GRAPS: Generalized Multi-Reservoir Analyses using probabilistic streamflow forecasts
Introduction
Water allocation among municipal, industrial, and agricultural sectors requires thorough integration of current supply and demand along with potential climate change, population growth and ecological considerations over the river basin (Singh et al., 2015). Most large river systems typically have multiple reservoirs that are regulated to meet its design uses (e.g., irrigation, water supply, hydropower) considering several ecosystem and environmental constraints (Wang et al., 2015a). Thus, multi-purpose multi-reservoir operations encompass detailed analyses considering trade-offs among conflicting uses (Kasprzyk et al., 2009). For instance, too little release may affect water quality and recreation, while too much release may cause flooding (Singh et al., 2015). The opposing nature of benefits associated with storing the water and profits associated with releasing the water contributes to the complexity of multi-reservoir system operations (Yeh, 1985; Koustosyiannis et al., 2003; Li et al., 2015). To understand the tradeoffs in multi-sectoral water allocation over the river basin, it is important the reservoir modeling framework should be capable of providing the tradeoffs under observed flows and forecasted flows, which is typically represented in the form of ensembles (Sankarasubramanian et al., 2009).
The main intent of this study is to develop and validate a multi-reservoir multi-purpose reservoir modeling framework that can take probabilistic seasonal/annual inflow forecasts for allocating water for multiple uses. The operation of a reservoir system is likely to be subjected to both supply and demand variations, which are typically provided as forecasts at subseasonal (weekly to monthly) to seasonal/annual time scale. It is important to analyze how these supply and demand variations impact the reliability of a given user and the probability of violating the target storage, which are specified as rule curves (Sankarasubramanian et al., 2009; Golembesky et al., 2009). Currently, reservoir modeling platforms typically use either deterministic forecasts, provided as forecast mean/median, which ignores the probabilistic information and the forecast uncertainty on the mean. A more rigorous approach is to analyze the multi-reservoir system using probabilistic inflow forecasts specified as ensembles to support proactive and adaptive water management policies. The utility of a multi-reservoir modeling system is to support reservoir managers and operators for meeting different target demands and testing adaptive strategies including drought contingency plans based on the potential supply and demand (Maurer and Lettenmaier, 2004).
Several formulations of multi-reservoir models have been in the literature, which are well documented in several review papers (Yeh, 1985; Labadie, 2004; Ahmad et al., 2014). Commonly used mathematical programming techniques include linear programming models (Loucks et al., 1981; Belaineh et al., 1999), network flow models (Hsu and Cheng, 2002) and interior-point method (Seifi and Hipel, 2001). Similarly, non-linear programming models have relied on sequential analyses to ensure convergence such as sequential linear programming (Barros et al., 2003), sequential quadratic programming (Finardi et al., 2005), and using generalized reduced gradient technique (Peng and Buras, 2000). Studies have also used both dynamic programming and stochastic dynamic programming models (Alaya et al., 2003). To reduce the dimensionality in the above mathematical programming models, studies have suggested using simulation-optimization models (Koustasyiannis and Economou, 2003; Sankarasubramanian et al., 2009). Application of several novel heuristic techniques such as genetic programming, tabu search and particle swarm optimization have also been used to solve multi-reservoir models (Rani and Moreira, 2009, Baltar and Fontane, 2008; Reddy and Kumar, 2007 and references therein).
Several agencies, universities and private corporations have also developed multi-reservoir modeling software packages. HEC-ResSim by U.S. Army Corps of Engineers is used to simulate reservoir operations for flood risk management, and real-time decision support (Klipsch and Hurst, 2013). Another popular software is MODSIM, a generalized river basin software designed as a tool for making improved basin-wide and regional strategies for management and water rights analysis (Labadie, 2010). California Department of Water Resources developed a general-purpose reservoir–river basin simulation model, CalSim, that permits specifications of system description and operational constraints through a new water resources engineering simulation language (Draper et al., 2004). A water resource planning tool, WEAP, developed by Stockholm Environment Institute, is capable of simulating water demand, supply, flows, and storage, and pollution generation, treatment and discharge (Sieber and Purkey, 2015). WaterWare is a proprietary, decision-support river-basin planning system that employs rule-based concepts for developing operating criteria and policies (Jamieson and Fedra, 1996). Another proprietary popular river basin modeling software is RiverWare developed by the Center for Advanced Decision Support for Water and Environmental Systems (CADSWES) (Zagona et al., 2001). RiverWare is a river basin modeling tool that includes an extensible library of modeling algorithms, solvers, and a language for the expression of operating policy and is extensively used by many operating agencies such as Bureau of Reclamation and Tennessee Valley Authority. Despite the availability of many multi-reservoir models, the implementation of these models under probabilistic inflow forecasts, represented as ensembles, requires running the model subsequently for each member or its deterministic form (i.e., mean/median of the forecast). However, detailed application of seasonal-to-interannual inflow forecasts for reservoir management shows the importance and incorporation of probabilistic constraints on target storage and release (Sankarasubramanian et al., 2009; Georgakakos and Graham, 2008), which cannot be handled by most of the above models.
The skill of seasonal climate forecasts over the last decade has improved considerably through a better understanding of teleconnection between the slowly evolving boundary conditions such as SSTs in the tropical oceans and local hydroclimatology (Goddard et al., 2003; Devineni et al., 2008 in GRL; Wang et al., 2015b). Low-frequency climate variability such as El Nino Southern Oscillation (ENSO) has been proven to influence streamflow in many parts of the world (Dettinger and Diaz, 2002). Utilizing these climate forecasts with updated and corrected land-surface conditions have resulted in improved streamflow and soil moisture forecasts (Wood et al., 2002; Sinha and Sankarasubramanian, 2013; Mazrooei et al., 2019). Despite these advancements, error propagation in downscaling and disaggregation of climate forecasts in developing streamflow forecasts (Wood et al., 2005; Sankarasubramanian et al., 2009; Mazrooei et al., 2015) have caused the application of climate forecasts for real-world water allocation to face challenges due to forecast uncertainty as well as due to institutional hierarchy (Pagano et al., 2001; Pagano et al., 1999; Broad et al., 2007). These challenges necessitate the translation of uncertainty in climate forecasts into corresponding uncertainty in reservoir releases and storages (Li et al., 2014; Lu et al., 2017).
Seasonal to interannual water allocation using a reservoir model based on climate-information requires combining the initial storage conditions with the conditional distribution of streamflow, specified as ensembles, to develop with the forecasted probability of meeting the target storage for the user-specified release (Sankarasubramanian et al., 2009). Georgakakos and Graham (2008) considered a single reservoir to obtain an optimal solution for minimizing the squared deviation from the end-of-the-season target storage under inflow forecast uncertainty. Maurer and Lettenmaier (2004) evaluated the long-lead hydrologic predictability, represented as deterministic inflow forecast, for improving hydropower generation from six reservoirs in the Missouri River basin using an aggregated reservoir system representation. Probabilistic inflow forecasts developed from combining multiple GCMs for a single reservoir, Falls Lake in North Carolina (NC), has been demonstrated to be valuable in invoking drought restrictions (Golembesky et al., 2009). Li et al. (2014) considered inter-basin transfer between two NC reservoirs – Falls Lake and Lake Jordan – using two separate single reservoirs for maintaining quality pool and water supply pool elevations under inflow forecast uncertainty. Wang et al. (2015a) used a single reservoir model to identify the trade-offs between hydropower generation and ecological demands under inflow forecast uncertainty. Lu et al. (2017) utilized multi-time scale forecasts, represented as ensembles, in a single reservoir model for improving hydropower generation and reducing flood risk for a major hydropower reservoir in India. Thus, most studies have used a single reservoir model or a simplified aggregated representation of a reservoir network for evaluating the utility of deterministic/probabilistic inflow forecasts to improve water allocation. To address this, we propose a detailed multi-reservoir simulation-optimization model, GRAPS (Generalized Reservoir Analyses using Probabilistic Streamflow forecasts), that considers the probabilistic inflow forecasts, specified as ensembles, along with probabilistic constraints on meeting the target storage (i.e., rule curves) to quantify the reliability of meeting the user-specified releases.
The manuscript is organized as follows: The generalized model formulation is presented in section two that can adapt to the complexity of interlinked reservoir systems by sequentially routing the flow from upstream to downstream. GRAPS is then applied to a system of reservoirs in Ceará, Brazil to demonstrate GRAPS’ capabilities in reservoir modeling and its abilities to accurately reproduce historical storage and flows. Results of the simulation are finally assessed under inflow forecasts and the performance of the forecast-based application is validated with historical observations.
Section snippets
GRAPS formulation
GRAPS is extended from a water allocation framework, as outlined in Arumugam et al. (2003) and Sankarasubramanian et al. (2009), that utilizes the benefits of ensemble forecasts of reservoir inflows to issue annual water contracts. Unlike many mainstream reservoir-modeling tools, GRAPS is well suited to handle streamflow ensembles, which translates forecast uncertainty into storage and release reliabilities. Fig. 1 provides an overview of variables, storages, inflows, and outflows, for a given
Study area: Jaguaribe valley, Ceará, Brazil
The purpose of this case study is to demonstrate GRAPS′ modeling capability to accurately simulate historical operations. The case is based on the Jaguaribe River Basin (Fig. 5), a basin situated in the semiarid state of Ceará in the northeastern part of Brazil. With a drainage basin covering an area of 75,961.07 km2, the Jaguaribe River extends for about 610 km and its discharge can range from zero to 7000 m3/s (Campos et al., 2000). The main water management challenge in the region is to
Results and discussion
The primary objectives of the case study are to demonstrate GRAPS′ capability to model a complex reservoir system and validate the program's ability to accurately compute flows and reservoir storages and to generate storage reliability curves from ensemble inputs. The multi-reservoir system is modeled for an entire calendar year and for a three year period with monthly time-steps. In this case, travel time for return flows it is not useful, so it is not considered. Simulation results are
Discussion and concluding remarks
GRAPS, a next-generation multi-reservoir simulation program, is presented and detailed as an optimization-simulation model. The program uses simulation for reservoirs and junction nodes and optimizes the releases for multiple users that maximizes the net benefit from allocation by considering deterministic constraints and probabilistic constraints on target storage and user deficits. In this study, we demonstrated the optimization using FSQP, but in principle, GRAPS can be called using any
Software availability
GRAPS is written in Fortran 90 and uses the Fortran Feasible Sequential Quadratic Programming (FFSQP) for optimization package (Zhou and Tits, 1992). GRAPS was developed by the authors of this article and is available as free and open-source software on GitHub at https://github.com/lcford2/GRAPS. Contained in the repository is the source code, along with pre-compiled executables for Linux and Windows. Compilation was performed using intel compilers for Fortran. This repository was made public
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This material is based on work supported by the National Science Foundation under Grant No. 1442909 and Grant No. 1805293. 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 National Science Foundation.
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