A wavelet-based approach to streamflow event identification and modeled timing error evaluation

Streamflow timing errors (in the units of time) are rarely explicitly evaluated but are useful for model evaluation and development. Wavelet-based approaches have been shown to reliably quantify timing errors in streamflow simulations but have not been applied in a systematic way that is suitable for model evaluation. This paper provides a step-by-step methodology that objectively identifies events, and then estimates timing errors for those events, in a way that can be applied to large-sample, high-resolution predictions. Step 1 applies the wavelet transform to the observations and uses statistical significance to identify observed events. Step 2 utilizes the cross-wavelet transform to calculate the timing errors for the events identified in step 1; this includes the diagnostic of model event hits, and timing errors are only assessed for hits. The methodology is illustrated using real and simulated stream discharge data from several locations to highlight key method features. The method groups event timing errors by dominant timescales, which can be used to identify the potential processes contributing to the timing errors and the associated model development needs. For instance, timing errors that are associated with the diurnal melt cycle are identified. The method is also useful for documenting and evaluating model performance in terms of defined standards. This is illustrated by showing the version-over-version performance of the National Water Model (NWM) in terms of timing errors.