Spectral properties of global surface temperature and uncertainties of global climate sensitivity are explored in this work through the medium of Energy Balance Climate Models (EBCMs) and observational surface temperature data. In part I, a complete series of 2D time-dependent non-orthogonal eigenmodes of global surface temperature are analytically derived and their geographic patterns are presented. The amplitudes of these modes have temporal characteristics and present exponentially decaying patterns. Theoretically, if the energy balance model is forced by white noise forcing in time, the autocorrelation functions of the mode amplitudes should present the same exponentially decaying patterns. When observed surface temperature data are projected onto these theoretical modes, the autocorrelation time scales of the mode amplitudes exhibit similar exponential decaying patterns. These modes are believed to be useful for surface temperature studies and model intercomparison. In part II, an objective means of deriving the probability density function (PDF) of global climate sensitivity is investigated. The method constrains the PDF by its fit to the present climate in terms of surface temperature. We found that a wide range of parameter combinations, which corresponds to a broad range of the sensitivity, shows equally good fits to the present climate. It means that the uncertainties in global climate sensitivity are very difficult to eliminate if climate models are tuned to fit observations of surface temperature alone. The origin of the skewness of the PDF is found in very simple terms.

Spectral properties of global surface temperature and uncertainties of global climate sensitivity are explored in this work through the medium of Energy Balance Climate Models (EBCMs) and observational surface temperature data. In part I, a complete series of 2D time-dependent non-orthogonal eigenmodes of global surface temperature are analytically derived and their geographic patterns are presented. The amplitudes of these modes have temporal characteristics and present exponentially decaying patterns. Theoretically, if the energy balance model is forced by white noise forcing in time, the autocorrelation functions of the mode amplitudes should present the same exponentially decaying patterns. When observed surface temperature data are projected onto these theoretical modes, the autocorrelation time scales of the mode amplitudes exhibit similar exponential decaying patterns. These modes are believed to be useful for surface temperature studies and model intercomparison. In part II, an objective means of deriving the probability density function (PDF) of global climate sensitivity is investigated. The method constrains the PDF by its fit to the present climate in terms of surface temperature. We found that a wide range of parameter combinations, which corresponds to a broad range of the sensitivity, shows equally good fits to the present climate. It means that the uncertainties in global climate sensitivity are very difficult to eliminate if climate models are tuned to fit observations of surface temperature alone. The origin of the skewness of the PDF is found in very simple terms.