Abstract
Abstract. 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.
Highlights
Common verification metrics used to evaluate streamflow simulations are typically aggregated measures of model performance, e.g., the Nash–Sutcliffe Efficiency (NSE) and the related root mean square error (RMSE)
Common verification metrics are calculated using the entire time series, whereas timing errors require a comparison of localized features or events in the data
From step 1 of our method, the wavelet transform is applied to the observations (Fig. 4b, left panel; Fig. 4c, left panel), revealing up to three event clusters, depending on the characteristic timescale examined (Fig. 4d)
Summary
Common verification metrics used to evaluate streamflow simulations are typically aggregated measures of model performance, e.g., the Nash–Sutcliffe Efficiency (NSE) and the related root mean square error (RMSE). Common verification metrics are calculated using the entire time series, whereas timing errors require a comparison of localized features or events in the data. This paper focuses explicitly on event timing error estimation, which is not routinely evaluated despite its potential benefit for model diagnostics (Gupta et al, 2008) and practical forecast guidance (Liu et al, 2011). Identifying events is typically subjective, time consuming, and not practical for large-sample hydrological applications (Gupta et al, 2014). A variety of baseflow separation methods, ranging from physically based to empirical, have been developed to identify hydrologic events (see Mei and Anagnostou, 2015, for a summary), though many of these approaches require some manual inspection of the hydrographs. The thresholds used for such analyses are often either based on historical percentiles
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