ADELM v1.0: a differentiable ecohydrological land model with learnable and diagnosable parameterization

Abstract. Land surface model (LSM) parameters translate vegetation, soil, snow, and hydrological properties into process controls on water, energy, and carbon exchange. Many of these parameters are not directly measurable at the grid scale, and their effective values depend on model structure, spatial aggregation, and observational constraints. Here we present the Adaptive Differentiable Ecohydrological Land Model (ADELM) v1.0, a fully differentiable LSM that combines process-based equations with machine learning, allowing each parameter to be prescribed or learned from observations and making parameterization itself a learnable and diagnosable part of the land model. ADELM couples canopy radiative transfer, soil hydraulics, photosynthesis, evapotranspiration, and snow and soil hydrology within a single automatic-differentiation graph, so that selected parameters can be learned directly from observed fluxes or states. Because a learned parameter can be expressed as a function of gridded environmental attributes, mappings trained at sparse sites can be applied across continuous spatial domains. We demonstrate ADELM in a European application using evapotranspiration and gross primary productivity constraints from eddy covariance sites. Mappings learned at the sites are evaluated across the 0.1° European grid, where observation-constrained learning improves evapotranspiration simulation and produces spatially coherent flux and parameter fields. Greater parameter flexibility can leave the learned parameters less identifiable, so learned parameterizations need to be judged by the stability and coherence of their parameter fields. Overall, ADELM provides a differentiable foundation for developing parameterizations that can be learned from observations, applied across space, and diagnosed for reliability.