The Use of Eigenvectors of Statistical Covariance Matrices for Interpreting Satellite Sounding Radiometer Observations

Abstract A new technique is formulated for using eigenvectors of covariance matrices to retrieve atmospheric parameters from spectral radiance observations. The eigenvector method permits the use of all spectral radiances in a simultaneous solution for cloud-free infrared sounding radiances from cloud-contaminated observations as well as for the vertical profiles of temperature, moisture and cloudiness. The effects of random observation errors are minimized without suppressing the influence of any real information structure contained in the spectral radiance distribution. Also, since the method provides for the most economical representation of any variable from a number of “terms required” point of view, computer storage and computation requirements are much less than those of other methods. The eigenvector method is tested using radiance observations synthesized for the Nimbus-6 infrared and microwave sounding instruments. Although the method has been successfully applied for the routine processing of o...