Three-dimensional gridding and mosaic of reflectivities from multiple radars with a two-step variational method

Doppler radar is an important tool for weather research, forecasting, and severe weather warnings. The most basic radar applications use a single radar field which in polar coordinates. However, single radar covers an area with a set of restrictions and individual characteristics. Such restrictions include a finite coverage area, spatial and temporal gaps in radar data coverage, and sensitivity to vertical temperature profiles in the atmosphere. Mapping multiple radar reflectivity fields onto a common 3D Cartesian grid can relieve some of these problems and allows applications to run over larger domains. Numerous approaches and techniques have been developed for gridding radar data in Cartesian space from spherical coordinate. Gridding radar data is challenging due to 1) the conical geometry of radar sampling and 2) the large volume of radar data sets. The distribution of radar data is non-uniform in space, with high resolution in the radial direction and low resolution in azimuthal and elevational directions, especially at far ranges. Additionally, it is possible to have more than one radar covering the same grid space. This provides valuable additional information, but how to retrieve the value at the grid. It requires the accurate interpolation of multiple observations. Variational method can avoid the problems mentioned above on certain degree. In this paper, gridding and mosaic of reflectivity are combined with a two-step variational method. First, a smoothed reflectivity field is retrieved at coarse grid space with a variational method. Then the retrieved reflectivity at the first step is used as background field at fine grid space with the variational method. The spatial smoothness penalty term is contained in the both cost function at the two steps. Before performing the analysis, the serious preprocessing must be performed. It has two processes: quality control and data correction to different type radars. The method is first tested with a single radar data- - . Compared to the observation from two aspects, the retrieved reflectivity is closed the observation. Then the method is easily expanded to utilize data from multiple radars and tested with Heifei and Maanshan radars.