Using regional scaling for temperature forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS)

Amador, Lenin Del Rio; Lovejoy, S.

doi:10.1007/s00382-021-05737-5

Cited by 15 publications

(20 citation statements)

References 65 publications

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“…Over the past years, many efforts have been devoted to study the climate memory effects 26,[28][29][30][31][32][33][34][35][36][37][38][39][40][41] . Beyond the classical energy-balance model (EBM) of a finite number of boxes 26,[28][29][30][31][32] , recent studies have introduced the concept of scaling among multiple time scales to lift the restrictions of a single e-folding time in a box model 33,34 .…”

Section: Introductionmentioning

confidence: 99%

The impact of long-term memory on the climate response to greenhouse gas emissions

et al. 2022

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Global warming exerts a strong impact on the Earth system. Despite recent progress, Earth System Models still project a large range of possible warming levels. Here we employ a generalized stochastic climate model to derive a response operator which computes the global mean surface temperature given specific forcing scenarios to quantify the impact of past emissions on current warming. This approach enables us to systematically separate between the “forcing-induced direct” and the “memory-induced indirect” trends. Based on historical records, we find that the direct-forcing-response is weak, while we attribute the major portion of the observed global warming trend to the indirect-memory responses that are accumulated from past emissions. Compared to CMIP6 simulations, our data-driven approach projects lower global warming levels over the next few decades. Our results suggest that CMIP6 models may have a higher transient climate sensitivity than warranted from the observational record, due to them having larger long-term memory than observed.

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Section: Introductionmentioning

confidence: 99%

The impact of long-term memory on the climate response to greenhouse gas emissions

et al. 2022

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“…The small-scale limit of the validity of the FEBE is not known, although it is likely to be ∼ 1 month (roughly the weather-macroweather transition timescale). Justification comes from the success of the high-frequency FEBE limit that successfully forecasts monthly and seasonal temperatures (Del Rio Amador and Lovejoy, 2019Lovejoy, , 2021aDel Rio Amador and Lovejoy, 2021b). As discussed earlier (Eq.…”

Section: The Amplitude Of the Internal Forcingmentioning

confidence: 99%

The fractional energy balance equation for climate projections through 2100

2022

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Abstract. We produce climate projections through the 21st century using the fractional energy balance equation (FEBE): a generalization of the standard energy balance equation (EBE). The FEBE can be derived from Budyko–Sellers models or phenomenologically through the application of the scaling symmetry to energy storage processes, easily implemented by changing the integer order of the storage (derivative) term in the EBE to a fractional value. The FEBE is defined by three parameters: a fundamental shape parameter, a timescale and an amplitude, corresponding to, respectively, the scaling exponent h, the relaxation time τ and the equilibrium climate sensitivity (ECS). Two additional parameters were needed for the forcing: an aerosol recalibration 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 rather predicted by the model itself: the internal variability response to white noise internal forcing. The 90 % credible interval (CI) of the exponent and relaxation time were h=[0.33, 0.44] (median = 0.38) and τ=[2.4, 7.0] (median = 4.7) years compared to the usual EBE h=1, and literature values of τ typically in the range 2–8 years. Aerosol forcings were too strong, requiring a decrease by an average factor α=[0.2, 1.0] (median = 0.6); 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. The key parameter ECS in comparison to IPCC AR5 (and to the CMIP6 MME), the 90 % CI range is reduced from [1.5, 4.5] K ([2.0, 5.5] K) to [1.6, 2.4] K ([1.5, 2.2] K), with median value lowered from 3.0 K (3.7 K) to 2.0 K (1.8 K). Similarly we found for the transient climate response (TCR), the 90 % CI range shrinks from [1.0, 2.5] K ([1.2, 2.8] K) to [1.2, 1.8] K ([1.1, 1.6] K) and the median estimate decreases from 1.8 K (2.0 K) to 1.5 K (1.4 K). As often seen in other observational-based studies, the FEBE values for climate sensitivities are therefore somewhat lower but still consistent with those in IPCC AR5 and the CMIP6 MME. Using these parameters, we made projections to 2100 using both the Representative Concentration Pathway (RCP) and Shared Socioeconomic Pathway (SSP) scenarios, and compared them to the corresponding CMIP5 and CMIP6 multi-model ensembles (MMEs). The FEBE historical reconstructions (1880–2020) closely follow observations, notably during the 1998–2014 slowdown (“hiatus”). We also reproduce the internal variability with the FEBE and statistically validate this against centennial-scale temperature observations. Overall, the FEBE projections were 10 %–15 % lower but due to their smaller uncertainties, their 90 % CIs lie completely within the GCM 90 % CIs. This agreement means that the FEBE validates the MME, and vice versa.

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“…7, we see that, taking the empirical value τ ≈ 4.7 years (Procyk et al, 2020), the HEBE lag is a little over a month. From the detailed maps in Donohoe et al (2020) (see also Ziegler and Rehfeld, 2020) I estimate that in the extratropical regions over land, the summer temperature maximum is typically 30-40 d after the solstice but only 20-30 d after the maximum forcing (insolation). For ocean, it is 60-70 d after the solstice but only 30-40 d after the maximum insolation.…”

Section: Empirical Estimates Of Complex Climate Sensitivitiesmentioning

confidence: 99%

“…The short dashed line (bottom) is the usual EBE (h = 1), the top line with long dashes is the classical heat forcing model, and the solid line is the (h = 1/2) HEBE. because of the strong albedo periodicity associated with seasonal ocean cloud cover (Stubenrauch et al, 2006;Donohoe et al, 2020). This delays the summer solstice forcing maximum over the ocean, potentially explaining the extra lag.…”

Section: Empirical Estimates Of Complex Climate Sensitivitiesmentioning

confidence: 99%

The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories

Lovejoy

2021

Earth Syst. Dynam.

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Abstract. The original Budyko–Sellers type of 1D energy balance models (EBMs) consider the Earth system averaged over long times and apply the continuum mechanics heat equation. When these and the more phenomenological box models are extended to include time-varying anomalies, they have a key weakness: neither model explicitly nor realistically treats the conductive–radiative surface boundary condition that is necessary for a correct treatment of energy storage. In this first of a two-part series, I apply standard Laplace and Fourier techniques to the continuum mechanics heat equation, solving it with the correct radiative–conductive boundary conditions and obtaining an equation directly for the surface temperature anomalies in terms of the anomalous forcing. Although classical, this equation is half-ordered and not integer-ordered: the half-order energy balance equation (HEBE). A quite general consequence is that although Newton's law of cooling holds, the heat flux across surfaces is proportional to a half-ordered (not first-ordered) time 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, and that the temperature–heat flux relationship is no longer instantaneous. I then consider the case in which the Earth is periodically forced. The classical case is diurnal heat forcing; I 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 of the forcing, I show how the HEBE can account for the phase lag between the summer maximum forcing and maximum surface temperature Earth response. In Part 2, I extend all these results to spatially inhomogeneous forcing and to the full horizontally inhomogeneous problem with spatially varying specific heats, diffusivities, advection velocities, and climate sensitivities. I consider the consequences for macroweather (monthly, seasonal, interannual) forecasting and climate projections.

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Using regional scaling for temperature forecasts with the Stochastic Seasonal to Interannual Prediction System (StocSIPS)

Cited by 15 publications

References 65 publications

The impact of long-term memory on the climate response to greenhouse gas emissions

The impact of long-term memory on the climate response to greenhouse gas emissions

The fractional energy balance equation for climate projections through 2100

The half-order energy balance equation – Part 1: The homogeneous HEBE and long memories

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