Enhancing Parameter Calibration in Land Surface Models Using a Multi-Task Surrogate Model within a Differentiable Parameter Learning Framework

Abstract. Land surface models (LSMs) are essential for simulating terrestrial processes and their interactions with the atmosphere. However, parameter calibration in LSMs remains a major challenge owing to complex process coupling and parameter uncertainty. For example, key parameters, such as plant function type (PFT), are often estimated using field measurements or empirical relationships, which are characterized by limited accuracy, resulting in systematic biases and inconsistencies. In this study, we introduce multiple-task differentiable parameter learning (MdPL), a deep learning framework that combines a multitask surrogate model with a differentiable parameter generator for more accurate and efficient LSM parameter calibration. The multitask surrogate learns both shared and task-specific features to predict multiple fluxes, and the differentiable generator infers site-specific parameters from meteorological forcings and land surface attributes. Calibrated across 20 sites spanning four PFTs, the MdPL-calibrated Integrated Land Simulator (ILS) achieved a 15 % decrease in RMSE for both sensible and latent heat flux simulations. Further, benchmarking using the PLUMBER2 dataset showed that the MdPL-calibrated ILS outperformed standard LSMs (CLM5, JULES, Noah, and GFDL), and its accuracy matched or exceeded those of LSTM-based approaches. The assessment of its transferability via leave-one-out cross-validation for evergreen forest, woodland, and cultivation sites showed reasonable transfer performance for evergreen forests and woodlands, with parameter sets yielding close-to-optimal flux simulations, even without site specification. However, for cultivation sites, PFT parameters exhibited strong site specificity, with parameter sets from the same PFT not reliably transferred. Despite its reduced effectiveness of the framework for cultivation sites under fixed PFT settings, it offers a scalable and physically grounded approach for enhancing parameter calibration in complex LSMs.