The TRMM Precipitation Radar (PR), the first of its kind in space, is an
electronically scanning radar, operating at 13.8 GHz that measures the 3-D
rainfall distribution over both land and ocean, and defines the layer
depth of the precipitation.

The primary objective of algorithm 3A25 is to compute the monthly rainfall
vertical structure and various statistics of rainfall and related
variables measured by PR.Data are derived on two spatial resolution: the
standard space scale of 5 degree by 5 degree latitude x longitude
cell and a high resolution of subset of the products over 0.5 degree x 0.5 degree
cells.The output variables include rainfall rate (mm/hour) profile at 2km, 4km, 6km,
10,km and 15 km, fractional rain, snow ice layer, and surface rain rate (mm/hour).
The output statistics include probabilities of occurrence, means and
standard deviations, histograms of storm and bright band height, and
correlation coefficients.The algorithm is applied to PR instantaneous
profiles of hydrometeors and heating from PR swath that are classified as
TRMM products 2a-21, 2a-23, 2a-25, and 1c-21.

The main issues regarding the 3A25 include the following:

1. All statistics in 3a-25, except near-surface rain rate, are computed
only when rain is judged in 1c-21 to be 'certain'.When rain is judged
in 1c-21 to be 'possible' the observation is treated as
a 'no-rain' observation.For the near-surface rain rate, the statistics
(mean, standard deviation and histogram) are computed for 'rain-possible' as
for the usual 'rain-certain'.

The near-surface rain rate statistics are computed under 'rain-possible' and
'rain-certain' conditions over two resolutions (low and high).For
low resolution (5 x 5 degrees) the products are:

- surfRainAllPix1(i,j):total counts of 'rain-possible' and 'rain-certain'
at (latitude, longitude) box = (i,j)
- surfRainAllMean1(i,j): mean rain rate (mm/h), given rain is present
surfRainAllDev1(i,j):standard deviation of the rain rate (mm/h), given
rain is present
- surfRainAllH(i,j,30):histogram classified into 30 bins

For high Resolution (0.5 x 0.5 degree) the products are:

- surfRainAllPix2(i,j):total counts of 'rain-possible' and
'rain-certain' at (latitude, longitude) box = (i,j)
- surfRainAllMean2(i,j): mean rain rate (mm/h), given rain is present
- surfRainAllDev2(i,j):standard deviation of the rain rate (mm/h), given
rain is present

Under 'rain-certain' condition, the statistics of near-surface rain rate
are computed over two resolutions.The products over low resolution include

- surfRainPix1(i,j):total counts of 'rain-possible' and 'rain-certain'
at (latitude, longitude) box = (i,j)
- surfRainMean1(i,j): mean rain rate (mm/h), given rain is present
- surfRainDev1(i,j):standard deviation of the rain rate (mm/h), given
rain is present
- surfRainH(i,j,30):histogram classified into 30 bins

The products over high resolution include:

- surfRainPix2(i,j):total counts of 'rain-possible' and 'rain-certain'
at (latitude, longitude) box = (i,j)
- surfRainMean2(i,j): mean rain rate (mm/h), given rain is present
- surfRainDev2(i,j):standard deviation of the rain rate (mm/h), given
rain is present

Because the 'rain-possible' cases are dominated by noise so that the
probability of false-alarm is high, the 'rain-certain' statistics should be
considered more representative of the TRMM radar data.

2.There are 2 definitions of zeta and nubf (from 2a-25).In both cases
the original definitions of these quantities are used; i.e., the first
element of the array.

3.The height levels are being defined relative to the ellipsoid and not
the local surface. This may cause difficulties in the interpretation of
the statistics over some land areas at the lower height levels because the
level can be below the local surface.In these cases, the rain rate is
always set to some flag value and is not counted in the statistics.On the
other hand, ttlPix1 (or ttlPix2), the total number of valid observations at
the low (high) resolution averaging box, will be incremented so that the
observations 'below the surface' will be counted as 'no-rain' events. This
will introduce a negative bias into the mean rain rate at the (lat,long) box
in question.

4. Missing data scans are being checked by monitoring the scanStatus flags
in 1C-21.If this indicates a missing scan, no processing is done for that
scan.Checks for
individual missing variables are not being done explicitly, however.

5. There are several subtle, interrelated issues regarding the definitions
of rain and no-rain and how these definitions affect the statistics.For
most of the output products from level 2, numbers that represent a physical
quantity (non-flagged values) are being output only if the minEchoFlag
variablein 1c-21 is set to 'rain-certain'.However, an important
category of products (Zt and rain rate from 2a-25 and Zm from 1c-21) are
being output under rain-possible conditions.With the exception noted
in 1.,only those products for which rain detection is classified
as 'certain' are included in the statistics (that is, the statistics
conditioned on rain being present).Although some rain events will be
missed, the advantage of this selection is that the set of products should
be self-consistent.

6. The quantity 'minEchoFlag' (from 1b-21 and 1c-21) provides information
on the presence/absence of rain along each of the 49 angle bins that
comprise the cross-track scan.To test whether rain is present at a
particular range bin or height above the ellipsoid, a threshold value must
be used. Presently, this threshold is dBZt > 0.01 dB so that if minEchoFlag
indicates the certainty of rain along the beam and if dBZt > 0.01 dBat a
particular range bin or height level, then the data(e.g., rain rate, dBZm,
dBZt, etc) are used in the calculation of the statistics (mean and standard
deviation).

A difficulty arises in defining the histograms for the rain rates. The
lowest histogram bin for dBZt and dBZm is taken from 0.01 dB to 12 dB; the
subsequent bins are taken equal to 2 dB so that the bin boundaries are 14
dB, 16 dB,..., 70 dB.Since the Z-R relationship that is used in 2a-25 can
change depending on the storm type and vertical structure, and because the
histogram bins must be fixed, the bins for the quantity 10 log R (where R is
the rain rate in mm/h) are determined from the nominal relationship Z = 200
R^{1.6 } or in dB:

dBR = 0.625 dBZ - 14.38 .

For example, the dBZ histogram bin from 12 dB to 14 dB corresponds to the
rain rate histogram bin from -6.88 dB to -5.63 dB.The lowest dBR value
(the lower boundary
of the first bin) is 0.625 * 0.01 - 14.38 = -14.32 dB.It is possible,
however, for dBR to be less than this because the actual Z-R relationship
used in 2a-25 differs from the nominal relationship.In order to count all
non-zero rain rates (under 'rain-certain' conditions), the lower boundary of
the first dBR histogram bin is set to -20 dB rather than -14.32 dB. The
reason for doing this is to ensure that the number of data points that are
categorized in the rain rate histogram are equal to the number of data
points used in the calculation of the mean and standard deviation of this
quantity.

7. There are 3 types of rain rates that are defined in 3a-25.
The first is a 'near-surface' rain rate that is obtained from the range bin
closest to the surface which is not corrupted by the surface clutter.Two
sets of products are being computed from these data:the first set of
statistics uses only those rain rate for which rain is classified as
'certain'; the second set uses those rain rates for which rain is classified
either as 'possible' or 'certain'.

The second type of rain rate is the path-averaged rain rate calculated by
summing the values from the storm top (first gate where rain is detected) to
the last gate (gate nearest to the surface uncontaminated by the surface
clutter) and dividing by the number of gates in the interval.

The third type of rain rate is that at a fixed height above the ellipsoid
(2, 4, 6, 10 and 15 km).For an arbitrary incidence angle there will be
several range gates that intersect the height: to estimate dBZm, dBZt and
rain rate at that height, a Gaussian weighting is done in dB space for the
reflectivity factors and in linear space for the rain rates. This resampling
lowers the minimum detectable threshold which, in turn, effects the
histogram counts in the 2 lowest bins.In other words, the histogram counts
at the lowest 2 bins will generally be larger for the height profiled
quantities than for the 'near-surface' or 'path-averaged'.

The data are stored in the Hierarchical Data Format (HDF).The low resolution
grids are in the Planetary Grid 1 structure and the high resolution grids
are in the Planetary Grid 2 structure.Each file size (each month) is about
16 mb.The description of file component objects and their size can be obtained
from the Volume 4 - Levels 2 and 3 File Specifications provided by the TRMM
Data and Information System (TSDIS). It is available at:

http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4.pdf .