Bayesian Learning of Climate Sensitivity I: Synthetic Observations

Abstract

The instrumental temperature records are affected by both external climate forcings—in particular, the increase of long-lived greenhouse gas emissions—and natural, internal variability. Estimates of the value of equilibrium climate sensitivity—the change in global-mean equilibrium near-surface temperature due to a doubling of the pre-industrial CO<sub>2</sub> concentration—and other climate parameters using these observational records are affected by the presence of the internal variability. A different realization of the natural variability will result in different estimates of the values of these climate parameters. In this study we apply Bayesian estimation to simulated temperature and ocean heat-uptake records generated by our Climate Research Group’s Simple Climate Model for known values of equilibrium climate sensitivity, T<sub>2x</sub> direct sulfate aerosol forcing in reference year 2000, F<sub>ASA</sub>, and oceanic heat diffusivity, ΔT<sub>2x</sub>. We choose the simulated records for one choice of values of the climate parameters to serve as the synthetic observations. To each of the simulated temperature records we add a number of draws of the quasi-periodic oscillations and stochastic noise, determined from the observed temperature record. For cases considering only values of ΔT<sub>2x</sub> and/or κ, the Bayesian estimation converges to the value(s) of ΔT<sub>2x</sub> and/or κ used to generate the synthetic observations. However, for cases studying F<sub>ASA</sub>, the Bayesian analysis does not converge to the “true” value used to generate the synthetic observations. We show that this is a problem of low signal-to-noise ratio: by substituting an artificial, continuously increasing sulfate record, we greatly improve the value obtained through Bayesian estimation. Our results indicate Bayesian learning techniques will be useful tools in constraining the values of ΔT<sub>2x</sub> and κ but not F<sub>ASA</sub> In our Group’s future work we will extend the methods used here to the observed, instrumental records of global-mean temperature increase and ocean heat uptake

Historical and future learning about climate sensitivity

“…Its three uncertain parameters are climate sensitivity ( S ); ocean vertical diffusivity ( κ ), controlling the rate of heat ocean uptake and the climate response time; and the aerosol radiative forcing strength ( α ), expressed as a factor multiplying the historical or projected forcing time series. These three parameters are generally assumed in climate sensitivity studies to be the most dominant physical uncertainties in the global temperature response [ Forest et al , ; Knutti et al , ; Urban and Keller , ; Ring and Schlesinger , ]. In addition, the initial temperature ( T 0 ) and ocean heat anomalies ( H 0 ) at the beginning of the model integration (the year 1850), and the standard deviation ( σ ) and annual autocorrelation ( ρ ) of the data model residuals, are also treated as uncertain parameters to be estimated.…”

“…Ring and Schlesinger [] produced an estimate of joint climate parameter learning (climate sensitivity, ocean diffusivity, and aerosol forcing) using an EBM with upwelling diffusive ocean. It considers Bayesian learning from surface temperature and radiative imbalance from ocean heat uptake, using synthetic historical and future observations generated from the EBM and a singular spectrum analysis of historical climate variability.…”

Bayesian estimation of climate sensitivity using observationally constrained simple climate models

“…Ring and Schlesinger 42 is a development from Ring et al 38 using a root-mean-square error method to estimate ECS, ocean heat diffusivity (K), and direct sulfate aerosol forcing (F SA ) parameters with an SCM. 42 Synthetic observations were employed to test a Bayesian estimation procedure to see if 'true' values of ECS, ocean diffusivity, and aerosol forcing could be determined. They found that ECS and K did converge given enough time but F SA was not found due to a low signal-to-noise ratio for the interhemispheric temperature difference used to constrain F SA .…”

“…Bayesian estimation has also been applied in related studies. Ring and Schlesinger is a development from Ring et al using a root‐mean‐square error method to estimate ECS, ocean heat diffusivity (K), and direct sulfate aerosol forcing (F SA ) parameters with an SCM . Synthetic observations were employed to test a Bayesian estimation procedure to see if ‘true’ values of ECS, ocean diffusivity, and aerosol forcing could be determined.…”