Climate change introduces substantial uncertainty to water resources planning and raises the key question: when, or under what conditions, should adaptation occur? A number of recent studies aim to identify policies mapping future observations to actions—in other words, framing climate adaptation as an optimal control problem. This paper uses the control paradigm to review and classify recent dynamic planning studies according to their approaches to uncertainty characterization, policy structure, and solution methods. We propose a set of research gaps and opportunities in this area centered on the challenge of characterizing uncertainty, which prevents the unambiguous application of control methods to this problem. These include exogenous uncertainty in forcing, model structure, and parameters propagated through a chain of climate and hydrologic models; endogenous uncertainty in human‐environmental system dynamics across multiple scales; and sampling uncertainty due to the finite length of historical observations and future projections. Recognizing these challenges, several opportunities exist to improve the use of control methods for climate adaptation, namely, how problem context and understanding of climate processes might assist with uncertainty quantification and experimental design, out‐of‐sample validation and robustness of optimized adaptation policies, and monitoring and data assimilation, including trend detection, Bayesian inference, and indicator variable selection. We conclude with a summary of recommendations for dynamic water resources planning under climate change through the lens of optimal control.

Managing water resources systems requires coordinated operation of system infrastructure to mitigate the impacts of hydrologic extremes while balancing conflicting multisectoral demands. Traditionally, recommended management strategies are derived by optimizing system operations under a single problem framing that is assumed to accurately represent the system objectives, tacitly ignoring the myriad of effects that could arise from simplifications and mathematical assumptions made when formulating the problem. This study illustrates the benefits of a rival framings framework in which analysts instead interrogate multiple competing hypotheses of how complex water management problems should be formulated. Analyzing rival framings helps discover unintended consequences resulting from inherent biases of alternative problem formulations. We illustrate this on the monsoonal Red River basin in Vietnam by optimizing operations of the system's four largest reservoirs under several different multiobjective problem framings. In each rival framing, we specify different quantitative representations of the system's objectives related to hydropower production, agricultural water supply, and flood protection of the capital city of Hanoi. We find that some formulations result in counterintuitive behavior. In particular, policies designed to minimize expected flood damages inadvertently increase the risk of catastrophic flood events in favor of hydropower production, while min‐max objectives commonly used in robust optimization provide poor representations of system tradeoffs due to their instability. This study highlights the importance of carefully formulating and evaluating alternative mathematical abstractions of stakeholder objectives describing the multisectoral water demands and risks associated with hydrologic extremes.

Managing socio-ecological systems is a challenge wrought by competing societal objectives, deep uncertainties, and potentially irreversible tipping points. A classic, didactic example is the shallow lake problem in which a hypothetical town situated on a lake must develop pollution control strategies to maximize its economic benefits while minimizing the probability of the lake crossing a critical phosphorus (P) threshold, above which it irreversibly transitions into a eutrophic state. Here, we explore the use of direct policy search (DPS) to design robust pollution control rules for the town that account for deeply uncertain system characteristics and conflicting objectives. The closed loop control formulation of DPS improves the quality and robustness of key management tradeoffs, while dramatically reducing the computational complexity of solving the multi-objective pollution control problem relative to open loop control strategies. These insights suggest DPS is a promising tool for managing socioecological systems with deeply uncertain tipping points.

Multireservoir systems require robust and adaptive control policies capable of managing hydroclimatic variability and human demands across a range of time scales. This is especially true for river basins with high intraannual and interannual variability, such as monsoonal systems that need to buffer against seasonal droughts while also managing extreme floods. Moreover, the timing, intensity, duration, and frequency of these hydrologic extremes may evolve with deeply uncertain changes in socioeconomic and climatic pressures. This study contributes an innovative method for exploring how possible changes in the timing and magnitude of the monsoonal cycle impact the robustness of reservoir operating policies designed assuming stationary hydrologic and socioeconomic conditions. We illustrate this analysis on the Red River basin in Vietnam, where reservoirs and dams serve as important sources of hydropower production, multisectoral water supply, and flood protection for the capital city of Hanoi. Applying our scenario discovery approach, we find that reservoir operations designed assuming stationarity provide robust hydropower performance in the Red River but that increased mean streamflow, amplification of the within‐year monsoonal cycle, and increased interannual variability all threaten their ability to manage flood risk. Additionally, increased agricultural water demands can only be tolerated if they are accompanied by greater mean flow, exacerbating food‐flood trade‐offs in the basin. These findings highlight the importance of exploring the impacts of a wide range of deeply uncertain socioeconomic and hydrologic factors when evaluating system robustness in monsoonal river basins, considering in particular both lower‐order moments of annual streamflow and intraannual monsoonal behavior.

Advances in modeling and control have always played an important role in supporting water resources systems planning and management. Changes in climate and society are now introducing additional challenges for controlling these systems, motivating the emergence of complex, integrated simulation models to explore key causal relationships and dependences related to uncontrolled sources of variability. In this brief, we contribute a massively parallel implementation of the evolutionary multiobjective direct policy search method for controlling large-scale water resources systems under uncertainty. The method combines direct policy search with nonlinear approximating networks and a hierarchical parallelization of the Borg multiobjective evolutionary algorithm. This computational framework successfully identifies control policies that address both the presence of multidimensional tradeoffs and severe uncertainties in the system dynamics and policy performance. We demonstrate the approach on a challenging real-world application, represented by the optimal control of a network of four multipurpose water reservoirs in the Red River basin in Northern Vietnam, under observed and synthetically generated hydrologic conditions. Results show that the reliability of the computational framework in finding near-optimal solutions increases with the number of islands in the adopted hierarchical parallelization scheme. This setting reduces the vulnerabilities of the designed solutions to the system's uncertainty and improves the discovery of robust control policies addressing key system performance tradeoffs

The Upper Basin of the Colorado River in the southwestern United States supports municipal, industrial, agricultural, and recreational activities worth an estimated $300 billion/year within the state of Colorado alone. The allocation of water to these activities is fundamentally shaped by water rights that in turn distribute risks among a diverse suite of sectors and stakeholders. In this study, we assess the vulnerabilities faced by the hierarchy of hundreds of water users in the portion of the Upper Basin within the state of Colorado, as a result of changes in hydrologic extremes, demand growth, and institutional and physical infrastructure in the basin. We also determine how robust the different users are to these potential changes, examining how their sensitivity to these factors depends on the magnitude and frequency of shortage they are unwilling to exceed. This advances previous robustness evaluation methods by formalizing an a posteriori exploration of alternative definitions of robustness tailored to each user's unique context. Our analysis reveals that robustness varies significantly not only across users but also across different definitions of acceptable performance for each user. We further show the importance of using scenario discovery to evaluate how the factors that drive consequential scenarios differ depending on the definition of robustness. Our results highlight the need for robustness and vulnerability frameworks to avoid broad categorical aggregations of stakeholder groups, to carefully capture complex institutional dependencies (e.g., water rights), and to facilitate a more transparent illustration of the implications of alternative definitions of robustness for specific stakeholders.

Multireservoir systems are designed to serve multiple conflicting demands over varying time scales that may be out of phase with the system's hydroclimatic inputs. Adaptive, nonlinear reservoir control policies are often best suited to serve these needs. However, nonlinear operating policies are hard to interpret, so water managers tend to favor simple, static rules that may not effectively manage conflicts between the system's multisectoral demands. In this study, we introduce an analytical framework for opening the black box of optimized nonlinear operating policies, decomposing their time‐varying information sensitivities to show how their adaptive and coordinated release prescriptions better manage hydrologic variability. Interestingly, these information sensitivities vary significantly across policies depending on how they negotiate tradeoffs between conflicting objectives. We illustrate this analysis in the Red River basin of Vietnam, where four major reservoirs serve to protect the capital of Hanoi from flooding while also providing the surrounding region with electric power and meeting multisectoral water demands for the agricultural and urban economies. Utilizing Evolutionary Multi‐Objective Direct Policy Search, we are able to design policies that, using the same information as sequential if/then/else‐based operating guidelines developed by the government, outperform these traditional rules with respect to every objective. Policy diagnostics using time‐varying sensitivity analysis illustrate how the Evolutionary Multi‐Objective Direct Policy Search operations better adapt and coordinate information use to reduce food‐energy‐water conflicts in the basin. These findings accentuate the benefits of transitioning to dynamic operating policies in order to manage evolving hydroclimatic variability and socioeconomic demands in multipurpose reservoir networks.

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