Estimates of Spatial Degrees of Freedom

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Abstract
The spatial degrees of freedom (dof) of atmospheric flows are estimated by comparing the variance of the theoretical standardized chi-squared distribution with the sum of the squared eigenvalues of a spatial correlation matrix, dof = N2/ΣI = 1Nλi2. The dof statistics are applied to monthly anomalies of ten-year datasets using daily 1000-mb heights of the T-21 representation of observations (ECMWF analyses 1980–89) and model simulations (ECHAM2) for the Northern Hemisphere mid- and higher latitudes (NH) and the eastern North Atlantic/European sector. Scales are distinguished by using unfiltered, low-, and bandpass filtered datasets. The following results are of interest: (i) The dofs of the observations are in qualitative agreement with the number of distinct weather types defined by phenomenological studies of the synoptic climatology on the hemispheric and regional scale. (ii) The larger number of dofs in summer (than in winter) can be associated with the reduced forecast performance of NWP models in the anomaly correlation sense. (iii) The larger number of ECHAM2 dofs for bandpass filtered anomalies (compared with observations) reveals the model's inability to activate as few modes as the atmosphere. (iv) Interannual variability is characterized by dof differences between daily anomalies taken from individual monthly averages and from the climate mean.