Using a simple post-processor to predict residual uncertainty for multiple hydrological model outputs

Regardless of the complexity of the hydrological model employed, uncertainty assessment (UA)is predominantly performed for the aggregated catchment response discharge. For coupled integrated models that simulate various hydrological states and fluxes on a grid cell basis, this represents a severe shortcoming. We test a simple data-driven technique (k-NN resampling)to evaluate its ability to provide reliable residual uncertainty estimates for the multi-variable (discharge, hydraulic head, soil moisture and actual evapotranspiration), deterministic output of two coupled groundwater-surface water models with different complexities. Being a nonparametric method, no explicit prior assumptions about the error distribution of different hydrological variables are required. When conditioning the algorithm, we propose to limit the number of error lags to be included based on inspection of the partial autocorrelation function (PACF). Our results confirm previous findings regarding reliability and robustness of the k-NN technique for discharge simulations and conclude that k-NN resampling also provides reliable and robust results for other variables like hydraulic head, soil moisture and actual evapotranspiration, even for underlying hydrological models with varying levels of performance. The 90% prediction intervals (PI)capture the observations in the testing period satisfactorily for all hydrological variables (92.6–97.3%), while Alpha indices (0.84–0.95)indicate very reliable PIs for all error quantiles. Differences in error structure between hydrological variables are successfully inferred from historical data and reflected in the results. We conclude that k-NN resampling represents a potent, cost-efficient UA technique for applications in operational hydrology, facilitating a near-simultaneous, easy uncertainty assessment for various outputs of computationally heavy hydrological models.