Fuzzy set based error measure for hydrologic model evaluation

Abstract

Traditional error measures (e.g. mean squared error, mean relative error) are often used in the field of water resources to evaluate the performance of models developed for modeling various hydrological processes. However, these measures may not always provide a comprehensive assessment of the performance of the model intended for a specific application. A new error measure is proposed and developed in this paper to fill the gap left by existing traditional error measures for performance evaluation. The measure quantifies the error that corresponds to the hydrologic condition and model application under consideration and also facilitates selection of the best model whenever multiple models are available for that application. Fuzzy set theory is used to model the modeler's perceptions of predictive accuracy in specific applications. The development of the error measure is primarily intended for use with models that provide hydrologic time series predictions. Hypothetical and real-life examples are used to illustrate and evaluate this measure. Results indicate that use of this measure is rational and meaningful in the selection process of an appropriate model from a set of competing models.