No abstract

Earth’s temperature variability can be partitioned into internal and externally forced components. Yet, underlying mechanisms and their relative contributions remain insufficiently understood, especially on decadal to centennial timescales. Important reasons for this are difficulties in isolating internal and externally forced variability. Here, we provide a physically motivated emulation of global mean surface temperature (GMST) variability, which allows for the separation of internal and external variations. To this end, we introduce the “ClimBayes” software package, which infers climate parameters from a stochastic energy balance model (EBM) with a Bayesian approach. We apply our method to GMST data from temperature observations and 20 last millennium simulations from climate models of intermediate to high complexity. This yields the best estimates of the EBM’s forced and forced + internal response, which we refer to as emulated variability. The timescale-dependent variance is obtained from spectral analysis. In particular, we contrast the emulated forced and forced + internal variance on interannual to centennial timescales with that of the GMST target. Our findings show that a stochastic EBM closely approximates the power spectrum and timescale-dependent variance of GMST as simulated by modern climate models. Small deviations at interannual timescales can be attributed to the simplified representation of internal variability and, in particular, the absence of (pseudo-)oscillatory modes in the stochastic EBM. Altogether, we demonstrate the potential of combining Bayesian inference with conceptual climate models to emulate statistics of climate variables across timescales.

Climate variability, that is variations in the statistics of climate parameters, characterizes Earth's dynamical system and is the primary influence on extreme events (Katz & Brown, 1992). Variability arises from unforced processes, internal to the climate system, and from forced processes, caused by external natural and anthropogenic drivers. Natural drivers include volcanic and solar forcing, contributing significantly to climate variability (Crowley & Unterman, 2013b). Due to anthropogenic activities, the recent trend of global mean surface temperature (GMST) and other variables has clearly emerged beyond the range of natural variability (

<div> <p>Reliable climate projections in face of global warming require a firm and detailed understanding of climate variability. Variations in climate can be externally-forced, for example by anthropogenic emissions, or internally-generated, for example from chaotic atmosphere and ocean dynamics. To investigate the climatic response to radiative forcing, a common concept is the equilibrium climate sensitivity (ECS). Many studies estimate the ECS by fitting simple energy balance models (EBMs) to observational data. This approach has benefitted from advances in numerical analysis and statistics, enabling a fully Bayesian analysis. Via Bayes theorem, it quantifies the probability of certain climate parameters given observations, for example of surface temperature. To this end, it combines the goodness of the model fit with assumptions on measurement errors and climate variability as well as prior information. Here, we analyse and discuss Bayesian inference of climate parameters such as ECS from global mean temperatures using multibox EBMs. We therefore present an R package which relies on the Markov Chain Monte Carlo algorithm and includes an extension of the one-box model with a time-dependent feedback parameter. Using measurements from the instrumental period as well as temperature reconstructions and model data from the last millennium, we validate and demonstrate the package. We find that the two-box model performs significantly better in fitting the observations than the one-box model, and generates 21<span>st</span> century projections that agree more closely with AR5 estimates. Further, we evaluate the robustness of the estimate against uncertainties in temperature and forcing data through synthetic experiments. To this end, we quantify how estimation errors depend on the strength of noise in temperature data and compare the influence of dating and amplitude uncertainties in forcing reconstructions. In summary, we provide an effective tool for Bayesian estimation of climate parameters and elaborate its potential for studying the response to external forcing. <span> </span></p> </div>