Multi-objective Optimization of Catchment Reforestation Robust to Uncertainty in Bayesian-Calibrated Watershed Model Parameters

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. Reforestation of urbanized catchments is one green infrastructure strategy to reduce stormwater volumes and nutrient exports. Reforestation designs must balance the benefits of flood flow reduction against the costs of implementation and the chance to exacerbate droughts via reduction in recharge that supplies low flows. Optimal locations and numbers of trees depend on the spatial distribution 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 streamflows across the catchment, which can lead to different optimal reforestation designs for different parameterizations.

Multi-objective robust optimization (MORO) has been proposed to discover reforestation designs that are robust to such parametric model uncertainty. However, it has not been shown that this actually results in better decisions than optimizing to a single, most likely parameter set, which would be less computationally expensive. In this work, the utility of MORO is assessed by comparing reforestation designs optimized using these two approaches with reforestation designs optimized to a synthetic true set of hydrologic model parameters. The spatially-distributed RHESSys ecohydrological model is employed for this study of a suburban-forested catchment in Baltimore County, Maryland, USA. Calibration of the model’s critical parameters is completed using a Bayesian framework to estimate the joint posterior distribution of the parameters. The Bayesian framework estimates the probability that different parameterizations generated the synthetic streamflow data, allowing the MORO process to evaluate reforestation portfolios across a probability-weighted sample of parameter sets in search of solutions that are robust to this uncertainty.

Reforestation portfolios are designed to minimize flooding, low flow intensity, and construction costs (number of trees). Comparing the Pareto front obtained from using MORO with the Pareto fronts obtained from optimizing to the estimated maximum a posteriori (MAP) parameter set and the synthetic true parameter set, we find that MORO solutions are closer to the synthetic solutions than are MAP solutions. This illustrates the value of considering parametric uncertainty in designing robust water systems despite the additional computational cost.