Optimization of geometry of infiltrating wadis-trenches for MAR schemes with flash flood and treated wastewater pulses in desert dunes

Interdunal areas in Oman are contemplated for Managed Aquifer Recharge (MAR) using flash flood and treated wastewater through the natural beds of dune valleys or constructed channels (see Al-Shukaili et al., 2019) which have a favorable dyad of porosity and hydraulic conductivity (m, Ks) for infiltration. However, the geometry of these channels, particularly the constructed once, can be optimized for further enhancement of the efficiency and performance of MAR application which is the scope of this study. We also present the results of sandbox experiments and numerical simulations in HYDRUS. Surface water impoundment in the channel during a single MAR-pulse lasts for time Te. In triangular trenches of an initial water width W0, depth H0 and length L, the dyad (W, H) vanishes at t->Te. The sooner the water seeps from the channel into the vadose zone, the better. The smaller the sizes of the W0, H0, the better. Similarly to Kacimov (1992), we formulate the cost function Cf (): Cf =c0 Te +c1 W0 +c2 H0 (1) where c0 (/hour), c1 (/m) and c2 (/m) are "weight" constants. Optimization problem: given L, volume of water to be infiltrated (fixed cross-sectional area A0=H0W0), the pentad (c0, c1, c2, m, Ks), determine the slope of the trench ωπ , 0