Modeling macroroughness contribution to fish habitat-suitability curves

Improved water management strategies necessitate a solid understanding of environmental impacts associated with various flow release policies. Habitat suitability models use hydrodynamic simulations to generate weighted usable area curves, which are useful in characterizing the ecological suitability of flow release rules. However, these models are not conveniently run to resolve the hydrodynamics at the smaller scales associated with macroroughness elements (e.g., individual stones), which produce wakes that contribute significantly to habitat suitability by serving as shelter zones where fishes can rest and feed. In this study, we propose a robust environmental indicator that considers the habitat generated by the wakes downstream of stones and can thus be used to assess the environmental efficiency of flow release rules for impounded streams. We develop an analytical solution to approximate the wake areas behind macroroughness elements, and the statistical distribution of wake areas is then found using the derived distribution approach. To illustrate the concept, we apply our theory to four exemplary river streams with dispersed stones having different statistical diameter size distributions, some of which allow for an analytical expression of the weighted usable area. We additionally investigate the impact of spatiotemporal changes in stone size distributions on the usable area and the consequent threshold flows. Finally, we include the proposed environmental indicator to solve a multiobjective reservoir optimization problem. This exemplifies its practical use and allows stakeholders to find the most favorable operational rules depending on the macroroughness characteristics of the impounded stream.