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. The effect of observational constraint on the ranges ofuncertain physical and chemical process parameters was explored in a globalaerosol–climate model. The study uses 1 million variants of the Hadley Centre General Environment Model version 3(HadGEM3) that sample 26 sources of uncertainty, together with over 9000monthly aggregated grid-box measurements of aerosol optical depth, PM2.5,particle number concentrations, sulfate and organic mass concentrations.Despite many compensating effects in the model, the procedure constrains theprobability distributions of parameters related to secondary organicaerosol, anthropogenic SO2 emissions, residential emissions, sea sprayemissions, dry deposition rates of SO2 and aerosols, new particleformation, cloud droplet pH and the diameter of primary combustionparticles. Observational constraint rules out nearly 98 % of the modelvariants. On constraint, the ±1σ (standard deviation) rangeof global annual mean direct radiative forcing (RFari) is reduced by33 % to −0.14 to −0.26 W m−2, and the 95 % credible interval (CI)is reduced by 34 % to −0.1 to −0.32 W m−2. For the global annualmean aerosol–cloud radiative forcing, RFaci, the ±1σrange is reduced by 7 % to −1.66 to −2.48 W m−2, and the 95 % CI by6 % to −1.28 to −2.88 W m−2. The tightness of the constraint islimited by parameter cancellation effects (model equifinality) as well asthe large and poorly defined “representativeness error” associated withcomparing point measurements with a global model. The constraint could alsobe narrowed if model structural errors that prevent simultaneous agreementwith different measurement types in multiple locations and seasons could beimproved. For example, constraints using either sulfate or PM2.5measurements individually result in RFari±1σ rangesthat only just overlap, which shows that emergent constraints based on onemeasurement type may be overconfident.

Robust observational constraint of uncertain aerosol processes and emissions in a climate model and the effect on aerosol radiative forcing