Decomposing the Performance of Streamflow Prediction into Errors of Timing and Distribution

Abstract:

Timing and distribution (magnitudes) are two important aspects of streamflow prediction that can have implications for water resources management and process understanding. Performance of streamflow predictions are often evaluated using generalized metrics like the sum of squared errors and Nash-Sutcliffe efficiencies, but these do not distinguish between errors of timing and distribution. Other metrics of performance are needed and often used, but additional metrics are often not directly relatable to the generalized performance metrics. Here we show how the sum of squared errors can be decomposed into errors of timing and distribution (magnitude) using predictions of daily streamflow across the United States. Streamflow timing is evaluated as the relative timing, quantifying the accuracy of the sequence of streamflow ranks. Streamflow distribution is evaluated by considering the accuracy of the simulated streamflow duration curve. The decomposition of an otherwise generalized metric identifies errors associated with model bias, the correlation of bias and magnitude, errors related to relative timing, errors related to streamflow distribution, and the correlation of errors in timing and distribution. These are presented as the sum of squared errors in timing and the sum of squared errors in distribution. While not advocated as a replacement for robust, multi-metric analysis of performance, this decomposition provides an elegant method to understand the source of errors in streamflow prediction for further investigation. After showing how this decomposition works in theory and in practice, we address the on-going discussions of how to appropriately use performance metrics derived from the sum of squared errors in water resources management.