Stochastic watershed model ensembles for long-range planning: Verification and validation

Deterministic watershed models (DWMs) are used in nearly all hydrologic planning, design, and management activities, yet they cannot generate streamflow ensembles needed for hydrologic risk management (HRM). The stochastic component of DWMs is often ignored in practice, leading to a systematic bias in extreme events. Since traditional stochastic streamflow models used in HRM struggle to account for anthropogenic change, there is a need to convert DWMs into stochastic watershed models (SWMs) to generate ensembles for use in HRM. A DWM can be converted to an SWM using a post-processing (pp) approach to add error to the DWM predictions. Many pp methods advanced in the area of flood forecasting are useful in HRM and for correcting extreme event biases. Selecting a suitable error model for pp is challenging due to nonnormality, skewness, heteroscedasticity, and autocorrelation. We develop a parsimonious pp method based on an autoregressive (AR) model of the logarithm of the ratio of the observations and simulations, which leads to AR model residuals that are approximately symmetric and independent. We document the value of pp for improving flood and low flow frequency analysis and we reintroduce the concepts of verification and validation of stochastic streamflow ensembles to ensure that the SWM can reproduce both statistics it was and was not designed to reproduce, respectively. These concepts are illustrated on a Massachusetts basin using the USGS Precipitation Runoff Modeling System, with an additional analysis indicating the approach may be applicable to 1,225 other sites across the United States.