Power Spectrum Sensitivity Analysis of the Global Mean Surface Temperature Fluctuations Simulated in a Two-Box Stochastic Energy Balance Model

Climate models used in theoretical studies and the long-term projections of climate change should be able to reproduce essential features of the Earth's climate system including natural global scale variability on timescales from years to decades. It is notable then, that models simulate a very wide range in unforced "natural" variability, for example showing a 2 1/2 fold range in standard deviation of decadal surface temperature. The global mean surface temperature (GMST) temporal fluctuations used as one of the main indicators of climate variability are usefully characterized by their power spectral density, which represents the distribution of temperature variance in the frequency domain. We applied a randomly-forced two-box energy balance model (EBM) with parameters that correspond to the Coupled Model Intercomparison Project Phase 5 (CMIP5) models to estimate the influence of such crucial aspects of the climate system as feedbacks, thermal inertia and deep ocean heat uptake on the power spectra of the GMST fluctuations (climate variability). These sensitivities can provide clues to allow us to better understand the reasons for the very wide range of climate variability derived from CMIP5 models. It is found that the influence of variations (uncertainties) in the EBM parameters on power spectra of the GMST fluctuations strongly depends on periods (frequencies) of these fluctuations. In particular, it was identified that the effect of variations in the feedback parameter significantly increases with increasing periods of GMST oscillations, while the influence of uncertainties in the climate thermal inertia parameter (effective heat capacity of the "atmosphere-mixed ocean layer" system) demonstrates the opposite behaviour. Variations in the deep-ocean heat uptake parameter tangibly affect GMST fluctuations on decadal and inter-decadal time scales. Meanwhile the uncertainty in the deep-ocean heat capacity parameter is minor for GMST fluctuations over all time scales.