The fractional energy balance equation for climate projections through 2100

Abstract. We produce climate projections through the 21st century using fractional energy balance equation (FEBE): a generalization of standard (EBE). The FEBE can be derived from Budyko–Sellers models or phenomenologically application scaling symmetry to storage processes, easily implemented by changing integer order (derivative) term in EBE value. is defined three parameters: fundamental shape parameter, timescale and an amplitude, corresponding to, respectively, exponent h, relaxation time ? equilibrium sensitivity (ECS). Two additional parameters were needed for forcing: aerosol recalibration factor ? account large uncertainty volcanic intermittency correction ?. A Bayesian framework based on historical temperatures natural anthropogenic forcing series was used parameter estimation. Significantly, error model not ad hoc but rather predicted itself: internal variability response white noise forcing. 90 % credible interval (CI) h=[0.33, 0.44] (median = 0.38) ?=[2.4, 7.0] 4.7) years compared usual h=1, literature values typically range 2–8 years. Aerosol forcings too strong, requiring decrease average ?=[0.2, 1.0] 0.6); ?=[0.15, 0.41] 0.28) ?=?=1. overpowered aerosols support revision global modern (2005) CI narrower [?1.0, ?0.2] W m?2. key ECS comparison IPCC AR5 (and CMIP6 MME), reduced [1.5, 4.5] K ([2.0, 5.5] K) [1.6, 2.4] ([1.5, 2.2] K), with median value lowered 3.0 (3.7 2.0 (1.8 K). Similarly we found transient (TCR), shrinks [1.0, 2.5] ([1.2, 2.8] [1.2, 1.8] ([1.1, 1.6] estimate decreases 1.8 (2.0 1.5 (1.4 As often seen other observational-based studies, sensitivities are therefore somewhat lower still consistent those MME. Using these parameters, made 2100 both Representative Concentration Pathway (RCP) Shared Socioeconomic (SSP) scenarios, them CMIP5 multi-model ensembles (MMEs). reconstructions (1880–2020) closely follow observations, notably during 1998–2014 slowdown (“hiatus”). also reproduce statistically validate this against centennial-scale temperature observations. Overall, 10 %–15 due their smaller uncertainties, CIs lie completely within GCM CIs. This agreement means that validates MME, vice versa.