Fig. 4: Emergent constraint on ΔC_s,τ as a function of global warming.

a Actual vs. estimated scatter plot for ΔC_s,τ for 2 °C of global warming. The vertical green line defines the observational constraint which is derived using observational data and the future spatial temperature field of each model (decadal average), and the shaded region represents the corresponding uncertainty (±1 standard deviation). The horizontal blue line represents our emergent constraint, with the shaded region showing the corresponding uncertainty (±1 standard deviation) which results from the differing future spatial warming patterns seen in the future spatial temperature fields across the ESMs, and the emergent relationship between the model data points (black line). b Probability density function showing the Gaussian distribution of ΔC_s,τ values from the unweighted prior model ensemble (black line) and the emergent constraint (blue line). c Constrained ΔC_s,τ values at different levels of global warming (blue), including the likely (±1 standard deviation) uncertainty bounds (shaded blue). Different effective global q₁₀ values shown for comparison; our emergent constraint is consistent with an effective q₁₀ ≈ 2.5 ± 0.6.