Pr( R | Tb ) = Pr(R) x Pr(Tb | R) (1)
where Pr(R) is the probability that a certain profile R will be observed and Pr(Tb | R) is the probability of observing the brightness temperature vector, Tb, given a particular rain profile R. The first term on the right hand side of Eq. (1) is derived from the a-priori database of rain profiles established by the radar/radiometer observing systems. The second term on the right hand side of Eq. (1), is obtained from radiative transfer computations through the cloud profiles in the a-priori database. While the mechanics of Bayesian inversions are fairly well understood, two important issues must be dealt with by the GPM program. The first issue that requires attention is the subsetting of the a-priori database. One can always construct databases by latitude, longitude and time of year. This, however, is viewed as a last resort as it does not capture changes in regimes such as ENSO or other expressions of variability in the Earth system. Not subsetting the databases, on the other hand, introduces variability that is undesirable in an already underconstrained problem. A second issue that the algorithm must deal with is the channels used in the Tb vector defined in Eq. (1). While it is straightforward to assume that all channels will be used, this is not necessarily the case for channels that are sensitive to the surface in cases in which the surface is simply not known (such as coastlines). This talk will summarize the status of the GPM radiometer algorithm development to date as well as plans going forward towards launch of the GPM Core satellite in the July 2013 timeframe.
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