The primary objective is to compute the path integrated attenuation (PIA) using the surface reference technique (SRT).  The surface reference technique relies on the assumption that the difference between the measurements of the normalized surface cross section within and outside the rain provides a measure of the PIA.

Two types of non-rain surface cross section (sigma-zero) reference estimates are used:  spatial and temporal.  In the spatial surface reference data set, the mean and standard deviation of the surface cross sections are calculated over a running window of Ns fields of view before rain is encountered. These operations are performed separately for each of the 49+2 incidence angles of TRMM (corresponding to the cross-track scan from -17 degrees to + 17 degrees with respect to nadir).  The 2 additional angle bins (making the total 51 rather than 49) are to account for non-zero pitch/roll angles that can shift the incidence angle with respect to nadir outside the normal range.
 
For the temporal surface reference data set, the running mean and standard deviation are computed over a 1 degree x 1 degree (latitude, longitude) grid.  Within each
1 degree x 1 degree grid, the data are further categorized into incidence angle categories (26).  The number of observations in each category, Nt, are also recorded.
Note that for the temporal reference data set no distinction is made between the port and starboard incidence angles so that instead of 49 incidence angles, there
are only 25 + 1, where the additional bin corresponds to angles greater than the normal range.

When rain is encountered, the mean and standard deviations of the reference sigma-zero values are retrieved from the spatial and temporal surface reference data
sets.  To determine which reference measurement is to be used, the algorithm checks whether Nt >= Ntmin and Ns >= Nsmin, where Ntmin and Nsmin are the minimum number of samples that are needed to be considered a valid reference estimate for the temporal and spatial reference data sets, respectively.  (Presently, Ntmin = 50 and
Nsmin = 8).   If neither condition is satisfied, no estimate of the PIA is made and the flags are set accordingly.  If only one condition is met, then the surface reference data which corresponds to this is used.  If both conditions are satisfied, the surface reference data is taken from that set which has the smaller standard deviation.

If a valid surface reference data set exists (i.e., either Nt >= Ntmin or Ns >= Nsmin or both) then the 2-way path attenuation (PIA) is estimated from the equation:

PIA  = <sigma-zero(reference value)> - sigma-zero(in rain)

where sigma-zero(in rain) is the value of the surface cross section over the rain volume of interest and <sigma-zero(reference value)> is the mean value obtained from either the temporal or spatial reference data sets, the choice of which depends on the considerations discussed above.

To obtain information as to the reliability of this PIA estimate we consider the difference between the PIA, as derived in the above equation, and the standard deviation as calculated from the no-rain sigma-zero values and stored in the reference data set.  Labeling this as std dev(reference value), then the reliability factor of the PIA estimate is obtained from:

reliabFactor = PIA - std dev(reference value)

When this quantity is large, the reliability is considered high and conversely. This is the basic idea.  Specific definitions of the reliability flag and reliability factors are given in the definitions of the output variables.

Description of the HDF output variables for 2a-21 can be found in Volume 4 - levels 2 and 3 file specifications provided by the TRMM Data and Information
System (TSDIS).  The document is available at:  http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4.pdf.

Description of the Processing Procedure:

At each angle bin, calculate the normalized surface cross section, sigma-zero, and check whether rain is present.  Also, find the (1 degree x 1 degree x angle bin)
element into which the measurement falls.

If rain is present, retrieve the mean and standard deviations from the temporal and spatial reference data sets (formed from previously measured data under no-rain conditions).  If both temporal and spatial reference data sets satisfy certain conditions, check which sample mean has the lower variance.  Using the sample mean associated with the smaller variance, compute an estimate of the path-integrated attenuation and an associated reliability factor.

If rain is absent, update the temporal statistics (mean and mean square) of sigma-zero at the relevant (1 degree x 1 degree x angle bin) element.  Also, update the spatial
statistics of sigma-zero.  Note that the surface reference measurement which will be used is that for which the sample variance is smaller.
 
Comments and Issues:

a. A gaussian beam approximation is used to represent the TRMM antenna pattern.

b. The radar return power used in computing sigma-zero is that for which a 2.5 dB correction has been made.  The factor  accounts for the logarithmic averaging loss. Like the rain, the surface is treated as a Rayleigh target.

c. Sigma-zero is being computed from that (single) gate where the return power is a (local) maximum.

d. The algorithm assumes that rain is present only if minEchoFlag = 2 (rain certain); minEchoFlag = 1 (rain possible) and and minEchoFlag = 0 (rain absent) are treated
as no-rain cases. Note that the minEchoFlag variable is read from 1B-21.

e. Images of path attenuation from 2a-21 sometimes show a striated (streaky) pattern where the attenuation estimates at one or more angles are larger than the estimates at adjacent angles.  This seems to occur more often at near-nadir angles where high values of the surface cross section are sometimes observed when rain is absent.  To avoid this kind of error, spatial surface reference values that are much larger than the mean value (as determined from large space-time regions) may need to be replaced either by the mean value itself or by the value determined by the temporal reference value.  Tests of this procedure will be carried out to evaluate whether it provides any improvement in the PIA estimates.
 
References:

Caylor I.J., G.M. Heymsfield, R. Meneghini, and L.S. Miller, 1997:  Correction of sampling errors in ocean surface cross-sectional estimates from nadir-looking  weather radar.  J. Atmos. Oceanic Technol., 14, 203-210.

Iguchi, T. and R. Meneghini, 1994:  Intercomparisons of single-frequency methods for retrieving a vertical rain profile from airborne or spaceborne radar data. J. Atmos. Oceanic Technol., 11, 1507-1516.

Kozu, T., 1995:  A generalized surface echo radar equation for down-looking pencil beam radar.  IEICE Trans. Commun., E78-B, 1245-1248.

Marzoug, M. and P. Amayenc, 1994:  A class of single- and dual-frequency algorithms for rain rate profiling from a spaceborne radar. Part I: Principle and tests from
numerical simulations.  J. Atmos. Oceanic Technol., 11, 1480-1506.

Meneghini, R. and K. Nakamura, 1990:  Range profiling of the rain rate by an airborne weather radar.  Remote Sens. Environ., 31, 193-209.