................................................................ readme_2a21_v5.06 Documentation for 2A-21, version 5.06 ................................................................ Algorithm 2A-21: Surface Cross Section Name of Contact: Bob Meneghini NASA/GSFC Ph: 301-614-5652 email: bob@meneg.gsfc.nasa.gov Date: 18 October 1999 1. Objectives and functions of the algorithm: The primary objective is to compute the path integrated attenuation (PIA) using the surface reference technique (SRT). The surface reference technique rests 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 normalized radar surface cross section (sigma-zero or NRCS) 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 used to take care of non-zero pitch/roll angles that can shift the incidence angle 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 cell, the data are further categorized into incidence angle categories (26). The number of observations in each category, Nt, are also recorded. Note that in 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 additionial bin is used to store data from angles outside 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 (see below). 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 a smaller sample 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(in rain) where sigma-zero(in rain) is the value of the normalized radar surface cross section over the rain volume of interest and 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 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 available at: http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4 Two comments should be made. i. The PIA is often defined as the one-way path attenuation rather than the 2-way attenuation used here. Note also that the PIA(2-way) is related to the specific attenuation or attenuation coefficient k (dB/km) by the equation: PIA(2-way) = 2 * integral [0, rs] k(s) ds where the path integral is taken along the direction of the main beam and where the integration limits range from the radar to the surface. Since the attenuation from the radar to the storm top is negligible, the integral can also be thought of as going from the storm top to the surface. ii. A case can be made for defining the reliability factor other than that given above. For example, we can define reliability factors by: Rel = [PIA - std dev(reference value)]/PIA Rel' = PIA - std dev(reference value) so that Rel= 1 (or Rel' going to infinity) would correspond to a perfect estimate whereas increasingly smaller values of Rel (including negative values) would correspond to lower reliabilities. Since the numerator and denominator of the expressions for Rel and Rel' can be computed from the output data, these quantities can be examined. 2a. Source Code: (on anonymous ftp site: priam.gsfc.nasa.gov, directory pub/trmm_code/v4_2a21/ ) f2a21_v5.06_HDF.f (118669 Bytes) {latest revision: 13 October 1999} read2a21_v5.06_HDF.f ( 22702 Bytes) {latest revision: 13 August 1999} 2b. Running the program (on priam.gsfc.nasa.gov): i. type: 'make -f Makefile_v5.06' [uses Makefile in same subdirectory] ii. type: 'f2a21_v5.06_HDF "input file" "output file" "int_tr" "int_tw" "int_s" "vfile"' where "input file" is the 1B-21 HDF file "output file" is the 2A-21 HDF output file "int_tr" is the read-only temporal intermediate file "int_tw" is the write-only temporal intermediate file "int_s" is the spatial intermediate file "vfile" is the verification (diagnostic) file note that the vi file is created in the program and should not exist prior to execution - A script file that executes the command line argument can be found in the present directory where the file name is: run_2a21_v5.06 2c. Output files: example for orbit 1332 on Feb. 20, 1998: i. 2A21_980220.1332.2.HDF - HDF output file [11 MBytes] ii. 2A21_980220.1332.2.DIAG - diagnostic file [0.717 MBytes] text iii. 2A21_980220.1332.2.INT_TR.dat - read-only temporal reference file [8.1 Mbytes] binary file 2A21_980220.1332.2.INT_TW.dat - write-only temporal reference file [8.1 Mbytes] binary file 2A21_980220.1332.2.INT_S.dat - spatial reference file [9.8 kBytes] binary file 3. Input Data: example of input file from orbit 1332 on Feb. 20, 1998: 1B21.980220.1332.2.HDF - HDF file, 149.4 MBytes variables used from 1B-21: geolocation(2, 49) (real*4) systemNoise(49) (real*4) minEchoFlag(49) (byte) binSurfPeak(49) (integer*2) scLocalZenith(49) (real*4) binEllipsoid(49) (integer*2) normalSample(140,49) (real*4) osBinStart(29) (integer*2) osSurf(5, 29) (real*4) peakPower, scAlt (real*4) scanTime (real*8) Total Input/ Scan: 30 kBytes 3 Internal Storage Requirements: Intermediate file 1: temporal surface reference (read-only and write-only) Includes the mean, mean square and number of points comprising these statistics at each (lat, long, angle-bin) variables: avs0nr(lat, long, mangle): running mean at (lat, long) and incidence angle bin 'mangle' sqs0nr(lat, long, mangle): running mean square " " " nccnr(lat, long, mangle) : number of observations " " " (lat = 72, long = 360, mangle = 26) storage required: 72 x 360 x 3 variables x 4 bytes = 8.1 MBytes since there are now 2 temporal intermediate files, the storage requirement is doubled to: 16.2 Mbytes Intermediate file 2: spatial surface reference. These files contain the last Ns no-rain estimates of the surface cross section (as well as the square of these cross sections) at each of 51 incidence angles. Separate matrices are defined for land, ocean and coastline surface types. (Ns = 8 with a maximum possible value of 20) variables: avocean(kkoc, mang), sqocean(kkoc, mang) avland(kkl, mang), sqland(kkl, mang) avcoast(kkcoast, mang), sqcoast(kkcoast, mang) (kkoc=kkl=kkcoast = 20 (maximum); presently, set equal to 8) (mang = 51; to account for incidence angles lying outside the standard 49 angle bins, 2 additional angle bins are introduced to account for non-zero values of pitch and roll.) Note that avocean contains the last kkoc measurements of the surface cross section at each of mang incidence angle bins for an ocean background and for thoses cases in which rain is not detected along the radar beam; sqocean is identical to avocean except that the square of the surface cross sections are stored. (avland, sqland) are defined in an identical way to (avocean, sqocean) but for land (avcoast, sqcoast) " " " " but for coastline The matrices sqocean, sqland, sqcoast are not essential since they can be obtained taking the square of the elements in avocean, avland, avcoast, respectively. maximum storage required: 6 variables x 4 bytes x 51 angles x 20 IFOVS = 25 kBytes 4a. Output Data Volume: The output products are sigma-zero, the path-attenuation, the incidence angle, the latitude, longitude of the peak surface return, two reliability parameters and a rain-flag. sigmaZero(49) (real*4) pathAtten(49) (real*4) incAngle(49) (real*4) geolocation(2, 49) (real*4) reliabFactor(49) (real*4) reliabFlag(49) (integer*2) rainFlag(49) (integer*2) Output per Scan: 1.372 kBytes Output per Orbit: 10.93 Mbytes 4b. Definitions of Output Variables sigmaZero(49) [real*4]: Normalized backscattering radar cross section of the surface (dB) (NRCS) for the 49 angles bins in the radar scan rainFlag(49) [integer*2]: Rain/no-rain flag (rain=1; no-rain = 0) The rain possible category from 1B-21 is included in the no-rain category; only the rain-certain category is considered rain incAngle(49) [real*4]: incidence angle wrt nadir (in degrees); pitch/roll correction is included pathAtten(49) [real*4]: Estimated 2-way path-attenuation in (dB) where pathAtten = 2*int[0,rs] k(s) ds where k(s) is the atten. coeff. in dB/km and integral runs from storm top to the surface. The path attenuation is often designated as the PIA, the path-integrated attenuation reliabFlag(49) [integer*2]: reliability Flag for the PIA estimate, pathAtten, where reliabFlag = 10000*iv + 1000*iw + 100*ix + 10*iy + iz where iv is a rain/no-rain indicator iw is an indicator of the reliability of the PIA estimate ix indicates the type of surface reference used iy provides information about surface detection iz gives the background type iv = 1 (no rain along path) = 2 (rain along path) iw = 1 (PIA estimate is reliable) - see definitions below = 2 ( is marginally reliable) = 3 ( is unreliable) = 4 ( provides a lower bound to the path-attenuation) = 9 (no-rain case) ix = 1 (spatial surface reference is used to estimate PIA) = 2 (temporal " " " PIA) = 3 (neither exists - i.e. insufficient # of data points) = 4 (unknown background type) = 5 (no-rain case & low snr - do not update temporal or spatial SRs) = 9 (no-rain case) iy = 1 (surface tracker locked - central angle bin) = 2 ( unlocked - central angle bin) = 3 (peak surface return at normally-sampled gate - outside central swath) = 4 ( not at normally-sampled gate - outside central swath) iz = 0 (ocean) = 1 (land) = 2 (coast) = 3 (unknown or of a category other than those above or 'mixed' type) Note: for missing data set reliabFlag = -9999 reliabFactor(49) [real*4]: reliability Factor for the PIA estimate, pathAtten, is given by reliabFactor = pathAtten/std dev(reference value) where PIA is the 2-way path-integrated attenuattion (dB), and std dev(reference value) is the standard deviation as calculated from the no-rain sigma-zero values. Both quantities are in dB. The parameter iw (in reliabFlag) is determined from reliabFactor and the SNR of the surface return (in dB). As presently defined: iw = 1 (reliable) if ((reliabFactor.ge.3).and.(SNR(dB).gt.3)) = 2 (marginally reliable) if: ((reliabFactor.ge.1) and (reliabFactor.lt.3) and (SNR(dB).gt.3)) = 3 (unreliable) if either (reliabFactor.lt.1) or ((SNR(dB).le.3).and.(reliabFactor.lt.3)) = 4 (lower bound) if ((reliabFactor.ge.3) and (SNR(dB).le.3)) [The iw = 4 case is defined because, while the attenuation estimate will be negatively biased because of a low signal-to-noise ratio, it may lead to the best rain estimate possible under the circumstances.] [SNR is the signal-to-noise ratio; expressed in dB this is given by the difference between the noise-corrected radar return power (dBm) and the radar noise power (dBm)] Note: for missing data, set reliabFactor = -9999.9 Note: pathAtten is output as long as the estimate is greater than 0, regardless of the value of iw. 5. Description of the Processing Procedure: At each angle bin, calculate the normalized radar 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. 6. Interfaces to other algorithms: The input data from this algorithm comes from 1B-21; the output is used by 2A-25, 3A-25 and 3A-26. 7. 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 or 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 observed under no-rain conditions. 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 a global mean value and the associated standard deviation. Tests of this procedure will be carried out to determine whether it provides any improvement in the PIA estimates and whether the operational 2a-21 algorithm should be changed. f. The diagnostic files now include outputs from the cross-track PIA estimate as well as the standard PIA output (either temporal, spatial or global). Over ocean, a quadratic function over the full swath is used as reference. Over land, a quadratic function over each half of the swath (greater than 0 and less than 0) is used. This latter choice is probably not a good representation for the NRCS over land and a more general polynomial fit would be better. This, however, has not been implemented as of 23 August, 1999. Two other ouputs to the diagnostic files have to do with comparisons between the old and new defintions of the reliability: write(7,*) 'rel-old,rel-new,pia,sds0,s0av,s0,scan-no,angle-no' write(7,881) (rel_old(mmm,nang),rel_new(mmm,nang), 1 ppia(mmm,nang),sig_s0(mmm,nang), s0aav(mmm,nang), 1 s000(mmm,nang), nncount(mmm,nang),nang, nang=1,49) and different calculations of sigma-zero write(7,*) 's0_old,s0_new,s0_interp,scan-no' write(7,882) (s0_old(mmm,nang),s0_new(mmm,nang), 1 s0_interp(mmm,nang),nscann(mmm,nang),nang,nang=1,49) 8. Description of Temporal Intermediate File Two temporal intermediate files are used to store (write-only file) and read (read-only file) the no-rain statistics of the normalized surface cross sections as a function of incidence angle (26 categories) and location (1 x 1 degree latitude-longitude grid). For the first month of data (December), the read-only and write-only temporal intermediate files are intialized to zero. During the processing of data from this month, the no-rain statistics are continuously updated and stored in the write-only file. At the end of the month, the write-only file for December is used as the read-only file for January and the write-only file is re-initialized to zero. This means that for the data processed in January, the statistics compiled in December will be used for the temporal reference data set. At the end of the processing of the January data, the write-only file, used to store the statistics for January, is used as the read-only file for the month of February. In general, the write-only file from the previous month is used as the read-only file (i.e. the reference data set) for the present month and where the write-only file is re-initialized at the beginning of each month. 9. 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., T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J.A. Jones, and J. Kwiatkowski, 1999: Use of the surface reference technique for path attenuation estimates from the TRMM Radar (submitted J. Appl. Meteor.) Meneghini, R. and K. Nakamura, 1990: Range profiling of the rain rate by an airborne weather radar. Remote Sens. Environ., 31, 193-209.