Rival framings: A framework for discovering how problem formulation uncertainties shape risk management trade‐offs in water resources systems

Abstract

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.

On the Value of ENSO State for Urban Water Supply System Operators: Opportunities, Trade‐Offs, and Challenges

“…To characterize the hydro‐climatological variability, we use an ensemble Ξ of 50 members containing 47‐year stochastic replicates of inflow and ONI. The optimization problem is then solved with Borg (Hadka & Reed, ), a self‐adaptive Multiobjective Evolutionary Algorithm that has been successfully employed in a few recent reservoir operation studies (e.g., Giuliani et al, ; ; Quinn et al, ). The initial population and number of function evaluations are set equal to 100 and 500,000, while the value of ε (used in the ε ‐dominance archive) is equal to 0.005 for all objectives, which are normalized between 0 and 1.…”

“…Among the various statistics available, we adopt the worst tenth percentile, so = quantile N {J i , 0.90}, where J i is the ith component of the vector J (the value of the objectives to be maximized is multiplied by −1 during the optimization process, so as to guarantee the correct verse of optimization). As recently discussed in Quinn et al (2017) and McPhail et al (2018), percentile-based statistics help design stable policies that generalize well on out-of-sample replicates. Note that the number of policy parameters to be optimized is 30 for the traditional policies and 48 for the ENSO-informed ones (see section 3.2.1)…”

Exploring How Changing Monsoonal Dynamics and Human Pressures Challenge Multireservoir Management for Flood Protection, Hydropower Production, and Agricultural Water Supply

“…The Borg algorithm requires that users specify “epsilons,” or significant levels of precision below which they are impartial to differences in performance, for each objective. Consistent with prior work in the basin (Giuliani et al, ; Quinn et al, ), we use epsilons of 0.05 for J Flood , 25.0 for , and 0.5 for J Hydro and run the multimaster Borg with five seeds using a 16‐master implementation with 400,000 function evaluations allocated to each master. The optimization was performed on the Texas Advanced Computing Center (https://www.tacc.utexas.edu/stampede/) using 512 cores per island for a total of 400,000 computational hours.…”

“…Map of the Red River basin (panel a) and schematization of the main components of the Red River basin model (panel b), reproduced from Quinn et al (). Flows to each of the reservoirs shown in panel b are generated synthetically, releases from the reservoirs are determined by operating policies discovered through multiobjective optimization, and flows through the delta are modeled by a dynamic emulator of a MIKE 11 model of the downstream hydraulics.…”

“…This scenario evaluation step is described in sections 3.5 and supporting information S3-S4, and the results of the analysis are presented in section 4.3. Quinn et al (2017) analyzed several rival framings for how the multiobjective Red River control problem should be formulated to best capture stakeholder objectives and preferences. Insights from that study were used to design the problem formulation described here, which is intended to capture the risk aversion of Vietnamese stakeholders with respect to extreme floods and droughts.…”