Fig. 5: The simple inertia model for hysteresis and reversibility.

a, Solution of the simple inertia model. The x and F correspond to climate state (for example, surface temperature and precipitation) and CO₂ forcing, respectively. They are normalized to have a range of 0 to 1. The trajectory shows the climate trajectory during increasing F (orange line) and decreasing F (blue line). The black dashed line is a static equilibrium solution where F is fixed. b–e, Comparison of the theoretical inertia curve with the experiment result. The normalized hysteresis area and Δx are calculated with varying λ using the simple inertia model (thick black line). For each grid point of the experiment output, the λ is fitted and normalized hysteresis area and Δx are calculated (Methods). The dots represent the result for each grid point and the colour shows the latitude of the dot. The results show normalized hysteresis area of surface temperature (b) and precipitation (d). The result for normalized Δx for surface temperature (c) and precipitation (e).