A wavelet-based approach to assessing timing errors in hydrologic predictions

Summary Streamflow predictions typically contain errors in both the timing and the magnitude of peak flows. These two types of error often originate from different sources (e.g. rainfall–runoff modeling vs. routing) and hence may have different implications and ramifications for both model diagnosis and decision support. Thus, where possible and relevant, they should be distinguished and separated in model evaluation and forecast verification applications. Distinct information on timing errors in hydrologic prediction could lead to more targeted model improvements in a diagnostic evaluation context, as well as better-informed decisions in many practical applications, such as flood prediction, water supply forecasting, river regulation, navigation, and engineering design. However, information on timing errors in hydrologic predictions is rarely evaluated or provided. In this paper, we discuss the importance of assessing and quantifying timing error in hydrologic predictions and present a new approach, which is based on the cross wavelet transform (XWT) technique. The XWT technique transforms the time series of predictions and corresponding observations into a two-dimensional time-scale space and provides information on scale- and time-dependent timing differences between the two time series. The results for synthetic timing errors (both constant and time-varying) indicate that the XWT-based approach can estimate timing errors in streamflow predictions with reasonable reliability. The approach is then employed to analyze the timing errors in real streamflow simulations for a number of headwater basins in the US state of Texas. The resulting timing error estimates were consistent with the physiographic and climatic characteristics of these basins. A simple post-factum timing adjustment based on these estimates led to considerably improved agreement between streamflow observations and simulations, further illustrating the potential for using the XWT-based approach for timing error estimation.