Comparing Robust Optimization Approaches for Addressing Hydrologic Model Uncertainty in Infrastructure Planning: A Green Infrastructure Example

Water resources planning depends upon hydrologic models to estimate flows and storage under candidate engineering designs. However, such models are calibrated with limited flow data relative to the many model parameters. This may result in different equifinal parameterizations that imply different optimal designs. To assess if and how this uncertainty should be considered, we compare three methods for multi-objective optimization of green infrastructure (GI): one that designs to the most likely parameterization and two robust alternatives that use several likely parameterizations with 1) likelihood-weighted objective functions, and 2) min-max objective functions. To evaluate these methods, we set synthetic true values for model parameters, use them to simulate "observed" streamflow, and then use Bayesian calibration to estimate parametric uncertainty. We compare results from optimization to the synthetic parameterization against the three alternatives. The GI optimizations aim to minimize flooding, low flow intensification, and cost. We find the two robust methods provide objective values and decisions that are closer to those optimized to the synthetic