A PASSIVE MICROWAVE TECHNIQUE FOR ESTIMATING RAINFALL AND VERTICAL STRUCTURE INFORMATION FROM SPACE .1. ALGORITHM DESCRIPTION

This paper describes a multichannel physical approach for retrieving r ainfall and vertical structure information from satellite-based passiv e microwave observations. The algorithm makes use of statistical inver sion techniques based upon theoretically calculated relations between rainfall rates and brightness temperatures. Potential errors introduce d into the theoretical calculations by the unknown vertical distributi on of hydrometeors are overcome by explicitly accounting for diverse h ydrometeor profiles. This is accomplished by allowing for a number of different vertical distributions in the theoretical brightness tempera ture calculations and requiring consistency between the observed and c alculated brightness temperatures. This paper will focus primarily on the theoretical aspects of the retrieval algorithm, which includes a p rocedure used to account for inhomogeneities of the rainfall within th e satellite field of view as well as a detailed description of the alg orithm as it is applied over both ocean and land surfaces. The residua l error between observed and calculated brightness temperatures is fou nd to be an important quantity in assessing the uniqueness of the solu tion. It is further found that the residual error is a meaningful quan tity that can be used to derive expected accuracies from this retrieva l technique. Examples comparing the retrieved results as well as the d etailed analysis of the algorithm performance under various circumstan ces are the subject of a companion paper.