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 one-box and two-box energy balance models. The software developed to perform the given analyses is publicly available as the R package INLA.climate.where σ dB(t) represents a white-noise forcing that gives rise to internal climate variability, and G is the response function, or Green's function, characterizing the relation between forcing and the temperature anomaly. A model of this form canPublished by Copernicus Publications on behalf of the European Geosciences Union.
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.
Fractional Gaussian noise (fGn) is a stationary time series model with long memory properties applied in various fields like econometrics, hydrology and climatology. The computational cost in fitting an fGn model of length n using a likelihood-based approach is O(n 2), exploiting the Toeplitz structure of the covariance matrix. In most realistic cases, we do not observe the fGn process directly but only through indirect Gaussian observations, so the Toeplitz structure is easily lost and the computational cost increases to O(n 3). This paper presents an approximate fGn model of O(n) computational cost, both with direct or indirect Gaussian observations, with or without conditioning. This is achieved Sigrunn H. Sørbye
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.
Temporal persistence in unforced climate variability makes detection of trends in surface temperature difficult. Part of the challenge is methodological since standard techniques assume a separation of time scales between trend and noise. In this work we present a novel Bayesian approach to trend detection under the assumption of long-range dependent natural variability, and we use estimates of historical forcing to test if the method correctly discriminates trends from low-frequency natural variability. As an application we analyze 2 • ×2 • gridded data from the GISS Surface Temperature Analysis. In the time period from 1900 to 2015 we find positive trends for 99% of the grid points. For 84% of the grid points we are confident that the trend is positive, meaning that the 95% credibility interval for the temperature trend contained only positive values. This number increased to 89% when we used estimates of historical forcing to specify the noise model. For the time period from 1900 to 1985 the corresponding ratios were 42 and 52%. Our findings demonstrate that positive trends since 1900 are now detectable locally over most of Earth's surface.
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