Evaluating Performance of Watershed Hydrology Simulations At Daily Time Step Using Autoregression.

Watershed models are calibrated to optimize the accuracy of simulated stream discharge. Typically, model validation statistics are calculated on monthly time periods, rather than the daily step at which models typically operate and discharge data are typically reported. This is because daily discharge exhibits large variability and skewness, while temporal aggregation provides a more straightforward performance target. But data transformation provides an option to reduce skew without losing detail. We empirically simulated transformed daily discharge (ln[Q]) for four South Fork Iowa River (SFIR) stream gages using autoregression, back-transformed results, and calculated model performance statistics for the autoregressive models and Soil and Water Assessment Tool (SWAT) output. Autoregressive models captured 93-97% of variation in ln(Q), while meeting a near-zero bias condition for convergence. Autoregressive model output, for three of four stations, had Nash-Sutcliffe efficiencies (NSE) of 0.77-0.82, and residual-standard-error (RSR) ratios of 0.37-0.41;  i.e., better than SWAT daily performance. The fourth gage, on Beaver Creek (BC), showed flashier hydrology and weaker autocorrelation. Consequently, SWAT outperformed autoregression at BC. Hydrologic variation among tributary watersheds had consequences for modeling success, and stream flashiness metrics helped assess this variation at the daily time step. Autoregression provides a statistical mimic of observed daily data and apparent potential to benchmark performance of watershed models at the daily scale. In this case, log-transformed SWAT output with NSE>0.9 and RSR<0.2 would be indistinguishable from a statistical reproduction of the measured data. Autoregressive models also produce confidence intervals, allowing the measured data to generate uncertainty estimates.