Universal differential equations for estimating terrestrial evaporation

Terrestrial evaporation (E) is an essential climate variable, linking water, energy and carbon cycles. As E is influenced by the state of the atmospheric boundary layer, vegetation and soil, its modelling is a complex task, resulting in a myriad of simulation approaches. To combine the strong predictive skills of data-driven models with the interpretability and physical consistency of process-based models (PBMs), a new research field of differentiable modelling has emerged1. Here, we present a differentiable framework for E estimation, facilitating online training of NNs as intermediate PBM components. It is inspired by the GLEAM framework for estimating E, which applies offline training (i.e., outside the PBM) of neural networks (NNs) predicting evaporative stress2,3. Building upon the Julia SciML ecosystem’s implementation of universal differential equations4, a wide array of numerical methods are available for solving the PBM’s ordinary differential equations (ODEs) and calculating the parameter sensitivities5. In this way, the effect of the numerical methods on the obtained hybrid model can be investigated, moving beyond the direct automatic differentiation through explicit Euler solutions of ODEs as often applied in other hydrological hybrid modelling approaches.