The present invention provides a new approach for processing hyper-spectral radiance data. It uses a transformation matrix to convert an instrument radiance spectrum into a pseudo-monochromatic radiance spectrum. The pseudo-monochromatic radiance spectrum is produced by an empirical transform of the instrument channel spectrum to a monochromatic equivalent spectrum (i.e., a pseudo-monochromatic spectrum). Eigenvector regression is used to produce the empirical transformation. Although the transformation does not produce the monochromatic radiance spectrum without error, the transformation error is generally well below nominal instrument noise levels for most spectral channels. The reduction in instrument noise results from a noise filtering effect of the eigenvector transformation. One of the advantages of the present invention is that it eliminates the need to build different fast radiative transfer models (RTMs) for different observing instruments, since the retrieval of geophysical parameters is based on an inversion of the monochromatic radiative transfer model. Although a different transformation matrix is required for different instrument spectral channel characteristics, the production of this transformation matrix is straightforward and simpler than the production of an accurate channel radiance fast model.