Multi-objective Optimization of Green Infrastructure Robust to Uncertainty in Bayesian-Calibrated Watershed Model Parameters

Abstract:

Urban land expansion is expected for our changing world, which unmitigated will result in increased flooding and nutrient exports that already wreak havoc on the wellbeing of coupled human-natural systems worldwide. Increasing canopy cover over urban surfaces with green infrastructure (GI) is one strategy to reduce stormwater volumes and excess nutrient exports. GI portfolio designs must balance the benefits of flood flow reduction with the costs of implementing GI and the chance to exacerbate droughts via reduction in recharge that supplies low flows. Optimal locations and sizes of GI depend on the locations and magnitudes of runoff and streamflow in a catchment; however, calibration data are often only available at the catchment outlet. Equifinal model parameterizations for the outlet can result in uncertainty in the locations and magnitudes of water flows across the watershed, which can lead to different optimal GI portfolios for different parameterizations.

Multi-objective robust optimization (MORO) is proposed to discover GI portfolios that are robust to such parametric model uncertainty. The spatially-distributed RHESSys ecohydrological model is employed for this study of a suburban-forested catchment in Baltimore County, Maryland. Calibration of the model’s critical parameters is completed using a Bayesian framework to estimate the joint posterior distribution of the selected parameters. The likelihood function describes the distribution of model errors for streamflow and nitrogen concentration. The Bayesian framework estimates the probability that different parameterizations generated the observed data, allowing the MORO process to evaluate GI portfolios across a probability-weighted sample of parameter sets in search of solutions that are robust to this uncertainty.

GI portfolios are designed to minimize flooding, low flow intensity, and the cost of GI implementation in the catchment. We compare the Pareto front obtained from the robust optimization to the Pareto front obtained by optimizing to the estimated maximum a posteriori parameter set and near-maximum a posteriori parameter sets. Differences between these Pareto fronts illustrate the importance of considering parametric uncertainty in designing robust water systems, even in the absence of urbanization and climate change.