Robust optimization of shading types to control the performance of water reservoirs

Abstract

Managing evaporation losses and water quality is critical in improving farm-level water reservoir performance. Applying shading cloths over water reservoirs reduces solar radiation and wind acting on the water surface, possibly affecting the evaporation losses and water quality therein. The complex thermal fluid dynamics, including biochemical reactions, make it difficult to answer the question of which color and intensity shading cloth best controls water reservoirs’ performance in a specific climate. This study aims to establish a systematic approach to determine the best portfolio of shading cloths in the framework of robust optimization with demonstrations in the arid and semi-arid climates of Jordan. Firstly, intensive experiments were conducted at a site in a steppe climate, using thirty class-A evaporation pans covered by ten different shading treatments, including the control. Secondly, a physical model was developed to represent the dynamics in each pan. The experimental results were utilized for the calibration-validation procedure for the physical model. Then, robust optimization problems are formulated with uncertainty sets, where numerical solutions of the physical model determine nominal values of evaporation rates. However, the experimental results exclusively do the uncertainty intervals of evaporation rates and the whole uncertainty sets of chlorophyll-a. Computational searches for optimal portfolios are performed to satisfy the necessary conditions according to the Karush-Kuhn-Tucker theorem. Significant results were obtained from the robust optimization, including the cases of no solution, the best single type of shading, and diverse types of shadings.