Sampling Theory for Asynoptic Satellite Observations. Part II: Fast Fourier Synoptic Mapping

Abstract

A one to one correspondence between alias-free asynoptic data and twice-daily synoptic maps is established in the Synoptic Retrieval Theorem. The uniqueness follows from an extension of the Sampling Theorem. A Fast Fourier Transform Scheme is defined for retrieving the unique sequence of synoptic maps from the asynoptic observations. The procedure involves the construction of space-time spectra from ?irregular,? combined asynoptic data. This is accomplished by application of the asynoptic form of the space-time transform. The ?regular? sequence of synoptic maps is then recovered by application of the synoptic form of the inverse space-time transform. Twice-daily, synoptic sequences retrieved in this fashion, contain exactly the correct spectral contribution resolvable in both types of data. The technique conserves information and fully utilizes the information content of combined, asynoptic observations. Furthermore, it is directly amenable to parallel processing of data over large ensembles of latitudes and pressure levels. Temporal evolution is retrieved equally well for both statistically stationary and nonstationary processes. Intermediate products of the synoptic inversion are global spectra. Their availability during the procedure allows the removal of latitudinally incoherent noise by low-pass filtering. It also makes possible the expansion of observed fields, or equivalently their wavenumber-frequency components, in arbitrary sets of spherical functions. In particular, the projection of remotely derived geopotential components onto Hough harmonics, facilitates the construction of ?global? wind fields, thereby circumventing the equatorial problem characteristic of geostrophic treatments.