Identification of Vertical Profiles of Radar Reflectivity for Hydrological Applications Using an Inverse Method. Part I: Formulation

Abstract

The vertical variability of reflectivity in the radar beam is one of the main sources of error in estimating rainfall intensity. This vertical variability, which has several origins, is characterized globally by a function called "vertical profile of reflectivity." The impact of this vertical profile of reflectivity on the radar measurement is quantified by incorporating this function in the radar equation. It is then possible to specify the influence of the characteristics of the radar, the distance, and the vertical profile on errors in estimating rain rates at the ground level. A method for determining the vertical profile of reflectivity is then described. This procedure requires the use of radar images from at least two different elevation angles. It is based on the evolution of theratio of reflectivities (reflectivity at high elevation divided by reflectivity at a lower elevation angle) versus distance. The ratio evolution is closely related to the vertical profile of reflectivity and to the conditions of radar operation. An inverse solution method is used to identify the vertical profile of reflectivity corresponding to the observed ratio of reflectivities. The advantages and limitations of the proposed method are discussed.