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, but parameter calibration remains challenging because of complex process coupling, parameter uncertainty, and limited observational constraints. In this study, we introduce multi-task differentiable parameter learning (MdPL), a deep learning framework that combines a multi-task neural surrogate with a differentiable parameter generator for efficient and diagnostically transparent LSM parameter calibration. The framework was evaluated at 20 PLUMBER2 sites spanning four plant functional types (PFTs). Because MdPL optimizes multiple parameters simultaneously through a neural surrogate, we first assessed surrogate–ILS consistency under joint parameter perturbations. Eighteen of the 20 sites satisfied the consistency criterion, defined as median Pearson’s R > 0.9 for both sensible and latent heat fluxes, and were retained for the main calibration analysis. Across these consistency-screened sites, the MdPL-calibrated Integrated Land Simulator (ILS) reduced RMSE by 14.1 % and 13.9 % at the PFT-mean level for sensible and latent heat flux simulations, respectively, relative to the default parameter set. Benchmarking with the PLUMBER2 dataset showed that the MdPL-calibrated ILS achieved competitive performance relative to standard LSMs, including CLM5, JULES, Noah, and GFDL, and performance comparable to an LSTM benchmark, although the relative advantage varied across variables, sites, and temporal resolutions. A comparison with a traditional calibration baseline based on Sobol sequence sampling at four representative sites further showed that MdPL identified competitive parameter solutions without exhaustive full-model evaluation, but its advantage remained site- and metric-dependent. An out-of-target evaluation using gross primary productivity (GPP) suggested that calibration based on sensible and latent heat fluxes did not lead to systematic degradation of a non-target carbon-related flux. Parameter plausibility analysis showed that some calibrated solutions approached predefined parameter bounds, indicating limited parameter identifiability under flux-only observational constraints. Therefore, the calibrated parameters should be interpreted as effective parameters under the given model structure and observational constraints, rather than as uniquely identifiable physical quantities. Overall, MdPL provides a scalable and diagnostically transparent approach for improving parameter calibration in complex LSMs.