On the Importance of the Jacobian of a DNN Observation Operator in Land Data Assimilation

Abstract

A recent study (Shan et al., 2024, https://doi.org/10.1016/j.rse.2024.114167) showed that using a Deep-Neural-Network (DNN)-based observation operator in land data assimilation (DA) does not guarantee improvements in surface soil moisture (WG2). Here, we conduct a synthetic experiment to explain this outcome by testing whether DNN-based operators reproduce physically consistent Jacobians (sensitivities) required by DA. The ISBA-A-gs land surface model is perturbed to generate “synthetic true” WG2 and leaf area index (LAI), and a Water Cloud Model (WCM) is used to generate synthetic backscatter. Two DNNs are trained taking simulated states from the open loop run as input and the synthetic backscatter as output. The first is trained on WG2 and LAI while the second uses LAI and soil moisture from multiple layers, that is including redundant inputs. The synthetic observations are then assimilated using the two DNNs and the WCM as observation operators. Results suggest that the assimilation using a DNN-based observation operator improves the estimates of WG2. However, DNN Jacobians are no longer physically plausible when the model simulations used as training inputs contain errors relative to the “true” data, or when redundant input variables are included. This confirms that a strong predictive performance does not automatically reflect accurate representation of underlying physical sensitivities which prove problematic in subsequent DA. This study has important implications for deep-learning-based DA and Earth system models (ESM): DA or ESM trained on reanalysis or simulations may learn inaccurate Jacobians if input contains errors and redundant variables. This potential limitation could remain hidden when evaluation focuses primarily on predictive performance.