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- Author or Editor: C. Eugene Buell x
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Abstract
The proper functions and values of a two-dimensional field (pollution concentration over St. Louis) were found using the discrete matrix method and a continuous integral equation method. For the matrix case, statistical tests were applied to determine the number of significant proper values/functions. In the integral equation case, the number of significant proper functions were determined from the self-consistency of equally valid quadrature methods. It was found that there were only about half as many significant proper functions using the integral equation formulation as were found using statistical methods.
Abstract
The proper functions and values of a two-dimensional field (pollution concentration over St. Louis) were found using the discrete matrix method and a continuous integral equation method. For the matrix case, statistical tests were applied to determine the number of significant proper values/functions. In the integral equation case, the number of significant proper functions were determined from the self-consistency of equally valid quadrature methods. It was found that there were only about half as many significant proper functions using the integral equation formulation as were found using statistical methods.
Abstract
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Abstract
Since the two point correlations of winds on an isobaric surface approximate those expected from a two-dimensional isotropic turbulence, it follows that in a flow that is geostrophic the two point correlations of wind and height must have a specific functional form. The form of the two point correlation function for wind and height is predicted from relations between this function and the correlation functions for the two point correlations of wind and the two point correlations of height. The theoretical predictions are compared with observational data and found to be reasonably well realized. The two point correlation function for wind and height is applied to height and wind observations at a point for the estimation of these quantities at a distance of several hundred nautical miles.
Abstract
Since the two point correlations of winds on an isobaric surface approximate those expected from a two-dimensional isotropic turbulence, it follows that in a flow that is geostrophic the two point correlations of wind and height must have a specific functional form. The form of the two point correlation function for wind and height is predicted from relations between this function and the correlation functions for the two point correlations of wind and the two point correlations of height. The theoretical predictions are compared with observational data and found to be reasonably well realized. The two point correlation function for wind and height is applied to height and wind observations at a point for the estimation of these quantities at a distance of several hundred nautical miles.
Abstract
The approximate relations between the correlation coefficient for geopotential, the longitudinal wind component, and the transverse wind component on an isobaric surface in the case of an homogeneous isotropic atmosphere are discussed briefly. Corresponding approximate relations for a nonhomogeneous and non-isotropic atmosphere are presented. The mixed correlations for wind component (longitudinal with transverse, and vice versa) are no longer identically zero (as was the case for the homogeneous isotropic atmosphere). Approximate expressions for these mixed correlation coefficient functions are presented in terms of the correlation coefficient for geopotential. It is shown that the general configuration of values computed from observed winds are those expected from theoretical considerations.
Abstract
The approximate relations between the correlation coefficient for geopotential, the longitudinal wind component, and the transverse wind component on an isobaric surface in the case of an homogeneous isotropic atmosphere are discussed briefly. Corresponding approximate relations for a nonhomogeneous and non-isotropic atmosphere are presented. The mixed correlations for wind component (longitudinal with transverse, and vice versa) are no longer identically zero (as was the case for the homogeneous isotropic atmosphere). Approximate expressions for these mixed correlation coefficient functions are presented in terms of the correlation coefficient for geopotential. It is shown that the general configuration of values computed from observed winds are those expected from theoretical considerations.
Abstract
The assumption that the two-point wind correlations are those expected from two-dimensional, homogeneous, isotropic turbulence leads to inconsistencies when applied to the wind-height correlations on the 500-mb surface in the summer. It is shown that these inconsistencies are due primarhy to the non-fulfihment of the homogeneity assumption. Modifications to take into account the magnitude of the horizontal gradient of the standard deviation of height are made. The modified results compare quite favorably with the observed data. The important modification developed consists of a change of the emphasis in the statistical assumptions made from an assumption that involves the wind correlations to an assumption regarding the nature of the height field and its two-point correlations.
Abstract
The assumption that the two-point wind correlations are those expected from two-dimensional, homogeneous, isotropic turbulence leads to inconsistencies when applied to the wind-height correlations on the 500-mb surface in the summer. It is shown that these inconsistencies are due primarhy to the non-fulfihment of the homogeneity assumption. Modifications to take into account the magnitude of the horizontal gradient of the standard deviation of height are made. The modified results compare quite favorably with the observed data. The important modification developed consists of a change of the emphasis in the statistical assumptions made from an assumption that involves the wind correlations to an assumption regarding the nature of the height field and its two-point correlations.
Abstract
A relation between the coefficients of variation for pressure, density and temperature is derived which must be satisfied if these statistical parameters are those of an atmosphere that satisfies the perfect gas law and the hydrostatic equation. Data on these parameters for Cape Kennedy, Fla., are adjusted on the basis of this relation. Corresponding adjusted values of the correlation coefficients rpT , rTρ , rρp are obtained. A parameter that measures the depth of pressure perturbation systems is also obtained for the levels from the surface to 90 km.
Abstract
A relation between the coefficients of variation for pressure, density and temperature is derived which must be satisfied if these statistical parameters are those of an atmosphere that satisfies the perfect gas law and the hydrostatic equation. Data on these parameters for Cape Kennedy, Fla., are adjusted on the basis of this relation. Corresponding adjusted values of the correlation coefficients rpT , rTρ , rρp are obtained. A parameter that measures the depth of pressure perturbation systems is also obtained for the levels from the surface to 90 km.
