A Cumulative Heat Framework Based on Anthropogenic Radiative Forcing

This work proposes a cumulative heat framework for quantifying the long-term thermal burden associated with anthropogenic radiative forcing. The framework converts annual radiative forcing into an equivalent annual heat load and integrates this quantity over time to obtain cumulative heat load. It introduces the Remaining Heat Margin (RHM) and Normalised Heat Margin (NHM) as measures of the remaining thermal capacity relative to specified critical heat-load benchmarks. The framework is illustrated using anthropogenic radiative forcing data from the IPCC Sixth Assessment Report under the SSP2-4.5 scenario. Benchmark calculations are presented for equivalent global mean ocean warming of 700 m and 1000 m, including the corresponding cumulative heat-load thresholds and projected crossover years. The Supplementary Information accompanying this record provides the numerical definitions, constants, annual forcing-derived values, cumulative heat-load calculations, RHM and NHM values, and benchmark results underlying the manuscript.