Hydropower representation in water and energy system models: a review of divergences and call for reconciliation

Reservoir-based hydropower systems represent key interactions between water and energy systems and are being transformed under policy initiatives driven by increasing water and energy demand, the desire to reduce environmental impacts, and interacting effects of climate change. Such policies are often guided by complex system models, whereby divergence in system representations can potentially translate to incompatible planning outcomes, thereby undermining any planning that may rely on them. We review different approaches and assumptions in hydropower representation in water and energy systems. While the models and issues are relevant globally, the review focuses on applications in California given its extensive development of energy and water models for policy planning, but discusses the extent to which these observations apply to other regions. Structurally, both water-driven and energy-driven management models are similar. However, in energy models, hydropower is often represented as a single-priority output. Water management models typically allocate water for competing priorities, which are generally uninformed by dynamic electricity load demand, and often result in a lower priority for hydropower. In water models, constraints are increasingly resolved for non-energy components (e.g. inflow hydrology and non-energy water demand); few analogues exist for energy models. These limitations may result in inadequate representations of each respective sector, and vastly different planning outcomes for the same facilities between the two different sectors. These divergent modeling approaches manifest themselves in California where poorly reconciled outcomes may affect decisions in hydropower licensing, electricity grid flexibility and decarbonization, and planning for environmental water. Fully integrated water-energy models are computationally intensive and specific to certain regions, but better representation of each domain in respective efforts would help reconcile divergences in planning and management efforts related to hydropower across energy and water systems.


Introduction
Water and energy infrastructure systems that enable access to energy and water services are critical for improving and sustaining quality of life in societies globally. Despite their co-dependency and the widely recognized need to model and manage them in an integrated fashion-e.g. the rise of 'nexus' disciplines such as the food-energy-water nexus (e.g. Endo et al 2017) and, more recently, MultiSector Dynamics (Reed et al 2022)-these water-energy systems are often planned separately and studied quasi-independently through the use of planning models that tend to focus on one sector (Khan et al 2017), with examples pervading the nexus literature (e.g. U.S. Department of Energy 2014, Dalla Fontana et al 2020, Liu et al 2021. This separate planning and modeling reflects the historically siloed approach to managing resource systems generally, as discussed by Howells and Rogner (2014) among many others (e.g. Vine 2008, Gallagher et al 2016, Artioli et al 2017, Foden et al 2019. As physical conditions and social objectives evolve-in particular toward greater environmental and social sustainability-energy and water system planners and managers face increasing pressure to adapt their respective systems accordingly and account for interdependencies. For example, energy systems are being transformed globally to both mitigate and adapt to climate change (Mitchell 2016, Markard 2018, Bogdanov et al 2021, while water systems globally face changes in water demand (UNESCO World Water Assessment Programme 2019, Boretti and Rosa 2019) and hydrologic extremes (Milly et al 2008, UNESCO World Water Assessment Programme 2020. Hydropower systems represent critical nexus points in water-energy-environmental (WEE) systems, where synergies and tradeoffs occur between WEE sectors (Lofman et al 2002, Zhang et al 2018b, Kuriqi et al 2021. Despite this centrality, hydropower operations are often represented differently between energy system and water system models, as with water-energy systems generally. These differences can potentially undermine any planning that may rely on hydropower modeling by introducing the risk of sacrificing the ability to meet energy objectives for water objectives or vice versa. Given a) the wide range of efforts globally to improve WEE system infrastructure configuration and operations to support sustainability across economic, social, and environmental dimensions and b) the strong interactions between water and energy systems in both policy and management, a better understanding is needed of explicit and implicit assumptions in hydropower modeling tools used for water and energy resources planning, the implications of differences in these assumptions, and how these differences might be overcome.
This planning concern and need for such a review is global in scope and particularly acute given both the prevalence of hydropower in the developed world and the rate at which new dams are being constructed globally generally (Zarfl et al 2015). Hydropower development is anticipated to continue across the globe where hydropower potential has not yet been fully realized, including, for example, in Brazil (De Souza Dias et al 2018), the Subcontinental Himalaya (e.g. Schulz and Saklani 2021), China (Li et al 2018), Southeast Asia (e.g. Intralawan et al 2019), and Ethiopia (e.g. Tiruye et al 2021). The adequacy of assumptions in hydropower modeling in WEE systems are also critical globally in the context of climate change impacts on hydrology (Schaefli 2015).
While the need for a review of hydropower modeling in WEE systems is global in scope, this review focuses on California, a highly managed region with a major world economy built on large, complex WEE systems (Lofman et al 2002), and where there is currently a concurrence of ambitious energy system decarbonization goals (California Public Utilities Commission 2018, Baik et al 2022, efforts to reduce the environmental footprint of managed water systems (Escobedo Garcia and Ulibarri 2022), history of drought and water management challenges (Pinter et al 2019), and high susceptibility to climate change impacts (Hayhoe et al 2004). The importance of connected water-energy systems in California, including the relevancy of hydropower, is noted, for example, by Reed et al (2022) in describing the scientific challenges and research vision of MultiSector Dynamics through 2030 (Reed et al 2022, Box 1.3). The planning challenges experienced by California are likely to be felt in other regions with substantial hydropower development-despite differences in region-specific hydrologic regimes-and even more pronounced in the future.
The goal of this review is to characterize hydropower modeling approaches in water and energy system models for regional planning of WEE systems and identify potential implications of divergences in approaches. The focus is on long-term (years to decades), regional planning models with sufficient spatiotemporal resolution for site-specific management, in contrast with the course resolution models emerging from systems-of-systems communities such as MultiSector Dynamics. This is achieved by reviewing (a) the role of hydropower in changing water and energy systems, (b) the broader characteristics of water and energy systems; (c) key differences in the methodological approaches for representing hydropower systems in water and energy system models, (d) the potential implications of such divergences, and (e) the need for improved sector integration in hydropower modeling. While this review recognizes the broader water-energy nexus policy and modeling concerns, these have been addressed by others, as noted below (see in particular Khan et al (2017) for a general discussion of issues and Vakilifard et al (2018) for a specific discussion of optimization modeling).

Hydropower in changing water and energy systems in California
Water and energy systems are being transformed in California given changing societal demands on water and energy resources, including better environmental stewardship. Here we describe hydropower in California, and, within this geographic context, the role of hydropower in changing water and energy systems. operations, even when only used for hydropower production, can have a major impact on other water management objectives in the state if poorly managed.
Of the 1576 dams and their connected reservoirs in California, 240 provide 60% of the state's total water storage (Escriva-Bou et al 2019, U.S. Army Corps of Engineers 2021). Approximately 80% of the state's hydropower is generated at a smaller number of large, low-elevation 'rim' reservoirs that provide both flood control and account for much of the state's water supply (Nover et al 2019, California Energy Commission 2021a. Additionally, these terminal rim dams and their operations have altered or blocked access to riverine aquatic habitats, often resulting in the extirpation or endangerment of native fish populations (Grantham et al 2017, Herbold et al 2018. Operations of most hydropower systems, particularly those adjoining dams, are regulated by constraints on releases to rivers below dams and diversions, including constraints on both flow magnitudes and rates of change. All of the above factors have major implications for the management of hydropower as they may significantly reduce operational flexibility.

Hydropower in a changing water system
Despite its energy value, hydropower rarely contributes directly to the core operational mission of water system operators. Hydropower in California, while important from an energy portfolio and reliability perspective, is a lesser and often conflicting priority to other water management objectives such as delivery to human uses and ecosystems (Willis et al 2022). This conflict persists despite the sometimes concurrent demand for both water and energy, when energy may be opportunistically generated through releases to penstocks and turbines when releasing for water deliveries. The potential loss of water reserves in storage reservoirs, when released only for hydropower, threatens water supply reliability for future demands, particularly during prolonged droughts. Conversely, optimal hydropower production in flood control reservoirs can threaten flood control operations, as the latter requires sufficient space to store flood water, thus reducing hydropower capacity due to loss of head and its operational flexibility to maximize economic value. Hydropower facilities and related operations can be detrimental to downstream ecosystems, including riverine and nearby terrestrial species and habitats due to changes in the flow regime (Ligon et al 1995, Bunn and Arthington 2002, Kuriqi et al 2021, such that any modification of releases for the environment necessarily affects hydropower. Finally, sporadic hydropower releases for peaking operations can adversely affect riverine ecosystems and human recreation alike, as both benefit from predictable magnitudes and rates of change (Fong et al 2016). Changes in each of these operational priorities, some of which are reviewed below, have significant potential to undermine hydropower assumptions in energy system planning models.
The water management context within which hydropower systems operate is evolving, particularly the environmental water context. However, there is no water sector corollary to the 'transformation' seen in the energy sector (i.e. deep decarbonization). While California is recognized for being environmentally progressive, its extensive river regulation has contributed to the decline of many river-dependent species (Howard et al 2015). This has led to ongoing efforts to drastically improve the environmental management of rivers through dam removal (e.g. in the Klamath River), re-regulation of reservoirs, and landscape modification . Re-regulation efforts are currently being discussed: for example, for the large, multipurpose rim dams and associated diversions that feed the San Joaquin River. These could entail substantial decreases in agricultural diversions, as proposed by the State Water Resources Control Board (SWRCB 2018), and/or other changes to make managed flow regimes more 'functional' (Yarnell et al 2015. Other aspects of water management are changing as well. There is movement toward forecast informed reservoir operations of large multipurpose reservoirs, which would increase the flexibility of reservoir operators to better meet multiple management objectives (Rheinheimer et al 2016, Delaney et al 2020 and could propagate to hydropower generation (Ahmad and Hossain 2020). Groundwater, long minimally regulated in California and resulting in unsustainably high groundwater withdrawals, is now being regulated under the California Sustainable Groundwater Management Act (Leahy 2015). This nascent groundwater regulation has implications for surface water management through conjunctive use, which could alter reservoir operation schemes (e.g. Goharian et al 2020). This evolution toward improved water and environmental sustainability will significantly alter water management dynamics, with cascading impacts on hydropower generation, though the exact implications are currently unknown.
While electricity generation is not valued in water systems as a primary output, and hydropower facilities can harm ecosystems, hydropower infrastructure and operations nonetheless align with broader water system management in several ways. First, single purpose hydropower reservoirs often offer limited flood attenuation, thereby reducing flood risk. Second, the revenue derived from electricity generation supports water system operations, contributing to financial sustainability and presumably to operations and maintenance of facilities. This broader benefit is seen frequently in California (e.g. the Hetch Hetchy system, owned and operated by the 'water first' San Francisco Public Utilities Commission), and could strengthen as hydropower value increases with the transformation of the energy system and with some warming, but may ultimately weaken with substantial warming as capacity for both load balancing and ancillary services decreases due to greater spill (Rheinheimer et al 2012, Forrest et al 2018. Finally, there are hints that reservoirs generally may provide some re-regulating buffers against climate change-induced hydrologic alterations (Null et al 2013, Rheinheimer and Viers 2015, Yun et al 2021, though this effect is limited by hydrology and reservoir capacity (Ehsani et al 2017). These beneficial uses of hydropower systems in the water sector, combined with the uncertainty around the future of these benefits, further imply a need to better represent hydropower operations in water and energy system planning models.

Hydropower in a changing energy system
Concerns regarding the environmental and social impacts of continued dependence on fossil fuels for energy production have motivated the transition of regional energy systems towards renewable and low-carbon energy resources, including hydropower. Several expansive hydropower-based energy projects are underway in China (Chang et al 2010), South Asia (Vaidya et al 2021), and other parts of Asia (Soukhaphon et al 2021) and throughout the Amazon and Congo basins (Oyewo et al 2018, Arias et al 2020. While this global boom in hydropower dam building is not entirely motivated by decarbonization goals (Zarfl et al 2015), and carries significant environmental impacts (Winemiller et al 2016, Tickner et al 2020, hydropower is nonetheless considered a critical component of the low-carbon energy economy. Such development will require coordinated planning to reduce ecosystem impacts (Rallings et al 2021, Schmitt et al 2021 and be resilient to climate change (Hamududu and Killingtveit 2017).
In California, multiple policies have been enacted to significantly decarbonize the state's economy, the fifth largest in the world. Notable examples include Senate Bill 100 (SB100), which mandates that 60% of the state's retail sales of electricity by met with eligible renewable resources by 2030 and 100% of such retail sales be met with eligible zero-carbon resources by 2045. This is complemented by policies such as SB350 that calls for an 80% reduction in economy-wide greenhouse gas (GHG) emissions below year 1990 levels by the year 2050. Policies along this spectrum have also been implemented across the U.S (Database of State Incentives for Renewables & Efficiency®-DSIRE n.d.). These efforts purposefully align with similar broader global efforts, as manifested most recently in the 2015 Paris Agreement, which similarly calls for major reductions in GHG emissions by 2050.
To better understand how regional electricity systems can meet these goals, long-term planning studies have explored the preferred resource mix to comply with these targets at lowest cost. Central to the role of developing low-cost but highly decarbonized and reliable electricity systems is the presence of dispatchable, zero-carbon electricity resources to manage variability from wind and solar generation, since these resources limit the scale of energy storage capacity needed to meet infrequent extreme peak load events (Sepulveda et al 2018. Hydropower resources are well-suited to provide this needed function through their ability to provide flexible generation without the emissions penalty of resources such as biogas-fueled turbines. As such, while hydropower capacity is not expected to expand in California to meet the state's SB100 goals, existing hydropower resources support the broader system's ability to do so (California Energy Commission 2021c). Other studies that focus on electricity systems of different scales also highlight the role of hydropower-particularly existing hydropower-in fulfilling a flexible but firm zero-carbon generation role (SDSN 2020). In addition to often providing hydropower, surface water reservoirs are increasingly seen as potential locations for floating solar photovoltaics (FPV); FPV-hydropower combinations are particularly promising (Farfan and Breyer 2018, Lee et al 2020). However, reservoirs with hydropower installations cannot be operated solely to support the electricity system as these assets also are needed to manage water supply and downstream ecosystems. In practice, the flexibility of hydropower electricity generation is constrained by a number of complex and interacting factors with their own economic drivers and regulatory frameworks.

Differences between water and energy systems
Differences in how hydropower operations are represented between water and energy system models, including decisions about how to simplify hydropower representation, arise from differences in both real-world operational priorities, as well as practical limitations in modeling ability. Real-world differences include the governance structure, priorities, and spatiotemporal resolutions of how water and energy infrastructure systems are operated in practice, while modeling limitations include human resources, lack of sufficient other-sector expertise, and modeling software. This section provides a high-level overview of relevant real-world water and energy system characteristics, while section 4 reviews the implications of these differences in the context of hydropower representation, followed by the policy implications of these differences with examples from California (section 5).

Decentralization vs. centralization of governance
At a fundamental level, water and energy systems differ in how the planning and operation of their respective infrastructure is governed with respect to the extent of centralization vs. decentralization of decisions for how infrastructure is planned and operated. The governance, planning, and management of water supply allocation to meet water demand, and inherently the expansion of infrastructure assets needed for water distribution, involves a large, decentralized array of organizational entities. There is no central body or mechanism to facilitate or coordinate water allocation operations between specific system owners. Some water systems are coordinated, such as the large State Water Project and Central Valley Project (figure 1), operated by the California Department of Water Resources and U.S. Bureau of Reclamation, respectively. This decentralized character of water systems stems from their relative flexibility to accommodate uncertainty, enabled by the widespread use of large reservoirs for storage, river channels for conduits, and extensive infrastructure for diversion and delivery; the impact of relatively small upstream decisions often can be accommodated without the need for coordination. Just as water systems can be relatively isolated locally, the state is mostly hydrologically isolated from other regions, with one exception being imports from the multi-state Colorado River basin. This contrasts with the energy system, which often has several large interties with other regions.
In California, the energy system (and particularly the electric grid) tends to be planned and operated in a more centralized manner. While the electricity system is not centrally planned and managed by a single entity, a relatively small set of entities collectively make the decisions for how the electric grid is operated and how the expansion and turnover of assets is conducted. For example, from an operational standpoint, electric utilities are the sole authorities for operation of the electric distribution system within their respective territories, and the balancing authority is the sole authority for the operation of the transmission system. In this case, the California Independent System Operator (CAISO) governs and moderates the markets that determine the dispatch of power plants and operation of transmission lines to facilitate the transfer of electricity from power plants to utilities for the vast majority of the state. Utilities are then tasked with operating the lower-voltage distribution system within their territories to transfer procured electricity supply to meet the demand of their customers. From a supply procurement standpoint, utilities are tasked with ensuring the procurement of sufficient supply to meet the spatiotemporal profile of electricity demand from a variety of sources such as building and owning generation assets in-house, developing contracts with individual supply facilities, or purchasing from the statewide electricity market. Investment in the expansion of assets is also the responsibility of the utility, governed by the California Public Utilities Commission.
While the above description applies to California, multiple regions across the U.S. have similar setups: a balancing authority responsible for operating the transmission system and facilitating the market between suppliers and consumers; and a set of utilities tasked with procuring supply to meet their customers' electricity demands. In some cases, the balancing authority for a region can also act as the electric utility. This setup means that, while these different entities must coordinate with each other, each has sole authority for operational decisions across large swaths of the state. For non-electric energy forms such as gas, gas utilities are the sole authority for the operation of gas infrastructure and the procurement of supply to meet demand. From a modeling standpoint, this means that relatively few decision actors need to be represented.

Operational priorities and objectives
Water and energy systems also differ in the plurality of objectives that govern their operation. Water systems are operated to meet several operational objectives, including urban and agricultural water supply, flood control, electricity generation, environmental water (quantity and quality), recreation, and other miscellaneous objectives (e.g. salinity management). Of these objectives, hydropower tends to have a relatively low priority in any given system. Even for water systems where hydropower is a dominant operational concern, meeting environmental water demand, typically in the form of minimum instream flows, is always prioritized over hydropower. Unlike energy systems, water systems are not operated explicitly using optimization methods. Nonetheless, water system operations can be informed by optimization methods, with operational rules and priorities represented as optimization constraints and costs, respectively. In the energy system (specifically the electric grid), power plants, transmission lines, and distribution lines are operated to fulfill supplier-utility contractual obligations and to minimize the system-wide cost of electricity at each hour. These objectives are pursued within the constraints of transmission and distribution line limits and operating reserve needs. Therefore, models of the electricity system are often governed by an optimization problem that seeks to minimize a single objective-electricity cost-with all other elements imposed as either constraints on that optimization problem or as exogenous input. This approach means, however, that most electricity system operational models are not suited to determine the operation of assets when subject to multiple priorities, especially when said priorities cannot be easily converted to a monetary cost.

Spatial and temporal resolution
Water and energy systems also differ in the spatial and temporal resolution across which resource supply must meet demand. These differences in system depiction and resolution result in fundamentally different models to capture different system dynamics. The appropriate spatial and temporal resolution of water system operations varies depending on the kind of operation. Spatially, water systems depend, like energy systems, on the physical system and governance structure, with physical systems ranging in size from a single reservoir and diversion to statewide and, though rarer, interstate projects (e.g. transfers from the Colorado River) (figure 1). However, operations can be in relative isolation from broader management needs. For example, flood control operations for a reservoir can be for a single reservoir, without consideration of broader system operations, even if in some cases multiple reservoirs are utilized together for flood control. Reservoirs generally allow for some operational disconnect between otherwise hydrologically connected systems. For example, upstream hydropower reservoirs in the Sierra Nevada can be operated independently of the major statewide projects due to the buffering capacity of large reservoirs downstream (Kondolf and Batalla 2005), some coordination of operations notwithstanding. Like energy systems, some operational decisions are at the short time step of hourly to daily (e.g. flood control and some hydropower), while others are at longer time steps of monthly to yearly (e.g. seasonal agricultural deliveries and reservoir carryover). In general, water systems tend to be more flexible than electricity systems with balanced energy load, as there is less of a need to maintain specific hydraulic conditions.
The electricity system is operated such that electricity supply must meet electricity demand over time periods of minutes to hours. Some ability exists in the electricity system to allow mismatches between supply and demand on very short timescales (seconds) through the physical inertia of system assets, but these differences must be corrected in a matter of seconds to prevent loss of electricity service to a subset of customers. From an operational standpoint, this is facilitated through the balancing authority electricity markets, which are intended to balance energy supply and demand. Typically, resources to meet demand are scheduled one day in advance based on a day-ahead forecast of demand to be met at each 5 min and 1 h interval; then additional resource adjustments (up or down) are called upon in real-time to compensate for errors in the day-ahead forecast. For an electricity system operation or planning model to provide a useful representation of system operations, the hourly timescale must be modeled at a minimum. Typical electricity system models rely on hourly resolution for one year as the default temporal representation. As reviewed in section 3.1, this process occurs over very large spatial areas: balancing authorities and utilities in California are each responsible for large swaths of the state.

Divergent assumptions in hydropower representation
A wide range of methods have been developed to represent hydropower operations in both water system and energy system models. Out of necessity, models in each of water and energy sectors make simplifying assumptions about the other sectors. Here we describe the modeling approaches and assumptions for dispatchable hydropower in water and energy system planning and/or operation models that have been used to help inform respective water and energy planning policy and actions. These approaches and assumptions are extracted from a review of prominent water-sector and energy-sector system models that have been used to perform research aimed at future planning of such systems, summarized in tables 1 and 2, respectively. More planning models have been developed than are included in these tables, as models with little emphasis on hydropower or without explicit hydropower (e.g. Kuczera 1992, Trindade et al 2020 are omitted. Water sector models have typically focused on informing the development of solutions for a diverse range of problems relevant to regional water resource allocation, while energy sector models have largely focused on informing the planning of highly renewable and deeply decarbonized electricity systems.

Hydropower optimization objectives and priorities
Key differences in modeling approaches to represent hydropower between water and energy sector system models are based on whether the real operational priorities of hydropower facilities are explicitly represented, and if so, what those priorities are assumed to be. These different approaches to representing operational objectives are typically manifestations of real-world differences in the interests and priorities of water-focused and energy-focused regulatory and planning agencies, as well as practical limitations in the ability of modelers to integrate other-sector priorities.
Water sector models typically focus on simulating the allocation of available water resources over a given spatial and temporal scale between multiple competing demands, most often using highly constrained optimization-linear programming (LP) in particular-as an allocation approach. Usually, this is sufficient, since water system models are often focused on allocations to non-hydropower users, and because there is typically a well-defined priority structure in actual operations, which are easy to model. Because modeling dispatchable hydropower operations requires additional complex hydro-economic considerations, this component is typically less of a priority than other operations, and therefore omitted or grossly simplified. Among the water sector models in table 2, all represent dispatchable hydropower as a fixed exogenous input of explicit water or energy demand and, in the case of priority-based models, priority or cost. This contrasts with the energy demand-driven approach of energy system models, noted above, and results in fairly poor representations of dispatchable hydropower. Non-dispatchable hydropower, such as run-of-river and opportunistic hydropower (e.g. smaller turbines at minimum flow release outlets), are represented with low relative priority; optimization (LP) routines ensure that low priority hydropower is generated opportunistically, consistent with actual practice. In some cases, a systems dynamics simulation approach is  used, such as with Stella (e.g. Teegavarapu and Simonovic 2014); in such cases, hydro-economic drivers of operations are omitted due to the limitations of the systems dynamics approach. Energy sector models, particularly those focused on electricity, often represent the operation of different electricity resources as seeking to minimize the cost of electricity across the entire balancing authority. This representation mimics the behavior of market-based balancing authorities. Among the energy sector models in table 2, two out of the twelve models reviewed do not represent the operational priorities of hydropower facilities and represent such facilities via exogenous input for electricity generation and associated water releases. The other ten models represent hydropower facilities as being operated primarily to maximize facility net revenue, where hydropower generation and the associated water releases are maximized when the grid-wide price of electricity is high and vice versa. However, this does not necessarily reflect actual operations, especially for reservoirs that have multiple purposes, in which case hydropower may not be so flexible. Energy-sector models differentiate their representation of hydropower in different aspects, as discussed in the following subsections.

Representation of hydropower operational constraints
Water and energy system models also differ by the types of constraints imposed on hydropower operations. Water system models tend to capture a more diverse array of physical and operational constraints that affect hydropower, particularly around infrastructure capacities and operational restrictions. All water system models include representation of physical constraints, such as reservoir and canal capacities. All water system models reviewed also have some capacity for setting minimum flow requirements below dams and diversions, since this is a common operational constraint. However, we note that these operational constraints are typically represented as demand, which may be unmet, rather than hard constraints.
Among the energy sector models reviewed (table 2), ten represented hydropower operation via a cost-minimizing optimization framework. Of these, all captured water availability constraints, but differed somewhat on the temporal scale over which this constraint was applied. For example, PROMOD applies a water availability constraint over a weekly or monthly time step, whereas CAPOW applies this constraint up to a daily time step. However, only seven of these models further captured the constraints of reservoir maximum and minimum fill levels, and only four explicitly capture minimum and maximum flow limits. Explicit representation of the type of flow limit (e.g. environmental flows) and their spatiotemporal variability are only represented explicitly by one of the ten models (CAPOW).
We thus see a substantial difference between water and energy models in representation of real-world constraints. The degree of divergence tends to be system-specific and related to the resolution and realism of operational objectives. The importance of these differences varies, but may be quite large for some operations. For instance, minimum flow requirements for downstream ecosystems can be quite complex, yet these are typically not represented well, if at all, in energy system models.

Spatial and temporal resolution
Water and energy sector models vary in their resolution of spatial and temporal scales over which hydropower operations are represented, driven generally by the real-world spatiotemporal needs noted above. Water system models can vary significantly in their spatial or temporal resolution, depending on the scope of the planning need. While some water system models can be quite large, spanning many reservoirs over large areas (e.g. Draper et al 2003), others can cover just a single reservoir for more detailed planning. Often, the temporal resolution scales with the spatial scope, with models of larger areas using a coarser resolution, though this is not always the case. For water allocation planning, time steps range from daily to monthly. Sub-daily time steps are typically only used if hydraulic routing is needed, such as for studies that include flood control or environmental flows. In contrast to energy models, water models can model across a single, contiguous time series spanning a long planning horizon (including more than 100 years for some planning studies). The large storage capacity of some reservoirs often obviates the need for hydraulic routing, especially in higher gradient systems, and allows for coarser (e.g. one month) time steps and/or smaller spatial extents compared to energy models. In California, for example, whereas the CAISO is necessarily the spatial unit for energy planning, water planning can occur for single reservoirs, even if they are ultimately hydraulically connected to other reservoirs.
Energy models tend to focus on the balancing authority as the smallest spatial unit (e.g. CAISO in figure 2(a)), with the geographic scope dependent on the specific study of interest from single zone balancing authorities, national grids with many subregions, and in some cases interconnected grids spanning multiple countries (e.g. in the European Union). As the hourly time step is most relevant to expansion planning, energy models operate at the hourly time step over relatively short modeling horizons (e.g. a week). All ten of the models summarized in table 2 simulate electricity system operation on at least an hourly timescale, with some such as PyPSA capable of simulating sub-hourly resolution with appropriate input data. Where electricity system models vary is in the time horizon over which electricity system operations are simulated. The capacity expansion models in table 2, for example, typically simulate representative 24 h periods from different parts of a year for different resource portfolio configurations. By contrast, load-balancing or production cost models typically simulate an entire continuous year for a given resource portfolio configuration. Models are also emerging that can handle both capacity expansion and production cost or dispatch functions, such as GenX (Jenkins et al 2022). Models will then be run with different input data to represent different environmental or demand scenarios.

Policy implications: examples from California
The modeling choice differences presented in sections 3 and 4 have implications for the applicability of water and energy system models aimed at informing policy and actions to meet their respective transformation goals. Here we discuss these implications generally, followed by specific needs for several major planning policies, frameworks, and general discourse in California.

The need for sector integration in hydropower modeling
This review found that long-term planning of regional-scale WEE systems are often conducted using system models that focus on one sector, with simplifying assumptions made about the sector(s) of lessor focus. These assumptions, while important to limit the complexity of system representation, may directly contradict other system models in the same region, and even be counterproductive. The high-level differences in the role hydropower plays in water and energy systems modeling are rooted in assumptions about, and representation of, operational priorities. Hydropower operations respond to varying types and strength of demands and constraints, as well as differences in the characterization of temporal and spatial resolution. This divergence in systems characterization is particularly true for dispatchable hydropower, whereby the operator has some real-time discretion over how much water to release, based on changing energy system needs (i.e. for load-following or peaking operations). As a result, modeling divergences can produce conflicting outcomes between water-centric and energy-centric model results.
These conflicts can potentially diminish the overall validity or usefulness of such models in informing policies for water and energy system transformation by inadequately representing real priorities or constraints that stem from the systems of secondary focus. Therefore, a need exists to explore the differences between how hydropower is represented in water and energy system models used to inform policies for transforming each system. Planning in water and energy sectors would improve if differences between planning tools (i.e. models) are understood and rectified for consistency.
Recognizing the need for sector integration is not new, as evidenced by the broader emergence of 'nexus' research fields involving water and energy, combined water-energy system models and modeling frameworks, and previous explicit calls for such integration. Related 'nexus' fields vary in scope, and include the water-energy nexus ( (Lofman et al 2002, Yazdandoost andYazdani 2019), and others. Many models and model frameworks exist in the literature to support these nexuses, as reviewed by others (e.g. Khan et al (2017) and Dai et al (2018) for the water-energy nexus), though historically relatively few system-focused models exist to co-optimize across systems (Vakilifard et al 2018, Gonzalez et al 2020. Of the 35 water-energy nexus models reviewed by Dai et al (2018), for example, we found none that resolve hydropower to the temporal resolution needed to plan and assess environmental flows, a key component of the WEE nexus affected by hydropower. However, some model developments are promising. Coupling the Water Evaluation And Planning System (WEAP) water system model (Yates et al 2005, Sieber 2006) and the Low Emissions Analysis Platform (LEAP) energy system model (Heaps 2022) conceivably could be used for high resolution hydropower operations, though we found no study that does so. Notably, climate change, land-use, energy and water strategies (CLEWS) integrates WEAP, LEAP and the agro-ecological zoning land use model into a regional scale planning package (Howells et al 2013). CLEWS has been applied in many water-energy contexts globally, including in policy-relevant contexts (Ramos et al 2021). While promising, CLEWS focuses on broader energy planning rather than site-specific operations, thereby missing a key analytical component. Resolution issues aside, use of water-energy system models do not yet reflect the norm for actual natural resource planning, and indeed are a motivation for further nexus model development (e.g. Liu et al 2021, Ramos et al 2021. Finally, two recent reports from the U.S. Department of Energy National Laboratories have noted the challenges of modeling hydropower from an energy perspective. Stoll et al (2017) notes how additional environmental, regulatory, and operational constraints in real hydropower operations are not present in operations of other energy system components, making hydropower that much more difficult to accurately represent. Voisin et al (2020) review the diversity in hydropower systems and models by science questions and applications, along with associated limitations of and research needs for representing hydropower in power system models for those different situations by summarizing the result of a workshop of 40 experts from both the water and energy sectors. Several broad themes from this workshop emerged, including data availability limitations, lack of effective validation and uncertainty characterization methods, and poor representation of actual-potentially non-economic-decision-making factors. Voisin et al (2020) also noted the need for cross-sector collaboration for improved representation of hydropower dynamics. Water and energy system model integration is thus an ongoing topic in general professional discourse amongst academic and practitioner systems modelers.

Policy implications for California
The lack of sector integration between water and energy planning models has broader, practical implications on policy. In California, three areas where model dissonance may have long-term impacts include hydropower licensing, energy sector planning for decarbonization, and environmental flow policies. While each policy area is affected differently, the cumulative impact of uncoordinated planning tools across these sectors could be severe.

Hydropower licensing
Non-federal hydropower projects are licensed by the U.S. Federal Energy Regulatory Commission (FERC) to operate for 30-50 years, whereby 'projects' comprise one or more individual hydropower facilities, including related infrastructure and surrounding land. Licenses specify operational conditions, including how water is managed for the downstream environment. The relicensing process typically takes five years, during which time project operators and stakeholders may develop models of the project to estimate implications of proposed revised operations. While projects are typically independent, relicensing efforts are in some cases coordinated where two or more projects are hydraulically connected to each other and have close license expiry dates.
In California, these FERC-licensed projects are predominantly located in the higher elevations of the Sierra Nevada (see Viers 2011). In general, there is no single planning model or model framework used in FERC-licensed projects in the region, consistent with the independent nature of projects and their respective licenses. However, because many of these high elevation facilities are integral to the power system in California Lund 2010, Rheinheimer et al 2014) and often affect particularly vulnerable species (Rehn 2009), their independent modeling in a license planning context represents the divergence between water and energy modeling. The implications of proposed license revisions on broader water and energy system objectives are not considered in the public component of relicensing efforts, and hydropower owners usually do not provide internal assessments on such issues. Conversely, regional water and energy planning studies may be undermined by unanticipated changes to hydropower operations that may emerge from license revisions. Despite these limitations, stakeholders and third-party researchers (e.g. academic researchers) may conduct modeling studies that, while unofficial from a relicensing process perspective, may nonetheless indirectly contribute to hydropower negotiations (Rheinheimer et al 2012).
Divergent assumptions among and between FERC and non-FERC planning models implies potential long-term diverging policy uncertainty around hydropower facilities, which is generally undesirable for both water and energy planning. These divergences are potentially further exacerbated by nature of FERC licenses, which are developed for operational certainty in a world increasingly defined by hydrologic and energy system change and uncertainty. As hydrology, energy needs and environmental needs change during the FERC license planning horizon, hydropower operators should be able to adapt to those changes to both fulfill energy needs and meet financial objectives; these adaptations are hampered by the current licensing and modeling approach. For example, including climate change modeling into FERC relicensing remains difficult (Viers 2011, Viers andNover 2018). FERC relicensing efforts would benefit from more aligned policy discourse, use of modeling frameworks for operational planning and impacts assessments that explicitly account for more nuanced representation of operational drivers (i.e. agricultural, environmental, and energy demands), and planning across a broad range of policy, socioeconomic, and environmental futures. In general, there appears to be a need to better integrate a systems view of hydropower systems beyond single projects. Aside from the general benefits of more cross-coordinated planning, this would enable a 'stress test' style modeling approach to adaptively improve system resilience across sectors given stressors such as droughts and blackouts (Viers and Nover 2018).

Electricity grid flexibility and decarbonization
Among regions in the United States, California has implemented one of the most aggressive goals for decarbonizing the regional electricity supply. This is exemplified by California Senate Bill 100 (SB 100), which established the requirement for 100% of the state's retail sales of electricity to be comprised of eligible zero-carbon resources by 2045. The California SB 100 Joint Agency Report (California Energy Commission 2021c) was commissioned to assist in evaluating and planning different strategies to meet this goal, relying on the RESOLVE capacity expansion model (Energy and Environmental Economics, Inc. 2023). Related policies exist to support this. For example, N-79-20 requires 100% of in-state sales of new passenger cars, trucks, and off-road vehicles and equipment be zero-emission by 2035 and for medium-and heavy-duty vehicles to be zero-emission by 2045 where feasible. From an electricity system standpoint, hydropower is a flexible, zero-carbon resource that is expected to fulfill a critical role in ensuring that time-varying electric load can be satisfied in electric grids with high penetration levels of variable renewable energy sources. Hydropower units can ramp up and down quickly to compensate for the variability of wind and solar; associated reservoirs can provide reserve capacity to fill in gaps in wind and solar generation. More broadly, hydropower belongs to a class of resources colloquially termed 'firm zero-carbon resources' (Sepulveda et al 2018), whose presence as a part of building a fully decarbonized grid is important for reducing the future scale of energy storage (and therefore costs) required to reliably satisfy electric load .
Models used to plan future decarbonized electric grids such as those in table 2 may not accurately represent the ability of hydropower to act as a flexible resource. For example, official modeling exercises for meeting California's SB 100 goals do not currently model the dynamics that control hydropower generation and for now, represents this resource via a static, historical generation profile. This modeling simplification can potentially have many implications for planning for SB 100, as well as other efforts such as N-79-20 that may use similar modeling approaches for planning.
First, using a fixed historical profile assumes that hydropower's bulk energy contribution to meeting future electricity demands will be equivalent to that in past years. Given the effects of climate change on altering hydrological regimes to have more extreme storm and drought events, hydropower's bulk energy contribution can vary widely from year to year. During dry extremes, the electric grid may need more capacity of other zero-carbon resources to stay compliant with the SB 100 goal.
Second, the effects of nonstationary climate may also affect the extent and timing with which constraints on hydropower's ability to shape its generation profile apply. For example, long droughts during the summer season may cause certain hydropower facilities to cease generation entirely if their reservoir elevation falls below the powerhouse intake heights, during the time of year where electric load (i.e. demand) in California is at its highest.
Third, without modeling how the competing obligations of hydropower reservoirs affect the timing and magnitude of water releases from these reservoirs, planning models may assume that hydropower will be more available during times of the year when practically it may not be. This is in addition to the effects of a nonstationary climate with extreme hydroclimatic events.
Finally, the lack of representation of hydropower operational dynamics, priorities, and constraints prevents the study of how hydropower can be operated to best support future, decarbonized grids within real-world contexts or how alleviating constraints can unlock beneficial hydropower flexibility.
To improve the understanding of hydropower's role in supporting regional electricity decarbonization efforts, planning models that are used to explore electricity resource needs to meet decarbonization goals should incorporate or at least communicate with a more detailed representation of hydropower facilities' competing priorities, constraints, and operational needs. As these resources fulfill important roles in supporting decarbonized grids, incorporating these representations into electricity system models will become more important.

Planning for environmental water
Environmental water needs have traditionally been well-represented in water system models. Because hydropower systems are typically lowest priority in water systems, and environmental requirements have traditionally been well-defined, modeling of environmental flows have been both straightforward and accurate, despite the need for some adjustments to account for operators' tendency to release more than minimal requirements. License requirements and other regional plans have prescribed specific target downstream flows from reservoirs, typically in the form of seasonal minimum instream flows and ramping rate limits .
In addition to changes in environmental flow targets developed through the relicensing process, California state agencies are increasingly emphasizing more nuanced, ecologically based flow requirements for individual facilities as well as watersheds developed using environmental impact assessment and ecological studies. Agencies such as the State Water Resource Control Board (SWRCB) and the California Department of Fish and Wildlife are empowered by state code to develop instream flow requirements through the Porter-Cologne Water Quality Control Act (Water Code § 13 000) and the Instream Flow Program (California Department of Fish and Wildlife n.d.), respectively. Many of the major river systems in California are also tied to the Sacramento-San Joaquin Delta (Delta), which is a hotspot for aquatic species conservation and governed by complex and far-reaching regulatory frameworks for managing tributary inflows. The SWRCB's Water Quality Control Plan for the Delta (Delta Plan) proposes full natural flow targets at several points along the San Joaquin River, one of the Delta's two major tributaries (SWRCB 2018). These flows are fed by a number of large reservoirs and complex, cascading hydropower facilities; new regulatory requirements will necessarily alter current upstream operations in order to meet these . Divergent (current) (a) and integrated (b) approaches to policy and modeling in water and energy systems. Water models depend on precipitation and assume decentralized decision-making for multiple resource management objectives, while energy models depend on renewable energy and assume centralized decision-making for resource management objectives. Integration assumes coordinated policy and data systems for multiple resource management objectives.
requirements. In this regulatory environment, tools have been developed to facilitate reoperations with an appropriate level of operational and ecological flexibility: the California Environmental Flows Framework (CEFF) has developed a theoretical framework focusing on functional flows  and practical tool for applications to reaches of watersheds (University of California, Davis n.d.). Currently, environmental water releases are represented with limited resolution in energy models. There are considerations for current and future regulation that restrict the flexibility of hydropower generation. However, there may be an opportunity on the part of hydropower operators to make operational judgments around environmental water releases, based in part on energy system needs, recognizing the flexibility of ecosystem water needs calculated through frameworks such as CEFF. Although environmental water is modeled in many water resources models, both water and energy models will require the appropriate temporal resolution in order to capture the impacts of increasingly nuanced and complex release characteristics (i.e. timing, frequency, duration, magnitude, and rate of change in environmental flows).
Environmental water targets may occur on hourly, daily, or seasonal scales (Yarnell et al 2015), all of which may have differential impacts on energy generation which capitalize on the timing releases at similar resolutions. Some environmental water will necessarily need to be valued to integrate with energy system models to appropriately assess the realistic flexibility of hydropower generation. This will likely be in the form of a high priority, non-negotiable minimum flow requirement accompanied by water that is valued in a manner comparable to energy. Valuation will likely be dynamic to address the need for probabilistic environmental water needs rather than needs known a priori. As climate change is integrated into environmental water planning, these trade-offs become more uncertain (Viers 2011); as reality and assumptions diverge, this gap in model representation of these releases may have more pronounced effects on modeled energy production.

Discussion and conclusions
This review summarized approaches to modeling water and energy systems, highlighting important divergences in assumptions and illustrating the implications of such divergences for planning initiatives in California. Water system models and studies prioritize detailed representation of water systems with poor approximations of energy drivers of hydropower, while energy system planning efforts use energy system models that only coarsely represent critical water management objectives and constraints, such as urban/agricultural water supply and environmental water needs. These approximations may or may not be appropriate, depending on the context and purpose of the planning effort. However, even in coarse resolution water system models, lack of accurate, energy-informed representation of upstream high value hydropower systems can result in decreased accuracy of large reservoir inflows and, consequently, poorer overall representation of system behavior.
The existence of divergent assumptions in both policy and modeling literature implies two major hydropower modeling needs. First, there is a need to explicitly identify the additional value gained from improvements in representation of other sector dynamics in hydropower models. Is a coarse approximation of hydropower drivers in a water system model (e.g. a fixed monthly energy demand rather than a full energy system optimization) adequate for water planning needs? Conversely, how much does omitting more nuanced water system drivers affect energy system model outcomes in an energy system planning context? These questions can be resolved through either sensitivity analyses with existing models or, where that is insufficient or not possible, through the coupling of existing water and energy system models with interactive feedbacks. Second, if findings of the first effort reveal that poor other-sector representation is indeed a significant limitation for planning studies involving hydropower, then a broader effort is needed to either substantially improve other-sector representation in sector models, or to focus on improving existing-or developing new-integrated water-energy system hydropower models. Implicit in the above is the need to include all water demands-including urban, agricultural, environmental and recreational-explicitly in energy system planning and models. This is particularly relevant for regions such as California, where there is a clearly defined water rights hierarchy (though with some limited water markets) and hydropower has the lowest priority in any given multipurpose system. Despite hydropower being low priority in the water sector (in contrast to its central role in energy systems), it is still typically not operated in a spatially consistent way. For example, high-elevation hydropower operators are not responsible for meeting downstream water needs. The implication is that the development of more integrated water-energy system models would need to recognize upstream-downstream connections. More broadly, policy studies could examine the option of better spatial integration of hydropower system operations for overall improvements in WEE system performance.
This recommended move from a divergent to integrated modeling approach-particularly in policy planning contexts-is depicted in figure 3. Such integration can be supported through novel information technology solutions, such that WEE models, even if loosely coupled, can draw from and report back to integrated data systems. While nexus research has made some progress in this area (e.g. Saif and Almansoori 2017), it has made little progress in supporting hydropower-related policy at temporal resolutions that are meaningful for modeling environmental flows, which requires at least the daily time step. Fortunately, new tools are emerging that could facilitate such integration. For example, the highly customizable water system modeling approach of Pywr (Tomlinson et al 2020) could be easily linked with an energy system model. An additional promising approach is the fully integrated water-energy network approach of Gonzalez et al (2020). Furthermore, accessible and efficient computational power continually advances, improving the ability to address the computational burden associated with more complex system models. However, integration also needs to be accompanied by novel user-facing tools, such as web applications (Voinov et al 2016), that make such integrated modeling more accessible to planning modelers and stakeholders.
Finally, we note two important limitations of this review. First, the focus is on models with site-specific relevancy. While this was an explicit decision to limit the review, within the broader water and energy nexus literature there are noted efforts to better integrate water and energy systems for long-term planning. However, as noted by Khan et al (2017), greater disaggregation is needed to truly capture the trade-offs and synergies between systems. Second, the review is biased toward water and energy policy and modeling in the United States generally and California in particular. While the issues discussed are relevant to other regions in the world, there may be some examples of exemplar integrated WEE system models from elsewhere that are not acknowledged. Similar reviews from other global hydropower centers are needed.

Data availability statement
No new data were created or analysed in this study.