Diagnosing Biases in Soil Moisture–Evaporation Coupling Metrics in Earth System Models using Covariance Discriminant Analysis

Various studies have validated Land-Atmosphere (L-A) coupling metrics from Earth system models against observations; however, challenges arise from limited in-situ data and random errors in satellite measurements. Tavakoli & Dirmeyer (2026) generated a global L-A coupling metrics dataset using observational gridded data, primarily satellite-based, by considering random observational errors in satellite soil moisture (SM) measurements within a Markovian framework. Since these datasets provide an independent benchmark for evaluating the accuracy of L-A coupling metrics derived from Earth system models, we quantified L-A coupling metrics, including correlation and the terrestrial coupling index between SM and evaporation (E), using Community Land Model (CLM) configurations. Since covariance matrices encode variance and covariance, and since correlation and the terrestrial coupling index are derived from these quantities, this study focuses on applying covariance discriminant analysis (CDA) to covariance matrices (model and observations) to identify the linear combinations of SM and E that yield the greatest separation between the two distributions. Using this comparison, we attempt to answer “Where is the model’s SM–E structure significantly different from observations? Is there a systematic seasonal pattern in this structure?” and “Is the disagreement dominated by SM variance, E variance, or their covariance? And how much are their contributions?” Therefore, we applied CDA to the covariance matrices of SM and E to identify directions and magnitudes in which the CLM model differs most from observations. For the observational dataset, we utilized the SM satellite from ESA CCI (The Climate Change Initiative) and GLEAM (Global Land Evaporation Amsterdam Model) as a surface heat flux dataset.The results show that there is a systematic seasonal pattern in the global over- and underestimation of the first and second modes. For instance, the CLM model underestimates variance along the first SM–E mode relative to the observed variance, particularly over semi-arid regions during JJA (June–July–August). However, the CLM model overestimates variance along the first SM–E mode compared with the observed variance, especially over humid and wetter regions during JJA. Additionally, disagreement between CLM and CCI-GLEAM, dominated by SM variance, is highest at high latitudes. This means that the CLM model struggles with hydrology problems or precipitation issues in these areas, while the contribution from E variance disagreement is highest in drier regions, indicating a land-surface parameterization issue in how CLM handles evaporation or transpiration. Disagreement dominated by the covariance of the SM-E contribution is mostly highest in transitional zones and monsoon regions, which are dynamic situations. This study can help us improve our understanding of ecosystem dynamics and climate variability, clarify the implications for global Earth system model simulations, and ultimately guide model development by targeting improvements in their parameterizations.