
(last update: April 6, 1998)
Two of the TRMM rainfall retrieval modules are "combined algorithms",
meaning that they combine inputs from the 2 instruments whose measurements are
directly responsive to the rain characteristics: the 13.8 GHz Precipitation Radar
(PR), and the 9channel passive TRMM Microwave Imager (TMI). The "instantaneous"
combined algorithm, referred to as 2B31, estimates the 3dimensional
structure of the particle size distribution within the PR swath, based on the PR
and TMI measurements within the swath. The "monthly areaaveraged" combined
algorithm, 3B31, generates monthly averages on a 5degree grid, based on the
outputs of 2B31 and algorithm 2A12, the TMIonly rain retrieval.
The basic approach adopted for algorithm 2B31 starts with
the premise that the radar measurements are significantly more detailed
(spatially) than the radiometer measurements, yet that both suffer from
intrinsic ambiguity, due to
 uncertainties and oversimplifications in the models relating the measurements
to the rain parameters
 inhomogeneous partiallyfilled beam(s), and
 fading and system noise.
The challenge is thus to fuse the data from the two instruments while
 giving each datum as much importance as its contamination by uncertainty
(or lack thereof) warrants
 avoiding any ad hoc "tricks" or "shortcuts" that might seem practical but would
be impossible to justify scientifically or empirically, and which might introduce
large biases in the estimates
 and using physical models that are close to the ones used in the PRonly and
TMIonly retrieval algorithms 2A25 and 2A12 respectively, so that the estimates
can be meaningfully compared.
The image at the top of this page shows the radaronly and
radiometeronly rain accumulations for february 1998. At the time,
the calibration of the instruments was not complete. However, the combined
algorithm does not require that the radar be absolutely calibrated. The
combinedalgorithm accumulations look like this:
Contrast the drought over Northern Australia and the Maritime Continent
with the aboveaverage precipitation over the Eastern Pacific. Neither one
of these two ElNino features is clear in the preliminary singleinstrument
maps.
How does the algorithm work? the current version starts with a standard
forward radiative transfer model to relate the measured 10.7GHz brightness
temperature (mean and standard deviation) to the rain parameters. It also uses
a standard inversion model to relate the measured radar reflectivities to the
rain parameters (mean and standard deviation). To combine passive and active
measurements and produce estimates of the rain parameter profiles, a Bayesian
approach is taken:
 Starting with a joint distribution for the raindrop shape parameters
based on statistical analyses of archived data (c.f. our
analyses of DSD data), use the radar inversion model to
produce estimates of the rain rate (mean and standard deviation).
 Continuing with this joint rainparameter probability distribution conditioned on
the radar measurements, use the radiometric forward model to predict the
corresponding brightness temperatures (mean and standard deviation)
 Produce the joint rainparameter probability distribution conditioned on the radar
and the passive measurements, by comparing predicted and measured
brightness temperatures.
The conditional means are the best estimates of the rain parameters (in the sense
that they are r.m.s.closest to all the possible solutions), and the conditional
standard deviation serves to quantify the confidence one can have in these
estimates: large standard deviations imply that the measurements are too
inconsistent with the physical model even after allowing for imperfections in the
models and noise in the measurements; small standard deviations indicate that the
models can indeed explain the measurements if the parameters are given the values
specified by the conditional means.
To retrieve a copy of the preprint describing the Day1 2B31 algorithm in more
detail:
Go back to the top page of the JPL TRMM site

