Observed versus Simulated Second-Moment Climate Statistics in GCM Verification

The observed and simulated (by the Hamburg GCM) Northern Hemisphere monthly surface air temperatures, averaged within different latitude bands, are statistically analyzed and compared. The objects used for the analysis are the two-dimensional spatial–temporal spectral and correlation characteristics, the multivariate autoregressive and linear regression model parameters, and the diffusion equation coefficients. A qualitative comparison shows that, generally, the shapes of the corresponding spectra and correlation functions are quite similar but that their numerical values and some features differ markedly, especially for the tropical regions. The spectra reveal a few randomly distributed maxima (along the frequency axis), the periods of which were not identical for both types of data. A comparative study of the estimates of the diffusion equation coefficients shows a significant distinction between the character of the meridional circulations of the observed and simulated systems. The approach developed gives approximate stochastic models and reasonable descriptions of the temperature processes and fields, thereby providing an opportunity for solving some of the vital problems of the theoretical and practical aspects surrounding validation, diagnosis, and application of the GCM. The methodology and the results presented make it clear that the formalization of the statistical description of the surface air temperature fluctuations can be achieved by applying the standard techniques of multivariate modeling and multidimensional spectral and correlation analysis to the data, which have been averaged spatially and temporally.