A Transformer-Based Framework for Parameter Learning of a Land Surface Hydrological Process Model

The effective representation of land surface hydrological models strongly relies on spatially varying parameters that require calibration. Well-calibrated physical models can effectively propagate observed information to unobserved variables, but traditional calibration methods often result in nonunique solutions. In this paper, we propose a hydrological parameter calibration training framework consisting of a transformer-based parameter learning model (ParaFormer) and a surrogate model based on LSTM. On the one hand, ParaFormer utilizes self-attention mechanisms to learn a global mapping from observed data to the parameters to be calibrated, which captures spatial correlations. On the other hand, the surrogate model takes the calibrated parameters as inputs and simulates the observable variables, such as soil moisture, overcoming the challenges of directly combining complex hydrological models with a deep learning (DL) platform in a hybrid training scheme. Using the variable infiltration capacity model as the reference, we test the performance of ParaFormer on datasets of different resolutions. The results demonstrate that, in predicting soil moisture and transferring calibrated parameters in the task of evapotranspiration prediction, ParaFormer learns more effective and robust parameter mapping patterns compared to traditional and state-of-the-art DL-based parameter calibration methods.