Regional Climate Sensitivity‐ and Historical‐Based Projections to 2100

Hébert, Raphaël; Lovejoy, S.

doi:10.1002/2017gl076649

“…Let's now apply the same approach but with an eye to longer macroweather timescales, notably the annual cycle. The climate sensitivity is an emergent macroweather quantity that is determined by numerous feedbacks that over the weather scales are quite nonlinear but over macroweather scales are considerably averaged (and at least for GCMs, [Hébert and Lovejoy, 2018]) are already fairly linear. In any event,…”

Section: Conductive Versus Conductive -Radiative Boundary Conditionsmentioning

confidence: 99%

The Half-order Energy Balance Equation, Part 1: The homogeneous HEBE and long memories

Lovejoy¹

2020

Preprint

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Abstract. The original Budyko–Sellers type 1-D energy balance models (EBMs) consider the Earth system averaged over long times and applies the continuum mechanics heat equation. When these and the more phenomenological zero (horizontal) – dimensional box models are extended to include time varying anomalies, they have a key weakness: neither model explicitly nor realistically treats the surface radiative – conductive surface boundary condition that is necessary for a correct treatment of energy storage. In this first of a two part series, we apply standard Laplace and Fourier techniques to the continuum mechanics heat equation, solving it with the correct radiative – conductive BC's obtaining an equation directly for the surface temperature anomalies in terms of the anomalous forcing. Although classical, this equation is half – not integer – ordered: the Half - ordered Energy Balance Equation (HEBE). A quite general consequence is that although Newton's law of cooling holds, that the heat flux across surfaces is proportional to a half (not first) ordered derivative of the surface temperature. This implies that the surface heat flux has a long memory, that it depends on the entire previous history of the forcing, the relationship is no longer instantaneous. We then consider the case where the Earth is periodically forced. The classical case is diurnal heat forcing; we extend this to annual conductive – radiative forcing and show that the surface thermal impedance is a complex valued quantity equal to the (complex) climate sensitivity. Using a simple semi-empirical model, we show how this can account for the phase lag between the summer maximum forcing and maximum surface temperature Earth response. In part II, we extend all these results to spatially inhomogeneous forcing and to the full horizontally inhomogeneous problem with spatially varying specific heats, diffusivities, advection velocities, climate sensitivities. We consider the consequences for macroweather forecasting and climate projections.

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“…This allows diverse forcings to be conveniently approximated by their equivalent radiative forcings. It also explains why -in spite of their highly nonlinear weather dynamics -that to a good approximation, GCM macroweather and climate responses to external perturbations are typically linear (as quantified for CMIP5 models in (Hébert and Lovejoy, 2018) but with stochastic internal variability.…”

Section: Introductionmentioning

confidence: 99%

The Fractional Energy Balance Equation for Climate projections through 2100

Procyk

¹

,

Lovejoy

²

,

Hébert

³

2020

Preprint

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Abstract. We produce climate projections through the 21st century using the fractional energy balance equation (FEBE) which is a generalization of the standard EBE. The FEBE can be derived either from Budyko–Sellers models or phenomenologically by applying the scaling symmetry to energy storage processes. It is easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value near 1/2. The FEBE has two shape parameters: a scaling exponent H and relaxation time τ; its amplitude parameter is the equilibrium climate sensitivity (ECS). Two additional parameters were needed for the forcing: an aerosol re-calibration factor α to account for the large aerosol uncertainty, and a volcanic intermittency correction exponent ν. A Bayesian framework based on historical temperatures and natural and anthropogenic forcing series was used for parameter estimation. Significantly, the error model was not ad hoc, but was predicted by the model itself: the internal variability response to white noise internal forcing. The 90 % Confidence Interval (CI) of the shape parameters were H = [0.33, 0.44] (median = 0.38), τ = [2.4, 7.0] (median = 4.7) years compared to the usual EBE H = 1, and literature values τ typically in the range 2–8 years. We found that aerosols were too strong by an average factor α = [0.2, 1.0] (median = 0.6) and the volcanic intermittency correction exponent was ν = [0.15, 0.41] (median = 0.28) compared to standard values α = ν = 1. The overpowered aerosols support a revision of the global modern (2005) aerosol forcing 90 % CI to a narrower range [−1.0, −0.2] W m−2 compared with the IPCC AR5 range [1.5, 4.5] K (median = 3.2 K). Similarly, we found the transient climate sensitivity (TCR) = [1.2, 1.8] K (median = 1.5 K) compared to the AR5 range TCR = [1.0, 2.5] K (median = 1.8 K). As commonly seen in other observational-based studies, the FEBE values are therefore somewhat lower but still consistent with those in IPCC AR5. Using these parameters we made projections to 2100 using both the Representative Carbon Pathways (RCP) and Shared Socioeconomic Pathways (SSP) scenarios and shown alongside the CMIP5/6 MME. The FEBE hindprojections (1880–2019) closely follow observations (notably during the hiatus, 1998–2015). Overall the FEBE were 10–15 % lower but due to their smaller uncertainties, their 90 % CIs lie completely within the GCM 90 % CIs. The FEBE thus complements and supports the GCMs.

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“…In this paper, we extend the approach of Hébert and Lovejoy ( 2018 ) to make climate projections through 2100. The approach is based on historical data and a simple model of the system memory based on scaling symmetries.…”

Section: Introductionmentioning

confidence: 99%

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

Hébert

¹

,

Lovejoy

²

,

Tremblay

³

2020

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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.

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Regional Climate Sensitivity‐ and Historical‐Based Projections to 2100

Cited by 23 publications

References 28 publications

The Half-order Energy Balance Equation, Part 1: The homogeneous HEBE and long memories

The Half-order Energy Balance Equation, Part 1: The homogeneous HEBE and long memories

The Fractional Energy Balance Equation for Climate projections through 2100

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

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