TRENDY-Emulator: A Bias-Corrected Deep Learning Emulator of Terrestrial Carbon and Water Dynamics

Terrestrial biosphere models are central to quantifying the global land carbon sink, with the TRENDY ensemble of Dynamic Global Vegetation Models (DGVMs) providing the land-surface estimates underpinning the annual Global Carbon Budget. Despite their widespread use, TRENDY models exhibit well-documented biases in simulated leaf area index (LAI), including errors in both magnitude and phenological phase, which propagate into uncertainties in carbon and water flux estimates.

Deep-learning emulators of Earth system models are increasingly adopted to improve computational efficiency, yet their potential as a structured mechanism for integrating process-based and data-driven approaches remains underexplored. Here, we use a deep-learning emulator not only to reproduce TRENDY ensemble behaviour, but also as a controlled framework to correct inherited LAI biases using observations, without discarding underlying process relationships. We first pre-train an emulator on the TRENDY ensemble mean across 14 carbon- and water-related key variables, and subsequently apply transfer learning using satellite-derived LAI observations. Training across all four TRENDY factorial experiments isolates the causal effects of CO₂ fertilisation, climate change and variability, and land-use change, thereby expanding the training space and improving extrapolation potential. The emulator uses a transformer architecture and is formulated as a point model, run independently at each location, with temporal memory carried only through autoregressively propagated state variables.

Emulating the TRENDY ensemble mean is largely successful. High accuracy is achieved for non-disturbance, deterministic fluxes (mean R² = 0.94), including gross and net primary production, ecosystem respiration, evapotranspiration, and surface runoff. State variables, including carbon pools, soil moisture, and LAI, show a modest reduction in performance due to autoregressive drift, but remain well constrained (mean R² = 0.87). In contrast, disturbance-related fluxes—specifically fire and land-use change emissions—are reproduced with substantially lower skill (mean R² = 0.27). The emulator accurately reproduces the effects of CO₂ fertilisation and climate change and variability across scenarios.

Transfer learning substantially reduces LAI errors in magnitude, phase, and spatial distribution, decreasing the mean LAI bias from 1.13 in the TRENDY ensemble mean to 0.01, while maintaining performance across other variables. The resulting emulator provides a highly computationally efficient predictor of land-surface dynamics, with improved LAI–evapotranspiration and LAI–gross primary production relationships relative to observations. This work highlights the potential of deep learning as a controlled bridge between process-based and data-driven land-surface modelling, with potential to extend the work toward multiple observational constraints.