Abstract
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.
Highlights
The behaviors and skills of models in many geosciences strongly depend on spatially-varying parameters that need calibration
This work broadly addresses geoscientific models across a wide variety of domains, including non-dynamical system models like radiative transfer modeling[1], as well as dynamical system models such as land models that are used in Earth
At the moderate training sampling density of 1/42, where 1/42 represents sampling one gridcell from each 4x4 patch, differentiable parameter learning (dPL) had nearly identical ending error metrics as SCE-UA (Fig. 2a, b). dPL’s marginal outperformance at 1/42 was a surprise to us, as one would expect an evolutionary algorithms (EAs) like SCE-UA to best capture the global minimum. This result attests to the uncompromising optimization capability of gradient descent
Summary
The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. System Models; hydrologic models that simulate soil moisture, evapotranspiration, runoff, and groundwater recharge[2]; ecosystem models that simulate vegetation growth and carbon and nutrient cycling[3]; agricultural models that simulate crop growth[4]; and models of water quality[5] and human-flood interactions[6] Besides scientific pursuits, these models fill the operational information needs for water supply management, pollution control, crop and forest management, climate change impact estimation, and many others. A calibration algorithm seeks to adjust the values of the unobserved parameters (θ) at each location, so that the difference between the model’s outputs (y) and some independent measurements (z) is minimized Uncertainties in these parameters, such as for those controlling the simulated land surface feedbacks of water and CO2 to the atmosphere, limit the confidence we have in the modeled results, such as simulated regional impacts caused by increasing CO2 levels[7]. These parameters are often sensitive to changes in spatial and/or temporal resolution[15], other model parameters, model version, and input data, continuously triggering the need to readjust previously calibrated parameters – a repetitive and tedious process[16]
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