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

Abstract

Abstract. Reliable quantification of the global mean surface temperature (GMST) response to radiative forcing is essential for assessing the risk of dangerous anthropogenic climate change. We present the statistical foundations for an observation-based approach, using a stochastic linear-response model that is consistent with the long-range temporal dependence observed in global temperature variability. We have incorporated the model in a latent Gaussian modeling framework, which allows for the use of integrated nested Laplace approximations (INLAs) to perform full Bayesian analysis. As examples of applications, we estimate the GMST response to forcing from historical data and compute temperature trajectories under the Representative Concentration Pathways (RCPs) for future greenhouse gas forcing. For historic runs in the Model Intercomparison Project Phase 5 (CMIP5) ensemble, we estimate response functions and demonstrate that one can infer the transient climate response (TCR) from the instrumental temperature record. We illustrate the effect of long-range dependence by comparing the results with those obtained from a 1-box energy balance model. The software developed to perform the given analyses is publicly available as the R-package INLA.climate.

The fractional energy balance equation

“…At first, scaling was invoked to directly mediate the forcing and the response: a scaling Climate Response Function (CRF: Rypdal, 2012; Van Hateren, 2013; Rypdal and Rypdal, 2014; Hebert, 2017; Myrvoll‐Nilsen et al ., 2020; Hébert et al ., 2021). Recently, it was suggested by Lovejoy (2019a) that this phenomenological approach could be made more physical (and realistic) by suggesting that rather than applying it to the CRF directly, that the scaling principle should instead be applied to the energy storage mechanisms.…”

“…As mentioned in the introduction, up until now the scaling principle has not been applied to the storage, but instead directly to the overall temperature response (Rypdal, 2012; Van Hateren, 2013; Rypdal and Rypdal, 2014; Hebert, 2017; Myrvoll‐Nilsen et al ., 2020; Hébert et al ., 2021). Scaling impulse (Dirac δ‐function) response CRFs are power laws: where H F is a scaling exponent.…”

“…Recently, Myrvoll‐Nilsen et al . (2020) have applied the original (Rypdal, 2012) infinite ECS model to twenty‐first century warming scenarios claiming that their model with “not well‐defined” ECS nevertheless “provides an accurate description of both forced and unforced surface temperature fluctuations”. Be that as it may, an additional attempt to justify their model as “a cost of the reduction of model complexity” cannot be sustained.…”

“…Alternatively, since even infinite ECS models have finite responses after finite times, their Transient Climate Responses (TCRs) will be finite, prompting Rypdal and Rypdal (2014) to argue that the TCR may be a more significant quantity than the ECS. In any event, an unsatisfactory consequence of the absence of energy balance is that when pure scaling models are used for climate projections, in order to avoid infinite temperatures, the forcings must return to zero (Rypdal, 2016; Myrvoll‐Nilsen et al ., 2020).…”