between the Mid-C and CAISO markets as well as outside markets,
so demands are met while accounting for imports and exports between the two regions and from other
external nodes (see figure 1). Imports and exports along these paths are generated synthetically based on
historical patterns and transmission capacity. The dispatch decisions are optimized for every hour over the
next 48 hours using perfect foresight. However, decisions are only implemented for the first 24 hours, and
then re-optimized for the next 48-hour window. This is performed over a 1-year horizon and run
independently across 100 different years. For a comprehensive understanding of the methodologies
originally employed in this study, readers are encouraged to consult the detailed exposition provided by [52],
especially its Supplementary Information.
While CAPOW is powerful in enabling us to predict the market impacts of changing reservoir
operations, it is too computationally expensive to couple with an optimization model. As such, we first ran
CAPOW over 1000 years of synthetic hydro-meteorological data and then used those model runs to build
statistical surrogates of electricity prices in the CAISO and Mid-C markets. The surrogate models are linear
regression equations (equations (3) and (4)) that predict daily prices in the two regions in $/Mwh as a
function of energy demands, exports, imports, solar, wind, and hydro generation:
PricesMidC
t=maxβ0+β1·DemandsMidC
t+β2·ExportsMidC
t+β3·WindMidC
t
+β5·HydroMidC
t+β6·ImportsMidC
t
+β7cos2πt
365 +β8sin2πt
365 +ϵMidC
t,10
(3)
PricesCAISO
t=maxβ0+β1·DemandsCAISO
t+β2·ExportsCAISO
t+β3·SolarCAISO
t
+β4·WindCAISO
t+β5·HydroCAISO
t+β6·ImportsCAISO
t
+β7cos2πt
365 +β8sin2πt
365 +ϵCAISO
t,10.
(4)
The models were trained over 800 of the 1000 years and their performance was tested on the remaining
200 years. The values of all predictors are reported in SI tables S3 and S4. Figure 4shows the actual vs
predicted values of the energy prices in the CAISO and informal Mid-C markets simulated by CAPOW vs.
our emulator over the test set. The emulators in both the markets provide a good fit with adjusted R2values
of 0.89 and 0.82 in CAISO and Mid-C, respectively. We reproduce remaining variability in our integrated
model by adding bootstrapped residuals (ϵMidC
tand ϵCAISO
t) from the emulators to their predictions,
conditioning the bootstrapping on the 10-percentile width bin in which the predictions lie, as in [55]. See SI
figure S3 shows the empirical cumulative distribution function of CAPOW prices vs. those simulated by our
surrogates with added residual noise.
2.6. Bonneville power administration financial model
The Bonneville Power Administration (BPA) is a power marketer in the U.S. Pacific Northwest, responsible
for selling the hydroelectricity generated at the 31 federal dams in the Federal Columbia River Power System
(FCRPS). Because this hydropower contributes 80% of BPA’s overall generation capacity [56], it is financially
vulnerable to temperature and hydrologic variability, which influence electricity demand and generation,
respectively. This vulnerability has been noted by credit rating agencies and internal reporting and has
contributed to the depletion of BPA’s line of credit with the U.S. government, one of its three primary risk
management tools [37,57–59]. Prior analysis has suggested that an inability to mitigate its
hydrometeorological risk could lead to losses of up to $200 million [60] and over $1 billion in costs [61].
7

Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 4. Actual vs predicted values of the statistical surrogates of the (a) Mid-C and (b) CAISO markets.
Adjusting the timing and volume of water releases and power generation can mitigate the impact of
hydrometeorological variability, but influences other system objectives.
To account for the linkage between hydropower production and financial outcomes, this work uses the
BPA financial model developed by [60] and refined by [61], which takes into account BPA’s existing risk
management tools (cash reserves, line of credit, and tariff adjustments). The model uses hydropower
generation and downscaled demand from CAPOW as inputs. Revenue is calculated daily, largely from
electricity sales to meet firm obligations at fixed prices. Surplus electricity is assumed to be sold directly on
the wholesale Mid-C electricity market or exported to and sold within the CAISO market, depending on
which market has higher prices. Should hydropower generation fall short of BPA’s fixed electricity delivery
obligations, BPA must purchase compensatory electricity to offset the deficit. In our model, this is either
purchased from the Mid-C or imported from CAISO, whichever is cheaper. Annual net revenues are
simulated by subtracting BPA’s operating costs, held constant at 2018 historical values, as in [60].
2.7. Formulation of multi-objective optimization problem
2.7.1. Formulation of objectives and constraints
In this study, we utilize Evolutionary Multi-Objective Policy Search (EMODPS; Giuliani [16]) to find a set of
non-dominated reservoir operating policies, p∗
θ, that minimize a vector of operating objectives¯
J:
p∗
θ=argmin
pθ
¯
J(5)
where
¯
J=|Jenv ,Jfld ,−Jrev ,Jfos |.(6)
Each element of ¯
Jis defined below, while the form of the operating policies pθis defined in section 2.7.2. The
outcome of the optimization is a set of non-dominated solutions, called the Pareto approximate set, in which
no solution outperforms another on all objectives.
Environmental spills. Let spillsi,trepresent the spills from reservoir ion day t, minSpilli,tbe the minimum
desired spills from reservoir ion day tto enable salmon migration through the dams, and maxSpilli,tbe the
maximum desired spills from reservoir ion day tto prevent supersaturation of dissolved gases above water
quality standards. The environmental spills objective is then defined by equation (7):
Jenv =1
Nd
Nr

i=1
Nd

t=1max0,spillsi,t−maxSpilli,t2+max 0,minSpilli,t−spillsi,t2.(7)
where Nris the number of reservoirs with spills regulations (see A2) and Ndis the number of days in the
simulation.
Flood protection. The flood objective, to be minimized, is calculated as the maximum water level at
Vancouver, WA, over the course of the simulation. This is defined by equation (8), where ZV
tis the water level
8

Environ. Res.: Energy 1(2024) 035010 S Singh et al
at Vancouver, WA at time t.
Jfld =max
t∈Nd
ZV
t.(8)
Fossil fuel generation. The fossil fuels objective, to be minimized, is calculated as the average daily fossil fuel
generation across the Mid-C and CAISO markets over the simulation horizon. Letting FossilstMidC represent
the fossil fuel generation in the Mid-C market on day t, and FossilstCAISO represent the fossil generation in
the CAISO market on day t, this is calculated by equation (9):
Jfos =1
Nd
Nd

t=1FossilstMidC +FossilstCAISO(9)
where FossilstMidC and FossilstCAISO are calculated using algorithm 1, provided in the appendix. This
algorithm describes how hydropower generated by our optimized policies in excess of HYSSR generation is
used to reduce fossil fuel generation in the two regions so that total power generation does not exceed total
demand. Excess hydropower is first used to reduce Mid-C fossil fuel generation down to a fixed minimum for
the region, capturing reserves. Any remaining excess hydropower is then exported to CAISO, where fossil fuel
generation is reduced down to a separate region-specific minimum. If total generation still exceeds total
demand, the remaining excess hydropower is curtailed. While this simplifies some elements of the power
system, it greatly reduces the cost of re-running CAPOW with the alternative operating rules, while showing
satisfactory performance in producing similar fossil fuel generation, as validated for one policy over three
years in SI figure S4.
BPA revenue. The final objective is to maximize BPA’s average annual net revenue in millions of U.S. dollars
(USD), calculated by the BPA Financial Model:
Jrev =1
Ny
Ny

y=1
NRy(10)
where NRyis BPA’s revenue in million USD ($M) in year yand Nyis the number of simulated years.
Non-Zero Storage Constraint. Finally, we include one constraint in the model that storage cannot be
negative at any of the reservoirs. While we also ensure this through mass balance constraints in the
simulation model, explicitly adding it as an optimization constraint prevented reservoirs from emptying
during the time series used for optimization.
Sres
t⩾Sres
min ∀res ∈RES (11)
where RES is the set of all model reservoirs and Sres
min is the minimum storage of reservoir res, ∀res ∈RES
Note that for this study, we set Sres
min to zero for all the four reservoirs.
2.7.2. Formulation of operating policies
In EMODPS, reservoir operating policies are parameterized within a certain family of functions describing
the release from the reservoirs as a function of different state variables. We employ Gaussian Radial Basis
Functions (RBFs) for these operating rules because [17] demonstrated their superior effectiveness in
representing reservoir operating policies compared to Artificial Neural Networks (ANNs) with hyperbolic
tangent activation functions. The RBF-based operating policies, described by equation (12), specify daily
normalized releases from the kth of Kreservoirs at a given time t, denoted as uk
t. These releases are
determined as a function of Btime-varying inputs, represented as vt, also normalized within the range [0,1]
uk
i=
N

i=1
wk
iexp
−
B

j=1vt,j−ci,j2
b2
i,j

.(12)
In this context, Nrepresents the total count of RBFs and vtis a vector comprising Binputs that have been
scaled to fall within the [0,1] range. (ci,j,bi,j) represent the center and radius of the jth input variable for the
ith RBF, and wk
isignifies the weight associated with the ith RBF for the kth reservoir. The weights are
constrained to add up to 1 for a given reservoir, k, representing a convex combination.
For the CRB system, we use N=8 RBFs, K=4 reservoirs, and B=7 inputs, resulting in
N(2B+K) = 144 optimized parameters. The seven RBF inputs are: the storage at each of the four reservoirs
9

Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 5. Policy performance of all optimized Pareto-approximate policies (colored lines) and HYSSR (black line) across (a) 15
years of synthetic flows used for optimization and (b) 100 years of synthetic flows used for validation.
whose operations we optimize (see table A1), the sum of interflows to the four reservoirs on the previous day
and a cyclic representation of time captured by sin2πt
365 and cos2πt
365 , all of which are normalized on [0,1].
The sum of interflows can be thought of as unregulated inflows that would be received by the reservoirs in
absence of operations. In the model, the true reservoir inflows are influenced by operations of upstream
reservoirs, whose releases are either determined by the optimized RBF policies or modeled by HYSSR.
Finally, when simulating reservoir operations described by these rules, the normalized release is first
un-normalized and then subjected to physical constraints to determine the true release. That is, if there is
insufficient water to release what is prescribed, only the available water is released. Likewise, if only releasing
what is prescribed would result in the reservoir exceeding its capacity, the excess is also released.
2.7.3. Multi-objective optimization algorithm
In our research, we employ the Borg multi-objective evolutionary algorithm (MOEA; Hadka and Reed [62])
in conjunction with the EMODPS framework to identify the optimal set of operating policy parameters,
denoted as θ. The Borg MOEA is particularly adept at handling complex multi-objective optimization
problems, boasting features such as epsilon-dominance archiving, mechanisms to detect when the search is
no longer making progress, randomized restarts to avoid being trapped in local optima, and the adaptive
selection of search strategies. Its efficacy is well-documented, with performance that matches or exceeds
other MOEAs across diverse problem scenarios, including reservoir operations [63].
For our computational needs, we utilized a multimaster parallelization of the Borg algorithm [64] using
two masters. Optimization was performed on the University of Virginia’s Rivanna High Performance
Computing (HPC) cluster across 240 cores for a total Number of Function Evaluations (NFE) of 800 000
across the two masters. The total wall-clock time was 16 hours.
2.8. Performance evaluation
Reservoir operations were optimized over a simulation of 15 years of stochastic data generated by CAPOW.
To evaluate the generalizability of the optimized operations, we resimulated the optimized rules over a
100-year out-of-sample data set.
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
3. Results and discussion
3.1. Performance evaluation across objectives
We first explore the tradeoffs found by our optimized Pareto-approximate reservoir operating rules across
the four system objectives. For reference, we compare these tradeoffs to the performance of existing
operating rules, as modeled by HYSSR. The parallel axis plots in figure 5show this comparison over
synthetic streamflows capturing historical hydrologic statistics. Figure 5(a) presents a set of 52 policies
derived from the multi-objective optimization over the 15 years of synthetic flows to which they were
optimized, while figure 5(b) displays their performance on a separate validation set of 100 years of synthetic
data. Each vertical axis in these plots represents performance for a specific objective, and each line represents
a single policy, intersecting the axes at its objective values. The color of the line represents its performance on
the fossil fuels objective, with dark blue indicating less emissions. The optimal direction on each axis is
down. The performance of historical operating rules simulated by HYSSR is shown in black.
Figure 5(a) shows that over 90% of the optimized policies dominate HYSSR over the 15 years used in
optimization, meaning they do better on all four objectives. While this decreases to 6% over the
out-of-sample validation set of streamflows (figure 5(b)), there clearly still exist better alternatives to
balancing these system objectives. While we are able to find policies that dominate existing rules, there are
still tradeoffs across the Pareto-approximate solutions. When lines cross between axes, it indicates tradeoffs
between the objectives of those policies. tradeoffs also exist when colors swap orders between non-adjacent
axes. This is clearly seen by the swapping colors between the fossil fuel use and flood objectives. This is
because reducing fossil fuel use requires increased hydropower production, which in turn requires higher
water storage levels in reservoirs for a greater head differential. However, keeping reservoirs full contradicts
the flood protection objective, as it reduces the capacity to store floodwaters. We explore how such operating
dynamics result in the observed tradeoffs in the following section.
3.2. Understanding water management tradeoffs
To understand how alternative operations result in the observed tradeoffs, we select the top four policies on
each objective from the Pareto set, as well as HYSSR, for a more detailed analysis. The performance of these
selected policies on the validation set of streamflows is illustrated in a parallel axis plot in figure 6(a), and the
values of their objectives are given in table A3. As noted before, a clear trade-off exists between fossil fuel
reduction and flood protection, as evidenced by the fact that the best policy for fossil fuel reduction is the
worst for flood protection. However, some objectives are positively correlated, such as fossil fuel use and BPA
Revenue (Spearman rank coefficient =0.922), since both are influenced primarily by hydropower
production. As can be seen in the figure, these objectives have nearly overlapping best policies in the Pareto
set. The environmental spills and flood protection objectives are also positively correlated (Spearman rank
coefficient =0.331), as lower water storage in reservoirs reduces spills and increases capacity for floodwater
storage. However, this correlation is not perfect, as can be seen by the stark performance differences of the
best policies for Environmental Spills and Flood Protection across objectives.
Figure 6also shows the average daily reservoir storage levels of each selected optimized policy and HYSSR
in the four optimized reservoirs over the validation set of 100 years of synthetic streamflows. Analyzing
average daily storage levels in these reservoirs reveals how varying operations help the select solutions achieve
near-optimal outcomes for specific objectives. GCL, the largest hydropower dam in the U.S., is consistently
operated at high storage levels across policies (figure 6(d)). All policies decrease storage at GCL in advance of
the spring snowmelt season, though, with those favoring flood protection and environmental spills drawing
storage down more dramatically and refilling later. HYSSR maintains lower storage levels at GCL throughout
the majority of the year. This requires less of a drawdown for flood protection in April, but still results in
significantly inferior performance than all four policies on Fossil Fuel use and than all but the Best Spills
policy on BPA Revenue.
Since the optimized policies prioritize hydropower generation at GCL to reduce fossil fuel use and
maximize revenue, they compensate by utilizing the other three optimized reservoirs for flood protection.
HYSSR, on the other hand, maintains higher storage in the other reservoirs, resulting in worse performance
on flooding and environmental spills than the policies favoring those objectives. HYSSR’s backward
coordination between GCL and the other reservoirs likely explains its inferior performance on all objectives
compared to the Best Flood policy. HYSSR could clearly improve the coordination of its operations if even
the policy that prioritizes flood protection maintains higher GCL storage.
It is clear from figure 6why the best policies for Fossil Fuel use and BPA Revenue do much better on these
objectives and worse on Environmental Spills and Flooding than the other policies because of their higher
storage at GCL (and DWR). However, it is not obvious from this figure why the Best Spills policy does so
much worse than the Best Flood policy on the flood objective. To understand this, it is critical to note which
11

Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 6. (a) Policies that perform best on each of the four objectives and HYSSR. (b)–(e) Average daily reservoir storage levels of
the four optimized policies that are best on each objective and HYSSR at (b) Libby, (c), Hungry Horse, (d) Grand Coulee and (e)
Dworshak.
reservoirs are subject to environmental spills regulations. Because fish migration does not occur upstream of
the Mid-Columbia, dams above GCL (LIB and HGH) are not subject to these regulations. Table A2 lists all
the reservoirs in the Mid-Columbia and Snake Rivers that have environmental spills regulations. Of these
reservoirs, we only optimize operations at GCL as all others behave as run-of-river dams on the daily time
step. Supplemental figure S1(a) illustrates spills at GCL from the Best Spills and Best Flood policies, and
figure S1(b) the resulting water level in Vancouver. In this figure, it can be seen that the Best Spills policy has
less spills at GCL than the Best Flood policy because its average storage is lower (as seen in figure 6(d)), but
the average storage of the other reservoirs, especially HGH (figure 6(c)), is higher, leading to increased flood
risk.
3.3. Understanding economic and environmental tradeoffs
The average storage levels shown in figure 6reveal useful insights into how alternative reservoirs in the CRB
favor different water management objectives, but provide little insight into why they achieve their economic
and environmental performance levels. However, unique to our integrated model of the
reservoir-electricity-economic system, we can also derive insights into these tradeoffs by exploring how these
average storage profiles influence spills and hydropower production, which in turn influence electricity
prices and utility revenue.
We explore the complexity of economic and environmental tradeoffs by investigating the average annual
time series of these variables in figure 7. Here we see that, generally speaking, when hydropower production
is high (figure 7(b)), net sales are as well (figure 7(d)), as surplus power can be sold on the market. Only in
rare cases (Best Spills policy in summer) does the average hydropower production fall too far below demand
such that even other PNW generators cannot meet demand, and BPA needs to purchase compensatory
power on the market. While power sales generally corresponds to increased BPA revenue (figure 7(e)), the
relationship is somewhat muddied by the fact that electricity prices are generally inversely related to
hydropower production (figure 7(c)). The complex, nonlinear relationship between hydropower production
and revenue resulting from these competing influences on prices and sales are best understood by comparing
the timing of generation across alternative policies.
In figure 7(b), it can be seen that HYSSR generates more hydropower than the other policies from June to
August, a strategic approach to maximize power output during periods of higher water availability. This
results in excess electricity that can be sold (figure 7(d)), enhancing the utility’s financial outcomes
(figure 7(e)), even if it decreases prices (figure 7(c)). However, this is also a period of low demands which
also leads to curtailment of other renewables. Our optimized operating policies instead distribute
hydropower generation more evenly throughout the year, resulting in greater generation, sales, and revenue
in the winter and fall. This explains how all of these policies achieve lower fossil fuel generation (see parallel
axis plot in figure 6(a)). For all but the Best Spills policy, this also results in greater revenue.
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 7. Average daily values of operational and economic variables over the year for the four selected policies and HYSSR. (a)
Squared deviations from spills targets at Grand Coulee (kcfs2); (b) Total Pacific Northwest (PNW) hydropower generation from
each policy and PNW electricity demands (MWh); (c) Mid-Columbia electricity prices ($/MWh); (d) Net Sales (>0)/Purchases
(<0) of electricity by the Bonneville Power Administration (BPA) ($M); (e) BPA Revenue ($M), representing economic returns
from power transactions.
To understand why the Best Spills policy does not also increase revenue, we also plot the time series of
average spills from GCL in figure 7(a). Across our Pareto front, we found that maximizing BPA revenue
corresponds to increasing hydropower generation by maintaining high storage, increasing the probability of
spills violations, while reducing fossil fuel use. However, the Best Spills policy achieves both lower spills and
fossil fuel emissions than HYSSR, but at a lower BPA revenue. Figure 7reveals that this anomalous tradeoff is
attributable to the timing of the releases, instead of simply the volumes released.
As can be seen in figure 7(a), the majority of spills at GCL from all policies occur during the late summer
and early fall, specifically from June to mid-August. Crucially, July is a period of relative scarcity in renewable
energy, as electricity demands begin to exceed hydropower supply (see figure 7(b)). This is especially true for
the Best Spills policy. The deficit in cheap renewable generation translates to an increase in Mid-C electricity
prices during this period (figure 7(c)), as more expensive thermal generators are activated to meet demand.
Compounding the decrease in hydropower generation and corresponding sales, BPA must also continue to
meet its fixed electricity delivery contracts and so is forced to purchase electricity at the high Mid-C price
(figure 7(d)). Consequently, although the spills-focused strategy may generate substantial hydropower at
other times of the year, the reduced revenue and increased costs during this peak period illustrate a
significant operational challenge that results in decreased BPA revenue. While HYSSR is able to generate
greater hydropower during this period to reduce prices and increase revenue, shifting hydropower seasonality
in this way comes at the expense of greater fossil fuels emissions over the course of the year.
This temporal misalignment underscores the need for strategically timed water releases to optimize both
environmental and economic outcomes in hydropower operations. The Best Revenue and Best Fossil Fuels
policies are able to better shift generation compared to HYSSR than the Best Spills policy so that reduced
fossil fuel use does not come at the expense of decreased revenue. However, their greater hydropower
production is still achieved by higher storage levels that result in greater environmental spills (figure 7(a)).
The Best Flood policy is able to strike the best balance. It refills GCL more slowly than all but the Best Spills
policy (figure 6(d)), resulting in less environmental spills violations than all but this policy as well. Yet its
faster refill at GCL than the Best Spills policy avoids the spikes in electricity prices and need to buy power on
the market at this price, ensuring its reduced fossil fuel use compared to HYSSR also results in greater BPA
revenue.
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
Figure 8. Storage percentiles of the Best Flood Policy at (a) Libby, (b) Hungry Horse, (d) Grand Coulee and (e) Dworshak across
validation set of 100 synthetic years, as well as the corresponding percentiles of (c) the water level at Vancouver, WA and (f)
Mid-C Fossil Fuels generation. Black lines represent the minimum, median (dashed), and maximum values simulated by HYSSR
over the same 100 years.
3.4. Performance evaluation across hydrologic years
Figures 6and 7illustrate how select reservoir operating policies behave on average across years, highlighting
the importance of properly timing releases to balance competing objectives. However, it also informative to
understand how operations differ across years to manage inter-annual variability. To understand this, figure 8
shows the behaviour of the Best Flood policy across 100 simulated years, not just on average. We select this
policy since it outperforms HYSSR on all objectives. The blue shaded regions in figure 8indicate percentiles
above the median, while the red regions indicate percentiles below the median. Black lines represent the
minimum, median (dashed), and maximum values when simulating HYSSR operations over the same years.
From figure 8, it is clear that the Best Flood policy makes use of the variables informing its releases
(storage at the four reservoirs, their total inflow and day of the year) better than HYSSR. Figure 6showed
that on average, the Best Flood Policy is generally able to maintain higher storages at GCL and release more
water for the hydropower objective. However, figure 8(c) shows that in advance of the flood peak, it makes
better use of information from the inflow state variable, drawing down more or less than HYSSR in advance
of the peak based on what is needed to improve flood protection. Figure 6showed these policies draw down
GCL storage to similar levels on average during the spring, masking the greater variability in storage seen by
the more dynamic Best Flood policy. While the Best Flood policy does occasionally empty the reservoir in the
driest of the validation years, this should not be of practical concern due to its low frequency (once in 100
years), and it could potentially be avoided by applying a harsher minimum storage constraint during
optimization (see equation (11)). Outside of the spring, the Best Flood policy refills GCL to higher levels
than HYSSR that it maintains the rest of the year to improve hydropower production. Interestingly, this shift
to higher storage levels applies to the whole storage distribution, with even the minimum optimized level
exceeding the maximum HYSSR level, not just their respective mean levels, as seen in figure 6.
Figure 8also gives us some more insights into how the reservoirs coordinate amongst themselves in the
network. As seen for the mean, in addition to keeping storage higher than HYSSR in GCL, the Best Flood
policy generally keeps storage lower in HGH and DWR, as they have greater storage capacity but lower
hydropower potential, making them better for flood protection. Storage in LIB is more similar on average,
but again, the within-year distribution changes to maintain higher levels in all but the spring, when it draws
down more in advance of the peak flow. Similar to GCL, we also see that the storage distribution of the
optimized policy at DWR is generally more variable than for HYSSR, adapting its operations more in
response to state information. Thus, the optimized policy represents a significant improvement over the
14

Environ. Res.: Energy 1(2024) 035010 S Singh et al
historical operation rules (HYSSR) by more effectively using storage and inflow information to balance
conflicting hydropower and flood protection objectives, improving performance on both.
The benefits of this improved coordination can be seen in figures 8(c) and (f) showing the distribution of
Vancouver water levels and total fossil fuel generation in Mid-C and CAISO. From January to late May, the
median water level at Vancouver is similar for the Best Flood Policy and HYSSR. However, the greater
drawdown at all reservoirs in April and May from the Best Flood policy reduces the median water level of this
policy from the peak in June through the end of the summer in August, once all the reservoirs have refilled.
This results in not only a lower median, but substantially lower peak as well (solid black and blue lines),
shifting the whole distribution down during the summer.
At the same time, figure 8(f) shows that the Best Flood policy effectively minimizes fossil fuel use as well.
From late winter through early spring, the entire distribution of fossil fuel use reduces for this policy
compared to HYSSR due to its elevated GCL storage that results in greater hydropower production that can
be exported to California when it exceeds Mid-C demands. At the end of the spring, the reservoirs all have
low storage and fossil fuel generation has to increase due to low hydropower production. However, this
increase is seen by HYSSR as well, with the distributions of fossil fuel generation behaving very similarly for
these to policies in the summer and fall. It is only during July–August at the highest percentiles that the Best
Flood Policy sometimes requires greater fossil fuel use than HYSSR due to the hydropower generation falling
short of demands, driven by lower inflows in those years. This sacrifice due to its greater storage variability
across years is outweighed by its benefits in reducing fossil fuel use across all years in the months of February,
March and April.
4. Discussion
The analyses above have illustrated many benefits to developing integrated models of the water, energy, and
economic components of hydropower systems. First, such models enable an understanding of how changing
hydropower operations impact objectives across all these areas. This can reveal interesting insights, which
may include both unforeseen conflicts and unexpected synergies. For example, here we observed unforeseen
conflicts in reducing fossil fuel use vs. increasing revenue when moving from HYSSR to the Best Spills policy
because of changes in the seasonality of releases. However, we also saw unexpected synergies in reducing
environmental spills and fossil fuel emissions while increasing revenue when moving from HYSSR to the Best
Flood policy. This was illustrated to be a byproduct of better coordination across reservoirs.
These insights were not only revealed because of the integrated model but through multi-objective
optimization. A chief benefit of multi-objective optimization is that many non-dominated policies can be
presented to stakeholders who can then deliberate with one another to arrive at an effective compromise
solution. This a posteriori deliberation is valuable [65], as stakeholders often select a different policy from a
non-dominated set than what their preferences solicited before optimization would imply [66]. Knowing
this, we do not recommend any particular policy in this study, but highlight some of the benefits and
drawbacks of different alternatives that could help inform that choice.
A stronger grasp of potential tradeoffs between competing objectives can also elucidate incentives or
regulations that could be used to produce more desirable outcomes. For example, the objectives used in this
model are tied to the river ecosystem (spills), BPA (revenues), households vulnerable to flooding (flood), and
the broader public (fossil fuels). To incentivize BPA to reduce system-wide fossil fuel emissions, carbon
credits could be granted for reductions enabled by switching operations. To incentivize BPA to reduce
environmental spills, stronger regulations or penalties could be imposed. Indeed, this leaves room for
additional work exploring how regulations interact across scales and governance levels. As Kosnik [67] notes,
excessive regulation can lead to the ‘Tragedy of the Anticommons,’ whereby excessive regulation leads to
sub-optimal usage. Combining integrated modelling with multi-objective optimization can help determine
effective levels of regulations to mitigate these impacts, hopefully leading to improved water resource
management.
5. Conclusions
This study uses the multi-reservoir Columbia River system in the U.S. Pacific Northwest to demonstrate the
power of integrated water-energy models in deriving insights into how to best balance competing
socio-economic and environmental objectives. Such insights can be gleaned through multi-objective
optimization of alternative reservoir operating rules for balancing these objectives. Insights from our
multi-objective optimization of the Columbia reservoir system include:
15

Environ. Res.: Energy 1(2024) 035010 S Singh et al
•producing non-dominated policies that can perform as well or better than the current reservoir operations
across all economic, environmental, flood protection and fossil fuels objectives;
•more effectively using storage and inflow information to coordinate reservoir operations for conflicting
hydropower and flood protection objectives across wet vs. dry hydrologic years, improving performance on
both;
•highlighting the importance of strategically timed water releases in hydropower operations to balance the
tradeoffs between environmental management and economic performance, especially during periods of
renewable scarcity when demand can outpace hydropower supply, impacting both revenue generation and
fossil fuel consumption.
While these findings are useful for informing how to adapt reservoir operations, many facets of the system
are likely to change in the near future. As such, future work should consider how such factors might
influence conclusions about how to best adapt operations. For example, it will be critical to understand how
shifting weather patterns and water availability under climate change could impact reservoir operations and
hydropower efficiency. Moreover, different technological development pathways, including the adoption of a
broader mix of renewable energy sources in the energy landscape, may significantly influence what
operations are most effective. Integrating these factors into the design of reservoir operations may reveal
synergies or tradeoffs between hydropower and other renewables. Understanding these impacts will enhance
our ability to reduce fossil fuel dependence and support sustainable energy production more effectively.
Data availability statement
All code for this project is available in online repositories. The code for CAPOW is available at https://github.
com/romulus97/CAPOW_PY36. All other model code can be found at: https://github.com/samarthsing/
CRB_reservoirs_optimization. All data files are available at https://doi.org/10.5281/zenodo.11962296.
The data that support the findings of this study are openly available at the following URL/DOI: https://
10.5281/zenodo.11962295.
Acknowledgments
This work was supported by funding from the University of Virginia School of Engineering and Applied
Science. The authors acknowledge Research Computing at The University of Virginia for providing
computational resources and technical support that have contributed to the results reported within this
publication (https://rc.virginia.edu). The authors would also like to thank Prof. Jonathan Lamontagne, Tufts
University and Steve Barton, Chief, Columbia Basin Water Management Division, USACE for helpful
discussions on model development. Any opinions, findings, and conclusions or recommendations expressed
in this material are those of the author(s) and do not necessarily reflect the views of the funding entities.
Appendix. Additional tables
Table A1. Reservoirs under optimization.
Reservoirs Abbreviations Storage capacity (kAF) Power capacity (MW)
Grand Coulee GCL 9107.2 6809
Dworshak DWR 3468.0 400
Hungry Horse HGH 3467.0 428
Libby LIB 5870.0 600
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Environ. Res.: Energy 1(2024) 035010 S Singh et al
Table A2. Reservoirs with environmental spills regulations.
Reservoir Abbreviation
Grand Coulee GCL
Chief Joseph CHJ
Lower Granite LWG
Little Goose LGS
Lower Monumental LMN
Ice Harbour IHR
Bonneville BON
Table A3. Objective values of select policies.
Selected policy
Environmental
spills violations
(kcfs2)Max flood level (ft) BPA revenue $ M/year)
Fossil fuels
generation
(GWh yr−1)
Lowest peak
flood
7319 30.8 394 238.0
Least spills 6839 32.8 343 242.0
Highest
revenue
7961 34.5 434 234.2
Lowest fossil
fuels
8086 34.5 432 233.8
HYSSR 7816 32.3 372 247.2
Algorithm 1. Pseudocode for Energy-mix curtailment.
1: for each timestep t
2: Ut←Hydro from the RBF releases
3: HydroMidC
t←Hydro from HYSSR
4: FossilsMidC
t←Initial fossils in the Mid-C
5: ExportsMidC
t←Initial energy exports in the Mid-C
6: FossilsCAISO
t←Initial fossils in the CAISO
7: ImportsCAISO
t←Initial energy imports in the CAISO
8: if Ut=HydroMidC
tthen
9: difference ←HydroMidC
t−Ut
10: FossilsMidC
t←FossilsMidC
t−difference
11: else
12: difference ←Ut−HydroMidC
t
13: FossilsMidC
t←FossilsMidC
t−difference
14: if FossilsMidC
t⩽min_fossils_constraint then
15: ca_exports_diff ←min_fossils_constraint −FossilsMidC
t
16: FossilsMidC
t←min_fossils_constraint
17: ca_exports_diff ←max(ca_exports_diff,max_exports_constraint)
18: ExportsMidC
t←ExportsMidC
t+ca_exports_diff
19: ImportsCAISO
t←ImportsCAISO
t+ca_exports_diff
20: FossilsCAISO
t←FossilsCAISO
t−ca_exports_diff
21: if FossilsCAISO
t⩽0then
22: hydro_curt ← −(FossilsCAISO
t)
23: Ut←Ut−hydro_curt
24: ExportsMidC
t←ExportsMidC
t−hydro_curt
25: ImportsCAISO
t←ImportsCAISO
t−hydro_curt
26: FossilsCAISO
t←0
27: end if
28: end if
29: end if
30: end for
ORCID iDs
Samarth Singh https://orcid.org/0000-0003-4564-9746
Julianne Quinn https://orcid.org/0000-0001-7806-4416
17

Environ. Res.: Energy 1(2024) 035010 S Singh et al
Jordan Kern https://orcid.org/0000-0002-1999-0628
Rosa Cuppari https://orcid.org/0000-0003-3530-3100
Greg Characklis https://orcid.org/0000-0001-9882-9068
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