Emergent Scale Invariance and Climate Sensitivity

Abstract

Earth’s global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a bridge between the decadal- and centennial-scale fluctuations in the instrumental temperature record, and the millennial-scale equilibration following perturbations in the radiative balance. In particular, the emergent scale invariance makes it possible to infer equilibrium climate sensitivity (ECS) from the observed relation between radiative forcing and global temperature in the instrumental era. This is verified in ensembles of Earth system models (ESMs), where the inferred values of ECS correlate strongly to estimates from idealized model runs. For the range of forcing data explored in this paper, the method gives best estimates of ECS between 1.8 and 3.7 K, but statistical uncertainties in the best estimates themselves will provide a wider likely range of the ECS.

Optimal Estimation of Stochastic Energy Balance Model Parameters

“…Maximum likelihood estimation is simple for one-box model parameters: given uniformly sampled data, estimation reduces to an ordinary least squares problem with a closed-form solution (Rypdal and Rypdal 2014). When more boxes are added, latent variables appear and the estimation problem becomes more difficult.…”

“…An important result of Fredriksen and Rypdal (2017) is that the stochastically forced three-box model produces a similar noise spectrum to so-called scale-invariant models, a related class of simple climate model. Parameters of scale-invariant models have been estimated by maximum likelihood (Rypdal and Rypdal 2014) and more recently using Bayesian inference (Rypdal et al 2018). The method of Rypdal et al (2018) is generally applicable to linear response models, including box models, although the authors only present results for the scale-invariant model.…”

Statistical estimation of global surface temperature response to forcing under the assumption of temporal scaling

“…Our best estimate is that the TCR is 1.43 K with a standard deviation of 0.29 K. This estimate falls right in the middle of the range put forward in the IPCC report (0.8-2.5 K), and the accuracy is consistent with the TCR obtained directly from the ESMs. The presented model has also given coherent estimates for the equilibrium climate sensitivity compared with running ESMs (Rypdal et al, 2018a).…”

“…However, there are several other modeling choices and compromises that contribute to the uncertainty (Flato, 2011). As a consequence, several studies have focused on constraining model results on climate sensitivity on observational data; see, e.g., the work of Annan and Hargreaves (2006) or the more recent studies of Cox et al (2018) and Rypdal et al (2018b, a). These studies focus on the equilibrium climate sensitivity (ECS) as an essential metric of the climate response, as have numerous paleocli-mate studies (Hansen et al, 2013;von der Heydt and Ashwin, 2017;Köhler et al, 2017).…”

“…(5). But on timescales up to approximately 10 3 years, the model provides an accurate description of both forced and unforced surface temperature fluctuations (Rypdal and Rypdal, 2014;Rypdal et al, 2015), and the millennial-scale climate sensitivity in the estimated fractional linear response model correlates strongly with ECS over the ensemble of models in the Coupled Model Intercomparison Project Phase 5 (CMIP5) (Rypdal et al, 2018a). Temporal-scale invariance in global temperature fluctuations is an empirical observation and we cannot deduce the parameters in the fractional linear response model from physical principles.…”