An observation-based scaling model for climate sensitivity estimates and global projections to 2100

Abstract

We directly exploit the stochasticity of the internal variability, and the linearity of the forced response to make global temperature projections based on historical data and a Green’s function, or Climate Response Function (CRF). To make the problem tractable, we take advantage of the temporal scaling symmetry to define a scaling CRF characterized by the scaling exponent H, which controls the long-range memory of the climate, i.e. how fast the system tends toward a steady-state, and an inner scale $$\tau \approx 2$$ τ ≈ 2 years below which the higher-frequency response is smoothed out. An aerosol scaling factor and a non-linear volcanic damping exponent were introduced to account for the large uncertainty in these forcings. We estimate the model and forcing parameters by Bayesian inference which allows us to analytically calculate the transient climate response and the equilibrium climate sensitivity as: $$1.7^{+0.3} _{-0.2}$$ 1 . 7 - 0.2 + 0.3 K and $$2.4^{+1.3} _{-0.6}$$ 2 . 4 - 0.6 + 1.3 K respectively (likely range). Projections to 2100 according to the RCP 2.6, 4.5 and 8.5 scenarios yield warmings with respect to 1880–1910 of: $$1.5^{+0.4}_{-0.2}K$$ 1 . 5 - 0.2 + 0.4 K , $$2.3^{+0.7}_{-0.5}$$ 2 . 3 - 0.5 + 0.7 K and $$4.2^{+1.3}_{-0.9}$$ 4 . 2 - 0.9 + 1.3 K. These projection estimates are lower than the ones based on a Coupled Model Intercomparison Project phase 5 multi-model ensemble; more importantly, their uncertainties are smaller and only depend on historical temperature and forcing series. The key uncertainty is due to aerosol forcings; we find a modern (2005) forcing value of $$[-1.0, -0.3]\, \,\,\mathrm{Wm} ^{-2}$$ [ - 1.0 , - 0.3 ] Wm - 2 (90 % confidence interval) with median at $$-0.7 \,\,\mathrm{Wm} ^{-2}$$ - 0.7 Wm - 2 . Projecting to 2100, we find that to keep the warming below 1.5 K, future emissions must undergo cuts similar to RCP 2.6 for which the probability to remain under 1.5 K is 48 %. RCP 4.5 and RCP 8.5-like futures overshoot with very high probability.

TransEBM v. 1.0: description, tuning, and validation of a transient model of the Earth's energy balance in two dimensions

“…We show that the model is most sensitive to changes in CO 2 and ice distribution, but the obliquity and land-sea mask have significant influence on modeled temperatures as well. We tune TransEBM to reproduce the 1960-1989 CE global mean temperature and the Equator-to-pole and seasonal temperature gradients of ERA-20CM reanalysis (Hersbach et al, 2015). The resulting latitudinal and seasonal temperature distributions agree well with reanalysis and the general circulation model (GCM) HadCM3 for a simulation of the past millennium (Bühler et al, 2020).…”

“…Observational records of climate and proxies are limited in both time and space (Schmidt et al, 2014;Hersbach et al, 2015). As such, climate models are vital for climate research since they can fill in gaps left by observational records.…”

The half-order energy balance equation – Part 2: The inhomogeneous HEBE and 2D energy balance models

“…Depending on the space-time statistics of the anomaly forcing, the HEBE justifies currentbased macroweather (monthly, seasonal) temperature forecasts (Lovejoy et al, 2015;Lovejoy, 2019, 2021a, b) that are effectively high-frequency approximations to the FEBE. Similarly, the low-frequency (asymptotic) power-law part can produce climate projections with significantly lower uncertainties than current general circulation model (GCM)-based alternatives (Hebert, 2017;Hébert et al, 2021) and work in progress directly using the HEBE (Procyk et al, 2020).…”

“…For example, the global value h = 0.5 ± 0.2 was found for the long-time behavior needed to project the Earth's temperature to 2100. Hebert (2017), Hébert et al (2021), andProcyk et al (2020), also using centennial-scale global temperature estimates but using the FEBE directly, found the less uncertain h = 0.38 ± 0.05. Using data at monthly and seasonal scales, Del Rio Amador and found and used the value h = 0.42 ± 0.03.…”

“…where the range of the integration = E is the entire surface of the Earth. This equation has only superficial links to equations studied in the literature such as the "generalized fractional advection-dispersion equation" (e.g., Meerschaert and Sikorskii, 2012;Hilfer, 2000). Now consider the system reaching equilibrium after a step forcing F (x, t) = F 0 (x) (t) (increase by F 0 (x) "turned on" at t = 0).…”