A robustness diagnostic framework for NMIP ensembles: Application to NMIP2 soil N₂O emission estimates

Abstract. Multi-model ensembles, such as the global N₂O Model Intercomparison Project (NMIP), are essential for quantifying terrestrial nitrous oxide (N₂O) fluxes; however, interpreting where ensemble results are reliable and where they are not remains challenging. Here, we propose a robustness diagnostic framework (RDF) that classifies each grid cell into four categories: Robust-increase, Robust-decrease, Divergent and Uncertain, based on the three metrics of ensemble-mean change, model agreement on the sign of change and inter-model standard deviation. By explicitly separating directional disagreement (Divergent) from quantitative disagreement (Uncertain), the RDF reveals the nature of model uncertainty rather than its magnitude alone. We applied the RDF to soil N₂O emission estimates from eight terrestrial biosphere models participating in NMIP phase 2 (NMIP2), comparing pre-industrial (1850s) and contemporary (2010s) periods. Of 56,852 valid grid cells, 40.8 % were classified as Robust-increase, 2.6 % as Robust-decrease, 36.1 % as Divergent and 20.5 % as Uncertain. Stratification by land-use type revealed that the nature of uncertainty differed fundamentally: cropland-dominated regions were dominated by Uncertain (72.6 %), indicating an agreement on the direction of N₂O increase but a large quantitative spread, whereas forest-dominated regions were dominated by Divergent (50.0 %), indicating disagreement on the direction of change itself. Pasture-dominated regions exhibited the highest robustness (59.1 % Robust-increase). The inter-model spread correlated strongly with nitrogen input intensity (Spearman ρ = 0.75), and the Divergent to Uncertain transition followed a gradient of cropland fraction. These contrasting patterns implied that different model improvement strategies were needed: observational benchmarking of emission magnitudes for croplands, and improved process understanding of the competition between carbon dioxide (CO₂) fertilization and warming effects in forests. The proposed framework is general and applicable to any multi-model ensemble of biogeochemical change.