Evaluating the use of “goodness‐of‐fit” Measures in hydrologic and hydroclimatic model validation

TLDR

Correlation‐based goodness‐of‐fit metrics are widely used in hydrologic modeling but are overly sensitive to outliers and fail to detect additive or proportional errors, sometimes misleadingly indicating good model performance. The paper aims to discuss alternative goodness‐of‐fit measures that address the shortcomings of correlation‐based metrics. The authors present and modify the coefficient of efficiency and index of agreement, along with other relative error metrics, to improve interpretability and overcome the limitations of correlation‐based measures. The study concludes that correlation‐based metrics should be avoided for model validation and recommends supplementing them with summary statistics and absolute error measures.

Abstract

Correlation and correlation‐based measures (e.g., the coefficient of determination) have been widely used to evaluate the “goodness‐of‐fit” of hydrologic and hydroclimatic models. These measures are oversensitive to extreme values (outliers) and are insensitive to additive and proportional differences between model predictions and observations. Because of these limitations, correlation‐based measures can indicate that a model is a good predictor, even when it is not. In this paper, useful alternative goodness‐of‐fit or relative error measures (including the coefficient of efficiency and the index of agreement) that overcome many of the limitations of correlation‐based measures are discussed. Modifications to these statistics to aid in interpretation are presented. It is concluded that correlation and correlation‐based measures should not be used to assess the goodness‐of‐fit of a hydrologic or hydroclimatic model and that additional evaluation measures (such as summary statistics and absolute error measures) should supplement model evaluation tools.