readme_3a25_5.02 ............................................................... Documentation for 3A-25, version 5.02 Date: 7 July 1999 ................................................................ Algorithm 3A-25: Space Time Statistics of Level 2 PR Products Name of Contact: Bob Meneghini NASA/GSFC Ph: 301-286-9128 email: bob@priam.gsfc.nasa.gov 1. Objective of the algorithm: To calcualte various statistics over a month from the level 2 PR output products. Four types of statistics are calculated: 1. probabilities of occurence (count values) 2. means and standard deviations 3. histograms 4. correlation coefficients The standard space scale is a 5 degree by 5 degree latitude x longitude cell A subset of the products, however, is also produced over 0.5 degree x 0.5 degree cells 2a. Source Code: (anonymous ftp site of priam.gsfc.nasa.gov: directory pub/trmm_code/v4_3a25/ f3a25_v5.02_HDF.f (210.6 kBytes) {latest revision: 7 July 1999} readinto_3a25_v5.02.f ( 19.7 kBytes) {latest revision: 7 July 1999} 2b. Running the program: i type: 'make' [uses Makefile in same subdirectory] ii type: 'f3a25_v5.02_HDF "1C-21 file" "2A-21 file" "2A-23 file" "2A-25 file" "3A-25 output file" \ "int file1" 'int file 2" "int file 3" "int file 4" "int file 5" "verification file" \ "begin/middle/end graule for month" "year" "month" ' Examples: f3a25_v5.02_HDF 1C21.970317.100.1.HDF 2A21_970317.HDF 2A23.970317.100.1.HDF \ 2A25.970317.100.1.HDF 3A25_970317_v4.5_B.hdf 3A25_970317_INT1 3A25_970317_INT2 \ 3A25_970317_INT3 3A25_970317_INT4 3A25_970317_INT5 3A25_970317_DIAG_B 'BEGIN' 1998 3 f3a25_v5.02_HDF 1C21.970317.100.1.HDF 2A21_970317.HDF 2A23.970317.100.1.HDF \ 2A25.970317.100.1.HDF 3A25_970317_v4.5_E.hdf 3A25_970317_INT1 3A25_970317_INT2 \ 3A25_970317_INT3 3A25_970317_INT4 3A25_970317_INT5 3A25_970317_DIAG_E 'END' 1998 3 3. Input Data: Data are read from 1C-21, 2A-21, 2A-23, and 2A-25. The data volumes per scan are approximately: 0.9 kbytes from 2a-21 0.4 kbytes from 2a-23 42.0 kbytes from 2a-25 17.0 kbytes from 1C-21 Total: 60 kbytes per scan 4. Output Data Volume (per month): Approximately 40 Mbytes 5a. Internal Storage Requirements: As noted above, 5 intermediate files are needed to store the running statistics. The storage needed for all 5 files is approximately 51 Mbytes. An example of the storage requirements for the 5 intermediate files is: 147464 bytes 3A25_980217.1288.4.HDF_INT1 728072 bytes 3A25_980217.1288.4.HDF_INT2 5391368 bytes 3A25_980217.1288.4.HDF_INT3 320264 bytes 3A25_980217.1288.4.HDF_INT4 44755208 bytes 3A25_980217.1288.4.HDF_INT5 5b. Output Variables: a. arrays for the calculation of probabilities [4-byte integers] example of notation used: rainPix1(16,72,6) = # of rain observations at each 5 x 5 degree x 1 mo. box at 5 heights and over full path rainPix1(i,j,1) @ h = 2 km; lat box i, longitude box j rainPix1(i,j,2) @ h = 4 km rainPix1(i,j,3) @ h = 6 km rainPix1(i,j,4) @ h = 10 km rainPix1(i,j,5) @ h = 15 km rainPix1(i,j,6) over full path Notes: - the same height convention is used for variables with height information - all heights are measured from the ellipsoid - the convention for the 16 latitude boxes are: box 1 runs from 40 S to 35 S box 16 runs from 35 N to 40 N - the convention for the 72 longitude boxes are: box 1 runs from 180 W to 175 W box 72 runs from 175 E to 179.99 E rainPix1(16,72,6) = # of observations at each 5 x 5 degree x 1 mo. box at 5 heights and over full path with rain present stratRainPix1(16,72,6) = same as above but for stratiform rain convRainPix1(16,72,6) = same as above but for convective rain surfRainPix1(16,72) = # of rain observations at range gate closest to surface ('rain-certain' only) surfRainAllPix1(16,72) = # of rain observations at range gate closest to surface ('rain-certain' and 'rain possible') wrainPix(16,72) = # of observations of warm rain (see 2a-23 documentation) ttlPix1(16,72) = # of observations (rain and no-rain) bbPixNum1(16,72) = # of observations for which BB is present epsilonPix1(16,72) = counts for epsilon when SRT value of PIA used (see 2a-25 documentation) ttlAnglePix1(16,72,4) = # of observations at each 5 x 5 degree x 1 mo. box at angles (approx) of 0, 5, 10, and 15 rainAnglePix1(16,72,4) = # of rain observations at each 5 x 5 degree x 1 mo. box at angles (approx) of 0, 5, 10, and 15 note: at (lat, long) = (i, j), and height k, the following probabilites, among others, can be calculated: Pr(rain) = rainPix1(i,j,k)/ttlPix1(i,j) Pr(stratiform rain) = stratRainPix1(i,j,k)/ttlPix1(i,j) Pr(convective rain) = convRainPix1(i,j,k)/ttlPix1(i,j) Pr(bright-band) = bbPixNum(i,j)/ttlPix1(i,j) Pr(stratiform rain| rain) = stratRainPix1(i,j,k)/rainPix1(i,j,k) Pr(convective rain| rain) = convRainPix1(i,j,k)/rainPix1(i,j,k) Pr(bright-band| rain) = bbPixNum(i,j)/rainPix1(i,j,6) note the difference among quantities of the following kind: Pr(stratiform rain| rain) = stratRainPix1(i,j,k)/rainPix1(i,j,k) Pr'(stratiform rain| rain) = stratRainPix1(i,j,k)/rainPix1(i,j,6) Pr''(stratiform rain| rain) = stratRainPix1(i,j,6)/rainPix1(i,j,6) Pr'' corresponds to what is the most common definition of the probability of stratiform rain: given that rain is present, what is the probability that it is stratiform. Pr is the probability that, given rain is present at a particular height level (denoted by the index 'k'), that the rain is stratiform. Pr' is the probability, given that rain is present somewhere along the beam, that rain is present at height level 'k' and that the rain is stratiform. b. means and mean squares [4-byte real] units of rain rates: millimeters/hour rainMean1(16,72,6): mean of rain rate (5 levels + path-av), conditioned on rain rainDev1(16,72,6): standard deviation of rain rate (5 levels + path-av), conditioned on rain stratRainMean1(16,72,6): mean of rain rate (5 levels + path-av), conditioned on stratiform rain stratRainDev1(16,72,6): standard deviation of rain rate (5 levels + path-av), conditioned on stratiform rain convRainMean1(16,72,6): mean of rain rate (5 levels + path-av), conditioned on convective rain convRainDev1(16,72,6): standard deviatione of rain rate (5 levels + path-av), conditioned on convective rain surfRainMean1(16,72): mean of 'near-surface' rain rate ('rain-certain' only) surfRainDev1(16,72): standard deviation of 'near-surface' rain rate ('rain-certain' only) surfRainAllMean1(16,72): mean of 'near-surface' rain rate ('rain-certain' and 'rain-possible') surfRainAllDev1(16,72): standard deviation of 'near-surface' rain rate ('rain-certain' and 'rain-possible') units of reflectivity factors: 10 log(Z), Z in (millimeters^6/meter^3) zmMean1(16,72,6): mean of dBZm (apparent refl. factor) (5 levels + path-av), conditioned on rain zmDev1(16,72,6): standard deviation of Zm (5 levels + path-av), conditioned on rain stratZmMean1(16,72,6): mean of Zm (5 levels + path-av), conditioned on stratiform rain stratZmDev1(16,72,6): standard deviation of Zm (5 levels + path-av), conditioned on stratiform rain convZmMean1(16,72,6): mean of Zm (5 levels + path-av), conditioned on convective rain convZmDev1(16,72,6): standard deviation of Zm (5 levels + path-av), conditioned on convective rain ztMean1(16,72,6): mean of Zt (refl. factor) (5 levels + path-av), conditioned on rain ztDev1(16,72,6): standard deviation of Zt (5 levels + path-av), conditioned on rain stratZtMean1(16,72,6): mean of Zt (5 levels + path-av), conditioned on stratiform rain stratZtDev1(16,72,6): standard deviation of Zt (5 levels + path-av), conditioned on stratiform rain convZtMean1(16,72,6): mean of Zt (5 levels + path-av), conditioned on convective rain convZtDev1(16,72,6): standard deviation of Zt (5 levels + path-av), conditioned on convective rain bbZmaxMean1(16,72): mean of maximum reflectivity in bright band bbZmaxDev1(16,72) std dev of same units of path-integrated attenuation (PIA) dB/km - PIA is the 1-way path attenuation piaSrtMean(16,72,4): mean of SRT PIA at 4 inc. angles (0, 5, 10, 15) piaSrtDev(16,72,4): standard deviation of of SRT PIA at same 4 inc. angles piaHbMean(16,72,4): mean of HB PIA at same 4 angles piaHbDev(16,72,4): standard deviation of HB PI at same 4 angles pia0Mean(16,72,4): mean of 0th-order PIA at same 4 angles pia0Dev(16,72,4): standard deviation of 0th-order PIA at same 4 angles pia2a25Mean(16,72,4): mean of 2a25-derived PIA at same 4 angles (7/7/99 - not yet in structure) pia2a25Dev(16,72,4): standard deviation of 2a25-derived PIA at same 4 angles (7/7/99 - not yet in structure) units of bright-band height, storm height, snow depth, etc, are all in meters bbHtMean(16,72): mean of height of BB bbHtDev(16,72): standard deviation of height of BB stormHtMean(16,72,3): mean of storm height (cond on rain type) stormHtDev(16,72,3): standard deviation of storm height (cond on rain type) sdepthMean1(16,72): mean of snow depth (only when BB is present) sdepthDev1(16,72): std dev of snow depth (only when BB is present) zpzmm(16,72): mean of (dBZ(at BB - epsilon) - dBZ(at BB + epsilon)) : NOT CALCULATED zpzmm2(16,72): std dev of (dBZ(at BB - epsilon) - dBZ(at BB + epsilon)): NOT CALCULATED bbwidthMean1(16,72): mean of width of bright band : NOT AVAILABLE FROM 2A23 bbwidthDev1(16,72): std dev. of same : NOT AVAILABLE FROM 2A23 following 6 quantities are unitless xiMean(16,72): mean of xi (see 2a-25 documentation) xiDev(16,72): standard deviation of xi nubfCorMean(16,72): mean of non-uniform beam filling correction factor (see 2a-25) nubfCorDev(16,72): standard deviation of non-uniform beam filling correction factor epsilonMean1(16,72): mean of epsilon conditioned on use of SRT in 2a-21 (see 2a-25) epsilonDev1(16,72): std dev of same c. histograms [2-byte integers]: see bin definitions in 5c : all histograms use 30 bins : histograms are simple counts - unitless rainH(16,72,30,6): histograms of rain rate; 6 height levels; unconditioned on rain type stratRainH(16,72,30,6): histograms of rain rate; 6 levels; for stratiform rain convRainH(16,72,30,6): histograms of rain rate; 6 levels; for convective rain surfrainH(16,72,30): histograms of near-surface rain rates; unconditioned on rain type ('rain-certain' only) surfrainAllH(16,72,30): histograms of near-surface rain rates; unconditioned on rain type ('rain-certain' and 'rain-possible') ztH(16,72,30,6): histograms of Zt (dB); 6 levels; unconditioned on rain type stratZtH(16,72,30,6): histograms of Zt (dB); 6 levels; for stratiform rain convZtH(16,72,30,6): histograms of Zt (dB); 6 levels; for convective rain zmH(16,72,30,6): histograms of Zm (dB); 6 levels; unconditioned on rain type stratZmH(16,72,30,6): histograms of Zm (dB); 6 levels; for stratiform rain convZmH(16,72,30,6): histograms of Zm (dB); 6 levels; for convective rain piaSrtH(16,72,30,4): histograms of SRT PIA at 4 angles piaHbH(16,72,30,4): histograms of HB-derived PIA at 4 angles pia0H(16,72,30,4): histograms of zeroth-order PIA at 4 angles pia2a25H(16,72,30,4): histograms of PIA at 4 angles as determined in 2a-25 (7/7/99- not yet in structure) BBHH(16,72,30): histogram of BB height stormHH(16,72,30): histogram of storm height (unconditioned on rain type) stratStormHH(16,72,30): histogram of storm height (conditioned on stratiform rain) convtStormHH(16,72,30): histogram of storm height (conditioned on convective rain) bbZmaxH(16,72,30): histogram of max Zt in bright-band (conditioned on presence of bright-band) snowIceLH(16,72): histogram of 'snow depth' (hstorm - hbb) (stratiform rain) zpzmH(16,72,30): histogram of dBZm(BB - eps) - dBZm(BB + eps): NOT CALCULATED nubfH(16,72,30): histogram of beam-filling factor (first argument of 2a-25 output) xiH(16,72,30): histogran of xi (first argument of 2a-25 output) epsilonH(16,72,30): histogram of epsilon conditioned on use of SRT in 2a-25 zmgradH: histogram of vertical gradient of Zm: NOT CALCULATED d. correlation coefficients (5 x 5 x 1 mo boxes) [all 4-byte real except ncoer and ncoepia which are 4-byte integers] - statistics compiled only when rain rates at 2 km, 4 km, and 6 km are all non-zero rainCCoef(16,72,3): correlation coefficient of rain rates at heights: (2 km, 4 km), (2 km, 6 km), (4 km, 6km) for all rain types stratRainCCoef(16,72,3): correlation coefficient of rain rates at heights: (2 km, 4 km), (2 km, 6 km), (4 km, 6km) for stratiform rain convRainCCoef(16,72,3): correlation coefficient of rain rates at heights: (2 km, 4 km), (2 km, 6 km), (4 km, 6km) for convective rain - following done only when all 3 PIAs exist and are reliable or marginally so piaCCoef(16,72,4,3): correlation coefficients of PIA values for (HB, SRT), (0th, SRT), (0th, HB) at 4 incidence angles - several correlation coefficient were defined but presently are not being computed: xiZmCCoef : corr. coeff. between xi and maximum value of Zm along path stormHtZmCCoef : corr. coeff. between storm height and maximum value of Zm along path e. high resolution statistics (0.5 x 0.5 x 1 mo boxes) i. counts (unitless; 4-byte integers) ttlPix2(148,720) total count number rainPix2(148,720,4) rain count number (all rain types) at 4 levels (2 km, 4 km, 6 km & path-av) stratRainPix2(148,720,4) stratiform rain counts at 4 levels (2 km, 4 km, 6 km & path-av) convRainPix2(148,720,4) convective rain counts at 3 levels (2 km, 4 km, 6 km & path-av) surfRainPix2(148,720) near-surface rain counts (all rain types) bbPixNum2(148,720) bright-band rain counts wrainPix2(148,720) warm rain counts surfRainPix2(148,720) near-surface rain rate counts ('rain-certain' only) surfRainAllPix2(148,720) near-surface rain rate counts ('rain-certain' and 'rain-possible') ii. rain rates (millimeters/hour; 4-byte real) rainMean2(148,720,4) mean rain rates at 4 levels (for all rain types) rainDev2(148,720,4) std dev of rain rates at 4 levels (for all rain types) stratRainMean2(148,720,4) mean rain rates at 4 levels (for stratiform rain) stratRainDev2(148,720,4) std dev of rain rates at 4 levels (for stratiform rain) convRainMean2(148,720,4) mean rain rates at 4 levels (for convective rain) convRainDev2(148,720,4) std dev of rain rates at 4 levels (for convective rain) surfRainMean2(148,720) mean near-surface rain rates ('rain-certain' only) surfRainDev2(148,720) std dev of same ('rain-certain' only) surfRainAllMean2(148,720) mean near-surface rain rates ('rain-certain' and 'rain-possible) surfRainAllDev2(148,720) std dev of same ('rain-certain' and 'rain-possible') iii. dBZ values (10 log Z; Z in mm^6/m^3; 4-byte real) zmMean2(148,720,4) mean dBZm at 4 levels (for all rain types) stratZmMean2(148,720,4) mean dBZm at 4 levels (for stratiform rain) convZmMean2(148,720,4) mean dBZm at 4 levels (for convective rain) ztMean2(148,720,4) mean Zt at 4 levels (for all rain types) stratZtMean2(148,720,4) mean Zt at 4 levels (for stratiform rain) convZtMean2(148,720,4) mean Zt at 4 levels (for convective rain) bbZmaxMean2(148,720) mean of maximum reflectivity in bright band : NOT COMPUTED bbZmaxDev2(148,720) std dev of same iv. heights of effective storm top, bright-band height, snow depth, etc. (meters; 4-byte real) stormHeightMean2(148,720,3) mean of storm height [meters] for: 1. stratiform rain 2. convective rain 3. all rain types stormHeightDev2(148,720,3) std dev of same bbHeightMean2(148,720) mean of bright-band height bbHeightDev2(148,720) std dev of same sdepthMean2(148,720) mean of snow depth sdepthDev2(148,720) std dev of same 5c. Definition of Bins for Histograms: for radar reflectivity factor histograms: ztH, convZtH, stratZtH zmH, convZmH, stratZmH the 31 bin boundaries are: data bhz/0.01,12.,14.,16.,18.,20., 22.,24.,26.,28.,30.,32.,34., 1 36.,38.,40.,42.,44.,46.,48., 1 50.,52.,54.,56.,58.,60.,62., 1 64.,66.,68.,70./ for all rain rate histograms: rainH, stratRainH, convRainH, surfRainH the 31 bin boundaries are (mm/h): 0.01 0.2050482 0.2734362 0.3646330 0.4862459 0.6484194 0.8646811 1.153071 1.537645 2.050482 2.734362 3.646330 4.862459 6.484194 8.646811 11.53071 15.37645 20.50482 27.34362 36.46331 48.62460 64.84194 86.46812 115.3071 153.7645 205.0482 273.4362 364.6331 486.2460 648.4194 864.6812 for bright band height histogram, HHBB, the 31 bin boundaries [km] are: data bhbb/0.01,0.25,0.5,0.75,1.,1.25,1.5,1.75,2.,2.25, 1 2.5,2.75,3.,3.25,3.5,3.75,4.,4.25,4.5,4.75,5., 1 5.25,5.5,5.75,6.,6.25,6.5,6.75,7.,7.5,20./ for storm height histograms, stormHH, stratStormHH, convStormHH, (in km), the 31 bin boundaries [km] are: data bhstorm/0.01,0.5,1.,1.5,2.,2.5,3.,3.5,4.,4.5,5., 1 5.5,6.,6.5,7.,7.5,8.,8.5,9.,9.5,10.,10.5, 1 11.,11.5,12.,12.5,13.,14.,15.,16.,20./ for distance from storm top to bright-band height histogram, snowIceLH, the 31 bin boundaries [km] are: data bhdepth/0.01,0.5,0.75,1.,1.25,1.5,1.75,2.,2.25, 1 2.5,2.75,3.,3.25,3.5,3.75,4.,4.25,4.5,4.75,5., 1 5.25,5.5,5.75,6.,6.25,6.5,6.75,7.,7.25,7.5,20./ !31 for the path-averaged attenuation estimate histograms, piaSrtH, piaHbH, pia0H, and pia2a25H, the 31 bin boundaries [dB] are: data bhpia/0.01,0.1,0.2,0.3,0.4,0.5,0.6,0.8,1.0,1.2,1.4,1.6,1.8, 1 2.0,2.5,3.0,3.5,4.0,4.5,5.0,5.5,6.0,6.5,7.0,7.5,8.0, 1 8.5,9.0,9.5,10.,100./ ! 31 for non-uniform beamfilling factor histogram, nubfH, the 31 bin boundaries [dimensionless] are: data bhnubf/0.,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.,1.1, 1 1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.,2.1,2.2,2.3, 1 2.4,2.5,2.6,2.7,2.8,2.9,3.0/ ! 31 for xi (=standard deviation of zeta/ mean of zeta) histogram, xiH, the 31 bin boundaries [dimensionless] are: data bhxi/0.,0.2,0.4,0.6,0.8,1.,1.2,1.4,1.6,1.8,2.,2.2,2.4, 1 2.6,2.8,3.,3.2,3.4,3.6,3.8,4.,4.2,4.4,4.6,4.8,5., 1 10.,20.,30.,50.,10000./ ! 31 for the parameter epsilon (see 2a-25) the 31 bin boundaries are: data bhepsilon/0.,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.,1.1, 1 1.2,1.3,1.4,1.5,1.6,1.7,1.8,1.9,2.,2.1,2.2,2.3, 1 2.4,2.5,2.6,2.7,2.8,2.9,3.0/ 5d. Other Input Parameters: c CAPPI heights relative to the ellipsoid data hh/2.,4.,6.,10.,15./ c angle bins at which the statistics of the various PIA estimates are to be evaluated c these angle bins approx. correspond to the port-side angles of c 0, 5, 10, and 15 degrees incidence: data jars/25, 32, 38, 45/ 5e. Definitions of low and high resolution grids The low resolution grid consists of 16 x 72 latitude-longitude elements corresponding to a 5 x 5 degree grid that covers the TRMM region from 40 S to 40 N where: lat index 1 -40 - -35 (40 S - 30 S) 2 -35 - -30 (35 S - 30 S) .... 16 35 - 40 (35 N - 40 N) longitude index 1 -180 - -175 (180 W - 175 W) 2 -175 - -170 (175 W - 170 W) .... 72 175 - 180 (175 E - 180 E) The high resolution grid consists of 160 x 720 latitude-longitude elements corresponding to a 0.5 x 0.5 degree grid that covers the TRMM region from 37 S to 37 N where: lat index 1 -37.0 to -36.5 (37 S to 36.6 S) 2 -36.5 to -36.0 (36.5 S to 36 S) .... 160 36.5 to 37.0 (36.5 N to 37 N) longitude index 1 -180 to -179.5 (180 W to 179.5 W) 2 -179.5 to -179. (179.5 W to 179 W) .... 720 179.5 to 180.0 (179.5 E to 180.0 E) 6. Processing Procedure: The basic steps in the procedure are: i. read in data (scan by scan) from 2a-21, 2a-23, 2a-25 and 1c-21 ii. adjust the numbering conventions so that Zm, Zt and R are aligned properly; this is done by using the achor point of binEllipsoid in 1c-21 and the corresponding bin ellipsoid of 2a-25 which, by convention, is the 80th element of Zt iii. find the coarse and fine resolution boxes to which each of the 49 observations belong. Note that a single scan is composed of 49 observations each at a different incidence angle. (coarse resolution boxes are 5 degree x 5 degree cells) (fine resolution boxes are 0.5 degree x 0.5 degree cells) iv. resample Zm, Zt and R from the range direction onto the vertical v. update the various statistics vi. if a month transition occurs within the granule, write the HDF output file and reinitialize the intermediate files 7. Comments and Issues: i. With the exception of one quantity, all statistics in 3a-25 are computed only when rain is judged in 1c-21 to be 'certain'. What this means is that when rain is judged in 1c-21 to be 'possible' the observation is treated as a 'no-rain' observation. The one exception to this rule is the near-surface rain rate. For this quantity, the statistics (mean, standard deviation and histogram) are computed for 'rain-certain' and 'rain-possible' as well as for the usual 'rain-certain' only. The near-surface rain rate statistics computed under 'rain-possible' and 'rain-certain' conditions are: -Low resolution products (5 x 5 degrees x 1 month) 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 -High Resolution products (0.5 x 0.5 x 1 month) 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 The statistics of near-surface rain rate computed only under 'rain-certain' conditions are denoted by: -Low resolution products (5 x 5 degrees x 1 month) 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 -High Resolution products (0.5 x 0.5 x 1 month) 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. ii. Several output variables are not being computed (& probably will not be unless the radar team or users of the product decide they are needed). zmGradH(16,72,30,3): histogram of vertical gradient of Zm at 3 heights zpzmH(16,72,30): histogram of difference of Zm at BB peak and in snow stormHtZmCCoef(16,72): correlation coeff. between storm height & maximum Zm xiZmCCoef(16,72): correlation coeff. between xi and maximum Zm iii. It is assumed in the program that the verification file does not exist; if it is already exists an error will occur. iv. 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. v. 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. vi. 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. vii. 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 variable in 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 above (in comment i.) 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. viii. 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 dB at 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 cateogorized 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. ix. 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' quantities. x. As noted in comment v., the rain rate statistics over mountainous regions at the height levels of 2 and 4 km will tend to underestimate the actual values; for these cases, the near-surface rain rate statistics (under 'rain-certain' conditions) should be more a more reliable indicator of the near-surface rain rate.