Stochastic post-processing of a regionalized monthly water balance model for the conterminous United States

Mathematical derivation has demonstrated that the deterministic use of an environmental simulation model for a single realization (a single stream of output derived from a single set of random variables and initial conditions) misrepresents the distributional characteristics of the modeled phenomenon. In deterministic streamflow modeling, these misrepresentations can be magnified in simulations of high- and low-flow portions of the measured streamflow record. The stochastic use of multiple realizations can improve the distributional properties of the simulations by incorporating the properties of model residuals back into the simulated output. We extend this approach to a deterministic rainfall-runoff model with a monthly water balance model (MWBM). Previous work regionalized the MWBM by aggregating 109,951 hydrologic response units across the conterminous United States into 110 regions calibrated to measured streamflow and modeled snow water equivalent for the period of record 1950 through 2010. The group-wise calibration resulted in each calibration region sharing a common parameter set that produced estimates of streamflow within each region. While simulated streamflow showed good correspondence with measured streamflow (median Nash-Sutcliffe Efficiency = 0.76), the greatest amount of model bias occurred in simulating high- and low-flow months. We introduced this approach of creating stochastic realizations based on the model residuals to the simulated streamflow time series in each MWBM region. This yielded multiple realizations of simulated monthly streamflow that can be used to better understand the spatial and temporal bias of the MWBM, allow for a more comprehensive representation of the range of outcomes, the development of confidence intervals, and an indication of predictive uncertainty for the model across the United States.