Introducing the Model Fidelity Metric (MFM) for robust and diagnostic land surface model evaluation

Abstract. The accurate evaluation of Land Surface Models (LSMs) is fundamental to their development and application. However, standard metrics such as the Nash-Sutcliffe Efficiency (NSE) and Kling-Gupta Efficiency (KGE) possess well-documented shortcomings. Relying on moment-based statistics such as mean, variance, and correlation often falls short for land surface modelling data, which are typically non-normal and skewed. These metrics can be misleading due to issues such as error compensation, instability when variability is low, and the confusion of magnitude and phase errors, leading to inaccurate model assessments. To address these fundamental flaws, we propose the Model Fidelity Metric (MFM), a novel evaluation framework constructed using robust statistics and information theory. MFM integrates three orthogonal dimensions of model performance within a Euclidean framework, including 1) Accuracy, which measure by the robust Normalized Mean Absolute p-Error (NMAEp) and penalized for timing issues via a Phase Penalty Factor (PPF); 2) Variability, quantified using the information-theoretic Scaled and Unscaled Shannon Entropy differences (SUSE); and 3) Distribution Similarity, assessed non-parametrically using the Percentage of Histogram Intersection (PHI). We evaluated MFM against with traditional metrics using targeted synthetic experiments and the large-sample CAMELS dataset. Our results demonstrate that MFM provides a more authentic and reliable assessment of model fidelity. MFM proved immune to error compensation effects that mislead KGE and remained stable in low-variability scenarios where NSE and KGE fail. Furthermore, MFM provides superior diagnostic capabilities by decoupling phase and magnitude errors and decomposing performance into its core components. This work highlights the need to move beyond traditional moment-based metrics. We advocate adopting robust, diagnostic frameworks such as MFM to support the development of more trustworthy LSMs.