H2MV (v1.0): Global Physically-Constrained Deep Learning Water Cycle Model with Vegetation

Abstract. The proposed hybrid hydrological model with vegetation (H2MV) uses dynamic meteorology and static features as input to a long short-term memory (LSTM) to model uncertain parameters of process formulations that govern water fluxes and states. In the hydrological model, we explicitly represent vegetation states by the fraction of absorbed photosynthetically active radiation (fAPAR), and by the maximum soil moisture capacity (SM_max), which are both learned and predicted by the neural networks. These parameters have an explicit role to model soil moisture (SM) storage and the partitioning of evapotranspiration (ET). The model is optimised concurrently against global observations and observation-based data of terrestrial water storage (TWS) anomalies, fAPAR, snow water equivalent (SWE), ET and gridded runoff in a 10-fold cross-validation setup. To this end, we infer where the model is under-constrained such that different processes could explain the observational constraints in the model due to equifinality. The model reproduces the observed patterns of global hydrological components and fAPAR, while emergent patterns of runoff ratio, evaporative fraction, and T/ET are consistent with our current understanding. Despite robustly predicted temporal patterns of TWS anomalies, we found that the mean soil moisture state is not well constrained causing uncertainty of mean TWS. This emphasizes the importance of SM_max and the necessity for associated enhanced constraints. The proposed model is open-source, and has a highly flexible and modular structure to facilitate future integration of carbon and energy cycles, advancing toward a hybrid land surface model.