Thermal decay modes of a 2-D energy balance climate model

A complete series of non-orthogonal thermal decay modes (TDMs) of climate is derived from a two-dimensional (2-D) Energy Balance Climate Model (EBCM) and their properties are investigated. The orthogonality property is broken by the presence of the land—sea distribution through the effective heat capacity function. In the model, these mode amplitudes decay exponentially when the same component of forcing is made to vanish. If the projection of forcing is white noise in time, the mode amplitudes will have Lorentz spectral densities (i.e. first order Markov or first-order Autoregressive Process (ARI)) making the autocorrelation functions decay exponentially as well. TheTDMhave familystyle shapes: all oceans, Eurasian—African family, North American family, etc. When actual data are projected onto the mode patterns their time-series exhibit the same exponential decay behaviour. These modes are proven useful in studying the global surface temperature field. The development of the TDM theory makes it possible to analyse more generally time-dependent surface-temperature problems in a framework with physical interpretation.