Estimates of Path Attenuation from Space-borne Radars using Normalized Surface Cross Section Data

Path attenuation estimates play an important role in methods of rain retrieval from radars that operate at frequencies at X-band and above. For many airborne radars, as well as the space-borne rain/cloud radars on the TRMM, CloudSat and GPM satellites, measurements of the normalized surface cross section, σ⁰, provide a way to estimate path attenuation by comparing measurements of σ⁰ within and outside the rain at the same incident angle. One way of forming the reference estimate is by using measurements of σ⁰ under rain-free conditions taken prior or subsequent to the rain event; the result is usually referred to as a ‘temporal reference’ estimate as distinguished from a ‘spatial reference’ estimate formed from nearby rain-free data from the same orbit . Presently, in the TRMM and GPM algorithms, statistics of rain-free σ⁰ data, accumulated over a fixed latitude-longitude grid of 0.5°, are used as the temporal reference. The database is compiled for each 3-month period and updated as additional data are acquired. For example, statistics of rain-free σ⁰data from the months of June-July-August for 2014-2016 will be used as the reference database for measurements that will be acquired during the summer of 2017 as well as in reprocessing data, acquired during this season, from earlier years.

Although the fixed grid database is convenient to use and update, it is not necessarily the best. For example, if a particular grid box includes surface types with different surface scattering properties (e.g., forest and bare soil over land or regions with different mean wind speeds over ocean) then the mean and standard deviation of the data will not be representative of either surface type. It can be shown that the variance of the rain-free σ⁰ data can be reduced by starting with a higher grid resolution and then performing a variable spatial averaging over the grid that minimizes the variance while accumulating a sufficient number of samples.

In addition to the variable-averaging procedure is a second alternative that involves overlaying orbits with similar trajectories. Although the GPM satellite does not have an exact orbital repeat cycle, for any given orbit we can usually find one or more orbits that are well matched to the target orbit in the sense that each scan line and viewing angle in the matched orbit is within less than 1/2 field-of-view (2.5 km) of the target orbit. Moreover, as more data are acquired the probability increases that at least one orbit can be found that is well-matched to a given orbit. In some sense, these nearly-matched orbits provide an ideal temporal reference in the sense that the spatial variations between σ⁰ measured within and outside the rain area are minimized. As the rain-free databases derived from the fixed grid, variable grid and the overlay orbits will differ, the path attenuations derived from them will differ as well. The presentation will show comparisons of the path attenuation derived from the three data bases and explore ways to identify the most accurate.