  The behaviors and skills of models in many geosciences (e.g., hydrology and
ecosystem sciences) strongly depend on spatially-varying parameters that need
calibration. A well-calibrated model can reasonably propagate information from
observations to unobserved variables via model physics, but traditional
calibration is highly inefficient and results in non-unique solutions. Here we
propose a novel differentiable parameter learning (dPL) framework that
efficiently learns a global mapping between inputs (and optionally responses)
and parameters. Crucially, dPL exhibits beneficial scaling curves not
previously demonstrated to geoscientists: as training data increases, dPL
achieves better performance, more physical coherence, and better
generalizability (across space and uncalibrated variables), all with
orders-of-magnitude lower computational cost. We demonstrate examples that
learned from soil moisture and streamflow, where dPL drastically outperformed
existing evolutionary and regionalization methods, or required only ~12.5% of
the training data to achieve similar performance. The generic scheme promotes
the integration of deep learning and process-based models, without mandating
reimplementation.
