Quantifying the sensitivity and stability of the performance of a multi-purpose reservoir to model, inflow, and operational uncertainties
Authors: Molakala Manvitha , Singh Riddhi 
Published: February 2023

Water resource management strategies are often identified and evaluated using performance metrics within a simulation-optimization framework. These metrics are likely to have varying levels of sensitivity to input variables such as inflows, model-related choices, and errors from the implementation of the strategies. Quantifying the sensitivity of the performance metrics to the aforementioned uncertain factors may therefore be useful for decision-makers in understanding the relative importance of these factors and their interactions. Furthermore, the total variation in the performance measures, arising as a consequence of the uncertain factors, may be useful to quantify the stability of the performance measures. Here, we quantify the first, second, and total order sensitivity of the performance metrics to uncertain factors using Sobol&#8217;s variance-based sensitivity analysis. The stability of the performance metric is quantified as the coefficient of variation of the metric evaluated for varying input factors.&#160;We then assess these sensitivity and stability indices for four performance metrics of the multi-purpose Nagarjuna Sagar reservoir, the largest reservoir in the Krishna river basin in southern India. The reservoir supplies water to meet irrigation, industrial and domestic demands while also generating hydropower with an installed capacity of 810MW. The performance metrics evaluated in this study are: (i) maximize hydropower generation, (ii) maximize the reliability of maintaining minimum environmental flows, (iii) maximize the reliability of avoiding high flow exceedance, and (iv) minimize demand deficits. We identify the Pareto approximate set of reservoir operation strategies using evolutionary multi-objective direct policy search (EMODPS), which employs a state-aware operating rule based on radial basis functions. We consider the following uncertain factors in our analysis: (i) the length of the planning horizon (varied from 1 to 15 years), (ii) model timestep (daily, 15-day, monthly timesteps), (iii) imperfect operations while applying optimized strategies, (iv) stochastic and deep uncertainties related to inflows. Our results show that the objective related to hydropower generation is the most sensitive to the model choices. In contrast, high flow non-exceedance reliability, demand deficits, and minimum environmental flow reliability objectives are most sensitive to deep uncertainties in inflows. We find that hydropower generation, environmental flow reliability, and demand deficits are not sensitive to the interaction effects of these factors. On the other hand, high flow non-exceedance-related objectives are sensitive to the interactions between deep uncertainties and model uncertainty. We also find that the first-order sensitivity indices can be calculated with a greater confidence level than the total-order sensitivity indices. We identify that the flood reliability objective is the most stable, and the demand deficits objective is the least stable when subjected to uncertainty. Our framework can be used to identify the relative importance of the uncertain factors and the stability of the performance measures in any water management problem.