Achieving high-quality probabilistic predictions from hydrological models calibrated with a wide range of objective functions

Abstract

Probabilistic predictions of streamflow are important in many environmental modelling applications. These predictions are often constructed using hydrological models combined with residual error models to describe predictive uncertainty. However, many objective functions commonly used to calibrate hydrological models make (implicit) assumptions that do not match the well-known heteroscedasticity and skewness of residual errors. Using a daily-scale hydrological model, we demonstrate that the use of such ‘inconsistent’ objective functions in combination with a commonly used residual error model introduces spurious flow dependencies in the mean of residual errors, which in turn leads to poor-quality probabilistic predictions. We then use residual error diagnostics to develop a simple enhanced error model, where the error mean depends linearly on the (transformed) simulated streamflow. The enhanced error model is compared with a commonly used reference error model that assumes a zero error mean. The empirical case study employs 54 perennial Australian catchments, the hydrological model GR4J, 9 common objective functions and 4 performance metrics (reliability, precision, volumetric bias and errors in the flow duration curve). The enhanced error model overcomes the loss of performance caused by inconsistent objective functions and achieves probabilistic predictions comparable to those obtained using consistent objective functions. These findings hold for all objective functions used in the case study. The enhanced residual error model is expected to facilitate the adoption of probabilistic predictions in the hydrological modelling community. In particular, it can be used to achieve high-quality probabilistic predictions from hydrological models calibrated with a wide range of common objective functions.