The GCM Validation
The GCM Validation
In this chapter 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 comparison shows that, generally, the shapes of the corresponding spectra and correlation functions are quite similar, but 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 theoretical and practical aspects surrounding validation, diagnosis, and application of the GCM. The methodology and results presented make it clear that 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. The idea of the statistical approach to the problems of GCM variability validation is contained in the comparison (observed vs. modeled) of the probability distributions of the different atmospheric and ocean processes and fields. At first, such a statement sounds like a standard statistical approach, and its solution would be obvious and simple if the number of climate processes taking place jointly were not huge and if they did not present a tremendously complicated (in its interrelationships and feedbacks) deterministic-stochastic system. As is known, the Stochastic System Identification Theory (see Eikhoff, 1983) deals mostly with the methodology for identifying linear systems, The interdependences of climatic processes and fields are not linear, and the application of this theory can give only highly approximate results.
Keywords: AR model and diffusion process, GCM diagnosis and verification, Hamburg GCM zonal temperature, diffusion, diffusion equation coefficients estimation, meridional circulation, surface air temperature
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