The Direct Estimation of Spatial Wavenumber Spectra of Atmospheric Variables

Abstract We attempt to determine the zonal kinetic energy and temperature spectra of the large-scale flow in the atmosphere by utilizing observations, unequally spaced, rather than objectively-analyzed grid point values of the wind and temperature variables. Sample correlation functions, are obtained by forming correlations from all possible pair-wise combinations of stations oriented along a parallel of latitude (∼52N). Formally, the estimated line spectrum is given by a Fourier transform of this sample correlation function, Here, owing to the unequal spacing of this sample function, the Fourier transform takes the form of a set of simultaneous, coupled, linear equations, which are poorly conditioned. Four different methods of effecting the solution are tried, all of which are directed at mitigating the ill-conditioning of the system of equations. Spectra of kinetic energy and temperature for the winter and summer seasons are obtained at 850, 500 and 200 mb. There is no significant difference in the shap...