Climate variability from annual to multi-decadal timescales in a two-layer stochastic energy balance model: analytic solutions and implications for general circulation models

A low-order stochastically forced two-layer global energy balance model (EBM) admitting an analytical solution is developed for studying natural inter-annual, decadal and multi-decadal climate variability, and ultimately to better understand forced climate change. The EBM comprises upper and lower oceanic layers with a diffusive coupling, a radiative damping term including feedbacks and stochastic atmospheric forcing. The EBM is used to analyse the influence of radiative forcing, feedbacks and climate system inertia on the global mean surface temperature variance (climate variability) and to understand why Coupled Model Intercomparison Project, Phase 5 (CMIP5) models exhibit such a wide range in the level of variability in globally averaged surface air temperature. We examine the influence of the model parameters on the climate variability on different timescales. To this end, we derive the Fokker–Planck equation for the EBM and then obtain the analytical expression that quantifies the sensitivity coefficients for all model parameters. For all timescales, the most influential factors are as follows: (1) the magnitude of the stochastic forcing, (2) the feedback mechanisms, (3) the upper layer depth, (4) the diffusion parameter and (5) the lower ocean depth. Results from the EBM imply that the range of stochastic forcing in the CMIP5 climate models is around twice as important as the strength of radiative feedback or upper layer depth in causing the model-to-model spread in the magnitude of globally averaged climate model variability