Tropical Rainfall Measuring Mission(TRMM)
Precipitation Radar Algorithm

Instruction Manual
For Version 7

TRMM Precipitation Radar TeamJapan Aerospace Exploration Agency (JAXA)
National Aeronautics and Space Administration (NASA)

July 20th, 2011

Table of Contents
0. INTRODUCTION ........................................................................... 1
0-1.

TRMM precipitation radar system description............................................1

0-2.

TRMM precipitation radar algorithms..........................................................2

0-3.

Altitude change of the satellite and modification of algorithms ...............3

0-4.

PR hardware switch from A-side to B-side .................................................3

0-5.

References .....................................................................................................4

1. LEVEL 1 ...................................................................................... 10
1-1.

1B21: PR received power ...........................................................................10

1-1. 1. Algorithm Overview ................................................................................................10
1-1. 2. File Format .............................................................................................................11
1-1. 3. Structure of output variables...................................................................................11
1-1. 4. Detailed description of output variables ..................................................................16
1-1. 5. Major changes in 1B21 algorithm for product version 7..........................................40
1-1. 6. Changes in 1B21 after the satellite boost in August 2001 ......................................41
1-1. 7. Comments on PR Level 1 products ........................................................................421-1. 8. References ............................................................................................................46
1-1. 9. DID access routine ................................................................................................47
1-1 10.

Main-lobe clutter rejection routine ........................................................................52

1-1. 11. Redefinition of the Minimum Echo Flag ..............................................................58

1-2.

1C21: PR radar reflectivity ........................................................................60

1-2. 1. Algorithm Overview ................................................................................................60
1-2. 2. File Format .............................................................................................................60
1-2. 3. Structure of output variables...................................................................................60
1-2. 4. Detailed description of output variables ..................................................................60
1-2. 5. Major changes in 1C21 algorithm for product version 7 .........................................62ii

2. LEVEL 2......................................................................................... 63
2-1.

2A-21: Surface Reference Technique (Version 7) ...................................63

2-1.1 Objectives and functions of the algorithm .................................................................63
2-1.2. Definitions of Output Variables ................................................................................65
2-1.3. Description of the Processing Procedure ................................................................68
2-1.4. Interfaces to other algorithms .................................................................................68
2-1.5. Comments and Issues.............................................................................................68
2-1.6. Description of Temporal Intermediate File ...............................................................69
2-1.7. The Cross-track or Hybrid Surface Reference Method............................................69
2-1.8. Revised Angle Bin Definitions..................................................................................70
2-1.9. Definitions of the Effective PIA, Variance and Reliability Factor ..............................71
2-1.10. Excluding Spatial Reference Data based on the refScanID Variable ....................74
2-1.11.

Excluding Temporal Reference Data ....................................................................75

2-1.12. Command line arguments..................................................................................75

References ..........................................................................................................................75

2-2.

2A23..............................................................................................................77

2-2.1. Objectives of 2A23 ..................................................................................................77
2-2.2. Main changes from the previous version .................................................................77
2-2.3.

Method used in 2A23 ..............................................................................................78

2-2.4.

Processing Flow......................................................................................................78

2-2.5.

Input data ................................................................................................................79

2-2.6.

Output data .............................................................................................................80

2-2.7.

Output file specifications .........................................................................................81

2-2.8.

Interfaces with other algorithms ..............................................................................88

2-2.9.

Special notes...........................................................................................................89

2-2.10.

References............................................................................................................90

Appendix. Some details of 2A23 .......................................................................................91

2-3.

2A25..............................................................................................................97

2-3. 1. Objectives...............................................................................................................97
2-3. 2. Changes from V6 to V7 ..........................................................................................97
2-3. 3. Algorithm Overview ................................................................................................98
2-3. 4. More Detailed Description of the Algorithm ............................................................98
2-3. 5. Input data..............................................................................................................101
2-3. 6. Output data...........................................................................................................102iii

2-3. 7. Interfaces with other algorithms............................................................................104
2-3. 8. Caveats ................................................................................................................104
2-3. 9. References ...........................................................................................................105
2-3.10. Detailed description of output variables...............................................................106
Appendix 1. Output data structure defined in the toolkit ..................................................127
Appendix 2. Parameters defined in “param_general_7.6.dat” .........................................130
Appendix 3. Parameters defined in “param_error_7.3.dat”..............................................132
Appendix 4. Parameters defined in “param_strat_4.dat” .................................................132
Appendix 5. Parameters defined in “param_conv_4.dat”.................................................134
Appendix 6. Parameters defined in “param_other_4.dat” ................................................136

3. LEVEL 3....................................................................................... 139
3-1.

3-2

3A-25: Space Time Statistics of Level 2 PR Products ..........................139

3-1.1.

Objective of the algorithm .....................................................................................139

3-1.2.

Output Variables ...................................................................................................140

3-1.2.1.

Variable naming convention ...............................................................................140

3-1.2.2.

Variable Definitions ...........................................................................................140

3-1.2.3.

Definition of Bins for Histograms ........................................................................151

3-1.2.4.

Other Input Parameters:.....................................................................................152

3-1.2.5.

Definitions of low and high resolution grids ........................................................152

3-1.3.

Processing Procedure: ..........................................................................................153

3-1.4.

Comments and Issues: .........................................................................................154

3-1.5.

Changed Variables in Version 6............................................................................157

3-1.5.1.

New variables.....................................................................................................157

3-1.5.2.

Deleted Variables

3-1.5.3.

Spelling Corrected..............................................................................................158

3-1.6.

New Variables in Version 7 ...................................................................................158...........................................................................................158

3A-26: Estimation of Space-Time Rain Rate Statistics Using a Multiple
Thresholding Technique ...........................................................................159
3-2.1. Objective of the algorithm......................................................................................159
3-2.2. Description of the Method .....................................................................................159
3-2.3. Relationship of 3a-26 outputs to those of 3a-25 ....................................................161
3-2.4. Relationship between 3a-26 and the fractional areas above particular thresholds...........................................................................................................................................162
3-2.5. Reliability estimates...............................................................................................164iv

3-2.6. Definition of the latitude-longitude boxes...............................................................164
3-2.7. Notes on the processing procedure.......................................................................164
3-2.8. Input Parameters (initialized in 3a-26) ...................................................................166
3-2.9. Output Variables....................................................................................................167
3-2.10. Processing Procedure .........................................................................................168
3-2.11.

Comments and Issues ........................................................................................168

References ........................................................................................................................170v

0.

Introduction

This instruction manual of TRMM PR algorithm is for PR version 7 algorithms
and products that were released to the public on July 1st, 2011. They aresummarized in Table 0-1.

0-1.

TRMM precipitation radar system description

The TRMM precipitation radar (PR) is the first spaceborne rain radar and theonly instrument on TRMM that can directly observe vertical distributions of rain.
The frequency of TRMM PR is 13.8 GHz. The PR can achieve quantitative rainfall
estimation over land as well as ocean. The PR can also provide rain height
information which is useful for the radiometer-based rain rate retrieval algorithms.
The footprint size of PR is small enough to allow for the study of inhomogeneous
rainfall effects upon the comparatively coarse footprints of the low frequency
microwave radiometer channels.
Major design and performance parameters of the PR are shown in Table 0-2[Kozu et al.,2001]. Observation geometry of PR is shown in Fig 0-1. During thenormal observation mode, PR antenna beam scans in the cross-track direction
over ±17 to results 220 km swath width from end to end. The antenna beam widthof the PR is 0.71 and there are 49 observation angle bins within the scanning
angle of ±17. The horizontal resolution (footprint size) is 4.3 km at nadir and about
5 km at the scan edge when TRMM takes the nominal altitude of 350 km. The
range resolution of TRMM PR is 250 m which is equal to the vertical resolution at
nadir.
The radar echo sampling is performed over the range gates between the sea
surface and the altitude of 15 km for each observation angle bin. For nadir
incidence, the “mirror image” is also collected up to the altitude of 5 km. In
addition, “oversample ” echo data are partially collected for surface return echoes(for scan angle within ±9.94) and for rain echoes (for scan angles within ±3.55 up
to the height of 7.5 km). These oversampled data will be used for precise
measurements of surface return echo level and melting layer structure.
The minimum detectable Z (corresponding to the noise-equivalent received
power) improved from 23.3 dBZ (based upon the specifications requirement) to
20.8 dBZ as determined from the pre-launch ground test and from the orbit test.
This is mainly due to the increased transmit power and the decrease of the receivernoise figure.

-1-

Actually the rain echo power is measured from the subtraction of the system noise
power from the total receiver power (rain echo power + system noise power). The
accuracy of rain echo power can be characterized by the effective signal-to-noise
ratio (S/N), that is the ratio of mean to standard deviation of rain echo power.
By considering these facts, the actual minimum detectable Z can be considered to
be about 16-18 dBZ after the detailed statistical calculation. The effective
signal-to-noise ratio (S/N) of 3 dB is obtained when Z -factor is 17 dBZ.

0-2.

TRMM precipitation radar algorithms

The TRMM PR standard algorithms are developed by the TRMM science team.
They are classified into Level 1 (1B21, 1C21), Level 2 (2A21, 2A23, 2A25) andLevel 3 (3A25, 3A26). Level 1 and Level 2 products are data in the IFOV. Level
3 data give the monthly statistical values of rain parameters mainly in 5° x 5° gridboxes required by the TRMM mission. The characteristics of TRMM PR algorithms
are summarized in Table 0-3 where numbers and the names of the algorithms,
contact persons, products, and brief descriptions of algorithms are shown. Also themutual relation of the algorithms are shown in Fig. 0-2.
The algorithm 1B21 produces engineering values of radar received power(signal + noise) and noise levels. It decides whether there exists rain or not in the
IFOV. It also estimates the effective storm height from the minimum detectable
power value. Algorithm 1C21 gives the radar reflectivity factor, Z, including rain
attenuation effects.
The algorithm 2A21 computes the spatial and temporal statistics of the surface
scattering coefficient 0 over ocean or land when no rain is present in the IFOV.
Then, when it rains in the IFOV, it estimates the path attenuation of the surface
scattering coefficient 0 by rain using no rain surface scattering coefficient 0 as areference [Meneghini, 2000]. The algorithm 2A23 tests whether a bright band exists
in rain echoes and determines the bright band height when it exists [Awaka,
1997] .The rain type is classified into the stratiform type, convective type and othersby the 2A23. It also detects shallow isolated rain whose height is below the melting
level height (zero degree Celsius). The algorithm 2A25 retrieves profiles of theradar reflectivity factor, Z, with rain attenuation correction and rain rate for eachradar beam by the combination of Hitschfeld-Bordan and surface reference
methods[Iguchi,2000].
As the 13.8 GHz frequency band selected for the TRMM PR is fairly heavily-2-attenuated by rain, the compensation of this rain attenuation becomes the major
subject in the rain retrieval algorithms.
Algorithm 3A25 gives the space-time averages of accumulations of 1C21,
2A21, 2A23 and 2A25 products. The most important output products are monthly
averaged rain rates over 0.5° x 0.5° and 5° x 5° grid boxes. It also outputs themonthly averaged bright band height over 0.5° x 0.5° and 5° x 5°grid boxes.
Algorithm 3A26 gives monthly averaged rain rates over the 5° x 5° grid boxes using
the multiple threshold method.

0-3.
Altitude change of the satellite and modification ofalgorithms
The TRMM satellite changed its altitude from 350 km to 402.5 km in August
2001 in order to save the fuel for altitude maintenance. Major impacts of theattitude change (hereafter boost) on the PR are 1) degradation of sensitivity by
about 1.2 dB and 2) occurrence of mismatch between transmission and reception
angles for one pulse among 32 onboard averaging pulses. The correction algorithm
for the latter was added in 1B21 algorithm (please see Chapter 1 for detail). Other
than the 1B21, algorithms were not changed according to the altitude change of thesatellite.

0-4.

PR hardware switch from A-side to B-side

The PR experienced a major anomaly on May 29, 2009, resulting in a loss ofdata. JAXA and NASA inferred that the FCIF/SCDP (Frequency Converter and
IF/System Control Data Processor) units were not working normally. JAXA andNASA successfully switched the FCIF/SCDP units from the original A-side(FCIF/SCDP-A) to the backup B-side (FCIF/SCDP-B) and restarted the PR toresume observation on June 17, 2009. The first granule of the B-side standard
products was acquired just after the PR panel temperatures were stabilized onJune 19, 2009. A PR B-side Task Force including JAXA carried out internal /external calibrations and carefully investigated the best way to calibrate the PR so
as to maintain continuity of PR products between the A-side and B-side.

-3-

0-5.

References

J. Awaka, T. Iguchi, H, Kumagai and K. Okamoto [1997], “Rain type classification
algorithm for TRMM precipitation radar,” Proceedings of the IEEE 1997
International Geoscience and Remote Sensing Symposium, August 3-8, Singapore,pp. 1636-1638.
R. Meneghini, T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J. A. Jones and J.
Kwiatkowski [2000], “Use of the surface reference technique for path attenuation
estimates from the TRMM precipitation radar,” J. Appl. Meteor., 39, 2053-2070.
K. Okamoto, T. Iguchi, T. Kozu, H. Kumagai, J. Awaka, and R. Meneghini [1998],“Early results from the precipitation radar on the Tropical Rainfall Measuring
Mission,” Proc. CLIMPARA’98, April 27-29, Ottawa, pp. 45-52.
T. Iguchi, T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto [2000], Rain-profilingalgorithm for the TRMM precipitation radar, J. Appl. Meteor., 39, 2038-2052.
T. Kozu, T. Kawanishi, H. Kuroiwa, M. Kojima, K. Oikawa, H. Kumagai, K. Okamoto,
M. Okumura, H. Nakatuka, and K. Nishikawa[2001], “Development of Precipitation
Radar Onboard the Tropical Rainfall Measuring Mission (TRMM) Satellite,”
Proceedings of the IEEE 2001 trans. Geoscience and Remote Sensing, 39,
102-116.

-4-

Table 0-1.

Major changes of PR algorithm from version 6 to version 7

Product No
1B21:
PR calibration

1C21:
PR reflectivities
2A21:
Sigma-zero

2A23:
PR qualitative

2A25:
PR profile

Major Changes
a. Improve clutter routine module.
b. Improve elevation data with SRTM30 over India, Tibet andSouth America.
c. Change “landOceanFlag” and “scOrientation”.
d. Change general data structure using PPS I/O toolkit.
e. Modification of calibration coefficients for B-side period.
a. Change general data structure using PPS I/O toolkit.
a. Introduction of 5 types of PIA
Temporal reference: increased spatial resolution
introduction of the reference data base with 0.1 deg. grid
Spatial reference: introduction of backward reference
b. Reference curve is determined piecewise in the hybrid
methodc. Introduction of the concept of distance from the reference
point in the spatial reference method
d. Introduction of effective PIA（PIAeff） and its error estimate
a. Introduced a concept of small rain cell, which isconvective. (Effect appreciable.)b. About 40% of shallow non-isolated is classified asconvective. (Effect appreciable.)c. GANAL data (Global analysis data by JMA) is used for
estimating 0C height.
d. When BB is detected, rain type is basically stratiform. But
an exception is introduced so that rain type can beconvective even when BB is detected, (Very infrequent
occurrence.)e. When storm top>15 km and without BB, rain type isconvective. (Low frequency of occurrence.)
f. Increased rain-type sub-categories.
a. Expected value to maximum likelihood value in estimating
αb. Adding 0.5 dB to PIA estimates over land from 2A21 tocompensate the wetting effectc. Changed the assumed vertical profile of specificattenuation k (α in k=αZeb ) (Changed the vertical profile ofthe mixing ratio of water to ice）
d. Introduction of a new DSD model (Z-R relation)e. Changed the uncertainty of ζ (α and Zm) in the
Hitschfeld-Bordan attenuation correction method
f. Introduction of NUBF correction
g. Correcting the smearing of BB in off-nadir beams-5-

3A25:Space-time average ofPR products

3A26:
Statistical method

a. New products:
Epsilon fit: statistics to characterize the slope of aregression line between zeta and a function of thepath-integrated attenuation derived from the SRT- PIA and zeta
a. Only minor changes

Table 0-2. Major parameters of TRMM PR

ItemSpecification

Frequency
13.796, 13.802 GHz
Sensitivity  0.7 mm/h (S/N /pulse  0 dB)
Swath width
220 km (from end to end)
Observable range
Surface to 15 km altitude
Horizontal resolution Vertical 4.3 km (nadir)resolution
0.25 km (nadir)
AntennaType128-element WG Planar array
Beam width
0.71° x 0.71°
Aperture
2.0 m x 2.0 m
Scan angle± 17° (Cross track scan)
Transmitter/receiverType
SSPA & LNA (128 channels)
Peak power 500 W (at antenna input)
Pulse width
1.6 s x 2 ch. (Transmitted pulse)
PRF
2776 HzDynamic range
 70 dB
Number of indep. samples
64
Data rate
93.2 kbps
Mass
465 kg
Power
250 W

-6-

Figure 0-1. Observation concept of the PR.

TRMM S/C(Alt.: 350 km)

Flight direction

PR
Scan angle:±17°

Range resolution : 250 m

Swath width: ~220 km
IFOV: ~4.3 km

The IFOV is about 5.0 km and the swath width is about 250 km after the boost of
the orbit.

-7-

Table 0-3. TRMM Standard PR Algorithms
Product
No.
1B21

Name

Contact Person

Products

Algorithm Description
Conversion of the count value ofradar echoes and noise level into
engineering value. Decision ofrain/no rain. Determination ofeffective storm height from minimum
detectable power value. Rejection of
mainlobe and sidelobe clutter.
Conversion of the power and noise
value to radar reflectivity factors Zm
without rain attenuation correction.

PRcalibration
Rain/No rain

JAXA/EORC(Japan)J. Awaka(Japan)T. Iguchi(Japan)Total received power,
Noise Level Clutter
contamination flag.

1C21

PR
reflectivities

JAXA/EORC(Japan)

2A21

Surfacescattering
coefficient 

R. Meneghini
(USA)

2A23

PR
qualitative

J. Awaka(Japan)

2A25

PR profile

T. Iguchi(Japan)

3A25

Space-time
average ofradar
products

R. Meneghini(USA)

Profiled Zm (radarreflectivity factors
without rain
attenuation
correction).
Path integrated
attenuation (PIA) of (in case of rain)
and its reliability. Database of  (ocean/land, in case of norain)
Detection of brightband, Bright bandheight, strength,
width, Rain typeclassification,
Detection of shallow
isolated rain. Outputof rain/no rain flag,height of storm top.
Range profiles ofattenuation-corrected
radar reflectivity
factors, rainfall rate.
Estimated nearsurface, and surface
rainfall rates, andaverage rainfall rates
between the two
predefined altitude(2,4 km).
Space-time averagesof accumulations of
1C21, 2A21, 2A23,
2A25.

3A26

Estimation of
space-timerain ratestatistics

R. Meneghini(USA)

Rain rate statistics
over 5 degree x 5
degree 1 monthspace-time regions
using a multiple
thresholding
technique.

-8-

Estimation of path integrated
attenuation and its reliability using
the surface as a reference target.
Spatial and temporal statistics ofsurface  and classification of 
into land/ocean, rain/no rain.
Whether a bright band exists in rainechoes or not, and determination ofbright band height when it exists.
The rain type is classified into
stratiform type, convective type orothers. Shallow isolated rain, theheight of which is below the 0 deg.,
is detected.
The rainfall rate estimate is given ateach resolution cell. This algorithm
employs a hybrid method of thesurface reference method and the
Hitschfeld-Bordan method.
Precipitation water content at 5
altitudes, and vertically integrated
precipitation water content are also
calculated.

Calculation of various statistics overa month from the level 2 PR output
products. Four types of statistics arecalculated. 1. probabilities ofoccurrence, 2. means and standard
deviations, 3. histograms, 4.
correlation coefficients.
Estimated values of the probability
distribution function of thespace-time rain rate at 4 levels, andthe mean, standard deviation, and soon.

Figure 0-2.

TRMM Precipitation Radar Algorithm Flow.

TRMM
Precipitation
Radar Standard
Algorithm Flow

Level 0
Unprocessed
Instrument Data
1B21
Calibrated Received Power
1C21
Radar Reflectivity(Z-factor)

2A23
PR Qualitative(Rain Type, BB)
3A26
Space-Time Averages
using Threshold Method

2A25
3-D Rain Profile(Z, Rain Rate)

3A25
Monthly Statisticsof PR Products

-9-

2A21
Surface Sigma-0
Rain Attenuation

1.

Level 1

1-1.

1B21: PR received power

1-1. 1.

Algorithm Overview

The 1B21 calculates the received power at the PR receiver input point from theLevel-0 count value which is linearly proportional to the logarithm of the PR
receiver output power in most received power levels.
To convert the count value to the input power of the receiver, internal calibration
data is used. The relationship between the count value and the input power isdetermined by the system model and the temperature in the PR. This relationshipis periodically measured using an internal calibration loop for the IF unit and thelater receiver stages. To make an absolute calibration, an Active Radar Calibrator(ARC) is placed at Kansai Branch of NICT and the overall system gain of the PR isbeing measured nearly every 3-6 months. Based on the data from the internal andexternal calibrations, the PR received power is obtained. Note that the calculation
assumes that the signal follows the Rayleigh fading, so if the fading characteristics
of a scatter are different, a small bias error may occur (within 1 or 2 dB).
Other ancillary data in 1B21 include:- Locations of Earth surface and surface clutter (range bin number).
Those are useful to identify whether the echo is rain or surface.
- System noise level: Four range bins data per angle bin.
This is the reference noise floor which is used to extract echo power from the"total" received power in 1B21 (echo + noise).
- Oversample data: In order to improve the accuracy of surface echo measurement,
and to obtain a better vertical rain profile, 125-m intervals data are available atnear-nadir angle bins for rain-oversample (up to 7.5 km) and ±10 deg. scanangles for surface-oversample.
- Minimum echo flag: A measure of the existence of rain within a beam.
There are multiple confidence levels and users may select up to what confidence
level they treat as rain.
- Bin storm height: The maximum height at which an echo exists for a specific anglebin.
- Land/ocean flag and Topographic height- 10 -

1-1. 2.

File Format

The main output of the Tropical Rainfall Measurement Mission (TRMM)/Precipitation Radar (PR) Level-1B product, 1B21 is “PR received power.”
The PR1B21 product is written in Hierarchical Data Format 4 (HDF4).
HDF was developed by the U.S. National Center for Supercomputing Applications(NCSA). HDF manuals and software tools are available via homepage at
http://www.hdfgroup.org/products/hdf4/

1-1. 3.

Structure of output variables

The PR Level-1B product, 1B21, "PR Power," is written as a Swath Structure. The
following sections describe the structure and contents of the format.
Dimension definitions:nscan: Number of scans in the granule.
nray (= 49): Number of angle bins in each scan.
Figure 1-1-1 through Figure 1-1-8 show the structure of this algorithm. The text
below describes the contents of objects in the structure, the C Structure Header
File and the Fortran Structure Header File.

- 11 -

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)

Figure 1-1-1. Data format structure for 1B21 (1/2)- 12 -

(23)
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
(33)

Figure 1-1-2. Data format structure for 1B21 (2/2)(6)

Figure 1-1-3. Data format structure for pr_cal_coef- 13 -

(7)Figure 1-1-4. Data format structure for ray_header(9)

Figure 1-1-5. Data format structure for ScanTime- 14 -

(13)Figure 1-1-6. Data format structure for scanStatus(14)

Figure 1-1-7. Data format structure for navigation- 15 -

(15)Figure 1-1-8. Data format structure for powers

1-1. 4.

Detailed description of output variables(1) FileHeader (Metadata)
FileHeader contains metadata common to all GPM products.
AlgorithmID:
The name of the algorithm that generated this product. For example, 1B21.
AlgorithmVersion:
The version of the algorithm that generated this product.
FileName:
The file name of this granule.
GenerationDateTime:
The date and time this granule was generated. The format is
YYYY-MM-DDTHH:MM:SS.sssZ, where YYYY is 4-digit year, MM is month
number, DD is day of month, T is "T", HH is hour, MM is minute, SS is second, sss
is millisecond, and Z is "Z". All fields are zero-filled.
StartGranuleDateTime:
The start time of the data in this granule. There may be overlap scans in the file
before the start time as described in NumberScans-BeforeGranule. The format is
the same as Generation-DateTime.
StopGranuleDateTime:
The stop time of the data in this granule. There may be overlap scans in the file
before the start time as described in NumberScans-BeforeGranule. The format is
the same as GenerationDateTime.

- 16 -

GranuleNumber:
The number of this granule, which starts as defined in GranuleStart. If theGranuleStart is identical to the orbit start, then the GranuleNumber will be the sameas the orbit number.
NumberOfSwaths:
The number of swaths in this granule.
NumberOfGrids:
The number of grid structures in this granule.
GranuleStart:
The starting place in the orbit of this granule. Currently defined values are"SOUTHERNMOST LATITUDE" and "NORTHBOUND EQUATOR CROSSING".
TimeInterval:
The time interval covered by this granule. Values are "ORBIT", "HALFORBIT","HOUR", "3 HOUR", "DAY", "MONTH".
ProcessingSystem:
The name of the processing system, e.g., "PPS".
ProductVersion:
The data version assigned by the processing system.
MissingData:
The number of missing scans.
InputFileNames:
InputFileNames contains a list of input file names for this granule.
InputAlgorithmVersions:
InputFileNames contains a list of algorithm versions of the input files for thisgranule.
InputGenerationDateTimes:
InputFileNames contains a list of algorithm versions of the input files for thisgranule.

- 17 -

(2) InputRecord (Metadata)
InputRecord contains a record of input files for this granule. This group appears in
Level 1 and Level 2 data products. Level 3 products have the same information
separated into 3 groups since they have many inputs.
InputFileNames:
InputFileNames contains a list of input file names for this granule. Since somealgorithms may have 2000 input files, this group is a "Long Metadata Group", which
has no elements. This group appears in Level 3 products.
InputAlgorithmVersions:
InputAlgorithmVersions contains a list of input algorithm versions for this granule.
Since some algorithms may have 2000 input files, this group is a "Long MetadataGroup", which has no elements. This group appears in Level 3 products.
InputGenerationDateTimes:
InputGenerationDateTimes contains a list of input generation datetimes for thisgranule. Since some algorithms may have 2000 input files, this group is a "Long
Metadata Group", which has no elements. This group appears in Level 3 products.

(3) NavigationRecord (Metadata)
NavigationRecord contains navigation metadata for this granule. This group
appears in Level 1 and Level 2 data products.
LongitudeOfMaximumLatitude:
The longitude of the maximum latitude of the orbit track of this granule.
SolarBetaAngleAtBeginningOfGranule:
The solar beta angle at the start of this granule.
SolarBetaAngleAtEndOfGranule:
The solar beta angle at the end of this granule.

- 18 -

(4) FileInfo (Metadata)
FileInfo contains metadata used by the PPS I/O Toolkit. This group appears in alldata products.
DataFormatVersion:
The version of the data format used to write this file. This version is separate foreach AlgorithmID. The order is: "a" "b" ... "z" "aa" "ab" ... "az" "ba" "bb" ...
TKCodeBuildVersion:
Usually TKCodeBuild-Version is "1". If the I/O routines built by TKIO change eventhough the DataFormatVersion is unchanged, then TKCodeBuild-Version
increments to "2", "3", ... If subsequently DataFormatVersion changes,
TKCodeBuildVersion becomes "1" again.
MetadataVersion:
The version of metadata used to write this file. This version is separate for each
AlgorithmID. The order is: "a" "b" ... "z" "aa" "ab" ... "az" "ba" "bb" ...
FormatPackage:
The underlying format of this granule. Values are "HDF4", "HDF5", "NETCDF","TKBINARY"
BlueprintFilename:
The filename of the primary blueprint file that defined the format used to write thisfile.
BlueprintVersion:
The BlueprintVersion of the format definition.
TKIOVersion:
The version of TKIO used to create I/O routines to write this file. TKIOVersion does
not define the format used to write this file.
MetadataStyle:
The style in which the metadata was written, e.g., "PVL". "PVL" means < parameter>=< value >;- 19 -

EndianType:The endian type of the system that wrote this file. Values are "BIG ENDIAN" and"LITTLE ENDIAN".

(5) JAXAInfo (Metadata)
JAXAInfo contains metadata requested by JAXA. Used by PR algorithms only.
CalibrationCoefficientVersion:
Version of the calibration coefficients.
GranuleFirstScanUTCDate:
Orbit First Scan UTC Date. Date is a 10 character string with the following
characters: YYYY/MM/DD, where YYYY = year, MM = month number, DD = day ofmonth and “/” is a literal. If the granule is empty, the value is ‘0/0/0’. In 2A-52, UTCdate is stored as “/” is replaced by “-”. In 1B-11 and 2A-12, UTC date is stored inseparate words for year, month and day of month.
GranuleFirstScanUTCTime:
Orbit First Scan UTC Time. Time is an 8 character string with the following
characters: HH:MM:SS, where HH = hour, MM = minute, SS = second, and “:” is a
literal. If the granule is empty, the value is ‘0:0:0’. In 1B-11 and 2A-12, UTC time isstored in separate words for hour, minute, and second.
GranuleFirstScanUTCMilliseconds:
Orbit First Scan UTC Milliseconds. Milliseconds is a 3 character string with thefollowing characters: MMM, where MMM = the number of milliseconds later thanthe last whole second.
GranuleLastScanUTCDate:
Orbit Last Scan UTC Date. See Orbit First Scan UTC Date.
GranuleLastScanUTCTime:
Orbit Last Scan UTC Time. Decided by L1A file header. See Orbit First Scan UTC
Time.
GranuleLastScanUTCMilliseconds:
Orbit Last Scan UTC Milliseconds. See Orbit Last Scan UTC Milliseconds.
SoftwareVersion:
Version of the Software.

- 20 -

DatabaseVersion:
Version of PR Database in the PR L1 software
TotalQualityCode:Total quality of the PR L1 product. Values are ‘G’, ‘F’, or ‘P’.
LongitudeOnEquator:
Longitude on the equator from the ascending node. Range is -180.000 to 179.999.
UTCDateOnEquator:
UTC date on the equator. See Orbit First Scan UTC Date.
UTCTimeOnEquator:
UTC time on the equator. See Orbit First Scan UTC Time.
UTCMillisecondsOnEquator:
UTC millisecond on the equator. See Orbit First Scan UTC Milliseconds.
CenterScanUTCDate:
UTC date at orbit center scan. See Orbit First Scan UTC Date.
CenterScanUTCTime:UTC time at orbit center scan. See Orbit First Scan UTC Time.
CenterScanUTCMilliseconds:
UTC milliseconds at orbit center scan. See Orbit First Scan UTC Milliseconds.
FirstScanLat:
Latitude of orbit first scan. Range is -40.000 to 40.000
FirstScanLon:
Latitude of orbit first scan. Range is -180.000 to 179.999.
LastScanLat:
Latitude of orbit last scan. Range is -40.000 to 40.000.
LastScanLon:
Longitude of orbit last scan. Range is -180.000 to 179.999.
NumberOfRainScans:
Number of rain scan whose minEchoFlag is rain certain (20) or rain possible (10,11, 12, 13).

- 21 -

(6) pr_cal_coef (Group)
Calibration coefficients consist of several parameters describing the PR electronic
performance. They are controlled by JAXA based on the results of PR calibration
data analysis. These coefficients are applied in 1B21 (PR received power)
calculations.
transCoef (4-byte float):
Transmitter gain correction factor.
receptCoef (4-byte float):
Receiver gain correction factor.
fcifIOchar [16] (4-byte float):
LOGAMP Input/Output characteristics. The power level at the IF unit corresponding
to the count value is calculated by a look-up table which represents input to output
characteristics of the IF unit measured by internal calibrations. PR received
power is then calculated from this power level and the receiver gain at RF stage.

(7) ray_header (Group)
The Ray Header contains information that is constant in the granule, such as theparameters used in the radar equation, the parameters in the minimum echo test,
and the sample start range bin number. These parameters are provided for eachangle bin.
rayStart [49] (2-byte integer):
Range bin number of starting normal sample. See note (a).
raySize [49] (2-byte integer):
Number of normal samples in 1 angle. See note (a).
angle [49] (4-byte float):
Scan angle (degree) is defined as the cross-track angle at the radar electriccoordinates which are rotated by 4 degrees about the Y-axis (Pitch) of spacecraft
coordinates, which is almost same direction with nadir. The angle is positive when
the antenna beam is rotated counter clockwise (CCW) from the nadir about the +X
axis of the radar electric coordinates.

- 22 -

startBinDist [49] (4-byte float):
Distance (m) between the satellite and the starting bin number of the normal
sample for the ray. See note (b).
rainThres1 [49] (4-byte float):
The threshold is used in minimum echo test.
rainThres2 [49] (4-byte float):
The threshold is used in minimum echo test.
transAntenna [49] (4-byte float):
Transmitted radar antenna effectiveness (dB).
recvAntenna [49] (4-byte float):
Received radar antenna effectiveness (dB).
onewayAlongTrack [49] (4-byte float):
Along track beam widths (radians) is recorded based on the fact that the PR main
beam is assumed to have a two-dimensional Gaussian beam pattern.
onewayCrossTrack [49] (4-byte float):
Cross track beam widths (radians) is recorded based on the fact that the PR main
beam is assumed to have a two-dimensional Gaussian beam pattern.
eqvWavelength [49] (4-byte float):
Equivalent wavelength (m). See note (c).
radarConst [49] (4-byte float):
Radar constant dC (units are dB), which relates Received Power to Radar
Reflectivity. See note (d).
prIntrDelay [49] (4-byte float):
The time (seconds) between when echo returns at antenna and when echo isrecorded in onboard processor. Set to 0.
rangeBinSize [49] (4-byte float):
Range Bin Size (rangeBinSize) is the PR range resolution and is the width at which
pulse electric power decreases 6dB (-6 dB width).

- 23 -

logAveOfset [49] (4-byte float):
Logarithmic Averaging Offset (logAveOffset) is the offset value between thelogarithmic average and the power-linear average. The PR outputs the data of 1
range bin which is the average of 64 LOGAMP outputs. "Received power" in the
PR1B21 output is corrected for the bias error caused by the logarithmic averageand is thus equal to normal average power.
mainlobeEdge [49] (1-byte integer):
Main Lobe Clutter Edge (mainlobeEdge) is a parameter previously used as thelowest range bin for the minimum echo test. This is the absolute value of thedifference in range bin number between the surface peak and the edge of theclutter from the main lobe.
sidelobeRange [3][49] (1-byte integer):
Absolute value of the difference in Range bin numbers between the bin number ofthe surface peak and the possible clutter position. A maximum of three range bins
can be allocated as "possible" clutter locations. "Zero" indicates no clutter.
Note (a)The Precipitation Radar (PR) has 400 internal (logical) range bins (A/D sample
points) and records “normal sample data (normalSample)” every other range bin
from “Ray Start (RayStart)” in order to sample radar echoes from 0-km (thereference ellipsoid surface) to 15-km height.
The number of recorded samples at an angle bin depends on the scan angle and isdefined by “Ray Size (RaySize).” The N-th normal sample data can be converted tothe internal logical range bin number as follows;
Logical range bin number at N-th normal sample= RayStart + 2  ( N  1)
Note (b)Starting Bin Distance is determined by the sampling timing of the PR. The distance
between the satellite and the center of the N-th normal sample bin is calculated asfollows:
Distance = “Starting Bin Distance (startBinDist)” + “Range Bin Size(rangeBinSize)”  (N  1)

- 24 -

This distance is defined as the center of a radar resolution volume
which extends  125 m .
Note (c)“Equivalent Wavelength (eqvWavelength)”  2c  f1  f2 
where c is the speed of light, and f1 and f2 are PR’s two frequencies.
Note (d)Radar Constant (radarConst) is defined as follows, and is used in the radar
equation:
2


K
3
18

C 0  10log 10
 2 10 ln2K  ε  1 / ε  2 
 : the relative dielectric constant of water2

K  0.9255

2

K is the calculated value at 13.8 GHz and 0 degree C based on Ray(1972).* 1 With this constant, users can convert from PR receiving
powers to rain reflectivity. (See the 1C products.)(8) SwathHeader (Metadata)
SwathHeader contains metadata for swaths. This group appears in Level 1 andLevel 2 data products.
NumberScansInSet :The scans read by TKreadScan are a "set". For single swath data, one scan is readso NumberScansInSet=1. In case of PR, NumberScansInSet=1.
MaximumNumberScansTotal :The maximum allowed number of total scans in this swath. Total scans = overlapscans before granule + scans in granule + overlap scans after granule.

1

Ray, P.S., 1972: Broadband complex refractive indices of ice and water. Appl.Opt., Vol.11, No.8, 1836-1844.

- 25 -

NumberScansBeforeGranule :The number of overlap scans before the first scan of the granule in this swath.
In case of PR, NumberScansBeforeGranule=0.
NumberScansGranule :The number of scans in the granule in this swath.
NumberScansAfterGranule :The number of overlap scans after the last scan of the granule in this swath.
In case of PR, NumberScansAfterGranule=0.
NumberPixels :The number of IFOV in each scan in this swath. In case of PR, NumberPixels=49.
ScanType :The type of scan in this swath. Values are: "CROSSTRACK" and "CONICAL". Incase of PR, ScanType="CROSSTRACK".

(9) ScanTime (Group)
Scan time is the center time of 1 scan (the time at center of the nadir beamtransmitted pulse).
Year [nscan] (2-byte integer):
4-digit year, e.g., 1998. Values range from 1950 to 2100 years.
Special values are defined as:-9999 MissingValue.
Month [nscan] (1-byte integer):Month of the year. Values range from 1 to 12 months.
Special values are defined as:-99 MissingValue
DayOfMonth [nscan] (1-byte integer):Day of the month. Values range from 1 to 31 days.
Special values are defined as:-99 MissingValue- 26 -

Hour [nscan] (1-byte integer):
UTC hour of the day. Values range from 0 to 23 hours.
Special values are defined as:-99 MissingValue
Minute [nscan] (1-byte integer):
Minute of the hour. Values range from 0 to 59 minutes.
Special values are defined as:-99 MissingValue
Second [nscan] (1-byte integer):
Second of the minute. Values range from 0 to 60 s.
Special values are defined as:-99 MissingValue
MilliSecond [nscan] (2-byte integer):Thousandths of the second. Values range from 0 to 999 ms.
Special values are defined as:-9999 MissingValue
DayOfYear [nscan] (2-byte integer):Day of the year. Values range from 1 to 366 days.
Special values are defined as:-9999 MissingValue(10) scanTime_sec [nscan] (8-byte float):
Scan time is the center time of 1 scan (the time at center of the nadir beamtransmitted pulse). Scan time is expressed as the UTC seconds of the day. Values
range from 0 to 86400 s.
Special values are defined as:-9999.9 MissingValue(11) Latitude [49][nscan] (4-byte float):
The latitude of the center of the IFOV at the altitude of the earth ellipsoid. Values
range from -90 to 90 degrees. Special values are defined as:- 27 -

-9999.9 MissingValue(12) Longitude [49][nscan] (4-byte float):
The earth longitude of the center of the IFOV at the altitude of the earth ellipsoid.
Values range from -180 to 180 degrees. Special values are defined as:-9999.9 MissingValue(13) scanStatus (Group)
missing [nscan] (1-byte integer):
Missing indicates whether information is contained in the scan data.
The values are:0 normal
1 missing (missing packet and calibration mode)2 No-rainvalidity [nscan] (1-byte integer):
Validity is a summary of status modes. If all status modes are routine, all bits in
Validity=0. Routine means that scan data has been measured in the normal
operational situation as far as the status modes are concerned. Validity does notassess data or geolocation quality. Validity is broken into 8 bit flags. Each bit = 0 if
the status is routine but the bit = 1 if the status is not routine. Bit 0 is the leastsignificant bit (i.e., if bit i = 1 and other bits = 0, the unsigned integer value is 2**i).
The non-routine situations follow:
Bit Meaning if bit = 1
0 Spare (always 0)
1 Non-routine spacecraft orientation (2 or 3)
2 Non-routine ACS mode (other than 4)
3 Non-routine yaw update status (0 or 1)
4 Non-routine instrument status (other than 1)
5 Non-routine QAC (non-zero)
6 Spare (always 0)
7 Spare (always 0)
qac [nscan] (1-byte integer):
The Quality and Accounting Capsule of the Science packet as it appears in Level-0- 28 -

data. If no QAC is given in Level-0, which means no decoding errors occurred,
QAC in this format has a value of zero.
geoQuality [nscan] (1-byte integer):
Geolocation quality is a summary of geolocation quality in the scan. A zero integer
value indicates 'good' geolocation. A non-zero value broken down into the following
bit flags indicates the following, where bit 0 is the least significant bit (i.e., if bit i = 1
and other bits = 0 the unsigned integer value is 2**i):Bit Meaning if bit = 1
0 latitude limit error
1 geolocation
2 attitude change rate limit error
3 attitude limit error
4 satellite undergoing maneuvers
5 using predictive orbit data
6 geolocation calculation error
7 not used
dataQuality [nscan] (1-byte integer):
Data quality is a summary of data quality in the scan. Unless this is 0 (normal), thescan data is meaningless to higher processing. Bit 0 is the least significant bit (i.e.,
if bit i =1 and other bits = 0, the unsigned integer value is 2**i).
Bit Meaning if bit = 1
0 missing
5 Geolocation Quality is not normal
6 Validity is not normal
SCorientation [nscan] (2-byte integer):
The positive angle of the spacecraft vector (v) from the satellite forward direction of
motion, measured clockwise facing down. We define v in the same direction as thespacecraft axis +X, which is also the center of the TMI scan. Values range from 0 to
360 degrees.
0:+x forward
180:-x forward
90:-y forward
Special values are defined as:-9999 MissingValue-8003 Inertial-8004 Unknown- 29 -

acsMode [nscan] (1-byte integer):
Value Meaning
0 Standby
1 Sun Acquire
2 Earth Acquire
3 Yaw Acquire
4 Nominal
5 Yaw Maneuver
6 Delta-H (Thruster)
7 Delta-V (Thruster)
8 CERES Calibration
yawUpdateS [nscan] (1-byte integer):
Value Meaning
0 Inaccurate
1 Indeterminate
2 Accurate
prMode [nscan] (1-byte integer):
Value Meaning
1 Observation Mode
2 Other Mode
prStatus1 [nscan] (1-byte integer):
The flags listed here indicate warnings of PR conditions (noise level, echo powerand echo position, and mode change). In data processing, users should becautions with the following as a scan with non-zero status includes questionable
range bins or angle bins.
Bit Meaning if bit = 1
0 LOGAMP noise limit error
1 Noise level limit error: The meaning of this warning is the same as "System Noise
Warning Flag".
2 Out of PR dynamic range: Surface echo is so strong that it exceeds the PR
receiver dynamic range. If this bit is ON, surface echo level may be questionable.
3 Not reach surface position: If Surface echo is out of range window, Bin Surface
Peak and related data become uncertain.
7 FCIF mode change- 30 -

prStatus2 [nscan] (1-byte integer):
In some cases, antenna sidelobes are directed to nadir receive surface echo
positions. When the main beam is off nadir, the timing of such nadir-surface
clutter can contaminate the rain echo. In "PR STATUS2," a warning flag is set ON(1) when the nadir surface echo (at the nadir angle bin #25) exceeds apredetermined threshold. When the flag is ON, please be careful about theechoes at all angle bins around the same logical range bin number as the
Bin-surface-peak at nadir (angle bin number 25).
Bit meaning if bit =1
0 Warning for clutter because of strong nadir surface echo.
FractionalGranuleNumber [nscan] (8-byte float):
The floating point granule number. The granule begins at the Southern-most pointof the spacecraft's trajectory. For example, FractionalGranuleNumber = 10.5
means the spacecraft is halfway through granule 10 and starting the descending
half of the granule.

(14) navigation (Group)
scPosX [nscan] (4-byte float):
The x component of the position (m) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time (i.e., time at the middle pixel/IFOV of the active
scan period). Geocentric Inertial Coordinates are also commonly known as Earth
Centered Inertial coordinates. These coordinates will be True of Date (rather than
Epoch 2000 which are also commonly used), as interpolated from the data in the
Flight Dynamics Facility ephemeris files generated for TRMM.
scPosY [nscan] (4-byte float):
The y component of the position (m) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time (i.e., time at the middle pixel/IFOV of the active
scan period). Geocentric Inertial Coordinates are also commonly known as Earth
Centered Inertial coordinates. These coordinates will be True of Date (rather than
Epoch 2000 which are also commonly used), as interpolated from the data in the
Flight Dynamics Facility ephemeris files generated for TRMM.
scPosZ [nscan] (4-byte float):
The z component of the position (m) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time (i.e., time at the middle pixel/IFOV of the active- 31 -

scan period). Geocentric Inertial Coordinates are also commonly known as Earth
Centered Inertial coordinates. These coordinates will be True of Date (rather than
Epoch 2000 which are also commonly used), as interpolated from the data in the
Flight Dynamics Facility ephemeris files generated for TRMM.
scVelX [nscan] (4-byte float):
The x component of the velocity (ms^-1) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time.
scVelY [nscan] (4-byte float):
The y component of the velocity (ms^-1) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time.
scVelZ [nscan] (4-byte float):
The z component of the velocity (ms^-1) of the spacecraft in Geocentric Inertial
Coordinates at the Scan mid-Time.
scLat [nscan] (4-byte float):
The geodedic latitude (decimal degrees) of the spacecraft at the Scan mid-Time.
scLon [nscan] (4-byte float):
The geodedic longitude (decimal degrees) of the spacecraft at the Scan mid-Time.
scAlt [nscan] (4-byte float):
The altitude (m) of the spacecraft above the Earth Ellipsiod at the Scan mid-Time.
scAttRoll [nscan] (4-byte float):
The satellite attitude Euler roll angle (degrees) at the Scan mid-Time. The order ofthe components in the file is roll, pitch, and yaw. However, the angles arecomputed using a 3-2-1 Euler rotation sequence representing the rotation orderyaw, pitch, and roll for the rotation from Orbital Coordinates to the spacecraft bodycoordinates. Orbital Coordinates represent an orthogonal triad in Geocentric
Inertial Coordinates where the Z-axis is toward the geocentric nadir, the Y-axis isperpendicular to the spacecraft velocity opposite the orbit normal direction, and the
X-axis is approximately in the velocity direction for a near circular orbit. Note this isgeocentric, not geodetic, referenced, so that pitch and roll will have twice orbital
frequency components due to the onboard control system following the oblate
geodetic Earth horizon. Note also that the yaw value will show an orbital frequency
component relative to the Earth fixed ground track due to the Earth rotation relative- 32 -

to inertial coordinates.
scAttPitch [nscan] (4-byte float):
The satellite attitude Euler pitch angle (degrees) at the Scan mid-Time. The orderof the components in the file is roll, pitch, and yaw. However, the angles arecomputed using a 3-2-1 Euler rotation sequence representing the rotation orderyaw, pitch, and roll for the rotation from Orbital Coordinates to the spacecraft bodycoordinates. Orbital Coordinates represent an orthogonal triad in Geocentric
Inertial Coordinates where the Z-axis is toward the geocentric nadir, the Y-axis isperpendicular to the spacecraft velocity opposite the orbit normal direction, and the
X-axis is approximately in the velocity direction for a near circular orbit. Note this isgeocentric, not geodetic, referenced, so that pitch and roll will have twice orbital
frequency components due to the onboard control system following the oblate
geodetic Earth horizon. Note also that the yaw value will show an orbital frequency
component relative to the Earth fixed ground track due to the Earth rotation relative
to inertial coordinates.
scAttYaw [nscan] (4-byte float):
The satellite attitude Euler yaw angle (degrees) at the Scan mid-Time. The order ofthe components in the file is roll, pitch, and yaw. However, the angles arecomputed using a 3-2-1 Euler rotation sequence representing the rotation orderyaw, pitch, and roll for the rotation from Orbital Coordinates to the spacecraft bodycoordinates. Orbital Coordinates represent an orthogonal triad in Geocentric
Inertial Coordinates where the Z-axis is toward the geocentric nadir, the Y-axis isperpendicular to the spacecraft velocity opposite the orbit normal direction, and the
X-axis is approximately in the velocity direction for a near circular orbit. Note this isgeocentric, not geodetic, referenced, so that pitch and roll will have twice orbital
frequency components due to the onboard control system following the oblate
geodetic Earth horizon. Note also that the yaw value will show an orbital frequency
component relative to the Earth fixed ground track due to the Earth rotation relative
to inertial coordinates.
SensorOrientationMatrix [3][3][nscan] (4-byte float):
SensorOrientationMatrix is the rotation matrix from the instrument coordinate frameto Geocentric Inertial Coordinates at the Scan mid-Time. It is unitless.
greenHourAng [nscan] (4-byte float):
The rotation angle (degrees) from Geocentric Inertial Coordinates to Earth Fixed
Coordinates.

- 33 -

(15) powers (Group)
radarTransPower [nscan] (2-byte integer):
The total (sum) power of 128 SSPA elements corrected with SSPA temperature inorbit, based on temperature test data of SSPA transmission power. The units are
dBm * 100. For example, -9436 represents -94.36 dBm.
transPulseWidth [nscan] (4-byte float):
Transmitted pulse width (s) corrected with FCIF temperature in orbit, based on
temperature test data of FCIF.

(16) systemNoise [49][nscan] (2-byte integer):
System Noise (dBm) is an average of the 4 measured system noise values,
multiplied by 100 and stored as a 2-byte integer. The units are dBm * 100. The
system noise consists of external noise and PR internal noise, and is recorded as
the total equivalent noise power at the PR antenna output. Missing data are given
the value of -32,734.

(17) sysNoiseWarnFlag [49][nscan] (1-byte integer):
System Noise Warning Flag indicates possible contamination of lower window
noise by high towers of rain. 0 means no possible contamination. If the system
noise level exceeds the noise level limit, the flag is set to 1. This will occur when
(1) a radio interference is received, (2) system noise increases anomalously, or (3)noise level exceeds the limit due to the statistical variation of the noise. In cases(1) and (2), data should be used carefully. In case (3), this flag may be neglected.
Received power levels in all range bins will increase in cases (1) and (2) as muchas the increase of the system noise.

(18) minEchoFlag [49][nscan] (1-byte integer):
This value shows the existence of the rain echo at each angle bin.
Six values are used in the Minimum Echo Flag: 0, 10, 20, 11, 12, and 13.
0: No rain. (Echoes are very weak.)- 34 -

10: Rain possible but may be noise.
(Some weak echoes above noise exist in clutter free ranges.)
20: Rain certain. (Some strong echoes above noise exist in clutter free ranges.)
11: Rain possible but may be noise or surface clutter.
(Some weak echoes exist in possibly cluttered ranges.)
12: Rain possible but may be clutter.
(Some strong echoes exist in possibly cluttered ranges.)
13: Rain possible but probably sidelobe clutter.
(Some strong echoes above noise exist but they are most likely caused bysidelobe clutter.)(19) binStormHeight [2][49][nscan] (2-byte integer):
Range Bin Number of the storm top, which is represented by the logical range binnumber (1 to 400). The Bin Storm Heights are generated in the procedure to
determine the Minimum Echo Flag. The first dimension is threshold, with values ofpossible[10] rain threshold and certain rain[20] threshold in that order. Missing data
are given the value of -9999.

(20) binEllipsoid [49][nscan] (2-byte integer):
The range bin number of the earth ellipsoid, which is represented by the logicalrange bin number (1 to 400). This is calculated by the following equation.
binEllipsoid = RayStart + (scRange - startBinDist)/rangebinSize x 2(21) binClutterFreeBottom [2][49][nscan] (2-byte integer):
The range bin number of the lowest clutter free bin. Clutter free bin numbers are
given for clutter free certain and possible, respectively. The clutter free certain bin
is always less than or equal to the clutter free possible bin number.
binClutterFreeBottom [0][]: clutter free certain,
binClutterFreeBottom [1][]: clutter free probable.
Missing data are given the value of -99.

- 35 -

(22) binDIDHmean [49][nscan] (2-byte integer):binDIDHmean represents the range bin number corresponding to the mean heightof all DID/SRTM30 data samples available in a 5 5km area that overlaps most withthe footprint. Here, DID stands for Digital Terrain Elevation Dataset (DTED)Intermittent Dataset (DID), and SRTM30 stands for Shuttle Radar Topography
Mission 30 arc-seconds. In V7, SRTM30 data were used instead of DID data insome wide area such as Tibet, India, and Andes.

(23) binDIDHtop [2][49][nscan] (2-byte integer):binDIDHtop[0][][] represents the range bin number corresponding to the highest
value (top) of all DID/SRTM30 data samples in a 5 x 5km box, andbinDIDHtop[1][][], the range bin number corresponding to the highest value in a 11x 11km box.

(24) binDIDHbottom [2][49][nscan] (2-byte integer):
The definition is the same as that of binDIDHtop except that the value represents
the lowest value (bottom) of all DID/SRTM30 samples in a 5 5km or 11 11km box.

(25) scLocalZenith [49][nscan] (4-byte float):
The angle, in degrees, between the local zenith and the beam's center line. The
local (geodetic) zenith at the intersection of the ray and the earth ellipsoid is used.

(26) scRange [49][nscan] (4-byte float):
Distance (m) between the spacecraft and the center of the footprint of the beam on
the earth ellipsoid.

(27) osBinStart [2][29][nscan] (2-byte integer):
The first dimension is the Bin Start of Oversample and Surface Tracker Status. The- 36 -

second dimension is the ray. The number of rays is 29 because this information
only applies to the rays that have oversample data (rays 11 to 39). The third
dimension is the scan. The Bin Start of Oversample is the starting range binnumber of the oversample (either surface or rain) data, counting from the top down,
which is represented by the logical range bin number (1 to 400). The Surface
Tracker Status has the value of 0 (Lock) or 1 (Unlock), where Lock means that (1)the on board surface detection detected the surface and (2) the surface detected
later by processing on the ground fell within the oversample bins. Unlock meansthat Lock was not achieved.

(28) landOceanFlag [49][nscan] (2-byte integer):Land or ocean information.
The values of the flag are:0 = ocean
1 = land
2 = coast (not water nor land)
3 = inland water
4 = ocean (surface peak is not correctly detected because of high attenuation)
5 = land (surface peak is not correctly detected because of high attenuation)
6 = coast (surface peak is not correctly detected because of high attenuation)
7 = inland water (surface peak is not correctly detected because of highattenuation)
In the product version 7, two categories are added in the landOceanFlag. The
new flags appear when the land (or ocean) surface position is not correctly
detected because of high attenuation relating to heavy rainfall. This is determinedby the Clutter routine in 1B21. The landOceanFlag is 4 when the surface peak is
not detected correctly over ocean. In this case, binSurfPeak is set at binEllipsoid.
If the phenomena happened over land or coast, landOceanFlag is 5 or 6 and thebinSurfPeak is recalculated using data between the binClutterFreeBottom andbinClutterFreeBottom+8 (bins) toward the Earth.

(29) surfWarnFlag [49][nscan] (2-byte integer):
The topographic mean height (m) of all DID samples in a 5 x 5km.

- 37 -

(30) binSurfPeak [49][nscan] (2-byte integer):
The range bin number of the peak surface echo, which is represented by the logicalrange bin number (1 to 400). This peak is determined by the post observation
ground processing, not by the on board surface detection. If the surface is notdetected, Bin Surface Peak is set to a value of -9999. Note that the echo peak may
appear either in the normal sample data or in the oversample data.

(31) normalSample [140][49][nscan] (2-byte integer):
Received power (dBm) of the normal sample, multiplied by 100 and stored as a
2-byte integer. The units are dBm * 100. Since each angle has a different numberof samples, the elements after the end of sample are filled with a value of -32767. If
a scan is missing, the elements are filled with the value -32734.

(32) osSurf [5][29][nscan] (2-byte integer):
Received power (dBm) of the surface echo oversample for the central 29 rays (raysnumber 11-39), multiplied by 100 and stored as a 2-byte integer. The units are dBm* 100. The PR records the oversampled data in five range bins around the surface
peak detected on board (not Bin Surface Peak) in a total of 29 angle bins (nadir 14
angles, angle bins 11 to 39) to examine the surface peak precisely. If the surface
tracker status is lock-off, the data position is unknown. To use the oversample data,
fill the five data starting at "Bin Start of Over_Surface (osBinStart)" in every otherlogical range bin, then merge with the interleaving normal sample data. If a scan is
missing, the elements are filled with the value -32734.

(33) osRain [28][11][nscan] (2-byte integer):
Received power (dBm) of the rain echo oversample for the central 11 rays (raysnumber 20-30), multiplied by 100 and stored as a 2-byte integer. The units are dBm* 100. The PR records the oversampled data at 28 range bins in a total of 11 angle
bins (nadir 5 angles: angle bins 20 to 30) to record the detailed vertical profile of therain.
The 125m interval dataset in heights from 0 km to 7.5 km can be generated byinterleaving the Normal Samples with the Surface Oversamples and rain

- 38 -

oversamples. The data are merged in the same way as the Surface Oversample.
The osBinStart expresses the start angle bin of rain oversample for the rainoversample angle bins and the surface oversample follows the rain oversample
continuously. Therefore, the logical range bin number of the Surface Oversample
and Rain Oversample is as follows:
Angle bin 11 - 19, 31-39 :Logical range bin number at Nth surface oversample = osBinStart +2(N-1)
Angle bin 20-30:
Logical range bin number at Nth rain oversample = osBinStart+2(N-1):
Logical range bin number at Nth surface oversample= osBinStart+56+2(N-1)- 39 -

1-1. 5.

Major changes in 1B21 algorithm for product version 7

1. Improvement of surface peak range bin number detection algorithm.
This routine is for the cases that the surface echo is fully attenuated by strong
rainfall. In this case, surface peak is searched again using the output from clutter
routine by Dr. Awaka. For the case of ocean, binSurfPeak is replaced bybinEllipsoid.

2. Refurbishment of calibration table
Discontinuity between linear fitting part and parabolic fitting part should becorrected. Modification of calibration table in order to be applicable to the dataaround December 15, 1997, when the NASDA performed initial check out of PR bychanging internal attenuation for various values.

3. Correction for a known error in the receiver calibration factor
It should be about -1.0 dB instead of -0.65dB. (input for 1B21)

4. Data format
Science data and meta data are defined by PPS I/O Toolkit. Some variable names
are renamed and added.

- 40 -

1-1. 6.

Changes in 1B21 after the satellite boost in August 2001

1. Outline of the boost
The TRMM satellite changed its altitude from 350 km to 402.5 km in August 2001 inorder to save the fuel for altitude maintenance. Major impacts of the attitudechange (hereafter boost) on the PR are 1) degradation of sensitivity by about 1.2
dB and 2) occurrence of mismatch between transmission and reception angles for
one pulse among 32 onboard averaging pulses. The latter causes unknown errorof the PR’s data because the mismatch pulse is averaged with other 31- nominal
pulses by onboard processor. In order to mitigate the mismatch error in PR data,
level one algorithm (1B21) added mismatch correction routine.

2. The mismatch correction algorithm in 1B21
The basic idea of the mismatch correction algorithm is to retrieve the power ofmismatch pulse received by PR based on the antenna pattern of mismatch pulse
as mentioned previous section. In the current correction algorithm of mismatch in
1B21 algorithm assumes followings: 1) mismatch pulse power can be expressed as
the average of power from current angle bin and one previous angle bin with 6 dBgain reduction, 2) the one previous angle bin data can be used without correction to
avoid the accumulation of error to the following angle bins, though it contains
mismatch error, and 3) the data of angle bin 1 (the first angle bin each scan)contains 31 normal pulse data and one noise data as mentioned in previous
section.
The correction algorithm is preferred to be expressed by simple equation and be
applied for various occasions such as rain echo and surface echo.
The equation of mismatch correction in 1B21 algorithm is expressed as 10 P  N  / 10  10 P  N 1 / 10    6  31
PcN    32  PN   10  log10

 

2

 

where N is angle bin number (angle bin to be corrected), P(N) is observed power at
a certain range bin of angle bin N in dBm (containing mismatch echo), P(N-1) is theone previous angle bin data of same distance from the PR used as the “reference”,
and Pc(N) is corrected power in dBm. In this equation, since the obtained data is
the result from averaging of 32 pulses, 32 times of P(N) stands for the total
received power.
The estimated correction error is less than 0.2 dB for rain echo and less than 0.3
dB for surface echo.
- 41 -

1-1. 7.

Comments on PR Level 1 products

1. Calibration accuracy
The TRMM Precipitation Radar (PR) has been working without any problem since
the first turn-on of the PR power in the beginning of December 1997 except PR
hardware switch from A-side to B-side on May 2009. The initial checkout of the PR
was completed by NASDA and CRL at the end of January 1998. The overall
calibration of the PR including the transmit and receiving antenna patternmeasurements were made by using an ARC. It was concluded that the ARC
calibration results are reasonable and consistent with the corresponding values
calculated by using the PR system parameters. Also the ocean surface sigma-0
obtained by the PR has been found to be quite consistent with those observed fromprevious airborne and satelliteborne scatterometers.

2. Sensitivity
The minimum detectable Zm (corresponding to the noise-equivalent received
power) improved from 23.3 dBZ (based upon the specifications requirement) to
20.8 dBZ as determined from the pre-launch ground test and from the orbit test.
This is mainly due to the increased transmit power and the decrease of the receivernoise figure. Actually the rain echo power is measured from the subtraction of thesystem noise power from the total receiver power (rain echo power + system noise
power). The accuracy of rain echo power can be characterized by the effective
signal-to-noise ratio (S/N), that is the ratio of mean to standard deviation of rainecho power. By considering these facts, the actual minimum detectable Zm canbe considered to be about 16-18 dBZ after the detailed statistical calculation. The
effective signal-to-noise ratio (S/N) of 3 dB is obtained when Zm is 17 dBZ.

3. Discrimination of rain from surface clutter
It is generally very difficult to discriminate rain echo from surface clutter especiallyin mountainous regions. An algorithm has been implemented which analyzes theradar echo range profile very carefully to determine the boundary between rain andsurface echoes. The result has been reflected into the surface location related
variables described in Item 6. Even though, there is a very small possibility that asurface echo is treated as a rain echo (and in mountainous regions, clutter position
when it rains can happen to become too high in a very rare occasion). Please be- 42 -

careful when you use the PR Level-2 data to study rain structure in mountainous
regions. Strong echoes near the surface are likely surface clutter and should be
excluded from rain analysis.

4. Surface clutter from the coupling between nadir-direction antenna sidelobe andstrong surface radar cross-section (NRCS)
It has been found that the echo strength from nadir direction is sometimes
extremely strong, which exceeds the anticipated value in the PR design. This
seems to occur wet and flat land areas rather than ocean. Even dry dessert regions,
the NRCS seems very strong in some cases. In such cases antenna sidelobes
directed to nadir receive surface echoes. When main beam is off-nadir, the timingof such nadir-surface clutter can contaminate the rain echo. In "PR STATUS2", awarning flag is set ON when the nadir surface echo (at the nadir angle bin, #25)
exceeds a pre-determined threshold. When it is ON, please be careful about theechoes in all angle bins at the same range bin number as the Bin_surface_peak(binSurfPeak) at nadir (angel bin number 25).

5. Discrimination of rain echo from noise
In order to help users utilization of the data, the 1B21 product contains the"Minimum Echo Flag" which indicates the existence of rain in the clutter free range
or in the clutter range. Since thermal noise, rain echo and resulting thermal noise
plus rain echo follow Rayleigh fading, the PR received echo is a result of theaveraging 64 number of independent samples. The averaged value still has small
fluctuations of about 0.7 dB to 1 dB, depending on signal-to-noise ratio. In order not
to miss weak echo which is sometimes useful to study rain structure, etc, thethreshold to set the flag = rain possible is currently about 90% value of the
cumulative distribution of thermal noise. This means quite a large fraction of data
having "rain possible" flag is only thermal noise. Since this rain/no-rain
discrimination is sometimes affected by the surface clutter at especiallymountainous area.
In the clutter region, rain/no-rain discrimination often misidentifies clutter as rain.
Minimum Echo Flag includes clutter flag.
There are five levels in the Minimum Echo Flag; 0, 10, 20, 11, and 12:
0: No rain. (Echoes are very weak.)
10: Rain possible but may be noise.

- 43 -

(Some weak echoes above noise exist in clutter free ranges.)
20: Rain certain. (Some strong echoes above noise exist in clutter free ranges.)
11: Rain possible but may be noise or surface clutter.
(Some weak echoes exist in possibly cluttered ranges.)
12: Rain possible but may be clutter.
(Some strong echoes exist in possibly cluttered ranges.)
13: Rain possible but probably sidelobe clutter.
(Some strong echoes above noise exist but they are most likely caused bysidelobe clutter.)
Therefore please be careful in using the Minimum Echo Flag except 0 and 20.
6. Bin_surface_peak (binSurfPeak) and oversample data
In PR 1B21, the data called Bin_surface_peak indicates the range bin number atwhich PR received power has the maximum within a range window centered at therange bin number determined from a Digital Elevation Model (DID or SRTM30). In
most cases, the Bin_Surface_Peak gives the correct location corresponding to thelocation of actual surface. There may be small number of cases where
Bin_surface_peak is wrong. One possibility a case in which DID/SRTM30 is in error,
and the other is a case in which rain echo is so strong so that surface echo ismasked by the rain echo. We expect those cases are rare, but please keep in mind
those may occur with a small probability.
The oversample data are recorded onboard based on the location of surface echo
peak detected by an onboard surface tracking function. Since this tracker may belocked-off in mountainous regions, there are cases in which oversample data arerecorded outside the location of surface echo. In such cases the oversample data
may not be useful because it may not be used for improving the accuracy of
surface echo power or for detailed study of vertical storm structure. The difference
between the location of surface echo estimated by the onboard tracker (Note 1)
and Bin_surface_peak is a measure of the goodness of oversample data in termsof its covering region in the radar range profile.
Note 1:The surface echo location estimated onboard (Y) can be obtained from
"Bin_start_oversample (osbinStart)" data.
Let X be Bin_start_oversample,
Y = X + 60 or + 61 (angle bins between 20 and 30) and Y = X + 4 or +5- 44 -

(between 11 and 19 and between 31 to 39).
We cannot judge either 60 or 61 (or 4 or 5) from 1B21 itself, however.

7. Interference from other radio services around 13-14 GHz
There have been several cases where PR suffered from interferences from otherradio services, mainly from satellite tracking and control stations using 13-14 GHz
bands. The probability is very small, and the impact to TRMM mission appears tobe negligible. In a typical interference case, the noise level increases a few toseveral decibels over entire range bins for a very short period (one or two scans).
In such a case, PR sensitivity to detect weak echo is degraded accordingly.

- 45 -

1-1. 8.

References

T. Kozu, T. Kawanishi, K. Oshimura, M. Satake, H. Kumagai; TRMM precipitation
radar: calibration and data collection strategies, Proc. IGARSS'94, 2215-2217,
Pasadena, 1994.
M. Satake, K. Oshimura, Y. Ishido, S. Kawase, T. Kozu: TRMM PR dataprocessing and calibration to be performed by NASDA, Proc. IGARSS'95, 426-428,
Florence, 1995.
N. Takahashi and T. Iguchi; Estimation and correction of beam mismatch of the
precipitation radar after an orbit boot of the Tropical Rainfall Measuring Mission
satellite, IEEE Trans. Geo. and Remote Sens., 42, 2362-2369, 2004.

- 46 -

1-1. 9.

DID access routine

1. Objectives
A DID access routine is used in a Level-1 PR algorithm, 1B21. Main objectives of
the DID access routine are:(a) To output the elevation information over a 5 km * 5 km box and an 11 km *11 km box using DID elevation data, with the center for the 5 km * 5 km box
being the same as the center for the 11 km * 11 km box.
(b) To output the land/water information over a 5 km * 5 km box, which is thesame as the 5 km * 5 km box for (a), using DID land/water data.
Note: DID stands for DTED (Digital Terrain Elevation Dataset) Intermediate Dataset.

2. Method used(a) Conversion of DID data having 1 km horizontal resolution to a 5 km * 5
km box and an 11 km * 11 km box.

3.

Flowchart

Opening of DID file

Clear cache memory when the memory is fullAccess 49 angle bins of data at one time

Conversion to 5km * 5km box and 11km * 11km box data
Closing of DID file- 47 -

4.

Some details of the algorithm(a) Height_mean
A mean of DID elevation over a 5 km * 5km box, Height_mean, is computedwith the following weights:
0.014,
0.028,
0.034,
0.028,
0.014,

0.028,
0.055,
0.069,
0.055,
0.028,

0.034,
0.069,
0.088,
0.069,
0.034,

0.028,
0.055,
0.069,
0.055,
0.028,

0.014,
0.028,
0.034,
0.028,
0.014.

(b) Land/water flag
The original land/water information having 7 categories is summarized into
the following information over the 5 km * 5 km box with 3 categories:(1) water if the 5 km * 5 km box has the following categories of data only,- deep ocean,- shallow ocean,- deep inland water,- shallow inland water.
(2) land if the 5 km * 5 km box has the following category only,- land.
(3) mixed if the 5 km * 5 km box includes- both land and water categories, or- at least one pixel is coast, or- at least one pixel is ephemeral inland water.
Computation of other quantities, such as maximum of DID elevation over the
5 km * 5 km box, is straightforward.

5.

Input data(a) DID data set.
(b) latitude/longitude

6.

Output data(a) int Height_mean[49],/* Unit in m (5km * 5km)

- 48 -*/

(b) int Height_max[49][2],(c) int Height_min[49][2],(d) int Hmedian[49],(e) int Hstd[49],(f) int LWflag[49],/* Unit in m (5km * 5km and 11km * 11km)/* Unit in m (5km * 5km and 11km * 11km)/* Unit in m (5km * 5km)/* Unit in m (5km * 5km)/* 0: water, 1: land, 2: coast,/ * 3: inland water

*/
*/
*/
*/
*/
*/

7. Output file specifications(a) int Height_mean[i]:Weighted sum of DID elevation over 5 km * 5 km box.
Unit is in [m].

(b) int Height_max[i][0]:Maximum of DID elevation over 5 km * 5 km box.
Unit is in [m].

int Height_max[i][1]:(c) int Height_min[i][0]:int Height_min[i][1]:

Maximum of DID elevation over 11 km * 11 km box.
Unit is in [m].
Minimum of DID elevation over 5 km * 5 km box.
Unit is in [m].
Minimum of DID elevation over 11 km * 11 km box.
Unit is in [m].

(d) int Hmedian[i]:Median of DID elevation over 5 km * 5 km box.
Unit is in [m].

(e) int Hstd[i]:Standard deviation of DID elevation over
5 km * 5 km box. Unit is in [m].

(f) int LWflag[i]:Land/water flag for 5 km * 5 km box.
LWflag[i] = 0: water,
1: land,
2: coast,
3: inland water.

where i runs from 0 to 48 (in C language).

8.

Interfaces with other algorithms

1B21 outputs some results of the DID access routine with the height being- 49 -

converted to the range bin number. 1B21 outputs the followings:===== In C language =====
int16

binDIDHmean[i]:Range bin number for Height_mean[i],int16binDIDHtop[i][0]:Range bin number for the maximum of DID
elevation over 5 km * 5 km box,

int16

binDIDHtop[i][1]:Range bin number for the maximum of DID
elevation over 11 km * 11 km box,

int16

binDIDHbottom[i][0]: Range bin number for the minimum of DID
elevation over 5 km * 5 km box,

int16

binDIDHbottom[i][1]: Range bin number for the minimum of DID
elevation over 11 km * 11 km box,

int16

landOceanFlag[i]:Land/water flag for 5 km * 5 km box,
plus additional information

where i runs from 0 to 48 and the range bin numbers are those for 125m
intervals.

===== In FORTRAN language =====INTEGER*2

binDIDHmean(j):Range bin number for Height_mean(j),INTEGER*2

binDIDHtop(1,j):

Range bin number for the maximumof DID elevation over 5 km * 5 km box,

INTEGER*2

binDIDHtop(2,j):

Range bin number for the maximumof DID elevation over 11 km * 11 km box,

INTEGER*2

binDIDHbottom(1,j): Range bin number for the minimumof DID elevation over 5 km * 5 km box,

INTEGER*2

binDIDHbottom(2,j): Range bin number for the minimumof DID elevation over 11 km * 11 km box,

INTEGER*2

landOceanFlag(j):Land/water flag for 5 km * 5 km box,
plus additional information.
- 50 -

where j runs from 1 to 49 and the range bin numbers are those for 125m
intervals.
9. SRTM30 patch to DID access routine
A patch to DID access routine is added in V7. In the patch, SRTM30 elevation
data are used instead of DID elevation data. The patched area includes overIndia, over Tibet, and over South America.
10.

Special notes (caveats)

None.

11.

References

None.

- 51 -

1-1 10.
1.

Main-lobe clutter rejection routine

Objectives of main-lobe clutter rejection routine

A main-lobe clutter rejection routine is developed to be included in the Level 1 PR
algorithm 1B21. The main objective is:(a) Determination of the boundary of clutter free region, where the clutter means
the main-lobe surface clutter.

2. Method used(a) Examination of the slope of Z profile at the top of surface clutter.

3.

Flowchart
Detection of phenomenon A(see Note 1)
Set offset for phenomenon A
and phenomenon G (see Note 2)
Determination of an upper bound for the height ofsurface clutter by an empirical formulausing DID/SRTM30 elevation information
Determination of the starting pointfrom which the slope of Pr is examined
Refinement (a kind of patch)
Determination of the clutter free bottom- 52 -

Note 1:

Description of phenomenon A and phenomenon G.

Phenomenon A:
Detected position of surface peak is too low from the actual position because of
inaccurate DID/SRTM30 elevation data, which indicates a too low height. Thisphenomenon was first observed in the data over the Andes area.
Phenomenon G:
Detected position of surface peak is too high from the actual position because of
inaccurate DID/SRTM30 elevation data, which indicates a too high height. Thisphenomenon was first observed in the data over the Guiana Highlands.
Note 2: Detection of phenomenon G is already made before the clutter rejection
routine is used in 1B21.

4.

Outline of the algorithm(a) Detection of phenomenon A:
When the radar echo at and around binSurfPeak, which is detected by surface
peak detection routine of 1B21, shows that the echo is eventually noise, there may
exist the following three possibilities:(1) Phenomenon A can occur due to an inaccuracy of DID/SRTM30
elevation data,(2) Strong attenuation makes the radar echo at and around binSurfPeak
very small, indistinguishable from noise,(3) The radar echo at and around binSurfPeak is actually very small
because of a specular reflection over a very flat surface when theantenna beam points away from the nadir direction.
When the radar echo at and around binSurfPeak is very small to beindistinguishable from noise, a search is made upper-wards until an appreciableecho is detected. If the appreciable echo has a peak and has a large slope at thebottom part of the peak, which is typical to the surface clutter, it is judged that thephenomenon A occurs.
(b) Offset:
Since the clutter rejection code is written in such a way to consult the DID/SRTM30- 53 -

elevation, offset is needed when phenomenon A or G occurs.

(c) Upper bound for the height of surface clutter:
Empirical upper bound for the height of surface clutter is obtained by using(i) nominal clutter offset for a flat surface,(ii) maximum height of DID/SRTM30 elevation over an 11 km * 11 km box.
(d) Starting position of the examination of slope:
A point where the received power, Pr, is 10 dB larger than the noise level is usedas the starting point from which the slope is examined. If the 10 dB up point is notfound, the empirical upper bound obtained by (c) is used as the starting point.
(e) Determination of the clutter free bottom:
First, whether the starting point obtained by (d) belongs to a rain region or not is
examined; if the echo above the starting point has appreciable value and slope issmall, it is judged that the starting point belongs to a rain region. If the starting
point belongs to a rain region, climb 'up' the surface peak until the slope becomesvery large, which is typical to the surface clutter. On the contrary, if the starting
point does not belong to a rain region, climb 'down' the surface peak as long as theslope is large.

5.

Input data
float normalSample_in[49][140],/* unit [dBm]; L1b21swathdata->normalSample */float osSurf_in[29][5],/* unit [dBm]; L1b21swathdata->osSurf*/

float osRain_in[11][28],/* unit [dBm]; L1b21swathdata->osRain

*/

int

/* L1b21swathdata->osBinStart*/

float systemNoise_in[49],/* unit [dBm]; L1b21swathdata->systemNoise*/

float zenith[49],/* unit [deg]; L1b21swathdata->scLocalZenith*/

float lat[49],/* unit [deg]*/float lon[49],/* unit [deg]*/float scRange[49],/* unit [m]; L1b21swathdata->scRange*/

int rayStart[49],/* L1b21header->rayHdr[].rayStart*/

osBinStart[29][2],- 54 -

int binEllips[49],/* L1b21header->binEllipsoid

int binSurfP_in[49],int Height_mean_in[49],/* L1b21swathdata->binSurfPeak*//* unit [m];*//* Mean of DID/SRTM30 elev. (5 km box)*//* unit [m];*//* Max. of DID/SRTM30 elev. [0]: 5 km, [1]: 11 km*//* unit [m];*//* Min. of DID/SRTM30 elev. [0]: 5 km, [1]: 11 km*//* unit [m];*//* Median of DID/SRTM30 elev. 5 km * 5 km*/

int Hstd[49],/* unit [m]; RMS dev.

*/

int LWflag[49],/* DID land/water/coast flag;

*/

/*

*/

int Height_max_in[49][2],int Height_min_in[49][2],int Hmedian_in[49],6.

*/5km * 5km

= 0: water (ocean),/*

1: land,*//*

2: coast,*//*

3: inland water.

*/

Output data
int binClutterFreeBottom[49][2],int ist[49].

/* bin number with 125 m resol.

*//* (valid range: 1 - 400, and -99)*//* status for each bin.

*/

/*

*/

ist[i] = 0: normal,/*

1: missing data input and/or/*

data corruption,

*/
*/

/*

2: bug (please notify author), *//*3: DID/SRTM30 elev. doubtful, *//*4: binSurfPeak doubtful- 55 -*/

/*

maybe due to large ATT,/*

5: binSurfPeak doubtful

/*

*/
*/

but not so serious as ist=4. */7. Output file specifications
The algorithm 1B21 outputs binClutterFreeBottom[49][2]:==== In C language ====
int16 binClutterFreeBottom[49][2]:binClutterFreeBottom[i][0]: range bin number (with 125 m interval)
for clutter-free-bottom certain
binClutterFreeBottom[i][1]: range bin number (with 125 m interval)
for clutter-free-bottom possible
where i stands for angle bin number running from 0 to 48, andbinClutterFreeBottom[i][0] <= binClutterFreeBottom[i][1]==== In FORTRAN language ====INTEGER*2 binClutterFreeBottom (2,49)
binClutterFreeBottom(1,j): range bin number (with 125 m interval)
for clutter-free-bottom certain
binClutterFreeBottom(2,j): range bin number (with 125 m interval)
for clutter-free-bottom possible
where j stands for angle bin number running from 1 to 49, andbinClutterFreeBottom(1,j) <= binClutterFreeBottom(2,j)

8.

Interfaces with other algorithms

The clutter information, binClutterFreeBottom[49][2], is included in the output of- 56 -

1B21 and 1C21 HDF files: binClutterFreeBottom[49][2] is used by Level 2
algorithms which need the main-lobe clutter information.

9.

Special notes (caveats)

Though SRTM30 patch is introduced in the product-ver. 7(V7), there still remains
the chance of occurring bad clutter free bottom (the occurrence of bad clutter freebottom is estimated to be less than 1 %, but not zero). Tibet and Andes are themost suspicious regions where bad clutter free bottom would still occur.
Main changes made in the V7 are as follows:(a) Only normal sample data are used,(b) In V7, binClutterFreeBottom is raised by the amount of one normal
range bin when compared to that in V7 on average.

10.

References

None.

- 57 -

1-1. 11.

Redefinition of the Minimum Echo Flag

1. Introduction
After the TRMM satellite was launched, it was found that sidelobe echoes from thesurface at nadir appeared in the radar received signal and that they sometimes
were misidentified as rain echoes. In order to decrease the number of such
misidentifications, the algorithm for defining the minEchoFlag was modified. A
new algorithm was added to redefined the minEchoFlag by using the radar echo
signals after removing some of the possible sidelobe echoes. The following
section describes the algorithm to remove sidelobe echoes from the original radar
echoes for this purpose.
Note, however, that the modified radar echoes are used only for this purpose
internally, i.e., to redefine the minEchoFlag in 1B21, and that the output data from
1B21 are original radar echoes.
Note also that since the parameters for the removal of sidelobe surface echoes arechosen in a conservative way in order not to miss a real rain echo, some of thesidelobe echoes remain to be identified as rain echoes.

2.

Sidelobe removal algorithm

The Precipitation Radar (PR) occasionally observes exceptionally large surface
echoes at nadir. Since the PR sensitivity turned out to be better than the minimum
requirement, a weak surface echo that is picked up by a sidelobe in the nadir
direction appears occasionally in the echo region above the surface when themainlobe is pointed offnadir. Such sidelobe surface echoes are sometimes
identified as rain echoes if they are strong and appear in successive range bins.
Since the sidelobe echoes are caused by the reflection of sidelobe signal at nadir,they appear only at the range equal to the nadir range to the surface regardless ofthe mainbeam direction. Although the magnitudes of the sidelobe echoes
naturally correlate with the magnitude of the mainlobe echo at the nadir, the ratio
fluctuates substantially from one scan to another. In fact, the sidelobe echoes atdifferent angle bins in a single scan do not correlate very well, either. Therefore, it
is not possible to estimate the magnitudes of the sidelobe echoes from themainlobe nadir return power and to subtract them from the radar echoes at slant
incidence angles to remove the sidelobe echoes.
The basic strategy of the sidelobe removing algorithm adopted is as follows:(1) Find a peak echo around the range corresponding to the nadir surface
range,- 58 -

(2) If this peak value is higher than the signal threshold and if the signals at 500
m above and 500 m below the peak are lower than the threshold, this peakecho and adjacent range bin echoes are identified as sidelobe clutter
echoes.
(3) The data identified as sidelobe clutter are replaced by the interpolated data.
However, there are exceptions:(4) Near the center of swath, the sidelobe range bin is too close to the surface
and the bin 500 m below it is totally contaminated by the mainlobe clutter.
In such an angle bin, only the comparison with the data above the expectedsidelobe bin is made (in a rather conservative way to avoid missing a true
rain echo).
(5) Except around the center of swath, the signal at the same height in theadjacent (inward) angle bin is also compared with the threshold, and unless
this signal is smaller than the threshold, the original peak is not identified assidelobe echo. This procedure is included to avoid misidentifying the brightband echo as a sidelobe echo.

3.

Redefinition of minEchoFlag

With the data modified in the way explained above, the new algorithm runs theminimum echo detection routine with the rain certain threshold in the same way as
the standard routine. If the result is low (not rain certain) and if the original
minEchoFlag=20 (rain certain), then the added routine replaces the minEchoFlag
of 20 by 13. If the result is high (rain certain) and if the original minEchoFlag=20,
then it keeps minEchoFlag as 20 but replaces the binStormHeight for rain certainby the range bin number at which the rain certain flag is first set with the modified
data.

- 59 -

1-2.

1C21: PR radar reflectivity

1-2. 1.

Algorithm Overview

The 1C21 calculates the effective radar reflectivity factor at 13.8 GHz (Zm) without
any correction of propagation loss (due to rain or any other atmospheric gas).
Therefore, the Zm value can be calculated just by applying a radar equation forvolume scatter with PR system parameters. The noise-equivalent Zm is about 21
dBZ. Through the subtraction of the system noise, the Zm value as small as 16 or
18 dBZ are still usable although the data quality is marginal. In 1C21, all echoes
stored in 1B21 are converted to "dBZ" unit.
This is not relevant for "non-rain" echo; however, this policy is adopted so that the
1B21 and 1C21 product format should be as close as possible except for thefollowing points:
Radar quantity is Zm in dBZ unit instead of received power (dBm).
Data at echo-free range bins judged in 1B21 are replaced with a dummy
value.

1-2. 2.

File Format

The 1C21 product is written in Hierarchical Data Format 4 (HDF4) as same with
1B21.

1-2. 3.

Structure of output variables

The structure of output variables is exactly the same as that of 1B21.

1-2. 4.

Detailed description of output variables

The main output of the PR Level-1C, 1C21, is the radar “reflectivity factor.”
All variables are copy of 1B21 products except for the replacement of the received
power by the radar reflectivity factor and noise (no echo range bin) by a dummy
value.
(31) normalSample [140][49][nscan] (2-byte integer):
Radar reflectivity factor (dBZ, mm6/m3) of the normal sample, multiplied by 100
and stored as a 2-byte integer. The units are dBZ * 100. For example, -9436- 60 -

represents –94.36 dBZ.
The radar equation used isPr(range) 

3 K

2

Pt  Gt  Gr  along  cross  c  pulse 1Zm
2 ln2
wavelength 2
range 210

dBZm  10log 10  Ps/10   10  Pn/10   C  20log(range)

Ps: 1B21 received power
Pn：1B21 noise level
range：DistanceC  Pt  Gt  Gr  10log along  cross   10log c  pulse   20log wavelength   C0
Pt: transmitter power (in power）
pulse：transmitter pulse width (in power）
Gt: transmit antenna gain (in ray header）
Gr: receive antenna gain (in ray header）
along：Along-track beam width (in ray header）
cross：Cross-track beam width (in ray header）
c：speed of lightwavelength：wave length (in ray header）
C0:Radar Constant (in ray header)If received power is below the noise level, the reflectivity is filled with a dummy
value of -32700.
*Note that the radar reflectivity factors given in 1C-21 are apparent values and include rain
or atmospheric attenuation.

(32) osSurf [5][29][nscan] (2-byte integer):
Radar reflectivity factor (dBZ, mm6/m3) of the surface echo oversample for thecentral 29 rays (rays number 11-39), multiplied by 100 and stored as a 2-byte
integer. The units are dBZ * 100.
(33) osRain [28][11][nscan] (2-byte integer):
Radar reflectivity factor (dBZ, mm6/m3) of the rain echo oversample for the central
11 rays (rays number 20-30), multiplied by 100 and stored as a 2-byte integer. The
units are dBZ * 100.
- 61 -

1-2. 5. Major changes in 1C21 algorithm for product version 7
1. Data format
Science data and meta data are defined by PPS I/O Toolkit. Some variable names
are renamed and added.

- 62 -

2.

Level 22-1.

2A-21: Surface Reference Technique (Version 7)

2-1. 1.

Objectives and functions of the algorithm

The primary purpose of 2A-21 is to compute the path-integrated attenuation (PIA) using thesurface reference technique (SRT). The surface reference technique rests on the assumptionthat the difference between the measurements of the normalized surface cross section
outside and within the rain provides an estimate of the PIA. The secondary purpose of 2A-21
is to compute the normalized radar cross sections (σ0 or NRCS) of the surface under rain-free
conditions.
A spatially or temporally averaged estimate of the rain-free normalized radar surface crosssection (σ0 or NRCS) is used as a reference value for computing the PIA. The algorithm
computes up to five alternative estimates of PIA (corresponding to five different σ0 reference
estimates, one temporal and up to four spatial). An effective PIA is obtained by weighting
the individual estimates by a factor proportional to the inverse of the variance of the estimate
and summing the results. Some of the reference estimates depend on the direction ofprocessing, so the orbit is processed twice—in the forward direction, and again backwardwith respect to the orbital direction. This provides two reference values for the
direction-sensitive methods. The estimates used are listed below:
Along-track Spatial Average: This is formed from an average of the Ns most recent
rain-free σ0 measurements in same angle bin and with the same surface type (currently Ns=8).
In version 7, two values of this reference are obtained by running the orbit forward andbackward.
Hybrid or Cross-Track: The hybrid reference data results from a quadratic fit of thealong-track spatial average data over the 49 angles bins within the cross-track swath. In
version 7, separate fits are done for the inner (less than 11.25°) and outer swath (greater than
11.25°). As with the along-track spatial reference, the cross-track hybrid is computed twice
by processing the orbit forward and backward.
Temporal Average: In versions prior to version 7, the temporal average was computed as
the monthly average of the rain-free σ0 data at 1°×1° latitude-longitude cells, categorized
into 26 incidence angles 0.75°  j, j=0,..,24 where a 26th category is defined to account forincidence angles beyond 18°. In version 7, the temporal reference data set are provided at a
0.1°0.1° latitude-longitude resolution where the data sets have been computed off-line foreach month using 12 years (1998-2009, inclusive) of rain-free σ0 measurements. As inprevious versions, the data are categorized into 26 incidence angles. Unlike earlier versions,however, three 0.1°0.1° files are computed for each month (for a total of thirty-six temporalreference files) for land, ocean and coastal backgrounds.
Different estimates for along-track and hybrid methods are obtained from forward andbackward processing. This provides up to five estimates of path attenuation—Forward
Along-track, Forward Hybrid, Backward Along-track, Backward Hybrid, andTemporal—for each rain observation. Note that the hybrid estimates are only available overocean since the cross-track fitting procedure does not work well over land. The different
reference estimates are filtered according to various criteria. For example, an along-track
estimate is dropped if the location of the reference data is too far from the observed rain

- 63 -

point. A temporal estimate is dropped if the number of prior rain-free observations in thereference cell is too few. The surviving estimates are weighted by the inverse of theirassociated variance. The weighted estimates are summed to yield an effective PIA,
pathAtten. The individual estimates, PIAalt, and their weights, PIAweight, areincluded in the 2A-21 product. A discussion of the weights and the effective PIA, variance,and reliability factor is given in section 9.
In addition to the sample mean of the NRCS as a function of angle bin, the reference data
sets also include the standard deviation and number of data points used to compute thesample mean.
The temporal surface reference data sets were computed from version-6 2A-21
sigmaZero data for each month for the 12 years 1998 to 2009 inclusive. Separate data sets
were computed for Ocean, Land, and Coast surface types so that a total of 36 temporalreference files are obtained. The statistics were computed over a 0.1°×0.1° (latitude,
longitude) grid. Within each 0.1°×0.1° cell, the data are further categorized into incidence
angle categories (26). The mean, standard deviation, and number of observations in eachcategory is recorded. In summary, 36 temporal reference files have been generated each withdimension (740, 3600, 26, 3) which correspond to the number of latitude, longitude,
incidence angles, and statistical bins (mean, standard deviation and counts), respectively.
Note that in the temporal reference data set no distinction is made between the port andstarboard incidence angles so that instead of 49 incidence angles, there is only 25+1, where
the additional bin is used to store data from angles outside the normal range.
In version 6, the temporal data set was computed over the previous month during regular
2A-21 processing. The latitude-longitude resolution was 1°×1°, and there was no
ocean-land-coast surface type distinction so that only one (rather than three) reference data
set was generated.
In the spatial (along-track) surface reference data set, the mean and standard deviation of the
NRCS are calculated over a running window of Ns fields of view before rain is encountered(currently, Ns=8). These operations are performed separately for each of the 49+2 incidence
angles of TRMM, corresponding to the cross-track scan from -18° to +18° with respect tonadir. The 2 additional angle bins (making the total 51 rather than 49) are used to account for
non-zero pitch/roll angles that can shift the incidence angle outside the normal range. Notethat the zenith angle increment is taken to be 0.75° so that the angle bins can be defined by0.75°  j, j=0,..,24.
When rain is encountered, the mean and standard deviations of the reference σ0 values are
retrieved from the along-track spatial (forward and backward), the hybrid (forward andbackward) and temporal surface reference data sets.
If a valid surface reference data set exists for one of the above estimates, then, denoting thisby the jth estimate, the 2-way path attenuation (PIA) for the jth estimate is computed fromthe equation:
0
PIA j   NR

j

 0

where <σ0NR>j is the jth reference estimate and σ0 is the value of the apparent normalized
radar surface cross section at the rain field of view of interest. The PIA(2-way) is related- 64 -

to the specific attenuation or attenuation coefficient k (dB/km) by the equation:rs

PIA(2 - way)  2  k ( s )ds
0

To obtain information as to the reliability of the jth PIA estimate we consider the ratio of
the PIA, as derived in the above equation, to the standard deviation as calculated from therain-free σ0 values and stored in the reference data set. Labeling this as std_devj(reference
value), then the reliability factor of the jth PIA estimate is defined as:

reliabFactorj 

PIA j
std_dev j (reference value)

When this quantity is large, the reliability is considered high and conversely.

The effective PIA, PIAeff, and the corresponding reliability factor can be expressed in similar
ways. From section 9, we have:
PIAeff  (u j ) 1 u j PIA j
Rel eff  (u j ) 1 / 2 u j PIA j

Where uj is the inverse of the variance, j2, associated with the jth reference data set:u j  1 /  2j

The summations are assumed to range over all valid reference data sets, even if the PIA’s arenegative. Over land, there can be a maximum of 3 valid reference data sets (forward andbackward along-track and temporal) while over ocean there can be as many as five since theforward/backward hybrid reference data sets may be valid as well. It is worth mentioningthat the definitions for the effective PIA and reliability factor reduce to those for theindividual estimate when only a single PIA estimate is available. Note, finally, that in thenotation used above: j  std _ dev j (reference _ value)

2-1. 2.

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 (unitless).

- 65 -

pathAtten(49) [real*4]
Estimated 2-way path-attenuation in (dB) where
rs

pathAtten  2  k ( s )ds0

where k(s) is the attenuation coefficient 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.
In the notation used above and in section 9:
pathAtten  PIAeff  (u j ) 1 u j PIA j

Where uj is equal to the inverse of the variance associated with the jth estimate of thePIA:
u j  1 /  2j

PIAalt(5,49) [real*4]
The path-integrated attenuation from the jth estimate, where
PIAalt(j=1, k)= PIA from forward along-track spatial at kth angle bin
PIAalt(j=2, k)= PIA from forward hybrid at kth angle bin
PIAalt(j=3, k)= PIA from backward along-track spatial at kth angle bin
PIAalt(j=4, k)= PIA from backward hybrid at kth angle bin
PIAalt(j=5, k)= PIA from temporal at kth angle bin
PIAweight(5,49) [real*4]

These are the weights of the individual PIA estimates used in deriving theeffective PIA. The sum of the weights should equal one.
wj 

1

 
2
j

1
 u j / u j
1

 2j

where
u j  1 /  2j

w 1
j

reliabFlag(49) [integer*2]
Reliability Flag for the PIAeff estimate,- 66 -

= 1 (PIAeff 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)reliabFactor(49) [real*4]
Reliability Factor for the effective PIA estimate, pathAtten. This is defined as:
reliabFact or  Rel eff  (u j ) 1/ 2 u j PIA j

RFactorAlt(5,49) [real*4]
The reliability factors associated with the individual PIA estimates.

RFactorAltj  Rel j  PIAj /  j ; j  1,...,5
rainFlag(49) [integer*2]

Rain/no-rain flag (rain=1; no-rain=0). The rain-possible category from 1B-21 isincluded in the no-rain category; only the rain-certain category is considered rain.
incAngle(49) [real*4]

Incidence angle with respect to nadir (in degrees); pitch/roll correction is included.
refScanID(2,2,49) [integer*2]
refScanID gives the number of scan lines between the current scan and the

beginning (or end) of the along-track reference data at each angle bin. The values
are computed by the equation: Current Scan Number - Reference Scan
Number. The values are positive for the Forward estimates and negative for the
Backward estimates. The Fortran indices are:
1,1 - Forward - Near reference
2,1 - Forward - Far reference
1,2 - Backward - Near reference
2,2 - Backward - Far reference
refMethodFlag(49) [integer*2][This flag is currently not used. The output variable PIAweight can be used toobtain the influence of an individual PIA on the effective PIA.].
surfaceTracker(49) [integer*2]= 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)- 67 -

surfTypeFlag(49) [integer*2]= 0 (ocean)= 1 (land)= 2 (coast)= 3 (unknown or of a category other than those above or ‘mixed’ type)2-1. 3.

Description of the Processing Procedure

In v7, the granule is processed twice, in the forward orbit sequence, and again backwards.
This is done because the along-track and hybrid methods use rain-free reference
observations near the rain observation. By processing the orbit backwards, an independent
estimate of rain attenuation is obtained. This gives up to 5 estimates that can be combined orfiltered to select a “best” estimate. The five estimates are Forward Along-track, Forward
Hybrid (Ocean only), Backward Along-track, Backward Hybrid (Ocean only), andTemporal.

2-1. 4.

Interfaces to other algorithms

All input data for this algorithm is from 1B-21; the outputs are used by 2A-25, 3A-25 and3A-26.

2-1. 5.

Comments and Issues

a. A Gaussian beam approximation is used to represent the TRMM antenna pattern.
b. The radar return power used in computing σ0 is that for which a 2.5 dB correction has
been made. The factor accounts for the logarithmic averaging loss. Like the rain, thesurface is treated as a Rayleigh target.
c. σ0 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/10 = 2 (raincertain); minEchoFlag/10 = 1 (rain possible) and minEchoFlag = 0 (rainabsent) are treated as no-rain cases. Note that the minEchoFlag variable is readfrom 1B-21.
e. Before version 6, images of path attenuation from 2A-21 sometimes showed astriated or streaky pattern where the attenuation estimates at one or more angles arelarger than the estimates at adjacent angles. This occurred more often at near-nadir
angles where high values of the surface cross section are observed under rain-free
conditions. Where it is used, the cross-track-spatial hybrid method appears toeliminate most of these streaky patterns. As pointed out by Seto and Iguchi (2007),
however, the quadratic function does not provide a good fit to the data over the fullswath. In version 7, separate quadratic fits for the inner swath (angles less than
11.250) and outer swath (angles greater than 11.250) are used to improve the fitting
function.
f. In previous versions of the algorithm (versions 1-4) the reliabFactor was
defined as the difference: pathAtten - std_dev(reference value). In version 5- 68 -

and 6, reliabFactor is defined as the ratio: pathAtten/std_dev(reference
value).
g. Prior to version 6, when the PIA < 0, pathAtten was set to 0.0. reliabFactor,
which in version 5 is proportional to PIA, was computed before pathAtten was
set to 0, so it could be negative; pathAtten was never less than zero. In versions 6
and 7, pathAtten is no longer set to zero. Negative values are possible, although
they will always be marked unreliable in the reliabFlag.

2-1. 6.

Description of Temporal Intermediate File

In version 7, three temporal files (for Ocean, Land, and Coast) were computed for eachmonth by averaging rain-free surface cross sections from 12 years of version 6 data. The
statistics are computed as a function of incidence angle (26 categories) and location(0.1°×0.1° latitude-longitude grid). The statistics include mean, standard deviation, andnumber of counts.

2-1. 7.

The Cross-track or Hybrid Surface Reference Method

In version 7, cross-track fitting of the data is done in the forward and backward directions for
ocean surfaces. Cross-track fitting is not used for land or coast. Unlike version 6, separate
cross-track fits are done for the inner (less than 11.25°) and outer swath (greater than
11.25°).
The input data for the cross-track fits are obtained from the spatial average for each angle bin.
As in the along-track method, the average is computed from the last 8 rain-free observations
over the same background type (i.e., ocean, land, or coast). The standard deviation from thespatial average is used as a weight in the fitting procedure. The fitted function is a quadratic
where the fitting routine is based on the LFIT routine from Numerical Recipes (Press, et. al.,1989).
The spatial average at the ith angle bin is the average of the last 8 rain-free surface
reflectivity values, σ0NR,0y i   NR
( i )

and, using “AS” to denote the along-track spatial reference, the standard deviation
is0
S AS ( i )  var( NR( i ))

The fit function for both the inner and outer swaths is the quadraticyfit( i )  a  b i  c i2

Letting j1 and j2 denote the angles -11.250 and 11.250 with respect to nadir, then for the
inner swath, the parameters a, b, and c are determined by minimizing- 69 -

 y  yfit( i )     i
S AS ( i ) i  j1 2

j2

2

A similar minimization is carried out over the angles from -180 to -11.250 and 11.250 to 180
249 y  yfit( i )  y  yfit( i )     i
    i
S AS ( i )  i j 21  S AS ( i ) i 1 
2

j11

2(In practice there is a 2-bin overlap between the fits of the inner and outer swaths to ensure
continuity.) The (2-way) cross-track or hybrid PIA is the difference between the Surface
Reference value, yfit(θi), and the apparent (attenuated) surface cross section, σ0i:
Ai  yfit( i )   i0

The standard deviation associated with this estimate is taken to be
std _ dev( S AS ) 

1 49 2
 S AS ( j )49 j 1

so that the reliability factor associated with the cross-track method is given byreliabFactor 

2-1. 8.

Ai
std _ dev( S AS )Revised Angle Bin Definitions

2A-21 defines two angle bins. The first, angle1, is computed from the absolute value of theincidence angle, and is used to categorize observations for the temporal Surface Reference
Technique (SRT). It ranges from 1 to 26 (Fortran array convention). The other angle bin,angle2, depends on the signed incidence angle, and is used for the spatial SRT. It ranges
from 1 to 51.
The angle bins angle1 and angle2 are defined such that

angle1 1 0.5    angle11 0.5angle2  26  0.5    angle21 0.5
where θ is the incidence angle and Δθ is the angle bin size.

- 70 -

These relations can be expressed more simply by 
angle1 int  1 0.5


 

angle2  int  26  0.5respectively.
There was a problem with the implementation of this algorithm before version 6: Δθ was
defined as the cross-track beam width, which is read from the 1B-21 Ray Header. The beam
positions (as opposed to the beam width) are uniformly spaced with equal steps of 0.75°.
One effect of the old angle bin definition is that the angle bins were not uniformly populated.
In general, each scan should have one beam position in each “angle2 bin” except for the
extra edge bins (1 and 51). In fact, some bins were under-populated and some wereover-populated because the angle bins did not correspond with the actual beam spacing.
In versions 6 and 7 of the 2A-21 algorithm, Δθ has been set to a constant value of 0.75°.

2-1. 9. Definitions of the Effective PIA, Variance and Reliability
FactorIn version 7 of 2A-21, multiple estimates of PIA are generated. These correspond todifferent surface reference estimates – i.e., the estimate of the rain-free NRCS or °NR.
Specifically, we have the following situation
0
PIAj   NR

j

 0

(1)

where the first term on the right-hand side is the jth surface reference value and the second
term is the apparent NRCS in rain. Note that there are as many as five reference values,
corresponding to forward along-track, forward hybrid (cross-track), backward along-track,backward hybrid (cross-track) and temporal. Over land and coast, however, only three
are used since the hybrid approach is not reliable. Associated with the jth reference data
set is a variance, j2:
0
var(PIAj )  var[  NR]   2j

(2)

j

From these PIA estimates we want to obtain an effective PIA.
written in the form:

PIAeff  w j PIAj

We assume it can be(3)

Where the weights, wj, are such that- 71 -

w j  1

(4)

We assume that the individual PIA estimates are statistically independent so that thevariance of PIAeff is:var( PIAeff )  w 2j  2j

(5)

To minimize this, subject to the side condition given by (4), we use the method of
Lagrange multipliers where the expression
w2j  2j   (w j  1)

(6)

is minimized with respect to the weights, wj.
with respect to wi, thenTaking the partial derivatives of (6)2wi i2    0  wi   / 2 i2(7)Also, using (4) gives
w j   ( / 2) (1 /  2j )  1    2 / (1 /  2j )(8)

Substituting (8) into (7) gives an expression for the weights:
wj 

1

 
2
j

1
 u j / u j
1

(9)

 2j

Where
u j  1 /  2j

(10)

The effective PIA is thenPIAeff  (u j ) 1 u j PIA j(11)

In previous versions of 2A-21, the reliability factor, Rel, was defined as the ratio of the
PIA to the standard deviation of the reference estimate, so that for the jth reference
estimate, we can write:

Rel j  PIAj /  j(12)

To apply this definition to the present situation, we define Releff by the equation:- 72 -

PIAeff  (u j ) 1 u j PIA j   eff Rel eff(13)

Computing Releff requires a value for the standard deviation of the effective PIA. Thiscan be found by substituting (9) into (5) and by noting that eff2 = var(PIAeff). This gives
1 /  eff2  (1 /  2j )   eff2  ((1 /  2j )) 1  (u j ) 1

(14)

Using (14) in (13) gives
Rel eff  (u j ) 1 / 2 u j PIA j(15)

Equations (9), (11) and (15) define, respectively, the weights, effective PIA, and effective
reliability factor as computed in version 7 of 2A-21.
There are several issues related to these equations. For example, what should be done if
none of the reference data sets exist? This situation can occur for measurements oversmall islands or small bodies of water or at coastal fields of view. For example, over asmall island, there may be an insufficient number of non-raining fields of view adjacent to
the rain area to form a valid spatial reference. In most cases, the temporal reference data
set would be used (j=1 in the above equations) and the other reference estimates would bediscarded. However, in some cases, there may be an insufficient number of data points inthe temporal file to provide a valid estimate. In this case, a flag is set indicating that novalid reference data are available and all the output variables are set to -999. (Definitionsof valid spatial and temporal reference data sets are discussed in sections 10 and 11
below.)
A somewhat different situation occurs if some of the reference data sets exist but all yield anegative PIA. For these cases, the individual variances will exist so that Releff, PIAeff andthe effective variance should all exist. Note that for these cases Releff, PIAeff will be
negative but the effective variance will be positive, as it should be.
A third type of situation occurs if one or more of the PIA estimates are positive and one ormore of the PIA estimates are negative. In this case, the negative PIAs will be includedin the definition of PIAeff. In general, as long as the reference data is considered to bevalid, the PIA will be used even if the value is negative.
According to these scenarios, there will be only one type of raining situation where theoutput variables will need to be set to some default value and this occurs when none of thereference data sets exist or are valid. This is expected to be a very small fraction relative
to the total number of rain cases.

- 73 -

2-1. 10. Excluding Spatial Reference Data based on the
refScanID VariableThis section addresses the conditions under which the spatial reference estimate is taken to
be valid. For the forward-going spatial reference, reference data will almost always
exist. An exception is if rain is encountered at the beginning of the orbit before Ns (=8)
rain-free fields of view have been measured at a particular incidence angle. A similar
exception occurs for the backward spatial methods: this occurs, however, at the end of
the orbit rather than the beginning. In all other cases, forward and backward spatialreference data should exist. The question is how to exclude a spatial reference estimate if
the data, used to form this estimate, are taken at locations far from the raining area. To
implement this, the variable refScanID (section 2) is used. This is defined by
refScanID(2,2,49) [integer*2]
refScanID gives the number of scan lines between the current scan and the

beginning (or end) of the along-track reference data at each angle bin. The values
are computed by the equation: Current Scan Number - Reference Scan
Number. The values are positive for the Forward estimates and negative for the
Backward estimates. The Fortran indices are:
1,1 - Forward - Near reference
2,1 - Forward - Far reference
1,2 - Backward - Near reference
2,2 - Backward - Far reference
The forward along-track spatial reference data will be assumed to be invalid (at angle bin j)
if:|refScanID(2,1,j)| > 100 for ocean and|refScanID(2,1,j)| > 50 for land and coast.
Similarly, the backward along-track spatial reference data will be assumed to be invalid (atangle bin j) if:|refScanID(2,2,j)| > 100 for ocean and|refScanID(2,2,j)| > 50 for land and coast.
The above conditions are equivalent to stating that, for a particular incidence angle, all the
spatial reference data must be taken within 50 scans of the scan at which rain is
encountered.
The criteria for the hybrid cross-track are more complicated because two quadratic fits areused for the inner and outer portion of the swath. Nominally, we will assume that if there
are 15 or more angle bins in the inner portion of the swath for which:|refScanID(2,1,j)|  100- 74 -

then the forward hybrid cross-track method will be applied. Note that the hybrid
cross-track is only applied to ocean backgrounds.
Similarly in the outer portion of the swath, if there are 15 or more angle bins in this portionof the swath for which:|refScanID(2,1,j)|  100
then the forward hybrid cross-track method will be applied.
Application of the backward cross-track follows the same rules using refScanID(2,2,j)instead of refScanID(2,1,j) .

2-1. 11.

Excluding Temporal Reference Data

Under raining conditions, the temporal data file that is accessed depends on the month andsurface type under which the raining measurement is made. The reference data at the
0.1°0.1° cell and angle-bin of interest consists of the mean, mean square and number ofrain-free data points, Nt, accumulated in the 12-year period from 1998 to 2009, inclusive.
The reference data are considered valid if Nt > 10; otherwise, the reference data areconsidered invalid and will not be used in the calculation of the effective PIA.

2-1. 12.

Command line arguments

jobname
1B21.inputfile.HDF
2A21.outputfile.HDF
2A21.tr_ocean.dat
2A21.tr_land.dat
2A21.tr_coast.dat
2A21.diag

PPS jobname
the 1B-21 HDF filethe 2A-21 HDF output file
the temporal file for ocean
the temporal file for land
the temporal file for coast
the verification (diagnostic) file

Note that the verification file is created in the program and should not exist prior to
execution.

References
Caylor I.J., G.M. Heymsfield, R. Meneghini, and L.S. Miller, 1997: Correction ofsampling 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.

- 75 -

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 forrain rate profiling from a spaceborne radar. Part I: Principle and tests from numericalsimulations. J. Atmos. Oceanic Technol., 11, 1480-1506.
Meneghini, R., T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J.A. Jones, and J. Kwiatkowski,
2000: Use of the surface reference technique for path attenuation estimates from the
TRMM Radar. J. Appl. Meteor., 39, 2053-2070.
Meneghini, R. and K. Nakamura, 1990: Range profiling of the rain rate by an airborne
weather radar. Remote Sens. Environ., 31, 193-209.
Meneghini, R., J.A. Jones, T. Iguchi, K. Okamoto, and J. Kwiatkowski, 2004: A hybridsurface reference technique and its application to the TRMM Precipitation Radar, J. Atmos.
Oceanic Technol., 21, 1645-1658.
Seto, S. and T. Iguchi, 2007: Rainfall-induced changes in actual surface backscatteringcross sections and effects on rain-rate estimates by spaceborne precipitation radar. J.
Atmos. Oceanic Technol., 24, 1693-1709.

- 76 -

2-2.

2A23

2-2. 1.

Objectives of 2A23

Main objectives of 2A23 are as follows:(a) Detection of bright band (BB) and determination of the height of BB, thestrength of BB, and the width (i.e. thickness) of BB when BB exists.
(b) Classification of rain type into the following three categories:- stratiform,- convective,- other,
where "other" means (ice) cloud only and/or maybe noise.
(c) Detection of shallow isolated and shallow non-isolated.
(d) Output of Rain/No-rain flag.
(e) Computation of the estimated height of freezing level.
(f) Output of the height of storm top.

2-2. 2.

Main changes from the previous version

The current product version of 2A23 is V7 (version 7).
Main changes are as follows:(a) Introduced a concept of small rain cell, which is classified as convective.
(Effect appreciable.)(b) About 40% of shallow non-isolated is classified as convective. (Effectappreciable.)(c) GANAL data (Global analysis data by Japanese Meteorological Agency,
JMA) is used for estimating 0C height, which was estimated using a
climatological data in V6.
(d) When BB is detected, rain type is basically stratiform. Exception is
introduced that even when BB is detected, rain type is convective if Z in therain region exceeds a threshold. (The occurrence of this turns out to bevery infrequent.)(e) When storm top > 15 km and BB is not detected, rain type is convective.

- 77 -

(Occurrence is small, but affects some 3A25 statistics).
(f) Increased rain-type sub-categories.

2-2. 3.

Method used in 2A23(a) Detection of bright band (BB):- Peak search by (1) using a spatial filter method [1], and (2) examining theslope in the upper part of BB profile. In the peak search, several conditions
are imposed on the height profile of BB.
(b) Determination of the width of BB:- By detecting upper and lower boundaries of BB along the slant path,then computing the thickness (i.e. width) of BB [2].
(c) Rain type classification:- Vertical profile method (V-method) [1][2],- Horizontal pattern method (H-method) [2][3].
(d) Detection of shallow isolated and shallow non-isolated:- A simple examination of the height of storm top being much lower than theestimated 0C height. When an isolation condition is satisfied, the type isshallow isolated, otherwise shallow non-isolated.
Here, the isolated
condition means that the shallow area is isolated from the non-shallow area.
(e) Rain/No-rain flag:- Almost identical to minEchoFlag recorded in 1C21 HDF file.
Difference occurs when rain probable is detected or, on rare occasion, whencorrupted input data are detected.
(f) Estimation of 0C height:- 0C height is computed using GANAL data in the standard product of 2A23.
A Temporal and spatial interpolation is made to obtain 0C height at a given
location and a given observation time.
- For a real time product, 0C height is estimated from a climatological surface
temperature data by assuming a constant lapse rate of 6.0 deg./km.
(g) Height of storm top:
- A simple conversion from range bin number to the height above the sea level.

2-2. 4.

Processing Flow

(1) Open files.

- 78 -

(2) Read in 1C21 metadata, and copy the metadata to 2A23 HDF file.
(3) Read in necessary GANAL data for the estimation of 0C height (freezH).
(4) Read in scan header from 1C21 HDF file.
(5) Repeat reading in 1C21 scan data until the end of 1C21 HDF file, and do thefollowing data processing for each scan:(a) Estimate freezH.
(b) Compute the height of storm top (stormH).
(c) Detect sidelobe clutter.
(d) Detect BB. When BB is detected, compute the height of BB, the strength ofBB, upper and lower boundaries of BB, and the width of BB, and set thestatus flag on BB detection.
(e) Classify rain type by V-method. Reject sidelobe clutter during thisprocessing.
(f) Detect shallow isolated and shallow non-isolated.
(g) Classify rain type by H-method. Reject sidelobe clutter during thisprocessing.
(h) Unify rain types.
(i) Set status flag.
(j) Write output to 2A23 HDF file.
(6) Close files and end the processing.

2-2. 5.

Input data(a) From 1C21 HDF file:(1) metadata(2) rayStart[49](3) startBinDist[49](4) ScanTime (structure)(5) scanTime_sec(6) scanStatus.missing(7) scanStatus.dataQuality(8) Latitude[49](9) Longitude[49](10) minEchoFlag[49](11) binStormHeight[49][2](12) binEllipsoid[49](13) binClutterFreeBottom[49][2]- 79 -(L1C21_RAY_HEADER)(L1C21_RAY_HEADER)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)

(14) binDIDHmean[49](15) scLocalZenith[49](16) scRange[49](17) osBinStart[29][2](18) landOceanFlag[49](19) binSurfPeak[49](20) normalSample[49][140](21) normalSample_scale[49][140](22) osSurf[29][5](23) osRain[11][28](L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(L1C21_SWATH)(b) Estimated height of 0C From GANAL for standard 2A23,
and a climatological SST data (sst-hou.grd) for real time 2A23.

2-2. 6.

Output data

(1) metadata(2) ScanTime (structure)(3) scanTime_sec(4) Latitude[49](5) Longitude[49](6) scanStatus (structure)(7) navigation (structure)(8) rainFlag[49](9) rainType[49](10) shallowRain[49](11) status[49](12) binBBpeak[49](13) HBB[49](14) BBintensity[49](15) freezH[49]---- same as that of 1C21---- same as that of 1C21---- same as that of 1C21---- same as that of 1C21---- same as that of 1C21---- same as that of 1C21
Rain/No-rain flag (1-byte integer)
Rain type (2-byte integer)
Shallow rain flag (1-byte integer)
Status (1-byte integer)
Range bin number for BB (2-byte integer)
Height of BB [m] (2-byte integer)
Strength of BB [dBZ] (4-byte float)
Estimated height of freezing level [m] (2-byte
integer)(16) stormH[49]Height of storm top [m] (2-byte integer)(17) BBboundary[49][2]Upper and lower boundaries of BB (2-byte integer)(BBboundary(2,49) in FORTRAN)(18) BBwidth[49]Width of BB [m] (2-byte integer)(19) BBstatus[49]Status flag for BB (1-byte integer)(20) spare[49]
Spare (2-byte integer)- 80 -

2-2. 7.

Output file specifications

This section describes details of items (8)-(19) in the previous section.
(a) int8 rainFlag[49]:= 0 : no rain
10 : rain possible
11 : rain possible
12 : rain possible
13 : rain possible
15 : rain probable
20 : rain certain-99 : data missing
Note:rainFlag is almost identical to minEchoFlag of 1C21 except for rainprobable case and the following very exceptional case.
The exception occurs if 2A23 detects data missing but 1C21 says the data
is normal - this can happen when the input data is corrupted. In normal
conditions, the rain certain case in rainFlag is identical to the rain certain
case in minEchoFlag of 1C21.

(b) int16 rainType[49]:
In V7 of 2A23, the flag rainType[i] (i=0 to 48) indicates the unified rain type by
3-digits numbers.
rainType[i]= 100: Stratiform.
When R_type_V[i] = T_stra,
and R_type_H[i] = T_stra.

(BB detected.)

105: Stratiform.
--- added in V7.
When R_type_V[i] = T_stra,(BB detected.)and R_type_H[i] = T_stra,
But storm top (determined by 2A23) is too high.
110: Stratiform.
When R_type_V[i] = T_stra,(BB detected.)and R_type_H[i] = T_other.
115: Stratiform.
--- added in V7.
When R_type_V[i] = T_stra,(BB detected.)- 81 -

and R_type_H[i] = T_other.
But storm top (determined by 2A23) is too high.
120: Probably stratiform. (BB may exist but not detected.)
When R_type_V[i] = T_other,and R_type_H[i] = T_stra.
130: Maybe stratiform.
When R_type_V[i] = T_stra,
and R_type_H[i] = T_conv.

(BB detected.)

135: Maybe stratiform.
--- added in V7.
When R_type_V[i] = T_stra,(BB detection certain.)and R_type_H[i] = T_conv.
But storm top (determined by 2A23) is too high.
140: Maybe stratiform. (BB hardly expected.)
When R_type_V[i] = T_other,and R_type_H[i] = T_stra.
152: Maybe stratiform:
When R_type_V[i] = T_other,
R_type_H[i] = T_stra,and shallowRain[i] = 20 or 21.
(Shallow non-isolated is detected.)
160: Maybe stratiform, but rain hardly expected near surface.
BB may exist but is not detected.
When R_type_V[i] = T_other,and R_type_H[i] = T_stra.
170: Maybe stratiform, but rain hardly expected near surface.
BB hardly expected. Maybe cloud only.
Distinction between 170 and 300 is very small.
When R_type_V[i] = T_other,and R_type_H[i] = T_stra.
200: Convective.
When R_type_V[i] = T_conv,
and R_type_H[i] = T_conv.
210: Convective.
When R_type_V[i] = T_other,and R_type_H[i] = T_conv;- 82 -

220: Convective
When R_type_V[i] = T_conv,
and R_type_H[i] = T_other;
230: Probably convective. ---> Re-introduced in V7.
When R_type_V[i] = T_stra;(BB exists)
R_type_H[i] = T_conv;
and Z below BB is strong.
235: Probably convective. ---> Added in V7.
When R_type_V[i] = T_other;
R_type_H[i] = T_stra;
But storm top (determined by 2A23) is too high.
237: Probably convective. ---> Added in V7.
When R_type_V[i] = T_other;
R_type_H[i] = T_stra;
But the cell size is small.
240: Maybe convective.
When R_type_V[i] = T_conv,
and R_type_H[i] = T_stra;
251: Convective.
When R_type_V[i] = T_conv,
R_type_H[i] = T_conv,
and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
252: Convective.
When R_type_V[i] = T_conv,
R_type_H[i] = T_conv,
and shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
261: Convective.
When R_type_V[i] = T_conv,
R_type_H[i] = T_conv;
and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
262: Convective.
When R_type_V[i] = T_conv,- 83 -

R_type_H[i] = T_other;and shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
271: Convective.
When R_type_V[i] = T_other,
R_type_H[i] = T_conv;
and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
272: Convective.
When R_type_V[i] = T_other,
R_type_H[i] = T_conv;
and shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
281: Convective.
When R_type_V[i] = T_conv,
R_type_H[i] = T_stra;and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
282: Convective.
When R_type_V[i] = T_conv,
R_type_H[i] = T_stra;and shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
291: Convective:
When R_type_V[i] = T_other;
R_type_H[i] = T_stra;and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
292: Convective:--- added in V7.
When R_type_V[i] = T_other;
R_type_H[i] = T_stra;and shallowRain[i] = 20 or 21;
Though this is shallow non-isolated, the appearance is'sporadic', hence convective.
297: Convective:--- added in V7.
When R_type_V[i] = T_other;
R_type_H[i] = T_stra;- 84 -

shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
But the cell size is small.
300: Other.
When R_type_V[i] = T_other;and R_type_H[i] = T_other;
This category includes very weak echo (possibly noise)
and/or cloud.
311: Others.
--- added in V7.
When R_type_V[i] = T_other,
R_type_H[i] = T_other;and shallowRain[i] = 10 or 11;(Shallow isolated is detected)
312: Other.
When R_type_V[i] = T_other,
R_type_H[i] = T_other;and shallowRain[i] = 20 or 21;(Shallow non-isolated is detected)
313: Other.
When R_type_V[i] = T_other,
R_type_H[i] = T_other;If sidelobe clutter were not rejected, shallow
isolated would be detected.
where T_stra, T_conv, and T_other are three distinctive values specifying rain
types. Three major rain categories, stratiform, convective, and other, can beobtained as follows:
When rainType[i] > 0,
rainType[i] / 100 =1: stratiform,
2: convective,
3: other.
When it is "no rain" or "data missing", rainType[i] contains the following values:-88 : no rain
-99 : data missing
Caution: When rainFlag[i]=10-15 (rain possible/rain probable), rainType[i]/100=3
because if it is rain, the type may not be startiform nor convective, suggesting thatthe type maybe other. However, 2A25 does not compute rainfall rate for rain
possible/rain probable. Please don’t examine rainType[i] for rainFlag[i]<20,- 85 -

otherwise users may find a paradoxical situation that the rain type is other but norainfall rate is calculated for rain possible/rain probable. Users should regard
rain possible/rain probable as no rain case, and should not be bothered by thecontent of rainType[i], which should be examined only when rainFlag[i]=20 (i.e.,rain certain).

(c) int8 shallowRain[49]:= 0 : no shallow isolated
10 : maybe shallow isolated
11 : shallow isolated (with confidence)
20 : maybe shallow non-isolated
21 : shallow non-isolated (with confidence)-88 : no rain
-99 : data missing(d) int8 status[49]: Status flag for the processing of 2A23.
This flag is meaningful when status >= 0, and indicates a confidence levelof 2A23 as follows:
0 <= status < 10 : good,
10 <= status < 50 : maybe good,
50 <= status < 100 : result not so confident (warning),
100<= status : bad (untrustworthy because of possible data corruption).
This flag also takes the following values:-88 : no rain
-99 : data missing(e) int16 binBBpeak[49]: Range bin number for the height of bright band peak.
> 0 : Range bin number corresponding to 125m intervals.
This also indicates that the bright band is detected.
= -1111 : No bright band
= -8888 : No rain
= -9999 : Data missing(f) int16 HBB[49]: Height of bright band.
> 0 : Height of bright band expressed in [m]This also indicates that the bright band is detected.
= -1111 : No bright band
= -8888 : No rain
= -9999 : Data missing
HBB[i] (i=0 to 48) is computed by the following formula:- 86 -

HBB[i] = (L1c21_swath_data->scRange[i] - rangeBB)* cos(zenith[i]);whererangeBB = (binBBpeak[i]- L1c21header->rayHdr[i].rayStart)*125+ L1c21header->rayHdr[i].startBinDist;(g) float32 BBintensity[49]: Bright band intensity in dBZ.
> 0 : Peak value of Z in BB [dBZ]= -1111.0 : No bright band
= -8888.0 : No rain
= -9999.0 : Data missing(h) int16 freezH[49]:Estimated 0C height obtained from GANAL data.
> 0 : Estimated 0C height [m]= -5555 : When error occurred in the estimation of freezH= -9999 : Data missing(In a real time version of 2A23, however, a climatological SST data
(sst-hou.grd) is used for computing freezH.)(i) int16 stormH[49]: Height of storm top.
> 0 : Height of storm top [m] (with high level of confidence)= -1111 : No stormH with high level of confidence= -8888 : No rain
= -9999 : Data missing
This height is computed only in the case of rain certain, i.e.,
minEchoFlag[i]=20.
It is computed bystormH[i] = (L1c21_swath_data->scRange[i] - range)* cos(zenith[i]);whererange = (binStormHeight[i][1]- L1c21header->rayHdr[i].rayStart)*125+ L1c21header->rayHdr[i].startBinDist;NOTE: Though 1C21 outputs the following two kinds of binStormHeight
for each angle bin,binStormHeight[i][0]: possible value,- 87 -

binStormHeight[i][1]: certain value,
2A23 converts only the certain value of binStormHeight to stormH.

(j) int16 BBboundary[49][2]: Upper and lower boundaries of BB.
This flag is meaningful when >0, and indicates
BBboundary[i][0]: range bin number for upper boundary of BB(BBboundary(1,i) in FORTRAN),
BBboundary[i][1]: range bin number for lower boundary of BB(BBboundary(2,i) in FORTRAN),
where range bin number specifies range with 125 m intervals.
(k) int16 BBwidth[49]: Width of BB (meaningful when >0).
At nadir (i=24 in C language), the width of BB [m] is computed simply
byBBwidth[24] = (BBboundary[24][1]- BBboundary[24][0])*125;
At other angles, the effect of oblique incidence is subtracted using an
Empirical formula (see item (4) in Appendix). In V7, BBwidth istrustworthy only at nadir direction.
(l) int8 BBstatus[49]:This flag indicates the quality of BB detection, BB boundaries, and BB
width in the following way:
BBstatus[i] = BB_detection_status * 16
+ BB_boundary_status * 4+ BB_width_status;
where, each status on the right hand side takes the following values
1: poor,
2: fair,
3: good.
BBstatus is meaningful when >0.

2-2. 8.

Interfaces with other algorithms(a) 2A23 uses 1C21 HDF file as an input file.
(b) 2A23 output is used by 2A25, 2B31, 3A25, and 3A26.

- 88 -

2-2. 9.

Special notes(a) Bright band (BB) detection has angle bin dependence because of the smearingof the shape of BB peak near the antenna scan edges.
(b) When 2A23 misses strong BB, rain type may sometimes be mis-classified asconvective. This possibility would be high for low-altitude BB which exists
near antenna scan edges.
(c) The height of BB shows a large variations mainly because of a relatively coarse
range resolution of 250m.
(d) Bright band detection is carried out for rain-certain case only, and rain typeclassification is meaningful only for rain-certain case.
(e) Rain type is expressed by 3-digits number inV7.
(f) Rain type of all the shallow isolated is convective in V7, though the echo
intensity of most of the shallow isolated is weak (see [4] for details). About
40 % of shallow non-isolated is convective in V7. Since most of shallow rain ismasked by the surface clutter near antenna scan edges, the count of shallow
rain shows dependence on antenna scan angle. In V7, the count of convective
rain also shows dependence on antenna scan angle because of the angle bin
dependence of shallow rain.
(g) Though rainType[i] for “rain possible/rain probable” is given by 2A23 V7 (andV6 as well), users should not use this information. The flag rainType[i] ismeaningful for the case of rain certain (i.e., rainFlag[i]=20) only. (See the noteat the end of the item (b) of 2-2.7.)(h) Effect of satellite boost from 350 km altitude to 400 km altitude on 2A23 issmall. When statistical analysis is made on 2A23 quantities (such as rain type
count and BB count), only a small difference shows up between the statistics of
2A23 quantities before the boost of the TRMM satellite and those after theboost.
(i) V7 outputs freezH even when there is ‘no rain’.

- 89 -

2-2. 10.

References[1] Awaka, J., T. Iguchi, and K. Okamoto, "Early results on rain type classificationby the Tropical Rainfall Measuring Mission (TRMM) precipitation radar," Proc.
8th URSI Commission F Open Symp., Aveiro, Portugal, 143-146, 1998.
[2] Awaka, J., T. Iguchi, and K. Okamoto, “TRMM PR standard algorithm 2A23
and its performance on bright band detection, “ J. Meteor. Soc. Japan, 87A,
31-57, 2009.
[3] Steiner, M., R.A. Houze, Jr., and S.E. Yuter, "Climatological characterization of
three-dimensional storm structure from operational radar and rain gauge
data," J. Appl. Meteor., 34, 1978-2007, 1995.
[4] Schumacher, C. and R.A. Houze, Jr., “The TRMM Precipitation Radar's View of
Shallow, Isolated Rain," J. Appl. Meteor., 42, 1519-1524, 2003.
[5] Fabry, F. and I. Zawadzki, “Long-term radar observations of the melting layerof precipitation and their interpretation," J. Atmos. Sci., 52, 838-851, 1995.
[6] Klaassen, W., “Radar observations and simulation of the melting layer ofprecipitation," J. Atmospheric Sciences, 45, 3741-3753, 1988.

- 90 -

Appendix. Some details of 2A23
(1) freezH[i] (i=0, ..., 48)
In the standard product of 2A23, the 0C height, freezH[i], is computed using
GANAL, which has a 1.25 x 1.25 degrees horizontal resolution and is available 4times a day at 0 LT (Local Time), 6 LT, 12 LT, and 18 LT.
The 0C height at an observing location is spatially and bi-linearly interpolated
at T1, which is 0LT or 6LT or 12 LT or 18 LT, and T1 satisfies T1 <= t < T1+6
[hours] where t is the observation time. The 0C height at the observing
location at T1+6 [hours] is also spatially and bi-linearly interpolated. Fromthus obtained 0C heights at T1 and T2, the 0C height for the observing location
at t is linearly interpolated with respect to time.
(In the real time product of 2A23, the 0C height, freezH[i], is computed from a
climatological surface temperature by assuming the lapse rate of thetemperature of 6.0 [deg/km].)(2) BB detection
In the BB detection, several conditions are imposed on BB, whose height isdesignated by HBB. Major conditions for the existence of BB are as follows:(a) BB has a peak,(b) HBB must be close to freezH-0.5km (within +/-2.5km) ,(c) Z must have a large slope at height above HBB,(d) HBB must be close to each other,(e) When Z at HBB, Z_hbb, exceeds 40 dBZ, Z below HBB should
not decrease rapidly.
Note:

The condition (e) is to avoid a false peak due to a strong
attenuation in the case of strong convective rain.

A two dimensional BB filter is introduced in 2A23 V7 to filter out the false BB.
(3) Upper and lower boundaries of BB
The lower boundary of BB is detected first. The lower boundary of BB isdefined as the point where there is the largest change in the slope of Z in theregion just below the BB peak (and of course the point is not far away from theBB peak).

- 91 -

The upper boundary of BB is determined by finding the following two points A
and B:
Point A: where there is the largest change in the slope of Z in the upper
region of BB peak.
Point B: where Z becomes smaller than Z at the lower boundary of BB for the
first time when Z is examined upward in the upper part of BB
starting from the BB peak.
When points A and B are the same, the upper boundary of BB is defined as thepoint A (which is the same as the point B in this case). When points A and B
are different, the upper boundary of BB is defined as either A or B which is
closest to the BB peak. Here, the definition of the lower boundary of BB is very
close to that by Fabry and Zawadzki [5], and the definition of the upperboundary is the one which is somewhere in between the definition by Fabry and
Zawadzki [5] and that by Klaassen [6].

(4) Width of BB
The width of BB in the nadir direction is computed as follows:
BBwidth[24] = (BBboundary[24][1]- BBboundary[24][0])*125;
where BBwidth[24] is the width of BB in the nadir direction, andBBboundary[24][0] and BBboundary[24][1] are respectively range bin number
for upper boundary of BB and that for lower boundary of BB (see section 2-2.7).
At other antenna scan angles, the effect of oblique incidence is subtracted using
the following empirical formula:
BBwidth[i] = (BBboundary[i][1] - BBboundary[i][0]– L sinTH[i] ) * cosTH[i] * 125;
where the index i denotes the angle bin number, TH[i] is the local zenith angle,
and L is given by
L = (Lo F) / (cosTH[i])^2
and where Lo is the footprint diameter of antenna beam (which is about 4.3 km
when the altitude of the TRMM satellite is 350 km), and F is an empiricalcorrection factor (F = 0.5).
The above formula for BBwidth[i] sometimes gives unrealistically small value,- 92 -

or in some cases even negative value. To avoid such a difficulty, a lower
bound for BBwidth[i] is set as follows:
If the above formula gives BBwidth[i] being smaller than 500*cosTH[i] meters(when normal sample data is used), the width of BB is computed by
BBwidth[i] = 500 * cosTH[i][m](for normal sample)

When oversample data is available, the lower bound for BBwidth[i] is given by
BBwidth[i] = 250 * cosTH[i][m](when oversample data is available)(5) Shallow isolated and shallow non-isolated.
The following two conditions are imposed for the detection of shallow isolated:(a) Shallow condition: Storm top is much lower than the 0C height.
(b) Isolated condition: Shallow isolated must be isolated from the othernon-shallow rain areas.
When the first condition (a) is satisfied, it then goes on to test whether theisolation condition is satisfied or not by examining the horizontal pattern of rain
types. Shallow non-isolated is the rain which satisfies the condition (a) only.
When shallow isolated is detected, shallowRain flag is set to 10 or 11 dependingon the level of confidence. Similarly, when shallow non-isolated is detected,
shallowRain flag is set to 20 or 21 depending on the level of confidence.
Hstorm < freezH - 1000 m (1.0 km)
 shallowRain[i] = 10: maybe shallow isolated,
20: maybe shallow non-isolated,
Hstorm < freezH - 1500 m (1.5 km)
 shallowRain[i] = 11: shallow isolated(with higher level of confidence),
21: shallow non-isolated(with higher level of confidence),
where freezH is the estimated 0C height.
If shallow isolated or shallow non-isolated is detected over land, the judgment isalways 'maybe shallow isolated’ or ‘maybe shallow non-isolated’ no matter how
low the height of storm top is because freezH may not be trustworthy over land.

- 93 -

(6) Rain type classification by V-method
The vertical profile method (V-method) classifies rain into three categories:
stratiform, convective, and other. Outline of the V-method is as follows:(a) When BB exists, rain is classified as stratiform,(b) When BB is not detected, and the maximum value of Z at a given angle bin
exceeds 40 dBZ, rain type for this angle bin is classified as convective,(c) Other type is defined as not-stratiform and not-convective.
It should be noted in (c) that other type of rain by the V-method is defined as
not convective and not stratiform: this means that(i) there exists appreciable radar echo but it is not strong enough to beconvective,(ii) BB is not detected.
Therefore the other type by the V-method consists of the following cases:(A) Cloud,(B) Actually stratiform, but BB detection fails,(C) Ambiguous because radar echo is not strong enough to be convective andBB does not exist,(D) Simply noise.

(7) Rain type classification by H-method
The horizontal pattern method (H-method) also classifies rain into three
categories: stratiform, convective, and other, but with the definitions of thesebeing different from those of the V-method. The H-method is based on the
University of Washington convective/stratiform separation method [3], which
examines the horizontal pattern of Z at a given height; where Z has a 2 km
horizontal resolution. In 2A23, the following modifications are made:(a) Instead of examining a horizontal pattern of Z at a given height, a horizontal
pattern of Zmax is examined; here, Zmax is the maximum of Z along therange for each antenna scan angle below freezH (minus 1 km margin).
(b) Parameters are changed so that they may be suitable for the TRMM datawith 4.3 km horizontal resolution. Choice of parameters was made before thelaunch of TRMM using a test GV data in such a way that a 4.3 km resolution
data produces almost the same result as that with a 2 km resolution data.

- 94 -

(c) Other type of rain is introduced to handle noise.
In the H-method, detection of convective rain is made first. If one of thefollowing condition is satisfied at a pixel, which correspond to the angle bindata being considered, it is judged that the pixel is a convective center:(A) Zmax exceeds 40 dBZ, or(B) Zmax stands out against the background area.
Rain type for a convective center is convective, and rain type for the (four)
pixels nearest to the convective center is also convective.
If rain type is not convective and if the rain echo is certain to exist, rain type isstratiform.
Rain type by the H-method is 'other' if the radar echo below freezH (with amargin) at a given angle bin is possibly noise.This means that the other type by
the H-method includes the case of (i) noise, and (ii) cloud.

(8) Unification of rain type
Since the algorithm 2A23 includes two independent methods for classifying rain
type, it would not be friendly to the users if 2A23 outputs the rain types by thetwo methods separately. To make the result user-friendly, 2A23 outputs theunified rain type (for details, see (b) of '2-2.7. Output file specifications'). The
unified rain type is expressed by 3 digits: the first digit indicates the rain type
(1: stratiform, 2: convective, 3: other), and the last two digits indicate subcategories.
Note that the rain types by V-method and H-method can be reconstructed fromthe unified rain type by using a suitable table (in other words, the unification ofrain type is made without loss of information).
(9) Small rain cell
When there is a single rain pixel or there are two adjacent rain pixels, those are
regarded as small cells, and the rain type for small cell pixels are classified asconvective in 2A23 V7.
(10) Rain type of shallow non-isolated
When shallow non-isolated appears “randomly” in one antenna scan, those- 95 -

“randomly” appeared shallow non-isolated are classified as convective in 2A23
V7. Here, “random” appearance of the shallow non-isolated is defined asfollows:(Definition) Examine one antenna scan data (which means that to examine thedata in the direction perpendicular to the satellite movement). When the countof shallow non-isolated is smaller than 3 or equal to 3 but not being contiguous,
it is judged that shallow non-isolated appears “randomly”.

- 96 -

2-3.

2A25

2-3. 1.

Objectives

The objectives of 2A25 are to correct for the rain attenuation in measured radarreflectivity (Zm) and to estimate the instantaneous three-dimensional distributionof rain from the TRMM Precipitation Radar (PR) data. The estimated verticalprofiles of attenuation-corrected radar reflectivity factor (Ze) and rainfall rate (R)are given at each resolution cell of the PR. The estimated rainfall rate at the actual
surface height and the average rainfall rate between the two predefined altitudes(2 and 4 km) are also calculated for each beam position.

2-3. 2.

Changes from V6 to V7

The major points of improvement in V7 are as follows:
The adjustment parameter  for  in the k-Ze relationship ( in k= Ze) is
estimated by the maximum likelihood method instead of calculating the
expected value of .
•

The vertical profile of α (phase state model) is substantially changed above
0 degree C height. The ratios of ice and water in a precipitation particle as afunction of height are redefined. The new profile assumes that particles
are 100% ice above -20℃ level. The value of  is linearly interpolated
between the top of bright band (for stratiform rain with a bright band) or
0℃ level and -20℃ level. (Note that the profile in V7 is different from whatis written in Iguchi et al. 2009.)•

A new drop size distribution (DSD) model which is defined in terms of theZ-R relation is introduced as the default DSD model. In the new stratiform
rain model, Z decreases by 0.5 dB. With this Z-R relation, R increases by
about 8%, if no adjustment is carried out.

new Ze-R and k-Ze relations are

introduced based on a non-spherical rain drop model. (R decreases forheavy rain)•

Errors in the PIA estimates from the surface reference technique (SRT) andin ζ are redefined. In V7, the fading noise in Zm is taken into account when
we calculate the error of ζ which depends on α and Zm.

- 97 -The error in thenon-uniform beam filling (NUBF) correction is also taken into account. As
a result the adjustment of the R-Z relation by change in ε decreases (Rincreases in regions where  is less than 1).
•

NUBF correction which was abandaned in V6 is re-introduced in V7. The
error in the NUBF correction formula in V5 was corrected.
The
introduction of NUBF correction will in general increase rain estimates forheavy rain.

•

Blurring of the bright band at off-nadir angle bins is compensated to someextent when Ze profiles are converted into R profiles.
Details of these changes except the compensation of blurring effect aredescribed in Iguchi et al. (2009).

2-3. 3.

Algorithm Overview

2A25 basically uses a hybrid of the Hitschfeld-Bordan method and the surface
reference method to estimate the vertical profile of attenuation-corrected effective
radar reflectivity factor (Ze).

(The hybrid method is described in Iguchi and

Meneghini (1994).) The vertical rain profile is then calculated from the estimatedZe profile by using an appropriate Ze-R relationship. One major difference fromthe method described in the above reference is that in order to deal with theuncertainties in measurements of the scattering cross section of surface as well as
the rain echoes, a probabilistic method is used. Since radar rain echoes from near
the surface are hidden by the strong surface echo, the rain estimate at the lowest
point in the clutter-free region is given as the near-surface rainfall rate for eachangle bin.

2-3. 4.

More Detailed Description of the Algorithm

The major input data to 2A25 are the measured radar reflectivity factor Zm, theapparent decrease of the surface cross section ( 0), its reliability, the rain typeand miscellaneous height information. The algorithm first defines the region forprocessing: It processes only the data between the rain top and the lowest height
above the surface that is free from the surface clutter. (The current algorithm
does not use any data below the surface, i.e., the mirror image.)- 98 -

The bright-band height and freezing height given by 2A23 are used to define theregions of liquid (water), solid (ice), and mixed phase of precipitating particles.
The initial values of the coefficients in the k-Ze and Ze-R relationships at different
altitudes are accordingly defined.
The attenuation correction is, in principle, based on the surface reference method.
This method assumes that the decrease in the apparent surface cross section iscaused by the propagation loss in rain. The coefficient  in the k-Ze relationship
k=Ze is adjusted in such a way that the path-integrated attenuation (PIA)
estimated from the measured Zm-profile will match the reduction of the apparent
surface cross section. The attenuation correction of Ze is carried out by the
Hitschfeld-Bordan method with the modified . Since  is adjusted, we call thistype of surface reference method the -adjustment method.
The -adjustment method assumes that the discrepancy between the PIA estimate
from  0and that from the measured Zm-profile can be attributed to the deviationof the initial  values from the true values which may vary depending on theraindrop size distribution and other conditions. It assumes that the radar isproperly calibrated and that the measured Zm has no error.
The surface reference method generally works rather well as long as the apparent
decrease in surface cross section  0 is much larger than the fluctuations of thetrue surface cross section. When the decrease is not significant, however, therelative error associated with this method in the estimates of rainfall rate becomeslarge since the fluctuation of surface cross section, which remains finite even when
there is no rain, translates to the absolute error of the rain estimates.
In order to avoid inaccuracies in the attenuation correction when rain is weak, ahybrid of the surface reference method and the Hitschfeld-Bordan method is used
[Iguchi and Meneghini, 1994]. In versions 5, 6 and 7 of 2A25, the errors in thesemethods are treated in a probabilistic manner. Because the relationship between
the error in  and that in the Hitschfeld-Bordan method changes substantially withthe attenuation, the relative weight on the surface reference method to the
Hitschfeld-Bordan method varies with the attenuation. When rain is very weak
and the attenuation estimate is small, the PIA estimate from the surface referenceis effectively neglected. With the introduction of the hybrid method, thedivergence associated with the Hitschfeld-Bordan method is also prevented.
When the PIA estimate from the surface reference ( 0) is unavailable, it is- 99 -

replaced by an equivalent  0c that would make the attenuation-corrected Ze-profile near the surface nearly constant vertically if the correction by the surface
reference method is applied with this equivalent  0c. This does not imply thatthe final vertical profile near the surface after the attenuation correction becomes
constant because of the use of the hybrid method. Note also that negative values of 0c are reset to zero. The use of  0c instead of  0 from the surface reference
seldom occurs.
The attenuation correction procedure requires two processing cycles. In the firstcycle, the correction is made without taking the attenuation by cloud liquid water(CLW), water vapor (WV) and molecular oxygen (O2) into account. From theattenuation-corrected profile, the rainfall rate at the surface is estimated. Basedon this rainfall rate and the statistical relationship between the surface rain rate
and the vertical profile of cloud liquid water, the attenuation of radar rain echocaused by CLW is estimated at each range bin. Similarly, the attenuation due to
WV is estimated from the estimated surface temperature and by assuming the 90%
relative humidity within the raining footprint and 70% outside the raining area.
The attenuation due to O2 is a simple function of the altitude. Then in the second
cycle, the vertical profile of Zm is corrected for the attenuation by CLW, WV andO2, and this attenuation-corrected Zm is corrected for the attenuation by rain.
The corrections for the non-uniform beam filling (NUBF) effect in the attenuation
correction and in the conversion from Ze to rainfall rate R are reintroduced in V7.
The non-uniformity of rain distribution within a field of view is estimated from thelow resolution variability of the PIA that is calculated from the PIAs at the angle
bin in question and the eight surrounding angle bins.
The rainfall estimates are calculated from the attenuation-corrected Ze-profiles byusing a power law: R=aZeb in which the parameters a and b are both functions of
the rain type, existence of bright-band, freezing height, storm height and absoluteheight. Effects of the difference in the raindrop size distribution by rain type, thephase state, the temperature, and the difference in terminal velocity due tochanges in the air density with height are taken into account. The parameters aand b are expressed as a function of the adjustment parameter () of  in the k-Ze
relation and adjusted in accordance with the -adjustment in the attenuation
correction.

- 100 -

2-3. 5.

Input data
Input files:
1C-21 HDF data file
2A-21 HDF data file
2A-23 HDF data file

Input swath data from 1C-21 which are used in 2A-25:
binClutterFreeBottom[][]binEllipsoid[]binStormHeight[][]binSurfPeak[]geolocation[][]minEchoFlag[]normalSample[][]scanStatus.dataQuality
scanStatus.missing
scanStatus.prStatus2
scanTime
scLocalZenith[]scRange[]
Input swath data from 2A-21 which are used in 2A-25:
pathAtten[]reliabFlag[]reliabFactor[]sigmaZero[]
Input swath data from 2A-23 which are used in 2A-25:
rainType[]
warmRain[]status[]freezH[]
HBB[]
Input header data from 1C21 used in 2A-25:
rayHdr[].rayStart
rayHdr[].mainlobeEdge
rayHdr[].sidelobeRange[]- 101 -

2-3. 6.

Output data

Output files:
2A-25 HDF data fileVI fileThe main part of 2A25 output data is stored in the variables listed below:
Output data (in alphabetical order):float attenParmAlpha[49][5];k- Ze parameter alpha at 5 nodes
float attenParmBeta[49];k- Ze parameter beta
float correctZFactor[49][80];attenuation-corrected Z factor in dBZ
float epsilon[49];correction factor with the hybrid method
float epsilon_0[49];correction factor with the SRT
float epsilon_alpha[49];correction factor for alpha (new)float epsilon_nubf[49]; correction factor for alpha due to NUBF (new)float errorRain[49];error estimate of rain rate near surface in dB
float errorZ[49];error estimate of Ze near surface in dB
float e_SurfRain[49];float freezH[49];short method[49];float nearSurfRain[49];float nearSurfZ[49];estimated rain rate at the actual surface
freezing height from 2A23
method used
estimated rain rate near surface
estimated Ze near surface

float nubfCorrectFactor[49][3]; non-uniform beam filling correction factors(new definitions)short parmNode[49][5]; bin numbers of 5 nodes for alpha, a and b
float pia[49][3];path-integrated attenuations from final Ze,
in surface clutter, and from 2A21
float pia_srt[49][6];6 PIA estimates by SRT (new)float precipWaterParmA[49][5]; PWC- Ze parameter a in PWC=a* Ze^b at 5
nodes
float precipWaterParmB[49][5];PWC- Ze parameter b in PWC=a* Ze^b at 5

nodes
float precipWaterSum[49][2];sum of PWC (2dimensional and new
definitions)short qualityFlag[49];quality flag
float rain[49][80];rainfall rate in mm/h.
float rainAve[49][2];average rainfall rate between 2 and 4 km

- 102 -

short rainFlag[49];status flag for rainfall estimate
short rainType[49];rain type from 2A23
short rangeBinNum[49][7]; bin numbers of BB, storm top, etc.
signed char reliab[49][80]; reliability of the output
float scLocalZenith[49]; spacecraft local zenith angle
float sigmaZero[49]; surface scattering cross section sigmaZero from 2A21
float spare[49][2];spare (New definitions)float stddev_zeta[49];standard deviation of zeta (new)float stddev_PIAsrt[49]; standard deviation of PIA by SRT (new)float stddev_alpha[49]; standard deviation of epsilon (new)float stddev_srt[49][6]; reliability factors corresponding to pia_srt[49][6](new)float stddev_Zm[49];standard deviation of epsilon_f (new)float zeta[49][2];integral of alpha*Zm^beta
float zeta_mn[49][2];mean of zeta over 3x3 IFOVs
float zeta_sd[49][2];standard deviation of zeta
float zmmax[49];maximum of Zm
float ZRParmA[49][5];Ze-R parameter a in R=a* Ze^b at 5 nodes
float ZRParmB[49][5];Ze-R parameter b in R=a* Ze^b at 5 nodes

L2A25_SCANTIME ScanTime;double scanTime_sec;
float Latitude[49];float Longitude[49];geolocation[][]scanTime

geolocation

L2A25_SCANSTATUS scanStatus;
L2A25_NAVIGATION navigation;

scanStatus
navigation data

ObsoletethickThPIZ[]
weightW[]xi[][]

range bin number where PIZ > threshPIZ
weight for the calculation of epsilonf
normalized standard deviation of PIA

For details, see section 2-3. 10.

- 103 -

2-3. 7.

Interfaces with other algorithms

As described in "Input data" section, 2A25 reads data from 1C21, 2A21 and 2A23.
The output data of 2A25 is used in 3A25 and 3A26.

2-3. 8.

Caveats

1. 2A25 produces many output variables. Please read section 2-3.10 carefully
before using them. For example, negative numbers are stored in rain[][] andcorrectedZFactor[][] when the data are missing or in the possibly cluttered
ranges.
(IMPORTANT)
If the input radar reflectivity factor Zm is below the noise level, the corresponding
rain estimate is set to 0. This procedure does not cause any serious problem
except when the measured Zm becomes smaller than the noise level by rain
attenuation. In such a case, even if some heavy rain exists near the surface, andthe actual rain rate there is rather large, the number in rain[][] is 0.
To know whether such low radar reflectivity factors are caused by large
attenuation or not, look at the fourth bit of 'reliab' and the fourth bit of 'rainFlag'.
2. The error estimates in 'rain' and 'correctZFactor' are given in 'errorRain[]' and'errorZ[]'. However, these estimates indicate only very crude estimates.
3. 2A25 processes data in 'rain certain' angle bins only. It processes all data
downward from 1 km above the height at which the first 'certain' rain echo isdetected. This new definition of the processing region in 2A25 is introduced inversion V5 and retained in V6 and V7.
4. Over some area with a very high surface reflectivity, surface echoes picked up
in antenna sidelobes may appear in the radar signal and they are sometimes
misidentified as rain echoes. The sidelobe clutter rejection routine in 1B21 and
2A25 removes some of the sidelobe clutters internally, but not all sidelobe signals
are completely removed.
5. 2A25 relies on the output of 1C21 to separate the surface cluttered ranges fromthe clutter free ranges. Because the clutter identification routine used in 1B21 is- 104 -

not perfect (it never can be), some surface clutter (mainlobe clutter) may beoccasionally misidentified as rain echoes in 2A25, particularly in mountain regions.
It is strongly suggested that you look at the vertical profile if the surface clutter
seems present in the data.
6. The range bin numbers in the output of 2A25 are all relative to the Earth's
ellipsoid (which is nearly equal to the mean sea level) with the ellipsoid range bincorresponding to 79. For example, if the range bin number is 75, its height fromthe ellipsoid is (79-75)*0.25 = 1.0 km. This number is NOT the height above theactual surface.


7. In V6 and V7, the value of  in the k-Ze Relationship (k =  Ze  at 5 nodal
points are given in attenParmAlpha[][].
The values in attenParmAlpha[][] are the initial values of  To obtain the valuesof alpha used in the final attenuation estimation, the initial values must be
multiplied by epsilon[].
8.

The values of a and b given in ZRParmA[][]and ZRParmB[][] are

the final values of a and b in the R-Ze Relationship (R = a Zeb) at the nodal points,
respectively. In the case of stratiform rain with a bright band, smearing effect due
to the canting scattering volume is compensated to some extent. In this case,mean values of a and b over the height profile of the scattering volume are used.
(In fact, the reciprocal of the mean of 1/a (and 1/b) with a weighting function
defined by the antenna pattern is used for smeared a (and smeared b).

2-3. 9.

References

Iguchi, T., and R. Meneghini, “Intercomparison of Single Frequency Methods for
Retrieving a Vertical Rain Profile from Airborne or Spaceborne Data,” Journal of
Atmospheric and Oceanic Technology, 11, 1507-1516 (1994).
Kozu, T., and T. Iguchi, “Nonuniform Beamfilling Correction for Spaceborne
Radar Rainfall Measurement: Implications from TOGA COARE Radar Data
Analysis,” J. Atmos. Oceanic Technol., 16, 1722-1735 (1999).
Iguchi, T., T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto, “Preliminary resultsof rain profiling with TRMM Precipitation Radar,” Proc. of URSI-F International
Triennial Open Symposium on Wave Propagation and Remote Sensing, Aveiro, Portugal,- 105 -

pp.147-150, 1998.
Iguchi, T., T. Kozu, R. Meneghini, J. Awaka, and K. Okamoto, “Rain-Profiling
Algorithm for the TRMM Precipitation Radar,” Journal of Applied Meteorology,
Vol.39, No.12, pp.2038-2052, 2000.
Meneghini, R., T. Iguchi, T. Kozu, L. Liao, K. Okamoto, J. A. Jones, and J.
Kwiatkowski, ”Use of the surface reference technique for path attenuation
estimation from the TRMM Precipitation radar,” Journal of Applied Meteorology,
Vol.39, No.12, pp.2053-2070, 2000.
Iguchi, T., T. Kozu, J. Kwiatkowski, R. Meneghini, J. Awaka, and K.
Okamoto, ”Uncertainties in the Rain Profiling Algorithm for the TRMM
Precipitation Radar,” Journal of the Meteorological Society of Japan, Vol. 87A, pp.
1-30, 2009.

2-3. 10.

Detailed description of output variables

New Output Variables
float epsilon_alpha[49];correction factor for alpha (new)float epsilon_nubf[49];correction factor for alpha due to NUBF (new)float pia_srt[49][6];6 PIA estimates by SRT (new)float stddev_zeta[49];standard deviation of zeta (new)float stddev_PIAsrt[49];standard deviation of PIA by SRT (new)float stddev_alpha[49];standard deviation of epsilon (new)float stddev_srt[49][6];standard deviation of pia_srt (new)float stddev_Zm[49];standard deviation of epsilon_f (new)New Definitions
int16

method[49]; (bit 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)

int16

qualityFlag[49]; (bit 2, 3, 4, 5, 11, 12, 13)

int16

rainFlag[49]; (bit 3, 4, 11)

float nubfCorrectFactor[49][3]; non-uniform beam filling correction factors(new definitions)float precipWaterSum[49][2];float32

sum of PWC (2dimensional and new definitions)pia[49][3];float spare[49][2];spare (New definitions)- 106 -

Obsolete (No data in V7)
int16

attenParmNode[49][5]; moved to parmNode[49][5];float32

pia2a25[49]; moved to pia[49][0]float32

thickThPIZ[49];float32

weightW[49]; replaced by epsilon_0[49]float32xi[49][2]; normalized standard deviation of PIA

int16

ZRParmNode[49][5]; moved to parmNode[49][5];List of 2A25 scan data
float32attenParmAlpha[49][5];int16

attenParmAlpha_scale[49][5];float32attenParmBeta[49];int16

attenParmBeta_scale[49];int16

attenParmNode[49][5];float32

correctZFactor[49][80];int16

correctZFactor_scale[49][80];float32

epsilon[49];float32

epsilon_0[49];Obsolete

float epsilon_alpha[49];New

float epsilon_nubf[49];New

float32

errorRain[49];float32

errorZ[49];float32

e_SurfRain[49];float32

freezH[49];float32

geolocation[49][2];int16

method[49];float32

nearSurfRain[49];float32

nearSurfZ[49];float32

nubfCorrectFactor[49][2];

int16

parmNode[49][5];float32

pia[49][3];float pia_srt[49][6];New

float32

pia2a25[49];Obsolete

float32

precipWaterParmA[49][5];float32

precipWaterParmB[49][5];float precipWaterSum[49][2];New dimension

int16

precipWaterSum_scale[49];int16

qualityFlag[49];- 107 -

float32

rain[49][80];int16

rain_scale[49][80];float32

rainAve[49][2];int16

rainAve_scale[49][2];int16

rainFlag[49];

int16

rainType[49];int16

rangeBinNum[49][7];int8

reliab[49][80];float64

scanTime;

float32

scLocalZenith[49];float32

sigmaZero[49];float32

spare[49][2];float stddev_zeta[49];New

float stddev_PIAsrt[49];New

float stddev_alpha[49];New

float stddev_srt[49][6];New

float stddev_Zm[49];

New

int16

thickThPIZ[49];Obsolete

float32

weightW[49];Obsolete

int16

weightW_scale[49];Obsolete

float32xi[49][2];Obsolete

float32

zeta[49][2];float32

zeta_mn[49][2];float32

zeta_sd[49][2];float32

zmmax[49];int16

ZRParmA_scale[49][5];float32

ZRParmA[49][5];int16

ZRParmB_scale[49][5];float32

ZRParmB[49][5];int16

ZRParmNode[49][5];

L2A25_SCANTIME ScanTime;

ObsoleteNew

double scanTime_sec;
float Latitude[49];float Longitude[49];geolocation[][]
L2A25_SCANSTATUS scanStatus;

New

L2A25_NAVIGATION navigation;

New- 108 -

Description of each output variableattenParmAlpha
float32attenParmAlpha[49][5];REAL*4attenParmAlpha(5,49)

Attenuation parameter alpha at nodes.
k = alpha*Z^beta.
"alpha" is given at five nodal points. These numbers are initial values of alpha.
The mean values of alpha used in the attenuation correction are obtained bymultiplying attenParmAlpha[49][5] by epsilon[49].
The alpha values between the nodes are calculated by linear interpolation.
The range bin numbers of the nodes are stored in ParmNode[49][5](in version 5, they were stored in attenParmNode[49][5]).

attenParmBeta
float32
REAL*4attenParmBeta[49];attenParmBeta(49)Attenuation parameter betak = alpha*Ze^beta.
beta is given for each angle bin.
A constant beta is used for all ranges in one angle bin.

correctZFactor
float32

correctZFactor[49][80];

REAL*4

correctZFactor(80,49)

Internally this quantity is stored as
int16 correctZFactor_scale[49][80] after multiplied (scaled) by 100.
Estimated effective Z-factor in dBZ at 13.8 GHz after attenuation correction.
If the input radar reflectivity factor Zm is below the noise level,or if the estimate is below 0 dB, correctZFactor is set to 0.0.
Everythingelse is the same as rain[49][80] (rain(80,49)).

- 109 -

epsilon
float32

epsilon[49];

REAL*4

epsilon(49)The multiplicative correction factor to zeta. alpha in the k-Ze relation is apart of zeta. Look at the description for epsilon_alpha below.

In V7, anon-uniform beam filling (NUBF) correction is also applied in the attenuation
correction.

In the final form of the modified Hitschfeld-Bordan attenuation

correction, zeta is multiplied by epsilon[] and nubfCorrectFactor[][0](thelatter is expressed by NUBF in Iguchi et al. 2009).
The value of epsilon is the maximum likelihood estimate with the likelihood
function of epsilon defined by the rain echo, surface echo and theiruncertainties.

epsilon_0
float32

epsilon_0[49];

REAL*4

epsilon_0(49)The multiplicative correction factor to alpha in the k-Ze relation if the weightto the path-integrated attenuation (PIA) given by the surface referencetechnique is 100%. This output is given only when the PIA estimate from 2A21
is either reliable or marginally reliable.
When it is not reliable, epsilon_0 is set to 0.

The exact formula used is as follows.
When pia[][0]>0, we define pia_ratio = (pia[][0]-pia[][1])/pia[][0].
If pia[][0]=0, pia_ratio=1.
att_f_bttm = pow(10.0,-(pia[][2] * pia_ratio)/10.0);
epsilon_0 = (1-pow(att_f_bttm,beta))/zeta;
I.e., the PIA estimate from 2A21 that represents the attenuation to the surface
is converted to the attenuation to the bottom of clutter-free range and thelatter is used for the calculation of epsilon_0.

epsilon_alpha (new)float epsilon_alpha[49]epsilon_alpha is the multiplicative correction factor to alpha in the k-Ze
relation. This value is used to modify the R-Ze and LWC-Ze relations. Note that- 110 -

zeta is modified by epsilon which is larger than epsilon_alpha. In other words,
the total adjustment of zeta is done by epsilon, but only a part of it isattributed to the DSD bias.

The latter adjustment corresponds to the adjustmentof alpha by epsilon_alpha.

epsilon_nubf (new)float epsilon_nubf[49]epsilon_nubf is the NUBF correction factor for the k-Ze relation, and its value
is between 0.8 and 1.0.

errorRainfloat32

errorRain[49];

REAL*4

errorRain(49)Error estimate of rain rate near the surface expressed in dB.

errorZ
float32

errorZ[49];

REAL*4

errorZ(49)Error estimate of correctZFactor near the surface expressed in dB.

e_SurfRain (New variable)
float32

e_SurfRain[49];

REAL*4e_SurfRain(49)Estimated rainfall rate at the actual surface. e_SurfRain is calculated byassuming a constant slope of dBZe from the bottom of the valid (clutter-free)rain echo. The assumed slope is 0 dB/km for all rain types except for the
stratiform rain over land where -0.5 dB/km toward the surface is assumed.
Note that 0 dB/km in Ze corresponds to -0.17 dB/km in rainfall rate (decreases
toward the surface).

freezH(New variable)

float32

freezH[49];

REAL*4freezH(49)- 111 -

Freezing height expressed in meter estimated from the climatological surface
temperature. This is a copy of freezH given in 2A23.(freezH in 2A23 isgiven as an integer, but it is stored as a float number in 2A25.)

geolocation
float32

geolocation[49][2];

REAL*4geolocation(2,49)

The earth location of the center of the IFOV at the altitude of the earth
ellipsoid. The first dimension is latitude and longitude, in that order.
Values are represented as floating point decimal degrees. Off-earth isrepresented as -9999.9.
Latitude is positive north, negative south. Longitude is positive east, negative
west. A point on the 180° meridian is assigned to the western hemisphere.

methodint16

method[49];INTEGER*2

method(49)Method (rain model) used in the retrieval of vertical profiles of Z and R
The default value is 0 (including no rain case).
The following meanings are assigned to each bit in the 16-bit integer.
(See flag_mthd)
0: (bit1) no rain

if rain0: (bit

1) over ocean

1: (bit

1) over land

2: (bit2) over coast, river, etc.

3: (bit2) others (impossible)+4: (bit3) PIA from constant-Z-near-surface assumption+8: (bit4) spatial reference+16: (bit5) temporal reference+32: (bit6) global reference+64: (bit7) hybrid reference+128: (bit8) good to take statistics of epsilon.

+256: (bit9) HB method used, SRT totally ignored+512: (bit 10) very large pia_srt for given zeta

- 112 -

+1024: (bit 11) very small pia_srt for given zeta
+2048: (bit 12) no ZR adjustment by epsilon+4096: (bit 13) no NUBF correction because NSD unreliable+8192: (bit 14) surface attenuation > 60 dB+16384: (bit 15) data partly missing between rain top and bottom
16th bit is currently not used.
The constant Z method is used only when the surface reference is unreliable.
This routine calculates the average slope of the Zm profile (expressed in dBZ)
near the bottom of radar echo and attributes the slope to the attenuation.
If there are not enough valid data points in the profile, it returns with
0 attenuation. The constant Z method is seldom used.

navigate
NAVIGATION

navigate;

Look at the TSDIS INTERFACE CONTROL SPECIFICATION (ICS) Vol. 3,
Appendix B “Navigation”

nearSurfRain
float32

nearSurfRain[49];

REAL*4

nearSurfRain(49)Near-surface rainfall rate estimate"Near-surface" is defined as the lowest point in the clutter free ranges
in almost all cases. However, if Zm at this point is below the noise level
and if zeta which corresponds to the estimated attenuation down to this pointis larger than the zeta_th_L defined in the parameter file (it is currently set
to 0.7 which approximately corresponds to 4 dB of attenuation),in other words,
if the first bit of reliab[][] = 0 and
if the forth bit of reliab[][] = 0,then the lowest range bin at which Zm is above the noise threshold is chosen
as the near-surface range bin. The actual value of this near-surface range bin
is stored in rangeBinNum[][6] in V6.

- 113 -

Specifically,
nearSurfRain[n_anglebin] = rain[n_anglebin][rangeBinNum[n_anglebin][6]];nearSurfRain(n_anglebin) = rain((rangeBinNum(7,n_anglebin)+1),n_anglebin)

nearSurfZ
float32
REAL*4

nearSurfZ[49];nearSurfZ(49)Near-surface Z-factor
See nearSurfRain[] for the definition of "Near-surface".
nearSurfZ[n_anglebin]=correctZFactor[n_anglebin][rangeBinNum[n_anglebin][6]];nearSurfZ(n_anglebin)=correctZFactor((rangeBinNum(7,n_anglebin)+1),n_anglebin)

nubfCorrectFactor (new definitions)float32
REAL*4nubfCorrectFactor[49][3];nubfCorrectFactor(3,49)'nubfCorrectFactor` is the non-uniform beam filling (NUBF) correction factor.
nubfCorrectFactor[][0] is the NUBF correction factor for the surface reference
and its range is between 1.0 and 10.0.
nubfCorrectFactor[][1] is the NUBF correction factor for the R-Ze relation.
nubfCorrectFactor[][2] is the NUBF correction factor for the LWC-Ze relation.
Note that the NUBF correction factor for the k-Ze relation is stored inepsilon_nubf.

parmNode
int16

parmNode[49][5];INTEGER*2 parmNode(5,49)
Range bin numbers of the nodal points at which
the attenuation parameter alpha and the Z-R parameters "a" and "b" are given
in attenParmAlpha[49][5] (attenParmAlpha(5,49)),
ZRParmA[49][5] (ZRParmA(5,49)), and- 114 -ZRParmB[49][5] (ZRParmB(5,49)), respectively.
For each angle bin, 5 nodal points are defined.
ParmNode[][] gives the range bin numbers of the 5 nodes at which
the values of attenuation parameter "alpha" and the Z-R parameters "a" and "b"are given in ParmAlpha[][], ZRParmA[][] and ZRParmB[][], respectively.
The values of alpha, a and b between the nodes are linearly interpolated.
The range of ParmNode is between 0 and 79. (See the note for rangeBinNum.)
In no-rain angle bins, ParmNode[][] is set to 0.
Note that the definition of range bin number in 2A25 is not the same as
1B-21 or 1C-21. The bin number shows the position in the 80-element arrayso that it takes a number between 0 and 79 (inclusive).
Bin number 79 corresponds to the surface of the ellipsoid which is approximately
equal to the sea surface.

pia
float32

pia[49][3];REAL*4pia(3,49)

pia[][0]Path-integrated attenuation from rain top to surface.
This attenuation is calculated from the attenuation-corrected Z-profile
in correctZFactor[][] and adjusted alpha.
The number represents the two-way attenuation to the actual surface.
pia[][1]Path-integrated attenuation between the clutter-free bottom and the surface.
This is the attenuation estimate in the range that is cluttered by the surface
echo.
pia[][2]Path-integrated attenuation to surface estimated by the surface referencetechnique in 2A21. This is an exact copy of pathAtten(49) in 2A21.

pia_srt (new)float32

pia_srt[49][6];REAL*4

pia_srt(6,49)- 115 -

The values of 6 kinds of path-integrated attenuation (PIA) given by 2A21.
pia_srt[][0]This value is used in 2A25. This is identical to pia[][2].
pia_srt[][1]This is an exact copy of PIAalt[][0] in 2A21.
pia_srt[][2]This is an exact copy of PIAalt[][1] in 2A21.
pia_srt[][3]This is an exact copy of PIAalt[][2] in 2A21.
pia_srt[][4]This is an exact copy of PIAalt[][3] in 2A21.
pia_srt[][5]This is an exact copy of PIAalt[][4] in 2A21.

precipWaterParmA
float32

precipWaterParmA[49][5];READ*4

precipWaterParmA(5,49)

Coefficient a in the relation between the precipitation water content (PWC)
and Ze at 5 nodal points. The unit of PWC is g/m^3 and that of Ze is mm^6/m^3.
PWC = a*Ze^b.
'a' is given at five nodal points.
These values are stored in the first 5 elements of the array.
'a' values between the nodes can be calculated by linear interpolation.
The range bin numbers of the nodes are stored in the ParmNode[49][5](ParmNode(5,49)).
Note that the sum of PWC’s calculated from Z=correctZFactor with formula
PWC = a*Ze^b where a and b from the interpoloted values of precipWaterParmA
and precipWaterParmB does not necessarily agree with precipWaterSum.
precipWaterSum also includes the precipitation water content in the surface
clutter range.

precipWaterParmB
float32

precipWaterParmB[49][5];- 116 -

READ*4

precipWaterParmB(5,49)

Coefficient a in the relation between the precipitation water content (PWC)
and Ze at 5 nodal points. The unit of PWC is g/m^3 and that of Ze is mm^6/m^3.
PWC = a*Ze^b.
'b' is given at five nodal points.
'b' values between the nodes can be calculated by linear interpolation.
The range bin numbers of the nodes are stored in the ParmNode[49][5](ParmNode(5,49)).

precipWaterSum(New dimension)

float32

precipWaterSum[49][2];

REAL*4

precipWaterSum(2,49)

Vertically integrated value of precipitation water content.
The unit is g km/m^3 or equivalently kg/m^2.
“precipWaterSum[0]” give the sum of the precipitation liquid water content
from the freezing height to the actual surface. The water content in the surface
clutter range is estimated with the same assumption that is used in theattenuation correction.
“precipWaterSum[1]” give the sum of the precipitation ice content from the
top of storm to the freezing height.

qualityFlag (New definition)
int16

qualityFlag[49];INTEGER*2

qualityFlag(49)Quality flag for each angle bin data
The default value is 0.
In V6, the definitions of bits 2, 3, 4, 5 are changed, and bits 13 and 14 areadded. The flags indicated by bits 4, 5 and 13 in V6 are moved from method flagin V5.
0: normal+1: unusual situation in rain average+2: NSD of zeta (xi) calculated from less than 6 points (flag_xi >= 2)- 117 -

+4: NSD of PIA calculated from less than 6 points (flag_nsd >= 2)+8: upper bound of nubfCFs ((status_nubf/4)%2==1)+16: lower bound of nubfCFs ((status_nubf/8)%2==1)+32: epsilon not reliable, epsi_sig <= 0.0 (flag_epsi==1)+64: 2A21 input data not reliable (flag_2a21>=3)+128: 2A23 input data not reliable (flag_2a23>99)+256: range bin error (flag_rbin)+512: sidelobe clutter removal (flag_sidelobe)+1024: lower bound of nubfCFkz ((status_nubf/2)%2==1)+4096: const Z is invalid+8192: reliabFactor in 2A21 is NaN (flag_2a21_rf!=0)+16384: data missing
16th bit (sign bit) is not used.
The contents are exact copy of internal variable flag_qlty.

rain
float32

rain[49][80];

REAL*4rain(80,49)

Internally this quantity is stored as
int16 rain_scale[49][80] after multiplied (scaled) by 100.
rainfall rate in mm/h
49 elements in the 2-D array correspond to the angle bins and 80 elements(first argument in FORTRAN convention) in the 2-D array correspond to the range
bins.
If the estimated Z-factor is below 0 dBZ, the rain rate is always set to 0.
If the input radar reflectivity factor Zm is below the noise level,
the corresponding rain estimate is set to 0. This procedure does not cause
any serious problem except when the measured Zm becomes smaller than the noiselevel by rain attenuation. In such a case, even if some heavy rain exists near
the surface,the number in this variable is 0.
To know whether such low radar reflectivity factors are caused by large
attenuation or not, look at the forth bit of 'reliab' and the forth bit of
rainFlag.

- 118 -

80 range bins are filled with data from top to bottom in height.
The last element corresponds to the ellipsoid height, i.e., 0 m high above
the model ellipsoid (not the actual surface). The first element corresponds to
the radar resolution cell about 20 km above in slant range along the beamfrom the footprint on the ellipsoid. The range resolution is 250 m.
If the radar data is missing, MISSING value of -99.99 is stored.
This situation may happen at range bins above 15 km high because JAXA only
guarantees the data collection below 15km.
(The highest edge of the radar's receiving window comes down to nearly 15km above
the sea level near the equator.)
The bin number of the lowest range bin that contains valid rain data is(rangeBinNum[][6] - 1 in C) or (rangeBinNum(7,.) - 1 in FORTRAN).
Below this level, CLUTTER value of -88.88 is stored.
If the estimated rainfall rate exceeds 300 mm/h, it is reset to 300 mm/h.

rainAve (New definition)
float32

rainAve[49][2];

REAL*4

rainAve(2,49)

rainAve[][0] :rainAve(1,*) : Average of rainfall rate between 2 and 4 km.

The unit is mm/h.

If the lowest bin processed is higher than 2 km, the average is taken between
the lowest altitude and 4 km.In this case, the 6th bit in rainFlag is set.
If the lowest bin processed is higher than 4 km, the average is not calculated.
In this case, 0 is stored, and the seventh bit of rainFalg is set.
rainAve[][1] :rainAve(2,*) : Integrated rainfall rate from the rain top to the bottom.
The unit in V6 and V7 is (cm/h)*km, and NOT (mm/h)*km. This odd unit is adopted
to avoid the overflow when the sum is stored as int16 after scaled by 100.
(It is not possible to use different scale factors for rainAve[][0]and rainAve[][1]. Cases with overflow were found in V5.)

- 119 -

rainFlag
int16

rainFlag[49];INTEGER*2

rainFlag(49)Rain flag for each angle bin (See flag_rain in Appendix 2.)
The default value is 0.
The following meanings are assigned to each bit in the 16-bit integer.
0: (bit1) no rain

+1: (bit1) rain possible (this bit is set even when rain is certain)+2: (bit2) rain certain+4: (bit3) zeta > zeta_th(=0.7) (PIA larger than approximately 4 dB)+8: (bit4) zeta is too large (zeta > zeta_max=5.0)+16: (bit5) stratiform+32: (bit6) convective+64: (bit7) bright band is detected+128: (bit8) warm rain

+256: (bit9) rain bottom above 2 km

+512: (bit 10) rain bottom above 4 km
+1024: (bit 11) rain rate is above upper limit+16384: (bit 15) data partly missing between rain top and bottom
12th to 14th bits are currently not used.
16th bit (sign bit) is not used either.

rainType
int16

rainType[49];INTEGER*2

rainType(49)This is an exact copy of rainType in 2A23.

rangeBinNum(New definition)

int16

rangeBinNum[49][7];INTEGER*2

rangeBinNum(7,49)

rangeBinNum[][0]: range bin number at the top of the intervalthat is processed as meaningful data in 2A-25.
This is 4 range bins (1 km) above the first (highest)- 120 -

rain-certain range bin.
rangeBinNum[][1]: range bin number at the top of the surface clutter
defined in 1B21.
rangeBinNum[][2]: range bin number at the actual surface.
rangeBinNum[][3]: range bin number of the bright band if it exits.
If not, the range bin number of the phase transition
height(estimated 0C height) is stored. (Read the note forfreezH.)rangeBinNum[][4]: the range bin number at which the path-integrated
Z-factor
first exceeds the given threshold.
If the path-integrated Z-factor does not exceed thethreshold, it is set to 79.
rangeBinNum[][5]: the range bin number at which the measured Z-factor is
maximum. If no rain, it is set to 79.
rangeBinNum[][6]: the range bin number at the bottom of the interval thatis processed as meaningful data in 2A-25.
The attenuation-corrected Ze and rainfall rate R at thisrange bin are defined as nearSurfZ and nearSurfRain.
See note below.
All these range bin numbers are indexed vertically from top to bottom with 0
at the highest elevation and 79 at the earth ellipsoid.
(All negative bin numbers are set to 0, and numbers larger than 79 are set to79.)
Exception: If the actual surface is lower than the ellipsoid, the number inrangeBinNum[][2] may be larger than 79.

This situation happens occasionally,

especially over Indian Ocean where the geoid surface is lower than the model
ellipsoid. The same situation may happen at a very low place over land, forexample, at Dead Sea where the surface is nearly 400 m below the sea level.
Range bin numbers are unitless.

Note 1: rangeBinNum[][1] contains the range bin number that is the top of thepossibly surface cluttered ranges.

This number is larger than the bin number

for the bottom of the clutter-free ranges by one.

- 121 -

Note 2: rangeBinNum[][6] contains the range bin number that corresponds to thebottom of the interval that is processed as meaningful data in 2A-25. This range
bin is one bin above the top of the region that is cluttered either by the surface
echo in the antenna mainlobe or by noise.

In the former case, this number is

identical to (rangeBinNum[][1]-1), but in the latter case, rangeBinNum[][6] isdifferent from (rangeBinNum[][1]-1).

The latter case may happen when the rainecho near surface becomes lower than the noise level by very large attenuation
due to heavy rain.

When rain is light and the echo near surface is below thenoise level, the data smaller than the noise level are treated as valid data
and the rainfall rate at that bin is set to zero.

reliabint8

reliab[49][80];BYTE

reliab(80,49)

Reliability parameter at each range bin
The default value is 0.
Each bit in the byte indicates the status shown below:
lowest (first) bit: 0 : measured signal below noise

lowest (first) bit: rainsecond bit: rain certain

third bit: bright band

forth bit: large attenuation

fifth bit

: weak return (Zm < 20 dBZ)

sixth bit

: estimated Ze < 0 dBZ

seventh bit: main-lobe clutter or below surface

eighth bit: missing data

For example, if the first bit is 0, i.e., if the number is an even number,then the measured signal in that range bin is below the noise level(noise threshold).

The large attenuation flag is set below the height at which the integral of
0.2*ln(10)*beta*alpha*Zm^beta first exceeds the given threshold.
In V 7, the threshold is 0.7 which approximately corresponds to the attenuationof 4 dB.

- 122 -

scanStatus
PR_SCAN_STATUS

scanStatus;

See the description of the 1B21 Scan Status in the TSDIS INTERFACE CONTROLSPECIFICATION (ICS) Volume 3.

scanTime
float64

scanTime;

REAL*8

scanTime

See the description of the 1B21 Scan Status in the TSDIS INTERFACE CONTROLSPECIFICATION (ICS) Volume 3.

scLocalZenith(New variable)

float32

scLocalZenith[49];

REAL*4scLocalZenith(49)Local zenith angle of the satellite at the center of the footprint.
The number corresponds to the incidence angle of the radar beam to the surface(ellipsoid surface).

sigmaZero(New variable)

float32

sigmaZero[49];

REAL*4sigmaZero(49)Exact copy of sigmaZero from 2A21.

spare(New definition)

float32

spare[49][2];

REAL*4spare(2,49)

spare[49][0] : distspare[49][1] : pia_error- 123 -

stddev_alpha (new)float32 stddev_alpha [49]
REAL*4 stddev_alpha (49)standard deviation of epsilon total which corresponds to the estimateduncertainty of alpha.
epsi_alpha=exp(log(epsilonf)*stddev_epsi*stddev_epsi/(stddev_epsi_f*stddev_epsi_f));

stddev_PIAsrt (new)float32 stddev_PIAsrt[49]
REAL*4 stddev_PIAsrt(49)standard deviation of PIA given by surface reference technique (SRT) used in
2A25. This value is different from the value from 2A21. Some minimum fluctuation
is assumed in the surface cross section measurement.
stddev_sigma;/* new */stddev_srt (new)float32 stddev_srt[49][6]
REAL*4 stddev_srt(6,49)
standard deviations of 6 kinds of PIA given by 2A21. stddev_srt[][0] is theactual value used in 2A25.

stddev_zeta (new)float32 stddev_zeta[49]
REAL*4 stddev_zeta(49)standard deviation of zeta

stddev_Zm (new)float32 stddev_Zm [49]
REAL*4 stddev_Zm (49)standard deviation of of epsilon_f
stddev_epsi_f=sqrt(stddev_epsi_total*stddev_epsi_total
stddev_epsi_nubf*stddev_epsi_nubf);

weightW
float32+(Obsolete. No data in V6 and V7. Can be calculated from epsilon andepsilon_0.)
weightW[49];- 124 -REAL*4

weightW(49)Internally this quantity was stored as
int16 weightW_scale[49] after multiplied (scaled) by 1000.
Weighting factor in the calculation of epsilon (SRT correction factor)
in the hybrid method. The number is always between 0 and 1 (inclusive).
Note that in V6 and V7, epsilon_0 is output instead of weightW.
The relationship among epsilon, epsilon_0 and weightW is as follows.
epsilon = 1 + weightW*(epsilon_0 - 1)

zeta
float32

zeta[49][2];

REAL*4zeta(2,49)

Integral of 0.2*ln(10)*beta*alpha*Zm^beta from rain top to the clutter-freebottom.
zeta[][0]: zeta = Integral of 0.2*ln(10)*beta*alpha*Zm^beta from the rain
top to the bottom (lowest altitude processed).
zeta[][1]: PIA_est = -10*(log10(1-zeta_cr))/beta where zeta_cr is a corrected
zeta (This zeta_cr is calculated by using the value ofepsilon in the first cycle of processing which isdifferent from the final estimate of epsilon.).
zeta is always between 0 and 100, typically between 0 and 2.

When it is larger

than 5, the 4th bit of rainFlag is set.
zeta is unitless.

zeta_mn
float32

zeta_mn[49][2];

REAL*4

zeta_mn(2,49)

Mean of zeta and PIA of 9 adjacent (3x3) beams.
At scan edges, the mean is calculated of 6 beams. At the scan edges of the firstand last scans of the granule, the mean is calculated from only 4 beams.

- 125 -

zeta_mn[][0]: zeta_mn = mean of zeta
zeta_mn[][1]: PIA_mn = mean of PIA_est
The range of output value is the same as zeta itself.
zeta_mn is unitless.

zeta_sd
float32

zeta_sd[49][2];

REAL*4

zeta_sd(2,49)

Standard deviation of zeta and PIA_est in 9 adjacent (3 x 3) beams.
At scan edges, it is calculated in 6 beams. At the scan edges of the first andlast scans of the granule, the mean is calculated from only 4 beams.
zeta_sd[][0]: zeta_sd = standard deviation of zeta
zeta_sd[][1]: PIA_sd = standard deviation of pia_est
zeta_sd is unitless.

zmmax
float32

zmmax[49];

REAL*4zmmax(49)zmmax is the maximum value of measured Z-factor expressed in dBZ at each IFOV.
The unit is dBZ or 10 log of mm^6/m^3.
0 and 100.

The range of the variable is between(Typically between 10 and 60.)

ZRParmA
float32

ZRParmA[49][5];REAL*4

ZRParmA(5,49)

Z-R parameter 'a' at nodal points.
R = a*Z^b.
'a' is given at five nodal points.
These values are stored in the first 5 elements of the array.
'a' values between the nodes are calculated by linear interpolation.

- 126 -

The

range

bin

numbers

of

the

nodes

are

storedin

ParmNode[49][5](ParmNode(5,49)).

ZRParmB
float32

ZRParmB[49][5];REAL*4

ZRParmB(5,49)

Z-R parameter 'b' at nodal points.

R = a*Z^b.
'b' is given at five nodal points.
The nodal points are the same as those for alpha.
'b' values between the nodes are calculated by linear interpolation.
The

range

bin

numbers

of

the

nodes

are

stored(ParmNode(5,49)).

ZRParmNode(Obsolete.

No data in V6)

int16

ZRParmNode[49][5];INTEGER*2

ZRParmNode(5,49);

This parameter is absorbed in parmNode[49][5].

Appendix 1. Output data structure defined in the toolkit#ifndef _TK_2A25_H_#define _TK_2A25_H_#ifndef _L2A25_NAVIGATION_#define _L2A25_NAVIGATION_
typedef struct {float scPosX;
float scPosY;
float scPosZ;
float scVelX;
float scVelY;
float scVelZ;
float scLat;- 127 -

in

ParmNode[49][5]float scLon;
float scAlt;
float scAttRoll;float scAttPitch;float scAttYaw;
float SensorOrientationMatrix[3][3];float greenHourAng;} L2A25_NAVIGATION;#endif#ifndef _L2A25_SCANSTATUS_#define _L2A25_SCANSTATUS_
typedef struct {signed char missing;
signed char validity;
signed char qac;signed char geoQuality;
signed char dataQuality;
short SCorientation;
signed char acsMode;
signed char yawUpdateS;
signed char prMode;
signed char prStatus1;
signed char prStatus2;
double FractionalGranuleNumber;} L2A25_SCANSTATUS;#endif#ifndef _L2A25_SCANTIME_#define _L2A25_SCANTIME_
typedef struct {short Year;signed char Month;signed char DayOfMonth;signed char Hour;signed char Minute;signed char Second;
short MilliSecond;
short DayOfYear;} L2A25_SCANTIME;#endif- 128 -

#ifndef _L2A25_SWATH_#define _L2A25_SWATH_
typedef struct {L2A25_SCANTIME ScanTime;double scanTime_sec;
float Latitude[49];float Longitude[49];
L2A25_SCANSTATUS scanStatus;
L2A25_NAVIGATION navigation;
float scLocalZenith[49];float rain[49][80];signed char reliab[49][80];float correctZFactor[49][80];float attenParmAlpha[49][5];float attenParmBeta[49];short parmNode[49][5];float precipWaterParmA[49][5];float precipWaterParmB[49][5];float ZRParmA[49][5];float ZRParmB[49][5];float zmmax[49];short rainFlag[49];short rangeBinNum[49][7];float rainAve[49][2];float precipWaterSum[49][2];float epsilon_0[49];short method[49];float epsilon[49];float epsilon_alpha[49];float epsilon_nubf[49];float zeta[49][2];float zeta_mn[49][2];float zeta_sd[49][2];float sigmaZero[49];float freezH[49];float nubfCorrectFactor[49][3];float stddev_zeta[49];float stddev_PIAsrt[49];float stddev_alpha[49];float stddev_Zm[49];short qualityFlag[49];float nearSurfRain[49];float nearSurfZ[49];float e_SurfRain[49];float pia[49][3];float pia_srt[49][6];- 129 -

float stddev_srt[49][6];float errorRain[49];float errorZ[49];float spare[49][2];short rainType[49];} L2A25_SWATH;#endif#ifndef _L2A25_CLUTTER_#define _L2A25_CLUTTER_
typedef struct {signed char mainlobeEdge[49];signed char sidelobeRange[49][3];} L2A25_CLUTTER;#endif#endifScale factors:#define L2A25_RAIN

100#define L2A25_CORRECTZFACTOR

100#define L2A25_ATTENPARMALPHA

10000000#define L2A25_ZRPARMA

100000#define L2A25_ZRPARMB

10000#define L2A25_RAINAVE

100#define L2A25_LIQWATERSUM

1000#define L2A25_ATTENPARMBETA#define L2A25_WEIGHTW

10000
1000

#define L2A25_NEARSURFRAIN

100#define L2A25_NEARSURFZ

100

Appendix 2. Parameters defined in “param_general_7.6.dat”
This parameter file for V7 is identical to that for V6. Note that nubf_cf’s are read but not usedin V7 of 2A25.

- 130 -

1 /* parameter file for v7.2 of 2A25. Aug. 21, 2010 */2 /* Do not delete empty lines. */3 /* Do not add or delete lines. Absolute line numbers are important. */4 1.0000 vratio[0]/* Terminal velocity ratio at 0 km */5 1.0396 vratio[1]/* Terminal velocity ratio at 1 km */6 1.0817 vratio[2]/* Terminal velocity ratio at 2 km */7 1.1266 vratio[3]/* Terminal velocity ratio at 3 km */8 1.1745 vratio[4]/* Terminal velocity ratio at 4 km */9 1.2257 vratio[5]/* Terminal velocity ratio at 5 km */10 1.2806 vratio[6]/* Terminal velocity ratio at 6 km */11 1.3394 vratio[7]/* Terminal velocity ratio at 7 km */12 1.4026 vratio[8]/* Terminal velocity ratio at 8 km */13 1.4706 vratio[9]/* Terminal velocity ratio at 9 km */14 1.5440 vratio[10]/* Terminal velocity ratio at 10 km */15 1.6234 vratio[11]/* Terminal velocity ratio at 11 km */16 1.7283 vratio[12]/* Terminal velocity ratio at 12 km */17 1.8404 vratio[13]/* Terminal velocity ratio at 13 km */18 1.9597 vratio[14]/* Terminal velocity ratio at 14 km */19 2.0867 vratio[15]/* Terminal velocity ratio at 15 km */20 2.2219 vratio[16]/* Terminal velocity ratio at 16 km */21 2.3658 vratio[17]/* Terminal velocity ratio at 17 km */22 2.5189 vratio[18]/* Terminal velocity ratio at 18 km */23 2.6819 vratio[19]/* Terminal velocity ratio at 19 km */24 2.8554 vratio[20]/* Terminal velocity ratio at 20 km */25 0.075
lprate/* 1/20 of the lapse rate per 250 m */26 1.0fhcf_strat/* FH correction factor for stratiform rain */27 1.2
fhcf_conv/* FH correction factor for convective rain */28 0.3
nsd_cnv_ocean[0] /* Conv. factor of NSD for stratiform */29 0.3
nsd_cnv_ocean[1] /* Conv. factor of NSD for convective */30 0.3
nsd_cnv_ocean[2] /* Conv. factor of NSD for default */31 0.3
nsd_cnv_land[0] /* Conv. factor of NSD for stratiform */32 0.5
nsd_cnv_land[1] /* Conv. factor of NSD for convective */33 0.3
nsd_cnv_land[2] /* Conv. factor of NSD for default */34 0.10zeta_min/* Threshold value of zeta for SRT */35 5.00
zeta_max/* Threshold for zeta to judge something wrong. */36 0.70
zeta_th_L/* Threshold for zeta to judge large attenuation. */37 0.00
z_offset/* Offset to be added to 1C21 Z factor in dB */38 0.00
z_slope[0][0] /* Slope for ocean strat in clutter. + for larger Z toward surf.
*/
39 0.00
z_slope[0][1] /* Slope of dBZ/km for ocean conv. in cluttered range */40 0.00
z_slope[0][2] /* Slope of dBZ/km for ocean others in cluttered range */41 -0.50
z_slope[1][0] /* Slope of dBZ/km for land strat in clutter. */42 0.00
z_slope[1][1] /* Slope of dBZ/km for land conv. in cluttered range */43 0.00
z_slope[1][2] /* Slope of dBZ/km for land others in cluttered range */44 1.00
epsi_init[0][0] /* initial offset factor of epsilon for ocean stratiform rain*/
45 1.00
epsi_init[0][1] /* initial offset factor of epsilon for ocean convective rain

- 131 -

*/46 1.00
47 1.00*/
48 1.00*/
49 1.00
50 0.08
51 7.70
52 90.0
53 70.0
54 2.00
55 -20.0
ice */

epsi_init[0][2] /* initial offset factor of epsilon for ocean other rain */epsi_init[1][0] /* initial offset factor of epsilon for land stratiform rain
epsi_init[1][1] /* initial offset factor of epsilon for land convective rain
epsi_init[1][2] /* initial offset factor of epsilon for land other rain */atten_O2_surf /* PIA due to O2 at 0 m from geoid */scale_h_O2/* scale height of O2 in km */r_humid_in_rain /* relative humidity inside the raining area */r_humid_out_rain /* relative humidity outside the raining area */scale_h_H2O/* scale height of H2O in km */temp_p_ice/* temperature of the height above which particles are 100%

Appendix 3.

Parameters defined in “param_error_7.3.dat”

Note that many of the parameters defined in this file are not used in V7.
The parameters marked with “n” are not used.
01 0.702 0.503 0.05
04 0.605 0.05
06 1.507 1.008 0.2
09 -0.2
10 1.011 0.3
12 -0.07
13 0.01
14 0.02
15 -0.005
16 1.3
17 -0.05
18 2.00
19 0.02
20 0.25*/
21 0.25
22 0.723 0.724 5.0d_Zm_typ/* Typical error (offset) in Zm in dB */d_alpha_typ/* Typical error in alpha in dB */d_beta_typ/* Typical error in beta in dB */d_zra_typ/* Typical error in a in dB */d_zrb_typ/* Typical error in b in dB */d_surf_typ/* Typical error in sigma^0 in dB */d_nubfCf_s/* Typical error in NUBF correct. factor for surf.*/d_nubfCf_zr/* Typical error in NUBF correct. factor for ZR */dv_dh/* Typical change of velocity per km in dB*/height_err_0C /* 0C height error in km */height_err_BB /* BB height error in km when it exists */dalpha_dT/* Change of alpha per 1 degree in dB */dbeta_dT/* Change of beta per degree in dB */da_dT/* Change of a in ZR per degree in dB */db_dT/* Change of b in ZR per degree in dB */d_alpha_id/* Error in alpha in dB caused by wrong ident. */d_beta_id/* Error in beta in dB caused by wrong ident. */d_zra_id/* Error in a in dB caused by wrong identification */d_zrb_id/* Error in b in dB caused by wrong identification */stddev_epsi_strat/* nominal error of epsilon for strat in linear unit
stddev_epsi_conv/* nominal error of epsilon for conv in linear unit */stddev_SRT_O/* nominal error of SRT over ocean in dB */stddev_SRT_L/* nominal error of SRT over land in dB */stddev_SRT_N/* nominal error of SRT in const-Z method in dB */Appendix 4.

Parameters defined in “param_strat_4.dat”- 132 -

1 /* parameter file for v6.9 of 2A25. January 18, 2008. SP0, Oblate */2 /* Do not delete empty lines. */3 /* Do not add or delete lines. Absolute line numbers are important. */4 /* stratiform parameters */5 /* coefficients for R-Z relationship: R = a * Z^b
6 log10(a) = zr_a_c0 + zr_a_c1*x + zr_a_c2*x*x
7 log10(b) = zr_b_c0 + zr_b_c1*x + zr_b_c2*x*x
8 where x = log10(alpha_final/alpha_initial) */9 /* initial coefficients of k-Z relationship: k = alpha * Z^beta */10 0.000031244 alpha_init[0][0]/* alpha for snow, no water */11 0.00012651 alpha_init[0][1]/* alpha for low density snow, 0.017 */12 0.00050167 alpha_init[0][2]/* alpha for high density snow, 0.170 */13 0.00031110 alpha_init[0][3]/* alpha for rain (stratiform) 0C */14 0.00030719 alpha_init[0][4]/* alpha for rain (stratiform) 20C */15 0.78069
beta_init[0]/* beta for stratiform column, strat */16 /* R-Ze coefficients */17 -1.7219 zr_a_c0[0][0]/* stratiform, bb.000*/
18 -1.8539 zr_a_c0[0][1]/* stratiform, bb.017*/
19 -2.3052 zr_a_c0[0][2]/* stratiform, bb.170*/
20 -1.6599 zr_a_c0[0][3]/* stratiform, 0C*/
21 -1.6085 zr_a_c0[0][4]/* stratiform, 20C*/
22
23 1.4946 zr_a_c1[0][0]/* stratiform, bb.000 */24 1.4974 zr_a_c1[0][1]/* stratiform, bb.017 */25 1.3411 zr_a_c1[0][2]/* stratiform, bb.170 */26 0.8867 zr_a_c1[0][3]/* stratiform, rain 0C */27 0.8766 zr_a_c1[0][4]/* stratiform, rain 20C */28
29 -0.2649 zr_a_c2[0][0]/* stratiform, bb.000 */30 -0.3013 zr_a_c2[0][1]/* stratiform, bb.017 */31 -0.4044 zr_a_c2[0][2]/* stratiform, bb.170 */32 -0.5135 zr_a_c2[0][3]/* stratiform, rain 0C */33 -1.2587 zr_a_c2[0][4]/* stratiform, rain 20C */34
35 -0.1144 zr_b_c0[0][0]/* stratiform, bb.000 */36 -0.1191 zr_b_c0[0][1]/* stratiform, bb.017 */37 -0.1380 zr_b_c0[0][2]/* stratiform, bb.170 */38 -0.1647 zr_b_c0[0][3]/* stratiform, rain 0C */39 -0.1752 zr_b_c0[0][4]/* stratiform, rain 20C */40
41 -0.0916 zr_b_c1[0][0]/* stratiform, bb.000 */42 -0.0801 zr_b_c1[0][1]/* stratiform, bb.017 */43 -0.0206 zr_b_c1[0][2]/* stratiform, bb.170 */44 0.1022 zr_b_c1[0][3]/* stratiform, rain 0C */45 0.1179 zr_b_c1[0][4]/* stratiform, rain 20C */46
47 0.1120 zr_b_c2[0][0]/* stratiform, bb.000 */48 0.1077 zr_b_c2[0][1]/* stratiform, bb.017 */49 0.0889 zr_b_c2[0][2]/* stratiform, bb.170 */50 0.0849 zr_b_c2[0][3]/* stratiform, rain 0C */51 0.2340 zr_b_c2[0][4]/* stratiform, rain 20C */52 /* LWC-Ze coefficients (log10 of a and b in LWC = a Ze^b) */- 133 -

53 -2.4161 zl_a_c0[0][0]54 -2.4881 zl_a_c0[0][1]55 -3.1290 zl_a_c0[0][2]56 -2.6994 zl_a_c0[0][3]57 -2.6502 zl_a_c0[0][4]58
59 1.5422 zl_a_c1[0][0]60 1.8509 zl_a_c1[0][1]61 1.8344 zl_a_c1[0][2]62 1.5283 zl_a_c1[0][3]63 1.5422 zl_a_c1[0][4]6465 -0.2365 zl_a_c2[0][0]66 -0.2254 zl_a_c2[0][1]67 -0.3571 zl_a_c2[0][2]68 -0.5889 zl_a_c2[0][3]69 -1.6158 zl_a_c2[0][4]7071 -0.1471 zl_b_c0[0][0]72 -0.1520 zl_b_c0[0][1]73 -0.1768 zl_b_c0[0][2]74 -0.2122 zl_b_c0[0][3]75 -0.2243 zl_b_c0[0][4]7677 -0.1056 zl_b_c1[0][0]78 -0.0915 zl_b_c1[0][1]79 -0.0442 zl_b_c1[0][2]80 0.0630 zl_b_c1[0][3]81 0.0751 zl_b_c1[0][4]82
83 0.1453 zl_b_c2[0][0]84 0.1357 zl_b_c2[0][1]85 0.1265 zl_b_c2[0][2]86 0.1913 zl_b_c2[0][3]87 0.4320 zl_b_c2[0][4]Appendix 5.
1
2
3
4
5
6
7
8
9
10
11
12

/* stratiform, bb.011, a=0.00383613 *//* stratiform, bb.02, a=0.00325046 *//* stratiform, bb.17, a=0.00074301 *//* stratiform, 0C ,a=0.00199806 *//* stratiform, 20C ,a=0.00223787 *//* stratiform, bb.011 *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 20C *//* stratiform, bb.011 *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 20C *//* stratiform, bb.011, b=0.71266 *//* stratiform, bb.02, b=0.70472 *//* stratiform, bb.17, b=0.66564 *//* stratiform, 0C,
b=0.61342 *//* stratiform, 20C,
b=0.59658 *//* stratiform, bb.011 *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 20C *//* stratiform, bb.011 *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 0C *//* stratiform, 20C */Parameters defined in “param_conv_4.dat”/* parameter file for v6.9 of 2A25. January 18 2008, SP0, Oblate*//* Do not delete empty lines. *//* Do not add or delete lines. Absolute line numbers are important. *//* convective rain parameters *//* coefficients for R-Z relationship: R = a * Z^b
log10(a) = zr_a_c0 + zr_a_c1*x + zr_a_c2*x*xlog10(b) = zr_b_c0 + zr_b_c1*x + zr_b_c2*x*xwhere x = log10(alpha_final/alpha_initial) *//* initial coefficients of k-Z relationship: k = alpha * Z^beta */0.000048144 alpha_init[1][0]/* alpha for snow, no water */0.000141036 alpha_init[1][1]/* alpha for low density snow, 0.011 */0.000428637 alpha_init[1][2]/* alpha for rain (convective) 0C */- 134 -

13 0.000428637 alpha_init[1][3]/* alpha for rain (convective) 0C */14 0.000432574 alpha_init[1][4]/* alpha for rain (convective) 20C */15 0.758892044
beta_init[1]/* beta for convective column, conv */16 /* R-Ze coefficients */17 -1.6071 zr_a_c0[1][0]/* convective, bb.000 */18 -1.6929 zr_a_c0[1][1]/* convective, bb.011, a=0.02027, a'= 174.09 */19 -1.4336 zr_a_c0[1][2]/* convective, 0C ,a=0.03484, a'= 159.44 */20 -1.4336 zr_a_c0[1][3]/* convective, 0C ,a=0.03484, a'= 159.44 */21 -1.3754 zr_a_c0[1][4]/* convective, 20C ,*/22
23 1.6925 zr_a_c1[1][0]/* convective, bb.000 */24 1.7174 zr_a_c1[1][1]/* convective, bb.011 */25 0.8576 zr_a_c1[1][2]/* convective, 0C */26 0.8576 zr_a_c1[1][3]/* convective, 0C */27 0.9149 zr_a_c1[1][4]/* convective, 20C */28
29 -0.4980 zr_a_c2[1][0]/* convective, bb.000 */30 -0.5336 zr_a_c2[1][1]/* convective, bb.011 */31 -1.1231 zr_a_c2[1][2]/* convective, 0C */32 -1.1231 zr_a_c2[1][3]/* convective, 0C */33 -2.0411 zr_a_c2[1][4]/* convective, 20C */34
35 -0.1215 zr_b_c0[1][0]/* convective, bb.000 */36 -0.1217 zr_b_c0[1][1]/* convective, bb.011, b=0.7556, 1/b=1.3234 */37 -0.1885 zr_b_c0[1][2]/* convective, 0C,*/
38 -0.1885 zr_b_c0[1][3]/* convective, 0C,*/
39 -0.1999 zr_b_c0[1][4]/* convective, 20C,*/
40
41 -0.1163 zr_b_c1[1][0]/* convective, bb.000 */42 -0.1163 zr_b_c1[1][1]/* convective, bb.011 */43 +0.0980 zr_b_c1[1][2]/* convective, 0C */44 +0.0980 zr_b_c1[1][3]/* convective, 0C */45 +0.0989 zr_b_c1[1][4]/* convective, 20C */46
47 0.1293 zr_b_c2[1][0]/* convective, bb.000 */48 0.1302 zr_b_c2[1][1]/* convective, bb.011 */49 0.1915 zr_b_c2[1][2]/* convective, 0C */50 0.1915 zr_b_c2[1][3]/* convective, 0C */51 0.3602 zr_b_c2[1][4]/* convective, 20C */52 /* LWC-Ze coefficients (log10 of a and b in LWC = a Ze^b) */53 -2.2070 zl_a_c0[1][0]/* convective, bb.011, a=0.00620868 */54 -2.4070 zl_a_c0[1][1]/* convective, 0C ,a=0.00391752 */55 -2.4070 zl_a_c0[1][2]/* convective, 0C ,a=0.00391752 */56 -2.4070 zl_a_c0[1][3]/* convective, 0C ,a=0.00391752 */57 -2.3522 zl_a_c0[1][4]/* convective, 20C ,a=0.004444 */58
59 2.0441 zl_a_c1[1][0]/* convective, bb.011 */60 1.5269 zl_a_c1[1][1]/* convective, 0C */61 1.5269 zl_a_c1[1][2]/* convective, 0C */62 1.5269 zl_a_c1[1][3]/* convective, 0C */63 1.5766 zl_a_c1[1][4]/* convective, 20C */64- 135 -

65 -0.5818 zl_a_c2[1][0]66 -1.0761 zl_a_c2[1][1]67 -1.0761 zl_a_c2[1][2]68 -1.0761 zl_a_c2[1][3]69 -2.2027 zl_a_c2[1][4]7071 -0.1618 zl_b_c0[1][0]72 -0.2377 zl_b_c0[1][1]
73 -0.2377 zl_b_c0[1][2]74 -0.2377 zl_b_c0[1][3]75 -0.2500 zl_b_c0[1][4]7677 -0.1259 zl_b_c1[1][0]78 0.0533 zl_b_c1[1][1]79 0.0533 zl_b_c1[1][2]80 0.0533 zl_b_c1[1][3]81 0.0545 zl_b_c1[1][4]82
83 0.1724 zl_b_c2[1][0]84 0.2681 zl_b_c2[1][1]85 0.2681 zl_b_c2[1][2]86 0.2681 zl_b_c2[1][3]87 0.5077 zl_b_c2[1][4]Appendix 6.

/* convective, bb.011 *//* convective, 0C *//* convective, 0C *//* convective, 0C *//* convective, 20C *//* convective, bb.011, b=0.68902 *//* convective, 0C,
b=0.57855 *//* convective, 0C,
b=0.57855 *//* convective, 0C,
b=0.57855 *//* convective, 20C,
b=0.56232 *//* convective, bb.011 *//* convective, 0C *//* convective, 0C *//* convective, 0C *//* convective, 20C *//* convective, bb.011 *//* convective, 0C *//* convective, 0C *//* convective, 0C *//* convective, 20C */Parameters defined in “param_other_4.dat”

1 /* parameter file for v6.9 of 2A25. January 18 2008, SP0, Oblate*/
2 /* Do not delete empty lines. */3 /* Do not add or delete lines. Absolute line numbers are important. */4 /* convective rain parameters */5 /* coefficients for R-Z relationship: R = a * Z^b
6 log10(a) = zr_a_c0 + zr_a_c1*x + zr_a_c2*x*x
7 log10(b) = zr_b_c0 + zr_b_c1*x + zr_b_c2*x*x
8 where x = log10(alpha_final/alpha_initial) */9 /* initial coefficients of k-Z relationship: k = alpha * Z^beta */10 0.000048144 alpha_init[2][0]/* alpha for snow, no water */11 0.000141036 alpha_init[2][1]/* alpha for low density snow, 0.011 */12 0.000428637 alpha_init[2][2]/* alpha for rain (convective) 0C */13 0.000428637 alpha_init[2][3]/* alpha for rain (convective) 0C */14 0.000432574 alpha_init[2][4]/* alpha for rain (convective) 20C */15 0.758892044
beta_init[2]/* beta for convective column, conv */16 /* R-Ze coefficients */17 -1.6071 zr_a_c0[2][0]/* convective, bb.000 */18 -1.6929 zr_a_c0[2][1]/* convective, bb.011, a=0.02027, a'= 174.09 */19 -1.4336 zr_a_c0[2][2]/* convective, 0C ,a=0.03484, a'= 159.44 */20 -1.4336 zr_a_c0[2][3]/* convective, 0C ,a=0.03484, a'= 159.44 */21 -1.3754 zr_a_c0[2][4]/* convective, 20C ,*/22
23 1.6925 zr_a_c1[2][0]/* convective, bb.000 */24 1.7174 zr_a_c1[2][1]/* convective, bb.011 */- 136 -

25 0.8576 zr_a_c1[2][2]/* convective, 0C */26 0.8576 zr_a_c1[2][3]/* convective, 0C */27 0.9149 zr_a_c1[2][4]/* convective, 20C */28
29 -0.4980 zr_a_c2[2][0]/* convective, bb.000 */30 -0.5336 zr_a_c2[2][1]/* convective, bb.011 */31 -1.1231 zr_a_c2[2][2]/* convective, 0C */32 -1.1231 zr_a_c2[2][3]/* convective, 0C */33 -2.0411 zr_a_c2[2][4]/* convective, 20C */34
35 -0.1215 zr_b_c0[2][0]/* convective, bb.000 */36 -0.1217 zr_b_c0[2][1]/* convective, bb.011, b=0.7556, 1/b=1.3234 */37 -0.1885 zr_b_c0[2][2]/* convective, 0C,*/
38 -0.1885 zr_b_c0[2][3]/* convective, 0C,*/
39 -0.1999 zr_b_c0[2][4]/* convective, 20C,*/
40
41 -0.1163 zr_b_c1[2][0]/* convective, bb.000 */42 -0.1163 zr_b_c1[2][1]/* convective, bb.011 */43 +0.0980 zr_b_c1[2][2]/* convective, 0C */44 +0.0980 zr_b_c1[2][3]/* convective, 0C */45 +0.0989 zr_b_c1[2][4]/* convective, 20C */42
47 0.1293 zr_b_c2[2][0]/* convective, bb.000 */48 0.1302 zr_b_c2[2][1]/* convective, bb.011 */49 0.1915 zr_b_c2[2][2]/* convective, 0C */50 0.1915 zr_b_c2[2][3]/* convective, 0C */51 0.3602 zr_b_c2[2][4]/* convective, 20C */52 /* LWC-Ze coefficients (log10 of a and b in LWC = a Ze^b) */53 -2.2070 zl_a_c0[2][0]/* convective, bb.011, a=0.00620868 */54 -2.4070 zl_a_c0[2][1]/* convective, 0C ,a=0.00391752 */55 -2.4070 zl_a_c0[2][2]/* convective, 0C ,a=0.00391752 */56 -2.4070 zl_a_c0[2][3]/* convective, 0C ,a=0.00391752 */57 -2.3522 zl_a_c0[2][4]/* convective, 20C ,a=0.004444 */58
59 2.0441 zl_a_c1[2][0]/* convective, bb.011 */60 1.5269 zl_a_c1[2][1]/* convective, 0C */61 1.5269 zl_a_c1[2][2]/* convective, 0C */62 1.5269 zl_a_c1[2][3]/* convective, 0C */63 1.5766 zl_a_c1[2][4]/* convective, 20C */64
65 -0.5818 zl_a_c2[2][0]/* convective, bb.011 */66 -1.0761 zl_a_c2[2][1]/* convective, 0C */67 -1.0761 zl_a_c2[2][2]/* convective, 0C */68 -1.0761 zl_a_c2[2][3]/* convective, 0C */69 -2.2027 zl_a_c2[2][4]/* convective, 20C */70
71 -0.1618 zl_b_c0[2][0]/* convective, bb.011, b=0.68902 */72 -0.2377 zl_b_c0[2][1]/* convective, 0C,
b=0.57855 */73 -0.2377 zl_b_c0[2][2]/* convective, 0C,
b=0.57855 */74 -0.2377 zl_b_c0[2][3]/* convective, 0C,
b=0.57855 */75 -0.2500 zl_b_c0[2][4]/* convective, 20C,
b=0.56232 */76- 137 -

77 -0.1259 zl_b_c1[2][0]78 0.0533 zl_b_c1[2][1]79 0.0533 zl_b_c1[2][2]80 0.0533 zl_b_c1[2][3]81 0.0545 zl_b_c1[2][4]82
83 0.1724 zl_b_c2[2][0]84 0.2681 zl_b_c2[2][1]85 0.2681 zl_b_c2[2][2]86 0.2681 zl_b_c2[2][3]87 0.5077 zl_b_c2[2][4]/* convective, bb.011 *//* convective, 0C *//* convective, 0C *//* convective, 0C *//* convective, 20C *//* convective, bb.011 *//* convective, 0C *//* convective, 0C *//* convective, 0C *//* convective, 20C */- 138 -

3.

LEVEL33-1.

3A-25: Space Time Statistics of Level 2 PR Products

3-1. 1.

Objective of the algorithm

The objective of the algorithm is to calculate various statistics over a month from the level 2 PR
output products. Four types of statistics are calculated:
1.
2.
3.
4.

Probabilities of occurrence (count values)
Means and standard deviations
Histograms
Correlation coefficients

In all cases, the statistics are conditioned on the presence of rain or some other quantity suchas the presence of stratiform rain or the presence of a bright-band. For example, to computethe unconditioned mean rain rate, the conditional mean must be multiplied by the probabilityof rain which, in turn is calculated from the ratio of rain counts to the total number ofobservations in the box of interest. Details of the procedure are given in section 8.
The standard space scale is a 5×5-degree latitude×longitude cell. A subset of the products,
however, is also produced over 0.5×0.5-degree cells.
The types of statistics computed include:
At 5×5-degree×1-month cells:
 Means, standard deviations, and count values (“pixel counts”)
 Histograms
 Correlation coefficients
 RZ coefficients, a and b, R = aZb
At 0.5×0.5-degree×1-month cells:
 Means, standard deviations, and count values
 RZ coefficients, a and b, R = aZb
The 5×5-degree statistics are stored in arrays dimensioned (16,72,*), with a product nameending with “1” (generally). There are 16 latitude cells, 72 longitude cells, and possibly otherdimensions, as noted, for height, rain type, etc. Histograms are dimensioned (16,72,30,*) with30 categories.
The 0.5×0.5-degree statistics are dimensioned (148,720,*), and have a product name ending
with “2”. There are 148 latitude cells and 720 longitude cells.

- 139 -

3-1.2.

Output Variables

3-1. 2.1. Variable naming convention
Variable names consist of a word or several words strung together describing the geophysicalquantity, and ending with an abbreviation designating the statistic type. For example, the
5×5-degree mean of stratiform rain rate is stratRainMean1. The statistic type designations are
Mean1
Dev1
Pix1
H
CCoef
rz..A1
rz..B1
Mean2
Dev2
Pix2
rz..A2
rz..B25×5-degree means
5×5-degree standard deviations
5×5-degree pixel counts
histograms
correlation coefficients
RZ-relation a-coefficient, 5×5 degrees; “rz” is a prefix
RZ-relation b-coefficient, 5×5 degrees
0.5×0.5-degree means
0.5×0.5-degree standard deviations
0.5×0.5-degree pixel counts
RZ-relation a-coefficient, 0.5×0.5 degrees
RZ-relation b-coefficient, 0.5×0.5 degrees

For example, a typical set of statistics, for rain rate is:
1-month mean, 5×5-degree cells
Standard deviation, 5×5-degree cells
Count, 5×5-degree cells
Histogram, 5×5-degree cells
1-month mean, 0.5×0.5-degree cells
Standard deviation, 0.5×0.5-degree cells
Count, 0.5×0.5-degree cells

rainMean1(16,72,6)
rainDev1(16,72,6)
rainPix1(16,72,6)
rainH(16,72,30,6)
rainMean2(148,720,4)
rainDev2(148,720,4)
rainPix2(148,720,4)

3-1. 2.2.

Variable Definitions

Number of observations (rain and no-rain)

integer
integer

ttlPix1(16,72)
ttlPix2(148,720)
Rain Rate Statistics
Rain rates in mm/h

CAPPIsConditioned on the detection of rain (‘rain-certain’ flag), computed at 5 heights +path-averaged. The heights are 2, 4, 6, 10, 15-km and full-path. High-resolution statistics arecomputed at 3 heights + path-averaged, 2, 4, 6-km and full path.

- 140 -

All rain types
rainMean1(16,72,6)
rainDev1(16,72,6)
rainPix1(16,72,6)
rainH(16,72,30,6)
rainMean2(148,720,4)
rainDev2(148,720,4)
rainPix2(148,720,4)

real
real
integer
integer*2
real
real
integerConvective rain
convRainMean1(16,72,6)
convRainDev1(16,72,6)
convRainPix1(16,72,6)
convRainH(16,72,30,6)
convRainMean2(148,720,4)
convRainDev2(148,720,4)
convRainPix2(148,720,4)

real
real
integer
integer*2
real
real
integer

Stratiform rainstratRainMean1(16,72,6)
stratRainDev1(16,72,6)
stratRainPix1(16,72,6)
stratRainH(16,72,30,6)
stratRainMean2(148,720,4
stratRainDev2(148,720,4)
stratRainPix2(148,720,4)

real
real
integer
integer*2
real
real
integer

Near-surface rain
Conditioned on the detection of rain (‘rain certain’), computed at the nearest range bin judged
free of ground clutter. The height in the input data varies with angle bin.

All rain types
surfRainMean1(16,72)
surfRainDev1(16,72)
surfRainPix1(16,72)
surfRainH(16,72,30)
surfRainMean2(148,720)
surfRainDev2(148,720)
surfRainPix2(148,720)

real
real
integer
integer*2
real
real
integerConvective rain
surfRainConvMean1(16,72)
surfRainConvDev1(16,72)
surfRainConvPix1(16,72)
surfRainConvH(16,72,30)
surfRainConvMean2(148,720)

real
real
integer
integer*2
real- 141 -

surfRainConvDev2(148,720)
surfRainConvPix2(148,720)

Stratiform rain
surfRainStratMean1(16,72)
surfRainStratDev1(16,72)
surfRainStratPix1(16,72)
surfRainStratH(16,72,30)
surfRainStratMean2(148,720)
surfRainStratDev2(148,720)
surfRainStratPix2(148,720)

realintegerreal
realinteger
integer*2
real
real
integer

Estimated surface rain
Conditioned on the detection of rain (“rain certain”), surface rain rate, estimated in 2A-25.

All rain types
e_surfRainMean1(16,72)
e_surfRainDev1(16,72)
e_surfRainPix1(16,72)
e_surfRainH(16,72,30)
e_surfRainMean2(148,720)
e_surfRainDev2(148,720)
e_surfRainPix2(148,720)

real
real
integer
integer*2
real
real
integerConvective raine_surfRainConvMean1(16,72)
reale_surfRainConvDev1(16,72)
realinteger
e_surfRainConvPix1(16,72)
e_surfRainConvH(16,72,30)
integer*2
e_surfRainConvMean2(148,720) reale_surfRainConvDev2(148,720) reale_surfRainConvPix2(148,720) integer
Stratiform raine_surfRainStratMean1(16,72) reale_surfRainStratDev1(16,72)
reale_surfRainStratPix1(16,72)
integer
e_surfRainStratH(16,72,30)
integer*2
e_surfRainStratMean2(148,720) reale_surfRainStratDev2(148,720) reale_surfRainStratPix2(148,720) integer
Shallow/Shallow-isolated rain
Near-surface rain, computed when rain is flagged “Shallow” or “Shallow-isolated”. The
categories Shallow and Shallow-isolated are mutually exclusive.

- 142 -

shallowRainMean1(16,72)
shallowRainDev1(16,72)
shallowRainPix1(16,72)
shallowRainH(16,72,30)
shallowRainMean2(148,720)
shallowRainDev2(148,720)
shallowRainPix2(148,720)

real
real
integer
integer*2
real
real
integershallowIsoRainMean1(16,72)
real
real
shallowIsoRainDev1(16,72)
shallowIsoRainPix1(16,72)
integer
integer*2
shallowIsoRainH(16,72,30)
shallowIsoRainMean2(148,720) real
shallowIsoRainDev2(148,720) real
shallowIsoRainPix2(148,720) integer
Measured reflectivity factors, Zm
dBZ, Z in mm6/m3

CAPPIsComputed at the same heights and conditions as rain CAPPIs. The count values are thecorresponding rain-rate pixel counts. 0.5×0.5-degree standard deviations are not computed.
All rain types
zmMean1(16,72,6)
zmDev1(16,72,6)
zmH(16,72,30,6)
zmMean2(148,720,4)

real
real
integer*2
real

Convective rain
convZmMean1(16,72,6)
convZmDev1(16,72,6)
convZmH(16,72,30,6)
convZmMean2(148,720,4)

real
real
integer*2
realStratiform rainstratZmMean1(16,72,6)
stratZmDev1(16,72,6)
stratZmH(16,72,30,6)
stratZmMean2(148,720,4)

real
real
integer*2
real- 143 -

Attenuation-corrected estimate of reflectivity factor, Zt (“Z-true”)
dBZ, Z in mm6/m3

CAPPIsComputed at the same heights and conditions as rain CAPPIs. The count values are thecorresponding rain-rate pixel counts. 0.5×0.5-degree standard deviations are not computed.
All rain types
ztMean1(16,72,6)
ztDev1(16,72,6)
ztH(16,72,30,6)
ztMean2(148,720,4)

real
real
integer*2
real

Convective rain
convZtMean1(16,72,6)
convZtDev1(16,72,6)
convZtH(16,72,30,6)
convZtMean2(148,720,4)

real
real
integer*2
realStratiform rainstratZtMean1(16,72,6)
stratZtDev1(16,72,6)
stratZtH(16,72,30,6)
stratZtMean2(148,720,4)

real
real
integer*2
real

Epsilon-0 and epsilon
Epsilon_0 is defined as the multiplicative factor of α (in the k=αZβ relation) such that the pathattenuation from Hitschfeld-Bordan estimate is equal to that from the surface referencetechnique (SRT). For small values of attenuation it is approximately equal to the ratio of thepath attenuation from the SRT to that of the Hitschfeld-Bordan path attenuation. It is
computed only when the path attenuation from 2A-21 is judged to be reliable or marginallyreliable (see 2A-21) and when bit 8 of the method flag from 2A-25 is set to one.

Epsilon is the multiplicative factor of α for the hybrid method of 2A-25. For small values ofattenuation it is approximately equal to the ratio of the path attenuation from 2A-25 to that of
the Hitschfeld-Bordan path attenuation. The epsilon values are stored only under theconditions for which the epsilon_0 data are stored. The number of counts for epsilon andepsilon_0 should be the same. Specifically,
epsilon0StratPix1 = epsilonStratPix1
epsilon0ConvPix1 = epsilonConvPix1
epsilon0StratPix2 = epsilonStratPix2
epsilon0ConvPix2 = epsilonConvPix2

Epsilon is the ratio of the path attenuation from 2A-25 to that of the Hitschfeld-Bordan pathattenuation (see 2a25).

- 144 -

epsilon0ConvMean1(16,72)
epsilon0ConvDev1(16,72)
epsilon0ConvPix1(16,72)
epsilon0ConvH(16,72,30)
epsilon0ConvMean2(148,720)
epsilon0ConvDev2(148,720)
epsilon0ConvPix2(148,720)

real
real
integer
integer*2
real
real
integer

epsilon0StratMean1(16,72)
epsilon0StratDev1(16,72)
epsilon0StratPix1(16,72)
epsilon0StratH(16,72,30)
epsilon0StratMean2(148,720)
epsilon0StratDev2(148,720)
epsilon0StratPix2(148,720)

real
real
integer
integer*2
real
real
integer

epsilonConvMean1(16,72)
epsilonConvDev1(16,72)
epsilonConvPix1(16,72)
epsilonConvH(16,72,30)
epsilonConvMean2(148,720)
epsilonConvDev2(148,720)
epsilonConvPix2(148,720)

real
real
integer
integer*2
real
real
integer

epsilonStratMean1(16,72)
epsilonStratDev1(16,72)
epsilonStratPix1(16,72)
epsilonStratH(16,72,30)
epsilonStratMean2(148,720)
epsilonStratDev2(148,720)
epsilonStratPix2(148,720)

real
real
integer
integer*2
real
real
integer

Storm height (meters)
Dimension 3 signifies that the statistics are conditioned on rain type where: 1=stratiform,
2=convective, 3=all rain.
stormHtMean(16,72,3)
stormHtDev(16,72,3)
stormHH(16,72,30)
convStormHH(16,72,30)
stratStormHH(16,72,30)
stormHeightMean(148,720,3)
stormHeightDev2(148,720,3)- 145 -

real
real
integer*2
integer*2
integer*2
real
real

Bright-band height (meters) and Maximum reflectivity in bright band (dBZ)
Bright-band statistics where height (Ht) is in meters and the maximum reflectivity statistics
refer to 10 log10 of the maximum radar reflectivity in the bright band.
bbHtMean(16,72)
bbHtDev(16,72)
bbPixNum1(16,72)
BBHH(16,72,30)
bbHeightMean(148,720)
bbHeightDev2(148,720)
bbPixNum2(148,720)

real
real
integer
integer*2
real
real
integerbbZmaxMean1(16,72)
bbZmaxDev1(16,72)
bbZmaxH(16,72,30)
bbZmaxMean2(148,720)
bbZmaxDev2(148,720)

real
real
integer*2
real
real

Nadir bright-band statistics
Height and width (meters) and maximum reflectivity (dBZ). The statistics are computed at thenadir angle bin only.
High-resolution (0.5 degrees) statistics are not computed (see 2a23).
bbNadirHtMean1(16,72)
bbNadirHtDev1(16,72)
bbNadirPix1(16,72)
bbNadirHH(16,72,30)

real
real
integer
integer*2

bbNadirWidthMean1(16,72)
bbNadirWidthDev1(16,72)
bbNadirWidthH(16,72,30)

real
real
integer*2

bbNadirZmaxMean1(16,72)
bbNadirZmaxDev1(16,72)
bbNadirZmaxH(16,72,30)

real
real
integer*2

Snow depth (meters)
Depth of layer from storm top to upper boundary of the bright-band.
Computed only when bright band is present. Pixel counts (number of occurrences) are
bbPixNum1 and bbPixNum2 for the low and high-resolution boxes, respectively.

real
real
real
real
integer*2

sdepthMean1(16,72)
sdepthDev1(16,72)
sdepthMean2(148,720)
sdepthDev2(148,720)
snowIceLH(16,72,30)- 146 -

Path-integrated attenuation (1-way) (dB/km)
Dimension 3 represents 4 angle bins (0, 5, 10, 15 degrees) and all 49 angle bins combined.
For example, piaSrtMean(i,j,2), piaSrtMean(i,j,5) represent the mean PIA
from the surface reference technique at the (i,j) box using data, respectively, from anincidence angle of 5 degrees and from all incidence angles. No adjustment is made for thediffering path lengths for the off-nadir angle bins. The 5-, 10-, and 15-degree bins combine
data from both sides of the scan. (This is a change from version 5, which included data fromone side only). Also note that the convention differs from that in 2A-21 where the 2-way pathattenuation is used.

Notation:‘Srt’ denotes the path attenuation determined from the surface reference technique in 2A-21.
Data are added to the computation only when the path attenuation is judged to be reliable or
marginally reliable.
‘Hb’ denotes the Hitschfeld-Bordan path attenuation from 2A-25. In some cases, the estimate
diverges so the estimates are not included in the statistics‘2a25’ denotes the final path attenuation estimate from 2a25
‘0’ denotes the zeroth-order estimate of path attenuation as determined from the integral ofαZmβ integrated from the storm top to the lowest range gate. α and β are estimated in 2A-25
piaSrtMean(16,72,5)
piaSrtDev(16,72,5)
piaSrtPix(16,72,5)
piaSrtH(16,72,30,5)

real
real
real
integer*2

piaHbMean(16,72,5)
piaHbDev(16,72,5)
piaHbPix(16,72,5)
piaHbH(16,72,30,5)

real
real
real
integer*2

pia0Mean(16,72,5)
pia0Dev(16,72,5)
pia0Pix(16,72,5)
pia0H(16,72,30,5)

real
real
real
integer*2

pia2a25Mean(16,72,5)
pia2a25Dev(16,72,5)
pia2a25Pix(16,72,5)
pia2a25H(16,72,30,5)

real
real
real
integer*2

Subset PIA statistics are the same as the above statistics, except that the input data are filtered
the same way as the epsilon statistics.
- 147 -

piaSrtssMean(16,72,5)
piaSrsstDev(16,72,5)
piaSrtssPix(16,72,5)
piaSrtssH(16,72,30,5)

real
real
real
integer*2

piaHbssMean(16,72,5)
piaHbssDev(16,72,5)
piaHbssPix(16,72,5)
piaHbssH(16,72,30,5)

real
real
real
integer*2

pia0ssMean(16,72,5)
pia0ssDev(16,72,5)
pia0ssPix(16,72,5)
pia0ssH(16,72,30,5)

real
real
real
integer*2

pia2a25ssMean(16,72,5)
pia2a25ssDev(16,72,5)
pia2a25ssPix(16,72,5)
pia2a25ssH(16,72,30,5)

real
real
real
integer*2

Xi (unitless)Xi is the normalized standard deviation of zeta (see 2A-25), zeta_sd/zeta_mn. Xi is nolonger a product in 2A-25, but zeta_sd and zeta_mn are available. In version 6, xi is now

computed in 3A-25. Xi is set to zero when zeta_mn is less than 0.01.
real
real
integer*2

xiMean(16,72)
xiDev(16,72)
xiH(16,72,30)

Non-uniform beam filling correction factor (unitless, see 2a25)
real
real
integer*2

nubfCorFacMean(16,72)
nubfCorFacDev(16,72)
nubfH(16,72,30)

RZ-relation coefficients, a and b, R = aZb
Computed near-surface (last array dimension = 1) and at 2-km (last dimension = 2).
At each lat-lon cell, a logR-logZ fit is computed for all pairs of points (logR, logZ) that are
estimated within the box (at either near-surface or 2 km) for the month. Note that R is rain rate
(mm/h) and Z is the attenuation-corrected reflectivity. If the a coefficient exceeds 10, the fit isassumed to have failed, and both a and b are set to -999.0.

All rain types
rzA1(16,72,2)
rzB1(16,72,2)

real
real
- 148 -

rzPix1(16,72,2)
rzA2(148,720,2)
rzB2(148,720,2)
rzPix2(148,720,2)

integerreal
realintegerConvective rain
rzConvA1(16,72,2)
rzConvB1(16,72,2)
rzConvPix1(16,72,2)
rzConvA2(148,720,2)
rzConvB2(148,720,2)
rzConvPix2(148,720,2)

real
real
integerreal
realinteger

Stratiform rainrzStratA1(16,72,2)
rzStratB1(16,72,2)
rzStratPix1(16,72,2)
rzStratA2(148,720,2)
rzStratB2(148,720,2)
rzStratPix2(148,720,2)

real
real
integerreal
realinteger

Correlation coefficients
Correlation of rain rate between pairs of heights.
The last dimension represents the height pairs, as follows:
1 (2 km, 4 km)
2 (2 km, 6 km)
3 (4 km, 6 km)

All rain types
rainCCoef(16,72,3)
rainCCoefPix(16,72,3)

real
real

Convective rain
convRainCCoef(16,72,3)
convCCoefPix(16,72,3)

real
real

Stratiform rainstratRainCCoef(16,72,3)
stratCCoefPix(16,72,3)

real
real

Correlation coefficients between storm height and maximum value of Zm along pathstormHtZmCCoef(16,72)
realCorrelation coefficients between xi and maximum Zm
xiZmCCoef(16,72)
real- 149 -PIA correlation coefficients
These are the correlations between various PIA estimates. Dimension 3 represents 4 angle bins
(0, 5, 10, 15 degrees) and all 49 angle bins combined. The last dimension represents the various
pairs amongst four PIA estimates, as follows:
1 [SRT,HB]
2 [SRT,0th-order]
3 [HB,0th-order]
4 [2a25,SRT]
5 [2a25,HB]
6 [2a25,0th-order]
piaCCoef(16,72,5,6)
piaCCoefPix(16,72,5)

real
real

ttlAnglePix1(16,72,4)
rainAnglePix1(16,72,4)

integer*2
integer*2

Epsilon Fit
Computed for each 5×5-degree cell. This is the slope of a regression between x and y,y   (rb )  l2a25.zeta(1, i)x  1  10 0.1 PIASRT

where i is the angle bin, and  l2a25.attenParmBeta(i)PIA SRT  l2a25.pia(3,i)

Points are included only when 2A-21 reliabFlag ≤ 2 (reliable or marginally reliable) andzeta > 0.1.
The inverse slope, 1/slope, is an estimate of epsilon. The intercept is forced to be zero.
slope 1  xyˆ  x2

epsilonFit  1/slope

sum square error   y 2 epsilonFitRMS 

21xy  2  x 2

ˆ
ˆ



sse
N 2
real
real

epsilonFit(16,72)
epsilonFitRMS(16,72)- 150 -

integer

epsilonFitPix(16,72)

3-1. 2.3.

Definition of Bins for Histograms

For radar reflectivity factor histograms:
ztH, convZtH, stratZtH
zmH, convZmH, stratZmH
bbZmaxH, bbNadirZmaxH,
the 31 bin boundaries are:0.01
12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0
32.0 34.0 36.0 38.0 40.0 42.0 44.0 46.0 48.0 50.0
52.0 54.0 56.0 58.0 60.0 62.0 64.0 66.0 68.0 70.0
For all rain rate histograms: rainH, stratRainH, convRainH, surfRainH, the 31 binboundaries 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:
0.01
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50
2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00
5.25 5.50 5.75 6.00 6.25 6.50 6.75 7.00 7.50 20.00
For storm height histograms, stormHH, stratStormHH, convStormHH, (in km), the 31
bin boundaries [km] are:0.01
0.5 1.0 1.5 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 8.5 9.0 9.5 10.0
10.5 11.0 11.5 12.0 12.5 13.0 14.0 15.0 16.0 20.0
For distance from storm top to bright-band heightbbNadirWidthH, the 31 bin boundaries [m] are:0.0
125.0 250.0 375.0 500.0 625.0
750.0 875.0 1000.0 1125.0 1250.0
1375.0 1500.0 1625.0 1750.0 1875.0
2000.0 2125.0 2250.0 2375.0 2500.0
2625.0 2750.0 2875.0 3000.0 3125.0
3250.0 3375.0 3500.0 3625.0 3750.0- 151 -

histogram,snowIceLH,

For the path-averaged attenuation estimate histograms, piaSrtH, piaHbH, pia0H, andpia2a25H, the 31 bin boundaries [dB] are: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 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
6.0 7.0 8.0 9.0 10.0 15.0 20.0 25.0 30.0 100.
For non-uniform beamfilling factor histogram, nubfH, the 31 bin boundaries [dimensionless]
are:
1.00
1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50
1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00
2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00

For xi (=standard deviation of zeta/mean of zeta) histogram, xiH, the 31 bin boundaries[dimensionless] are:0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0
4.2 4.4 4.6 4.8 5.0 10.0 20.0 30.0 50.0 10000.
For the parameters epsilon and epsilon0 (see 2a25) the 31 bin boundaries are:0.0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

3-1. 2.4.

Other Input Parameters:

CAPPI heights relative to the ellipsoid: 2, 4, 6, 10, 15 km.
Angle bins at which the statistics of the various PIA estimates are to be evaluated: 5,
12, 18, 25, 32, 38, 45, which correspond approximately to angles of 0, 5, 10, and 15
degrees incidence (port and starboard).

3-1. 2.5.

Definitions of low and high resolution grids

The low resolution grid consists of 16×72 latitude-longitude elements corresponding to a
5×5-degree grid that covers the TRMM region from 40 S to 40 N where:
latitudeindex
1-40 to -35
2-35 to -30…

(40 S to 30 S)(35 S to 30 S)- 152 -

16

35 to 40

(35 N to 40 N)

longitudeindex
1-180 to -175 (180 W to 175 W)
2-175 to -170 (175 W to 170 W)…
72
175 to 180 (175 E to 180 E)
The high resolution grid consists of 160×720 latitude-longitude elements corresponding to a
0.5×0.5-degree grid that covers the TRMM region from 37 S to 37 N where:
latitudeindex
1-37.0 to -36.5 (37.0 S to 36.5 S)
2-36.5 to -36.0 (36.5 S to 36.0 S)…
160
36.5 to 37.0 (36.5 N to 37.0 N)
longitudeindex
1-180.0 to -179.5 (180.0 W to 179.5 W)
2-179.5 to -179.0 (179.5 W to 179.0 W)…
720
179.5 to 180.0 (179.5 E to 180.0 E)

3-1. 3.

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 isdone by using the anchor 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
belongs. Note that a single scan is composed of 49 observations each at a different
incidence angle.
(coarse resolution boxes are 5×5-degree cells)(fine resolution boxes are 0.5×0.5-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 andreinitialize the intermediate files.
- 153 -

3-1. 4.

Comments and Issues:i.

In version 6, the rain statistics are computed only when the ‘rain-certain’ flag is set
in 1C-21. The ‘rain-possible’ flag is treated the same as a ‘no-rain’ flag. Products
defined in version 4 (which contained the term ‘All’ in the product name) and which
included ‘rain-certain’ and ‘rain-possible’ data, have been deleted from the list ofversion 6 products.

ii.

It is assumed in the program that the verification file does not exist; if it is alreadyexists an error will occur.

iii.

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.

iv.

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 areasat the lower height levels because the level can be below the local surface. In thesecases, 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 theobservations ‘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.

v.

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.

vi.

There are several subtle, interrelated issues regarding the definitions of rain andno-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) is being output under rain-possible conditions. With the
exception noted above 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 selectionis that the set of products should be self-consistent. The above was valid for version
4. In versions 5 and 6 the rain-possible flag is always treated as a no-rain occurrence(see comment i.).

vii.

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 thecross-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- 154 -

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 subsequentbins 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 thenominal relationship Z = 200R1.6 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 differsfrom 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 numberof data points that are categorized in the rain rate histogram are equal to the numberof data points used in the calculation of the mean and standard deviation of thisquantity.
viii.

There are 4 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 thesurface that is not corrupted by the surface clutter. In version 4, two sets of products
were being computed from these data: the first set of statistics used only those rain
rate for which rain is classified as ‘certain’; the second set used those rain rates forwhich rain is classified either as ‘possible’ or ‘certain’. For version 5, thedetermination was made to eliminate products using the ‘rain-possible’ flag (seecomment i).
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 (gatenearest 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 thatintersect 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 therain rates. This resampling lowers the minimum detectable threshold that, in turn,affects 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.
The fourth type, added in version 6, is an estimated surface rain rate. See 2a25 for a
discussion.

- 155 -

ix.

As noted in comment v., the rain rate statistics over mountainous regions at theheight levels of 2 and 4 km will tend to underestimate the actual values; for thesecases, the near-surface rain rate statistics (under ‘rain-certain’ conditions) should bea more reliable indicator of the near-surface rain rate.

x.

All of the statistics in 3a25 are conditioned on the existence of one or more variables.
To compute the unconditioned statistic, it is necessary to compute the probabilitiesof the events upon which the statistic is conditioned. For example,
rainMean1(i,j,k) is the conditional mean rain rate in the box (i,j) at the kth
height level. To convert this into an unconditional mean rain rate, Rm say, it isnecessary first to compute the probability of rain at the appropriate
latitude-longitude box and height:
rainPix1(i, j,k)
ttlPix1(i, j)
Rm (i, j,k)  Pr (i, j,k)  rainMean1(i, j,k)
Pr (i, j,k) To convert this to an accumulation (in mm) over a time period consisting of N hours,
a multiplication of Rm by N would be used. For example, the accumulation in mm in
a 30 day month N = 720.
Similarly, to compute the unconditional mean rain rate for stratiform rain, RmStrat, at(i,j,k):stratRainPix1(i, j,k)
ttlPix1(i, j)
Strat
Strat
Rm (i, j, k )  Pr (i, j, k )  stratRainMean1(i, j, k )PrStrat (i, j,k) Note also the following probabilities:bbPixNum(i, j)
ttlPix1(i, j)
stratRainPix1(i, j,k)Pr stratiform rain rain 
rainPix1(i, j,k)
convRainPix1(i, j,k)Pr convective rainrain 
rainPix1(i, j,k)
bbPixNum(i, j,k)Pr bright - band rain 
rainPix1(i, j,k)Pr bright - band 

Note the difference among quantities of the following kind:stratRainPix1(i, j,k)rainPix1(i, j,k)stratRainPix1(i, j,k)Prstratiform rain rain 
rainPix1(i, j,6)
stratRainPix1(i, j,6)Prstratiform rain rain
rainPix1(i, j,6)Pr stratiform rain rain - 156 -

Pr'' corresponds to what is the most common definition of the probability ofstratiform 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 that, given rain is present
somewhere along the beam, that rain is present at height level k and that the rain is
stratiform.

3-1. 5. Changed Variables in Version 6
3-1. 5.1. New variables
bbNadirPix1
bbNadirHtMean1
bbNadirHtDev1
bbNadirHH
bbNadirWidthMean1
bbNadirWidthDev1
bbNadirWidthH
bbNadirZmaxMean1
bbNadirZmaxDev1
bbNadirZmaxH
e_surfRainPix1
e_surfRainMean1
e_surfRainDev1
e_surfRainH
e_surfRainPix2
e_surfRainMean2
e_surfRainDev2
e_surfRainConvPix1
e_surfRainConvMean1
e_surfRainConvDev1
e_surfRainConvH
e_surfRainConvPix2
e_surfRainConvMean2
e_surfRainConvDev2

e_surfRainStratPix1
e_surfRainStratMean1
e_surfRainStratDev1

e_surfRainStratPix2
e_surfRainStratMean2
e_surfRainStratDev2
e_surfRainStratH
epsilon0ConvPix1
epsilon0ConvMean1
epsilon0ConvDev1
epsilon0ConvH
epsilon0ConvPix2
epsilon0ConvMean2
epsilon0ConvDev2
epsilon0StratPix1
epsilon0StratMean1
epsilon0StratDev1
epsilon0StratH
epsilon0StratPix2
epsilon0StratMean2
epsilon0StratDev2

epsilonStratMean1
epsilonStratDev1
epsilonStratH
epsilonStratPix2
epsilonStratMean2
epsilonStratDev2
pia0Pix
pia2a25Pix
piaHbPix
piaSrtPix
piaCCoefPix
piaSrtssPix
piaSrtssMean
piaSrsstDev
piaSrtssH
piaHbssPix
piaHbssMean

epsilonConvPix1
epsilonConvMean1

epsilonConvDev1
epsilonConvH
epsilonConvPix2
epsilonConvMean2
epsilonConvDev2
epsilonStratPix1- 157 -

piaHbssDev
piaHbssH
pia0ssPix
pia0ssMean
pia0ssDev
pia0ssH
pia2a25ssPix
pia2a25ssMean
pia2a25ssDev

pia2a25ssH
convCCoefPix
stratCCoefPix
rainCCoefPix
rzPix1
rzA1
rzB1
rzPix2
rzA2
rzB2
rzConvPix1
rzConvA1
rzConvB1
rzConvPix2
rzConvA2
rzConvB2
rzStratPix1

rzStratA1
rzStratB1
rzStratPix2
rzStratA2
rzStratB2
shallowIsoRainPix1
shallowIsoRainMean1
shallowIsoRainDev1
shallowIsoRainH
shallowIsoRainPix2
shallowIsoRainMean2
shallowIsoRainDev2
shallowRainPix1
shallowRainMean1
shallowRainDev1
shallowRainH
shallowRainPix2

shallowRainMean2
shallowRainDev2
surfRainStratPix1
surfRainStratMean1
surfRainStratDev1
surfRainStratH
surfRainStratPix2
surfRainStratMean2
surfRainStratDev2
surfRainConvPix1
surfRainConvMean1
surfRainConvDev1
surfRainConvH
surfRainConvPix2
surfRainConvMean2
surfRainConvDev2

3.1.5.2. Deleted Variables
bbwidthMean1
bbwidthDev1
epsilonPix1
epsilonMean1
epsilonDev1
epsilonH

stormHtZmCCoef
wrainPix1
wrainPix2
xiZmCCoefzmGradH
zpzmH

3.1.5.3. Spelling CorrectedstratZtH; was “startZtH”

3.1.6. New Variables in Version 7
epsilonFit
epsilonFitRMS
epsilonFitPix- 158 -

surfRainAllPix1
surfRainAllMean1
surfRainAllDev1
surfRainAllH
surfRainAllPix2
surfRainAllMean2
surfRainAllDev2

3-2. 3A-26: Estimation of Space-Time Rain Rate Statistics Using a
Multiple Thresholding Technique3-2. 1. Objective of the algorithm
The primary objective of 3A-26 is to compute the rain rate statistics over 5-degree(latitude)×5-degree (longitude)×1-month space-time regions. The output products include theestimated values of the probability distribution function of the space-time rain rates at 4“levels” (2 km, 4 km, 6 km and path-averaged) and the mean, standard deviation, andprobability of rain derived from these distributions. Three different rain rate estimates are used
for the high-resolution rain rate inputs to the algorithm: the standard Z-R (or 0th-order estimate
having no attenuation correction), the Hitschfeld-Bordan (H-B), and the rain rates taken from
2a-25. (Fits based on the high-resolution inputs from the surface reference technique are output
to the diagnostic file for evaluation).
This algorithm is based on a statistical procedure. Although the radar team believes that astatistical method of this type should be implemented for TRMM, the method is relatively new
and the testing has been carried out only on simulated data and on preliminary TRMM data.
Caution on the use of the results is well warranted.

3-2. 2.

Description of the Method

A general understanding of the method can be gained by noting that the amount of attenuationin the TRMM radar signal depends on the 2-way path attenuation down to the range gate ofinterest. This attenuation increases as the range gate is taken deeper into the storm (closer to thesurface) and as the rain rate increases. Although some general features of the rain are used in
2a-25, the rain rate estimates are obtained at each instantaneous field of view (IFOV) of the
instrument. The space-time statistics of these high-resolution estimates are done in 3a-25. Most
users of the TRMM radar data will be interested in the output data from 3a-25 and not the datafrom 3a-26.
Algorithm 3a-26 serves as an alternative way of estimating the space-time rain statistics. The
idea behind the method is that because of attenuation at high rain rates and low signal to noise
ratios at light rain rates, there will usually exist an intermediate region over which the rain rateestimates are most accurate. Using only these estimates and an assumption as to the form of theprobability distribution function (log-normal), the parameters of the distribution can be foundby minimizing the rms difference between the hypothetical distribution and the values of the
distribution obtained directly from the measurements. Once the distribution is estimated, themean and standard deviation of the distribution can be calculated [Refs. 1-2, Ref. 6].
Useful by-products from the calculation of the probability distribution of rain rates are thefractional areas above (or below) particular rain rate thresholds. These data can be used as
inputs to some of the area-time integral (ATI) methods that have been proposed [Refs. 3-5].
Although the data can be used to implement the ATI method, the method used in 3a-26 is itself
not an ATI method.
The behavior of the estimates depends strongly on the magnitude and type of threshold as wellas the method that is used to determine the high-resolution rain rates. There are 3 methods thatare used to determine the high-resolution rain rates: the Z-R (0th order without attenuation
correction), the Hitschfeld-Bordan (H-B), and the hybrid method of 2a-25. A fourth method,
based solely upon the surface reference method, is implemented in the code but the results are- 159 -

output only to a diagnostic file for evaluation. For the 3 estimates of rain rate (Z-R, HB and2a-25), Q (or zeta as defined in 2a-25) is used as the threshold parameter. What this means isthat if the threshold is set to a particular value, Q*, then if the measured value of Q is less thanQ*, the corresponding rain rate is accepted - that is, it is used to update the distribution functionof rain rates. On the other hand, if Q exceeds Q* the corresponding rain rate estimate is rejected- that is, it is not used to update the distribution function. As the threshold value, Q, is increaseda larger percentage of the rain rates will be accepted. The converse holds so that as Q isdecreased a smaller percentage of the rain rates will be used in estimating the distributionfunction. It should be noted that Q is a proxy for the attenuation and usually assumes a value
between 0 and 1.
If the Z-R method (without attenuation correction) of estimating the high resolution rain rates is
considered, the corresponding output files include the rain rate distribution function,
zeroOrderpDf, and the mean, standard deviation, and probability of rain derived from the
distribution, zeroOrderFit, for 6 different values of the Q threshold. The six values of Q
are: 0.1, 0.2, 0.3, 0.5, 0.75 and 0.9999. Which set of values corresponding to which thresholdshould be used? Simulations suggest that if the total number of rain points is on the order of 500
to 1000, the best accuracy is usually obtained by using a threshold value of 0.3. This
corresponds to the 3rd array element so that the monthly mean rain rate (using the Z-R method)over the 5×5-degree box (lat, long) at height level, ih, is given by:mean = zeroOrderFit(lat, long, 1, ih, iq = 3)

The standard deviation and probability of rain are given by:
std dev = zeroOrderFit(lat, long, 2, ih, iq = 3)
Pr (Rain) = zeroOrderFit(lat, long, 3, ih, iq = 3)

Simulations indicate that for a large number of rain points (N > 5000), the use of smaller
threshold values (Q = 0.2) may lead to better estimates of the mean space-time rain rate. In thecase of Q = 0.2 we have:mean= zeroOrderFit(lat, long, 1, ih, iq = 2)
std dev = zeroOrderFit(lat, long, 2, ih, iq = 2)
Pr (Rain) = zeroOrderFit(lat, long, 3, ih, iq = 2)

A useful set for comparison is the choice: Q = 0.999 (array element 6). In this case nearly all of
the Z-R rain rate estimates are accepted so that the method reduces to fitting almost all the Z-R
derived rain rates to a lognormal distribution:mean= zeroOrderFit(lat, long, 1, ih, iq = 6)
std dev = zeroOrderFit(lat, long, 2, ih, iq = 6)
Pr (Rain) = zeroOrderFit(lat, long, 3, ih, iq = 6)

The estimate of the mean as determined from the zeroOrderFit HDF output variable
should be considered the primary output of the algorithm. Since Q = 0.3 is considered,nominally, as the optimum choice of threshold, the variable, rainMeanTH, has been defined
to store these values. In particular:- 160 -

rainMeanTH(lat,long,ih) = zeroOrderFit(lat,long,ih,1,3)

The accuracy of the results at other Q thresholds and the statistics derived from the
Hitschfeld-Bordan (hbFit) and rain rates from 2a-25 (fit2A25) will be evaluated asadditional data from the TRMM radar become available.

3.2- 3.

Relationship of 3a-26 outputs to those of 3a-25

In comparing the statistics from 3a-25 and 3a-26 there are 2 differences between these data setsthat should be kept in mind. The first is that the statistics produced from 3a-25 are conditioned
either on the presence of rain or on the presence of a particular type of rain (stratiform orconvective). For the 3a-26 products the means and standard deviations derived from thezeroOrderFit, hbFit and fit2A25 arrays are unconditioned - that is, the statistics
include both rain and no-rain events. The second difference is that the set of heights for the
3a-26 products is a subset of the heights used for the (low resolution) products of 3a-25.
For the 3a-26 products, the height levels relative to the ellipsoid are:hlevelHeight above ellipsoid

1
2
3
4

2 km
4 km
6 km
Path-average

For the low-resolution 3a-25 products, the height levels relative to the ellipsoid are:hlevelHeight above ellipsoid

1
2
3
4
5
6

2 km
4 km
6 km
10 km
15 km
Path-average

In earlier versions of the program, the height levels were defined relative to the local surface. In
the latest versions of 3a-25 and 3a-26 (version 3 and later) all heights are measured relative tothe earth's ellipsoid.
As an example, assume that the monthly rain accumulations, MRA (millimeters/month), are to
be computed over the 5-degree×5-degree latitude-longitude box specified by (lat, long) for therain rates measured at a height level given by hlevel.
From 3a-25, the mean rain rate (mm/hr), conditioned on rain being present at height level, ih,
is given by:- 161 -

rainMean1(lat, long, ih).

To convert this to an unconditioned mean rain rate the quantity is first multiplied by theprobability of rain. This can be approximated by the ratio of the number of rain counts(rainPix1(lat,long,ih)) to the total number of observations over the month(ttlPix1(lat,long)). To convert this to a monthly accumulation, the unconditioned rain
rate is multiplied by the number of hours in a (30 day) month, 720, so that the monthly rain
accumulation, MRA (mm/month), as derived from the 3a-25 products, is:MRA(3a-25) = rainMean1(lat,long,ih)*PrRain(lat,long,ih)*720

where
PrRain(lat,long,ih) = rainPix1(lat,long,ih)/ttlPix1(lat,long)From the 3a-26 products, the MRA (mm/month), using the zeroth-order estimate (Z-R), and thesame conversion from mm/h to mm/month (720), is:MRA(3a-26) = zeroOrderFit(lat,long,ih,1,iqthres)*720

For the 3rd threshold, Q = 0.3, the MRA is
MRA(3a-26) = zeroOrderFit(lat,long,ih,1,3)*720

or, equivalently,
MRA(3a-26) = rainMeanTH(lat,long,ih)*720

3-2. 4. Relationship between 3a-26 and the fractional areas above
particular thresholds
The single threshold technique (ATI) uses the fractional area above a particular rain rate
threshold as a linear estimator for the area-average rain rate. Estimates of the fractional areas
above a threshold can be obtained from the estimated distribution functions described above.
As noted above, the counts, which are proportional to the probability distribution functions ofrain rate, are stored in the arrays:
zeroOrderFit(16, 72, 4, 3, 6)
hbFit(16, 72, 4, 3, 6)
fit2A25(16, 72, 4, 3, 6)

where the 5 dimensional array refers to: latitude, longitude, height, fitting parameter, Q
threshold)and where
fitting parameter = 1 (mean value of log-normal distribution)= 2(standarddeviation of log-normal distribution)- 162 -

= 3

(probability of rain)

It is important to note that these counts only include rain counts. To add in the no-rain counts,
note that the total number of counts, ntot(lat,long), and the total number of rain counts(at level ih), nrain(lat,long,ih), are output variables so that
N_no-rain(lat,long,ih) = ntot(lat,long) - nrain(lat,long,ih)

The probability distribution function, zeroOrderpDf' (unnormalized), that includes the
no-rain cases, is given by:
zeroOrderpDf'(lat,long,ir,ih,iq) =zeroOrderpDf(lat,long,ir,ih,iq) + N_no-rain(lat,long,ih)
for

ir = 1,..,25
iq = 1,..,6

the formulas for hbpDf and pDf2a25 are identical
The variable zeroOrderpDf'(lat,long,irainth,ih,iqthres) is the number ofrain counts above the rain rate threshold corresponding to the 'ir' indice. Denote this rain rateby RR(ir). The fractional area below the rain rate threshold RR(ir) at height level ih at theQ threshold, iq, using the Z-R estimates of rain rates is:
Fr_Area{R < RR(ir)}(lat,long,ih) =zeroOrderpDf'(lat,long,ir,ih,iq)/ntot(lat,long)

The fractional area above this threshold is:
Fr_Area_RR > RR(ir)(lat,long,ih) = 1 - Fr_Area{R < RR(ir)}(lat,long,ih)

For example, to compute the fractional area above the threshold of 2.05 mm/h (ir = 9 - see
definition of the rain rate threshold categories in 3b below) at the Q threshold of 0.9999 (iq =6) at a height of 2 km above the ellipsoid (ih =1) the following equations are used:
zeroOrderpDf'(lat,long,ir=9,ih=1,iq=6) =zeroOrderpDf(lat,long,ir=9,ih=1,iq=6) + N_no-rain(lat,long,ih=1)
N_no-rain(lat,long,ih=1) = ntot(lat,long) - nrain(lat,long,ih=1)
Fr_Area{RR<2.05}(lat,long,ih=1) =zeroOrderpDf'(lat,long,ir=9,ih=1,iq=6)/ntot(lat,long)
Fr_Area{RR>2.05}(lat,long,ih=1) = 1 - Fr_Area{RR<2.05}(lat,long,ih=1)

So that the fractional area above 2.05 mm/h over the 5×5-degree box (lat, long) over the month(which uses the Z-R derived rain rates and nearly all the data, iq = 6) can be expressed in termsof the HDF outputs:- 163 -

zeroOrderpDf(lat,long,ir=9,ih=1,iq=6)
nrain(lat,long,ih=1)
ntot(lat,long)

3-2. 5.

Reliability estimates

The reliability is defined as the rms difference between experimentally determined values of thepDf and the fitted values of the pDf at those values for which the experimentally-determined
pDf increases monontonically.
reliabZeroOrder(16,72,4,6)
reliabHB(16,72,4,6)
reliabSRT(16,72,4,6)

In version 7, several changes have been made to subroutine fncfit3 to eliminate occurences ofInf and NaN. One consequence is that several of the error flags have been changed, new error
flags added and some old flags deleted. The error flag definitions for version 7 are given
below.
one or more of the fitting parameters have been set to NaN
set fitting parameters & reliab factor to -222.
errors in one or more of the fitting coefficientsset fitting parameters & reliab factor to -333.
large (or possibly negative) rms error in fit
set fitting parameters & reliab factor to -444.
concave parameter less than 0
set fitting parameters & reliab factor to -666.
insufficient # of thresholds or n1 or n2 = 0
set fitting parameters & reliab factor to -777.
insufficient # of points for accurate fit
set fitting parameters & reliab factor to -999.
Note that the old flag values -555 and -888 have been eliminated since these error conditions
are covered by those above.

3-2. 6.

Definition of the latitude-longitude boxes

The products are defined on a 5-degree×5-degree×1 month grid that covers the TRMM orbit.
The latitude boxes are labeled from 1 to 36 where box 1 covers from 40 S to 35 S and box 36
covers from 35 N to 40 N. The longitude boxes are labeled from 1 to 72 where box 1 runs from
180 W to 175 W and box 72 runs from 175 E to 179.999 E.

3-2. 7. Notes on the processing procedure
1. Assume that 1 granule of data corresponds to 1 orbit.

- 164 -

2. The program is set up to read a scan line of data at a time from 1C-21, 2A-21, 2A-23 and
2A-25 until the full granule of data has been processed.
3. As all the output products are over a 5-degree×5-degree×1 month space-time region,
after each granule is processed, the program will write the partially accumulated
products to temporary storage. When the next processing cycle begins, these products
will be read from temporary storage, and then overwritten once the updated statistics arecompleted.
4. At the end of the processing cycle (1 month), a subroutine within the program will be
used to output the statistics to the HDF file.
5. For the 0th and HB estimates of rain rate, the EDR (effective dynamic range) is basedon the quantity zeta (as defined in 2a-25) or Q (as defined in 3a-26), where:r

Q    0.2ln   Z m
0where Zm is the measured or apparent reflectivity factor, k  Z  , and k is theattenuation coefficient or specific attenuation (dB/km), and Z is the actual reflectivity
factor (mm6/m3). The coefficients α, and β are read from the 2a-25 output. Note that as
Q = ζ goes to one, the path-integrated-attenuation (pia) increases without bound if k-Z
relationship is exact.
As noted above, the 3a-26 products are defined for height levels of 2 km, 4 km, and 6
km referenced to the ellipsoid. For a height of 2 km, for example, r is that range gate thecenter of which is closest to the surface drawn 2 km above the ellipsoid.
6.
7. For the multiple threshold method, a necessary condition is that the random variable(that characterizes the radar-measured quantity) be a monotonic function of the quantitythat we wish to measure. For example, in the presence of attenuation, the apparent
reflectivity factor at the surface Zm(surface) [or the rain rate estimate based on Zm] is a
non-monotonic function of the true rain rate; as such it is not an appropriate choice forthis method. On the other hand, Q (or ζ) is a monotonic function of the path-integrated
rain rate and is appropriate for the 0th order and HB estimates of RR.

8. For the path-integrated attenuation (PIA) as derived from the surface referencetechnique (and the corresponding rain rate), an appropriate proxy variable is the SRT
estimate of PIA itself. Results based on the SRT are output only to a diagnostic file.
9. The motivating principle of the multiple threshold method is that for area-wide
estimates of the rain rate it is more accurate to extrapolate to the low and high regions ofrain rate than to attempt to measure the distribution of these values directly. Reasons forthe possible poor performance of the radar at high and low rain rates are:i. low SNR at low rain rates
ii. signal attenuation at high rain rates
iii. higher variability in Z-R laws at low rain rates
10. In the multiple threshold method, an effective dynamic range (EDR) is selected. The
EDR is defined as the region over which the rain rates or Zm estimates are expected to- 165 -

have the highest accuracy (where the signal-to-noise ratio is high and attenuation islow).
11. Currently, the maximum number of thresholds within the EDR is taken to be 25 (theoptimum number is still an issue and will depend upon the number of samples and therange of the variable).
12. If the number of samples of the histogram is small, then the estimated pDf is generally
unreliable. To circumvent this, we assume that the total number of IFOVs over the
averaging domain, with rain present be larger than some number, iqqmin. Presently,
iqqmin = 200.

3-2. 8. Input Parameters (initialized in 3a-26)
Thresholds:
data QUthres0th /0.1,0.2,0.3,0.5,0.75,0.9999/
data QUthresHB /0.1,0.2,0.3,0.5,0.75,0.9999/
data QLsrt/1.5,1.,0.8,0.6,0.4,0.1/! Q-thresholds for Z-R and 2a-25! Q-thresholds for HB! PIA-thresholds for SRT

The rain rate distribution functions consist of the count values in the following 25 rain ratecategories
data RRcategories ! In mm/hr/0.205, 0.27, 0.3646, 0.4863, 0.648, 0.865,
1.153, 1.537, 2.050, 2.734, 3.646, 4.862,
6.484, 8.6468, 11.531, 15.376, 20.505, 27.344,
36.463, 48.625, 64.84, 86.47, 115.31, 153.76, 205.048/

At present, a lognormal fitting through the points of the rain rates distribution is made only
when the following condition is satisfied:
iqqmin = 200! Minimum number of valid rain occurrences needed for fitting to be done.

In identifying the number of valid thresholds, we require that the count value increase by acertain amount from between successive rain rates thresholds; in fact, the upper rain rate
threshold can be identified as that threshold beyond which the count value does not increase byat least nfu counts, where:
nfu = 30

- 166 -

3-2. 9. Output Variables
Arrays for the calculation of probabilities [int*4].
ttlCount(16,72)

Number of observations at each 5×5-degree box over the month.
rainCount(16,72,4)
Number of rain observations at each 5×5-degree box over themonth. Note that all height levels are measured relative to theellipsoid.
nrain(i,j,1)
nrain(i,j,2)
nrain(i,j,3)
nrain(i,j,4)

h = 2 kmh = 4 kmh = 6 km
path-averaged

Arrays for output of “truncated” histograms at each 5×5×1 month box for 3 RR estimates/4 “levels”.
zeroOrderpDf(16,72,25,4,6)
Number of counts in the probability distribution function (25categories) using 0th order (Z-R) rain rate estimate at heights
with respect to the ellipsoid of 2, 4, 6 km and path-av for 6 Q
thresholds.
hbpDf(16,72,25,4,6)Same as above except using the HB estimate of rain rate.
pDf2A25(16,72,25,4,6)Same as above except using the rain rate estimates from 2a-25.
Convention for zeroOrderpDf(16,72,25,4,6), hbpDf(16,72,25,4,6), andpDf2A25(16,72,25,4,6)
first argument: latitudesecond: longitude
third: rain rate category for pDf
fourth: height “level”: 1 = RR @ 2 km
2 = RR @ 4 km
3 = RR @ 6 km
4 = path-averaged RR
fifth: Q threshold

Mean, std dev, Pr(Rain) derived from log-normal assumption to rain rate distribution
zeroOrderFit(16,72,4,3,6)
3 statistics [mean, std dev, Pr(R)] of distribution fit of the rain rates asderived from the 0th (Z-R) method for 6 thresholds at 4 “levels”.
hbFit(16,72,4,3,6)Same as above except Hitschfeld-Bordan method used for rain rateestimates.
fit2A25(16,72,4,3,6)Same as above except data from 2a-25 are used for rain rates estimates.

- 167 -

Reliability factors:
reliabOrderFit(16,72,4,6)
reliabHBfit(16,72,4,6)
reliab2A25fit(16,72,4,6)

See section 3.2.1.4 for details on computation of the reliability factors.

3-2. 10.

Processing Procedure

The basic steps in the procedure are (first 4 are similar to 3a-25 algorithm):i.

Read in data (scan by scan) from 2a-21, 2a-23, 2a-25 and 1c-21

ii.

Adjust the range gate numbering conventions so that Zm, Zt and R are aligned
properlyiii.

Find the coarse boxes to which the 49 IFOVs belong (coarse resolution boxes are
5-degree×5-degree latitude-longitude boxes)

iv.

Resample Zm, Zt and R from the range direction onto the verticalv.

Update the estimated probability distribution function for the various rain rate
methods at each 5×5-degree box at the various heights, and for threshold values.

vi.

If the granule crosses the month boundary, do a nonlinear least squares fit to the
distributions determined in step 5, assuming a log-normal distribution; from thefitting parameters, calculate the mean, standard deviation and probability of rain foreach distribution.

vii.

Re- initialize the intermediate file

3-2. 11. Comments and Issuesi.

It is assumed in the program that the verification file does not exist; if it alreadyexists an error will occur.

ii.

Differences exists between the height levels at which the 3a-25 and 3a-26 statistics
are calculated; for 3a-25 the levels are [2, 4, 6, 10, 15] km and the path-average
while for 3a-26 the levels are [2, 4, 6] km and the path-average.

iii.

Presently, the height levels are being defined relative to the ellipsoid and not the
local surface.

iv.

Resampling of the radar data from the range direction to the vertical is done
differently in 3a-25 and 3a-26. In 3a-25, the estimate of the reflectivity factor at aparticular height is done by a gaussian weighting of the range gates that intersect- 168 -

that height. 3a-26 uses only a single value of Z and R - that gate, the center of which
is closest to the height of interest.
v.

The Z-R or 0th method refers to the zeroth order solution of the reflectivity factor
from the basic weather radar equation. In this approximation, no compensation ismade for attenuation so the reflectivity factor is directly proportional to themeasured radar return power. This approximate reflectivity factor is sometimes
called the apparent or measured reflectivity factor. In converting any estimate of thereflectivity factor, Z(est), to rain rate, R, the power-law approximation is used: R =aZ(est)b where a and b are obtained from 2a-25.
The HB or Hitschfeld-Bordan solution to the reflectivity factor, Z, is obtained byusing a specific attenuation-reflectivity factor (k-Z) relationship and then solving
the weather radar equation for Z.
Description of the rain rates from 2a-25 is given in the documentation for thisalgorithm.

vi.

In version 5 and higher versions of the algorithm, additional error flags have been
added that are used to specify the behavior of the second derivative of the estimateddistribution function, F, at a rain rate of 0.01 mm/h. Since F is assumed to be
log-normal, then for R>0 it can be written:
F (R)  0.5 p[1  erf(u)]1 uerf(u)  exp(t 2 )dt

 0
ln R  u
s 2

The sign of the second derivative can be determined by:
d dF
0
dR dR
d dF
if (ì - lnR) < s2, then
0
dR dR

if (ì - lnR) > s2, thenwhere in the code, R is evaluated at R = 0.01 mm/h.
If

d dF 0 , then an error flag is set (see above).
dR dR

The following rule can be shown to give a more stable estimate of rain rate:d dF. If this is greater than 0 then accept the
dR dR
d dF
parameters of this distribution. However, if 0 , increase Q and evaluatedR dR

Begin with Q = 0.3 and evaluate- 169 -

d dF
d dF
again; continue this until a Q is found for which 0 at which point
dR dR
dR dR
accept the corresponding distribution.

References[1] Meneghini, R., 1998, J. Appl. Meteor., 37, 924-938.
[2] Meneghini, R., and J. Jones, 1993, J. Appl. Meteor., 32, 386-398.
[3] Short, D.A., K. Shimizu, B. Kedem, 1993, J. Appl. Meteor., 32, 182-192.
[4] Kedem, B., L.S. Chiu, G.R. North, 1990, J. Geophys. Res., 96, 1965-1972.
[5] Atlas, D., D. Rosenfeld, D.A. Short, 1990, J. Geophys. Res., 95, 2153-2160.
[6] Meneghini, R., J.A. Jones, T. Iguchi, K. Okamoto, and J. Kwiatkowski, 2001, J. Appl.
Meteor., 40, 568-585.

- 170 -