Meta-modelling of carbon fluxes from crop and grassland multi-model outputs

Abstract

We evaluated five stacking-based meta-models-Multiple Linear Regression, Random Forest, XGBoost, and also Random Forest and XGBoost with environmental covariates (RF+ and XGB+, respectively)-against the multi-model median (MMM) and best individual process-based models for gross primary production (GPP), ecosystem respiration (RECO) and net ecosystem exchange (NEE) at two cropland and two grassland sites. We tested two validation strategies for GPP and RECO (70%/30% training/validation approach and the time-aware leave-one-year-out (LOYO) method), and three strategies for NEE (70%/30%, complete LOYO and independent validation using the meta-model based RECO-GPP). All meta-models were associated with improved RMSE, bias and correlation. Based on the LOYO validation strategy, average correlation increase was ∼ 2 % for GPP (0.2 %–4.4 %), 9 % for RECO (5 %–13.6 %) and 8 % for NEE (0.5 %–12.5 %). In the case of the independent validation strategy correlation increase was ∼ 40 % for NEE (24.5 %–64 %). Bias was nearly eliminated except at one cropland site. Wilcoxon signed-rank tests confirmed that improvements were statistically significant for 72 % of model-site-variable combinations, with particularly robust results for grassland sites where all meta-models significantly outperformed MMM, while one cropland site with limited data showed no significant improvements. SHapley Additive exPlanations (SHAP) analysis of XGB+ showed that diverse individual models, not always the top performers, contributed most, and that temperature-especially for RECO in croplands and NEE in grasslands-was the dominant environmental driver, while precipitation had minor effects. These findings highlight the predictive and diagnostic advantages of meta-modeling approaches over MMM, with potential applications across agroecosystem, Earth system and environmental model ensembles.