Constructing Rain-Free Surface Cross Section Data Sets for the Estimation of Path Attenuation

It has long been recognized that the path-integrated attenuation (PIA) can be used to improve precipitation estimates from high frequency space-borne radar. One approach that provides an estimate of PIA is the surface reference technique (SRT) that has been used as one of the standard retrieval algorithms for the Global Precipitation Measurement (GPM) Dual-frequency Precipitation Radar (DPR) as well as for the Tropical Rain Measuring Mission (TRMM) Precipitation Radar (PR).

The SRT relies on the assumption that the difference between the normalized radar cross section of the surface (NRCS or σ₀) in rain and a rain-free reference value can be attributed to the PIA associated with precipitation along the radar beam. The rain-free reference data are either spatial or temporal: in the former case, the reference data are generally taken over rain-free field of view (FOV) adjacent to the raining FOV at the same incidence angle; in the latter case, the sample mean and standard deviation are computed over a latitude-longitude-incidence angle grid based on prior rain-free measurements. The temporal reference data are particularly useful around islands, rivers and coastlines where spatial reference data are often sparse or missing.

Using the TRMM PR data, it has been shown that the size of the resolution cell (latitude-longitude) for the temporal reference data is directly related to the accuracy of PIA estimates. As the resolution is decreased from a 1º×1º to 0.1º×0.1º, temporal data become more useful because the sample variance associated with the σ₀ data is decreased. However, as the GPM satellite was only recently launched, the DPR data volume is still not large enough to build a temporal reference data set at high resolution. Nevertheless, there are sufficient data to construct a temporal reference look-up table over a fixed latitude-longitude grid of 0.5º×0.5º. This will be referred to as the standard grid.

We are exploring some ideas on constructing lower variance temporal look-up tables that should lead to more accurate estimates of PIA. The first attempt to decrease the variance of reference data is to make separate look-up tables for land, ocean and coast at the same grid resolution (0.5 degree). This reduces the high variance in pixels at land-water boundaries.

The main strategy is to begin the construction over a high resolution grid (in our case 0.2 degree) and then expand the sampling area at each grid cell until a sufficient number of data points is obtained. There are several ways to proceed including uniform and step-wise expansion from the initial area. The final strategy is to construct templates that include all possible area permutations for a given set of pixels. Although the template approach guarantees the minimum variance solution, the search procedure becomes prohibitive for large numbers of pixels. The various strategies will be described and evaluated according to computational efficiency and the average standard deviation of the data.