Technical note: Diagnostic efficiency – specific evaluation of model performance

Abstract

A better understanding of the reasons why hydrological model performance is unsatisfying represents a crucial part of meaningful model evaluation. However, current evaluation efforts are mostly based on aggregated efficiency measures such as Kling–Gupta efficiency (KGE) or Nash–Sutcliffe efficiency (NSE). These aggregated measures provide a relative gradation of model performance. Especially in the case of a weak model performance it is important to identify the different errors which may have caused such unsatisfactory predictions. These errors may originate from the model parameters, the model structure, and/or the input data. In order to provide more insight, we define three types of errors which may be related to their source: constant error (e.g. caused by consistent input data error such as precipitation), dynamic error (e.g. structural model errors such as a deficient storage routine) and timing error (e.g. caused by input data errors or deficient model routines/parameters). Based on these types of errors, we propose the novel diagnostic efficiency (DE) measure, which accounts for these three error types. The disaggregation of DE into its three metric terms can be visualized in a plain radial space using diagnostic polar plots. A major advantage of this visualization technique is that error contributions can be clearly differentiated. In order to provide a proof of concept, we first generated time series artificially with the three different error types (i.e. simulations are surrogated by manipulating observations). By computing DE and the related diagnostic polar plots for the reproduced errors, we could then supply evidence for the concept. Finally, we tested the applicability of our approach for a modelling example. For a particular catchment, we compared streamflow simulations realized with different parameter sets to the observed streamflow. For this modelling example, the diagnostic polar plot suggests that dynamic errors explain the overall error to a large extent. The proposed evaluation approach provides a diagnostic tool for model developers and model users and the diagnostic polar plot facilitates interpretation of the proposed performance measure as well as a relative gradation of model performance similar to the well-established efficiency measures in hydrology.