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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The temporal fluctuations in global mean surface temperature are an example of a geophysical quantity that can be described using the notions of long-range persistence and scale invariance/scaling, but this description has suffered from lack of a generally accepted physical explanation. Processes with these statistical signatures can arise from nonlinear effects, for instance, through cascade-like energy transfer in turbulent fluids, but they can also be produced by linear models with scale-invariant impulse-response functions. This paper demonstrates that, on time scales from months to centuries, the scale-invariant impulse-response function of global surface temperature can be explained by simple linear multibox energy balance models. This explanation describes both the scale invariance of the internal variability and the lack of a characteristic time scale of the response to external forcings. With parameters estimated from observational data, the climate response is approximately scaling in these models, even if the response function is not chosen to be scaling a priori. It is also demonstrated that the differences in scaling exponents for temperatures over land and for sea surface temperatures can be reproduced by a version of the multibox energy balance model with two distinct surface boxes. [ABSTRACT FROM AUTHOR]

This paper studies regional climate variability for the time period 1900-2013 using parsimonious stochastic models. Instrumental data records on 5° × 5°, 2° × 2°, and equal-area grids are examined. A long-range dependent (LRD) stochastic process is used as a simplified description of the multitude of response times in the climate system. Fitting a linear trend to the global mean surface temperature (GMST) implies a warming of 0.08 decade−1, which is highly significant under an LRD null hypothesis ( p < 10−4). The regional trends are distributed around the global mean trend, while the fluctuation levels increases when going from global to regional scale. The temperature fluctuations of the tropical oceans are observed to be strongly influenced by El Niño-Southern Oscillation (ENSO) and, therefore, more consistent with autoregressive processes of order 1 [AR(1)]. A likelihood-ratio test is used to systematically determine the best null model [AR(1) or LRD]. About 80% of the regional warming trends are found to be significant (with a 5% significance level). [ABSTRACT FROM AUTHOR]

In order to have a scaling description of the climate system that is not inherently non-stationary, the rapid shifts between stadials and interstadials during the last glaciation (the Dansgaard-Oeschger events) cannot be included in the scaling law. The same is true for the shifts between the glacial and interglacial states in the Quaternary climate. When these events are omitted from a scaling analysis the climate noise is consistent with a 1/f law on timescales from months to 105 years. If the shift events are included, the effect is a break in the scaling with an apparent 1/fβ law, with β > 1, for the low frequencies. No evidence of multifractal intermittency has been found in any of the temperature records investigated, and the events are not a natural consequence of multifractal scaling. [ABSTRACT FROM AUTHOR]

Understanding the global mean surface temperature response to radiative forcing is essentialto assess the risks of global climate change. We present the statistical methodology for arealistic stochastic model that includes forcing contributions and accounts for chaoticatmospheric dynamics. This is achieved by using a long-memory stochastic process to modelthe temporal dependence observed in global temperature variability. This implies thatinference on the resulting model becomes computationally challenging, which is resolved byintroducing an approximation for the long memory process. The resulting model isincorporated in a latent Gaussian modeling framework and Bayesian inference is obtainedusing the methodology of integrated nested Laplace approximations (INLA). As an exampleof application the model will be fitted to the historical runs of the Earth System Models(ESMs) in the CMIP5 ensemble. The resulting model parameters will be used toobtain estimates of the transient climate responses (TCRs), which are comparedto the responses that arise from the ESMs directly. Estimations of the TCR forinstrumental temperature data is also obtained using forcing from the different ESMs.The presented method is implemented within the R-package INLA.climate. [ABSTRACT FROM AUTHOR]

Simple stochastic models suggest that there is a relation between the statistical properties of unforced climate variability and the temperature response to radiative forcing. In the framework of stochastic linear response models there are general results that link the low-frequency limit in power spectral density of the climate noise to the equilibrium climate sensitivity (Rypdal et al. Climate 2018). More generally there are fluctuation-response relations that link scale-dependent climate sensitivity to the second-order statistics of the climate noise, and these results can in principle provide methods for constraining climate sensitivity. In this work we present analyses of the relation between unforced variability and the climate response using different types of experiments in the CMIP5 ensemble, and we discuss the challenges of constraining equilibrium climate sensitivity using data in the instrumental era. We also use simple models to analyze how "slowing down" associated with non-linear feedbacks and accelerated warming affect fluctuation-response relations. [ABSTRACT FROM AUTHOR]