Tropical Rainfall Measuring Mission（TRMM）
Precipitation Radar Algorithm
Instruction Manual
For Version 6

TRMM Precipitation Radar TeamJapan Aerospace Exploration Agency (JAXA)
National Aeronautics and Space Administration (NASA)Jan 11th, 2005

Tropical Rainfall Measuring Mission
Precipitation Radar Algorithm Instruction Manual
For Version 6
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. On this instruction manual of TRMM PR...............................................................3
0-5. References ...................................................................................................................4

1. LEVEL 1 .................................................................................................. 10
1-1. 1B21: PR received power, 1C21: PR radar reflectivity........................................10
1-1. 1. Algorithm Overview.............................................................................................................. 10
1-1. 2. File Format ............................................................................................................................ 11
1-1. 3. Changes in 1B21 after the satellite boost in August 2001 .................................................... 29
1-1. 4. Major changes in 1B21 algorithm for product version 6 ...................................................... 30
1-1. 5. Comments on PR Level 1 products ....................................................................................... 30
1-1. 6. Planned Improvements .......................................................................................................... 35
1-1. 7. References ............................................................................................................................. 35

1-2. DID access routine ...................................................................................................36
1-2. 1. Objectives.............................................................................................................................. 36
1-2. 2. Method used .......................................................................................................................... 36
1-2. 3. Flowchart............................................................................................................................... 36
1-2. 4. Some details of the algorithm................................................................................................ 37
1-2. 5. Input data............................................................................................................................... 37
1-2. 6. Output data ............................................................................................................................ 38
1-2. 7. Output file specifications....................................................................................................... 38
1-2. 8. Interfaces with other algorithms............................................................................................ 39
1-2. 9.

Special notes (caveats) ......................................................................................................... 40

1-2.10.

References ........................................................................................................................... 40-i-1-3. Main-lobe clutter rejection routine ........................................................................41
1-3. 1. Objectives of main-lobe clutter rejection routine.................................................................. 41
1-3. 2. Method used .......................................................................................................................... 41
1-3. 3. Flowchart............................................................................................................................... 41
1-3. 4. Outline of the algorithm ........................................................................................................ 42
1-3. 5. Input data............................................................................................................................... 43
1-3. 6. Output data ............................................................................................................................ 44
1-3. 7. Output file specifications....................................................................................................... 45
1-3. 8. Interfaces with other algorithms............................................................................................ 46
1-3. 9. Special notes (caveats) .......................................................................................................... 46
1-3.10. References............................................................................................................................ 46

1-4. Redefinition of the Minimum Echo Flag................................................................47
1-4. 1. Introduction ........................................................................................................................... 47
1-4. 2. Sidelobe removal algorithm .................................................................................................. 47
1-4. 3. Redefinition of minEchoFlag ................................................................................................ 48
Appendix. Detail information of the metadata ................................................................................. 49

2. LEVEL 2 .................................................................................................... 58
2-1. 2A-21: Surface Cross Section..................................................................................58
1. Objectives and functions of the algorithm.................................................................................... 58
2. Command line arguments: ............................................................................................................ 61
3. Definitions of Output Variables.................................................................................................... 61
4. Description of the Processing Procedure:..................................................................................... 64
5. Interfaces to other algorithms: ...................................................................................................... 64
6. Comments and Issues: .................................................................................................................. 64
7. Description of Temporal Intermediate File .................................................................................. 66
8. The Cross-track Hybrid Surface Reference Method..................................................................... 67
9. Revised Angle Bin Definitions..................................................................................................... 69
10. References .................................................................................................................................. 70ii

2-2. 2A23...........................................................................................................................71
2-2.1. Objectives of 2A23................................................................................................................. 71
2-2.2. Main changes from the previous version................................................................................ 71
2-2.3.

Method used in 2A23 ............................................................................................................ 72

2-2.4.

Processing Flow..................................................................................................................... 73

2-2.5.

Input data ............................................................................................................................... 74

2-2.6.

Output data ............................................................................................................................ 75

2-2.7.

Output file specifications....................................................................................................... 75

2-2.8.

Interfaces with other algorithms ............................................................................................ 82

2-2.9.

Special notes.......................................................................................................................... 83

2-2.10.

References ........................................................................................................................... 84

Appendix. Some details of 2A23 ..................................................................................................... 85

2-3. 2A25...........................................................................................................................91
2-3. 1. Objectives.............................................................................................................................. 91
2-3. 2. Changes from V5 to V6......................................................................................................... 91
2-3. 3. Algorithm Overview.............................................................................................................. 92
2-3. 4. More Detailed Description of the Algorithm ........................................................................ 92
2-3. 5. Input data............................................................................................................................... 95
2-3. 6. Output data ............................................................................................................................ 96
2-3. 7. Interfaces with other algorithms............................................................................................ 97
2-3. 8. Caveats .................................................................................................................................. 98
2-3. 9. References ........................................................................................................................... 100
2-3.10. Detailed description of output variables............................................................................. 101
Appendix 1. Output data structure defined in the toolkit ............................................................... 124
Appendix 2. Parameters defined in “param_general_6.61.dat”...................................................... 126
Appendix 3. Parameters defined in “param_error_6.61.dat”.......................................................... 128
Appendix 4. Parameters defined in “param_strat_1.dat”................................................................ 129
Appendix 5. Parameters defined in “param_conv_1.dat”............................................................... 131
Appendix 6. Parameters defined in “param_other_1.dat” .............................................................. 133

iii

3. LEVEL 3 .................................................................................................. 135
3-1. 3A-25: Space Time Statistics of Level 2 PR Products.........................................135
1. Objective of the algorithm .......................................................................................................... 135
2. Output Variables......................................................................................................................... 136
3. Processing Procedure:................................................................................................................. 151
4. Comments and Issues: ................................................................................................................ 151
5. Changed Variables in Version 6 ................................................................................................. 155

3-2. 3A-26: Estimation of Space-Time Rain Rate Statistics Using a Multiple
Thresholding Technique..................................................................................................157
1.

Objective of the algorithm ......................................................................................................... 157

2. Description of the Method.......................................................................................................... 157
3. Relationship of 3a-26 outputs to those of 3a-25 ........................................................................ 160
4.

Relationship between 3a-26 and the fractional areas above particular thresholds .................... 162

5. Reliability estimates ................................................................................................................... 165
6. Definition of the latitude-longitude boxes ................................................................................. 166
7. Notes on the processing procedure............................................................................................. 166
8. Input Parameters (initialized in 3a-26)....................................................................................... 168
9. Output Variables ........................................................................................................................ 169
10.

Processing Procedure ............................................................................................................... 171

11. Comments and Issues ............................................................................................................... 171
12. References ................................................................................................................................ 173

PR TEAM MEMBERS............................................................................... 174
PR Team Leader:.............................................................................................................174
1B21, 1C21 Algorithm Developers:................................................................................174
2A21, 3A25, 3A26 Algorithm Developer: ......................................................................175
2A23 Algorithm Developer: ............................................................................................175
2A25 Algorithm Developer: ............................................................................................175

iv

0.

Introduction

This instruction manual of TRMM PR algorithm is for PR version 6 algorithms
and products that were released to the public on 1 June 2004. The major changes of
PR standard algorithms after the release of PR products on 1 November 1999 are
involved. They are summarized 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 width of
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 thereceiver noise 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 scienceteam. 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
the mutual 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 thesurface scattering coefficient σ0 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 thesurface scattering coefficient σ0 by rain using no rain surface scattering coefficient
σ0 as a reference [Meneghini, 2000]. The algorithm 2A23 tests whether a brightband 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 typeand others by 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 the radar reflectivity factor, Z, with rain attenuation correction and rain
rate for each radar beam by the combination of Hitschfeld-Bordan and surface
reference methods[Iguchi,2000].

-2-

As the 13.8 GHz frequency band selected for the TRMM PR is fairly heavily
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 of algorithms

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 fordetail). Other than the 1B21, algorithms were not changed according to the altitudechange of the satellite.

0-4.

On this instruction manual of TRMM PR

The file content description for level 2 and 3 algorithms can be found in theInterface Control Specification (ICS) between the Tropical Rainfall Measuring
Mission Science Data and Information System (TSDIS) and the TSDIS Science User
(TSU) Volume 4: File Specification for TSDIS Products-Level 2 and 3 File
Specifications. It is available at:
http://tsdis02.nascom.nasa.gov/
PR team would like to express its sincere gratitude to Ms. Hiraki of JAXA for
her help with editing this manual.

-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 ofPrecipitation 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 after the last version (version 6.0)
Product No
1B21:
PR calibration

1C21:
PR reflectivities
2A21:
Sigma-zero
2A23:
PR qualitative

2A25:
PR profile

3A25:
Space-time average ofPR products

3A26:
Statistical method

Major Changes
a. Modification of calibration look up tables
outside of main routine
b. Correct RX power calibration factor by 0.35 dB
c. Improve mainlobe clutter routine
No changea. Implement hybrid surface reference over ocean
b. Change in angle bin definitionc. Use of scOrientation parameter
Rain type flag: 2 digits to 3 digits
Change criteria for “other type”, whose count decreases
in Version 6.
All the “shallow isolated” is convective
Introduced “shallow non-isolated”.
Change BB detection code, allowing Z below BB can belarger than Z at BB peak.
When BB is detected, rain type is stratiform.
Introduce BB boundaries and BB width.
Introduce rain probable (no effect on other products)
Removal of the 4 known bugs.
Improvement of estimation rain rate in the rangethat is cluttered by the surface echo.
Outputting the statistical expectation of rainfall rate R
and radar reflectivity factor Z by using Bayesian method.
Addition and modification of output variables.
Removal of unrealistically large values of Z and R
due to graupel or hail
Introduce the effect of gaseous attenuation.
Change initial DSD model.
a. New products:- Nadir bright-band products (from 2A23)- Estimated surface rain rate (from 2A25)- Near surface rain rate (from 2A25)- a, b parameters in R=aZb (from 2A25)- New rain categories (from 2A23)- ε, ε0 statistics
b. Modification of PIA statistics
c. Add counts for:- Correlation of RR at several height levels-Numberofreliable/marginallyreliableSRTobservations
a. Only minor changes-5-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 µs 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-7-

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

Name

Contact Person

Products

Algorithm Description

PR calibration
Rain/No rain

JAXA/EOC(Japan)J. Awaka (Japan)
T. Iguchi (Japan)

Total received power,
Noise Level Clutter
contamination flag.

1C21

PR
reflectivities

JAXA/EOC(Japan)

2A21

Surfacescattering
coefficient σ0

R. Meneghini(USA)

Profiled Zm (radarreflectivity factors
without rain attenuation
correction).
Path integrated
attenuation (PIA) of

Conversion of the count value of radar
echoes and noise level into engineeringvalue. Decision of rain/norain.Determination of effective storm
height from minimum detectable power
value. Rejection of mainlobe andsidelobe clutter.
Conversion of the power and noise
value to radar reflectivity factors Zm
without rain attenuation correction.

σ0 (in case of rain) and
its reliablility. Data base

2A23

PR qualitative

J. Awaka(Japan)

2A25

PR profile

T. Iguchi (Japan)

3A25

Space-time
average ofradar products

R. Meneghini
(USA)

3A26

Estimation of
space-timerain ratestatistics

R. Meneghini(USA)of σ0 (ocean/ land, incase of no rain)
Detection of brightband, Bright bandheight, strength, width,
Rain type classification,
Detection of shallow
isolated rain. Output ofrain/no rain flag, heightof storm top.
Range profiles ofattenuation-corrected
radar reflectivity
factors, rainfall rate.
The estimated nearsurface, and surface
rainfall rate, andaverage rainfall rate
between the two
predefined altitude(2,4 km).
Space-time averages ofaccumulations of 1C21,
2A21, 2A23, 2A25.

Rain rate statistics over5 degree x 5 degree 1
month space-time
regions using a multiple
thresholding technique.

-8-

Estimation of path integrated
attenuation and its reliability using thesurface as a reference target. Spatial andtemporal statistics of surface σ0 andclassification of σ0 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 or others. Shallow
isolated rain, the height of which is
below the 0 deg., is detected.
The rainfall rate estimate is given ateach resolution cell. This algorithm
employs hybrid method of the surface
reference method and
Hitschfeld-Bordan method.
Precipitation water content at 5
altitudes, and vertically integrated
precipitation water content are also
calculated.

Calculation of various statistics over amonth 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 the space-timerain rate at 4 levels, and the mean,
standard deviation, and so on.

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, 1C21: PR radar reflectivity

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 2 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).
The 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 echomeasurement, and to obtain a better vertical rain profile, 125-m intervals data
are available at near-nadir angle bins for rainoversample (up to 7.5 km) and±10 deg. scan angles for surfaceoversample.
- 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 specificangle bin.
- Land/ocean flag and Topographic height- 10 -

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 thatthe 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.

1-1. 2.

File Format

1-1.2.1. 1B21 PRODUCT FILE

The main output of the Tropical Rainfall Measurement Mission (TRMM)/Precipitation Radar (PR) Level-1B product, 1B21 is “PR received power.”
The file name convention at JAXA EOC is as follows:
T1PRYYYYMMDDnnnnn_1B21F00vv.01
PR1B21.YYYYMMDD.nnnnn
YYYYMMDD: Observation Date, nnnnn: granule ID, vv: product version
number
The PR1B21 product is written in Hierarchical Data Format (HDF).
HDF was developed by the U.S. National Center for Supercomputing
Applications (NCSA).
HDF manuals and software tools are available via anonymous ftp at ftp.ncsa.
uiuc.edu.
The file structure of 1B21 products is shown in Table 1-1.

- 11 -

Table 1-1. 1B21 product file structure
Name
Data Granule

FormatNote(Data object per granule)

Metadata
Calibration Coefficients72 bytetable 1-2.

Ray Header

60 byte*49

table 1-3.

Swath Data

(Data object per scan =0.6 sec.)

Scan Timefloat64

scantime[nscan]

Geolocation

float32

geolocation[2][49][nscan]latitude, longitude

Scan Status

table

15 byte*[nscan]table 1.-4.

Navigationtable

88 byte*[nscan]table 1-5.

Power

table

6 byte*[nscan]table 1-6.

System Noise

int16

systemNoise[49][nscan]unit: dBm*100

System Noise Warning Flag

int8

sysNoiseWarnFlag[49][nscan]

Minimum Echo Flag

int8

minEchoFlag[49][nscan]First Echo Height

int16

binStromHeight[49][nscan]

range bin number

Range Bin Number of Ellipsoid

int16

binElliposid[49][nscan]

range bin number

Range Bin Number of
Clutter-free Bottom
Range Bin Number of Mean DID

int16

binClutterFreeBottom[2][49][nscan]

range bin number

int16

binDIDHmean[49][nscan]

range bin number

Range Bin Number of Top of DID

int16

binDIDHtop[49][nscan]

range bin number

binDIDHbottom[49][nscan]

range bin number

Range Bin Number of Bottom of DID int16
Satellite Local Zenith Angle

float32 scLocalZenith[49][nscan]unit: deg

Spacecraft Range

float32 scRange[49][nscan]unit: mBin Start ofoversample

int16

osBinStart[2][29][nscan]

Land/Ocean Flag

int16

landOceanFlag[49][nscan]

Topographic Height

int16

surfWarnFlag [49][nscan]unit: mBin Number of Surface Peak

int16

binSurfPeak[49][nscan]

range bin number

Normal Sample

int16

normalSample[140][49][nscan]unit: dBm*100

Surfaceoversample

int16

osSurf[5][29][nscan]unit: dBm*100

Rain Oversample

int16

osRain[28][11][nscan]unit: dBm*100

Note.
nscan: number of total packets (scans) in one granule(one orbit from southernmost point to the next southernmost point).
In PR, one granule (about 91 minutes) has about 9100 scans because the PR performs
one scan every 0.6 seconds.
dBm*100: For example, -9436 represents –94.36 dBm- 12 -

1. Metadata (CoreMetadata.0, ArchiveMetadata.0)
Metadata are defined as the inventory information of the TRMM data.
EOSDIS 1 has divided the metadata elements into two types: core metadata(EOSDIS Core System (ECS) metadata; CoreMetadata.0) and product-specificmetadata (ArchiveMetadata.0). Core metadata are common to most Earth
Observing System (EOS2) data products. Product-specific metadata include thespecific information of each product.
The detailed information is provided in the Appendix.

2. Calibration Coefficients (PR_CAL_COEF)
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.

Table 1-2. Calibration coefficients
Name

FormatTransmitter gain correction factor

float32transCoef

Receiver gain correction factor

float32

receptCoef

LOGAMP Input/Output characteristics

float32

fcifIOchar[16]Note

The power level at the IF unit corresponding to the count value is calculated bya look-up table which represents input to output characteristics of the IF unit
measured by internal calibrations. PR received power is then calculated fromthis power level and the receiver gain at RF stage.

1
2

EOSDIS: EOS Data and Information System (NASA)
EOS: Earth Observing System (NASA)- 13 -

3. Ray Header (RAY_HEADER)
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 each angle bin.
Table 1-3. Ray Header

Ray Start

Name
int16

FormatrayStart[49]

Ray Size

int16

raySize[49]Scan Angle
Starting Bin Distance

float32 angle[49]float32 startBinDist[49]Rain Threshold #1
Rain Threshold #2
Transmitter Antenna Gain
Receiver Antenna Gain
One-way 3dB
Along-track Beam Width
One-way 3dB
Cross-track Beam Width
Equivalent Wavelength
Radar Constant
PR Internal Delayed Time
Range Bin Size
Logarithmic Averaging Offset
Main Lobe Clutter Edge
Side Lobe Clutter Range

float32
float32
float32
float32
float32

rainThres1[49]rainThres2[49]transAntenna[49]recvAntenna[49]onewayAlongTrack[49]Noterange bin number ofstarting normal sample,
see Note (a)number of normal samples
in 1 angle
see Note (a)unit deg, see Note (b)distance (m) between
the satellite and the starting bin
sample. unit m,see Note (c)see Note (d)see Note (d)unit: dB
unit: dB
unit: rad, see Note (e)float32 onewayCrossTrack[49]unit: rad, see Note (e)float32
float32
float32
float32
float32
int8
int8

unit: m, see Note (f)unit: dB, see Note (g)set to 0
unit: m, see Note (a), (h)unit: dB, see Note (i)see Note (j)see Note (k)eqvWavelength[49]radarConst[49]prIntrDelay[49]rangeBinSize[49]logAveOffset[49]mainlobeEdge[49]sidelobeRange[3][49]Notes: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.

- 14 -

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)b) Scan Angle (angle) 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.* 3 The angle is positive when the antenna beam isrotated counter clockwise (CCW) from the nadir about the +X axis of the radarelectric coordinates.
c) 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 as follows:
Distance = “Starting Bin Distance (startBinDist)” + “Range Bin Size(rangeBinSize)” × (N − 1)This distance is defined as the center of a radar resolution volume
which extends ± 125 m .
d) Rain Thresholds (rainThres1 and rainThres2) are used in the minimum echo
test.
e) Beam widths, both along track beam width and cross track beam width(onewayAlongTrack and onewayAcrossTrack), are recorded based on the factthat the PR main beam is assumed to have a two-dimensional Gausian beam
pattern.
f) “Euivalent Wavelength (eqvWavelength)” = 2c ( f1 + f2 )where c is the speed of light, and f1 and f2 are PR’s two frequencies.

3

If there is no attitude error, +X (or sometimes –X, see Spacecraft Orientation in Scan Status) is along the spacecraft
flight direction, +Z is along the local nadir, and +Y is defined so that the coordinates become a right-hand Cartesiansystem.

- 15 -

g) Radar Constant (radarConst) is defined as follows, and is used in the radar
equation:
2


K
3
−18

C 0 = 10log π
10
 2 10 ln2

K = (ε − 1) / (ε + 2 )ε : 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
4(1972).* With this constant, users can convert from PR receiving
powers to rain reflectivity. (See the 1C products.)h) Range Bin Size (rangeBinSize) is the PR range resolution and is the width atwhich pulse electric power decreases 6dB (-6 dB width).
i) Logarithmic Averaging Offset (logAveOffset) is the offset value between thelogarithmic average and the power-linear average. The PR outputs the dataof 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
average and is thus equal to normal average power.
j) 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.
k) Absolute value of the difference in Range bin numbers between the binnumber of the 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: Items j) and k) are not useful for detailed examination of radar echo range
profile, especially over land. Please refer to 14 (“Range Bin Number of Clutter-free
Bottom”), 23 “Bin Number of Surface Peak” and so on.

4Ray, P.S., 1972: Broadband complex refractive indices of ice and water. Appl.Opt., Vol.11, No.8, 1836-1844.

- 16 -

4. Scan Time (float64

scan_Time[nscan])

Scan Time is the center time of 1 scan (the time at center of the nadir beamtransmitted pulse)
It is expressed as the UTC seconds of the day.

5. Geolocation (float32

geolocation[2][nscan])The earth location of the beam center point per angle bins at the altitude of theearth ellipsoid.
This is recorded as latitude and longitude, in that order.
If the earth location cannot be calculated, the geolocation output becomes-9999.9 (dummy output).
Positive number of latitude indicates north latitude, and positive number of
longitude indicates east longitude.

- 17 -

6. Scan Status (pr_scan_status[nscan])The status of each scan, that is, quality flags of spacecraft and instrument, arestored.
Table 1-4. Scan Status
Name

FormatNote

Missing

int8 missing

The values are:0: normal
1: missing (missing packet and calibration mode)
2: No-rain

Validity

8-bit validity

The summary of operation mode.
If all items are normal, zero is recorded.

QAC

8-bit qac

Geolocation
Quality

8-bit geoQuality

Data Quality

8-bit dataQuality

Spacecraft
Orientation

int8 scOrient

Bit meaning if bit=1<bit1>: Non-routine spacecraft orientation (2 or 3 or 4)<2>: Non-routine ACS mode (other than 4)<3>: Non-routine yaw update status (0 or 1)<4>: PR operation mode (other than 1)<5>: Non-routine QAC (QAC bit 2, 6 or 7 is not zero)
Quality information regarding demodulation statusat Level-0 processing (quality accounting capsule)<bit1>: RS header error<2>: Data unit length code wrong<3>: RS frame error<4>: CRC frame error<5>: Data unit sequence count error<6>: Detected frame error during generation ofthis data unit
<7>: Data unit contains fill data
Bit meaning if bit =1<0>: latitude limit error<1>: geolocation discontinuity<2>: attitude change rate limit error<3>: attitude limit error<4>: maneuver<5>: using the predictive orbit data
<6>: geolocation calculation error
If geolocation quality is not zero,
the geolocation accuracy is not assured.
Total summary of scan data.
If this is not zero, the data is not processed in 1C.
Bit meaning if bit =1<0>=1: Missing (No data)<5>=1: Bad Geolocation Quality<6>=1: Bad Validity
The information in spacecraft Attitude
Control System.
Value 0 and 1 is normal.
Value Meaning
0:+x forward
1:-x forward
2:-y forward
3:CERES calibration- 18 -ACS mode

int8 acsMode

Yaw Update
Statusint8 yawUpdateS

PR Modeint8

PR status #1

8-bit prStatus1

PR status #2

8-bit prStatus2

Fractional Orbit
Numberfloat32 fracOrbitN

prMode4:Unknown orientation
The mode of spacecraft Attitude Control System.
Value: Meaning
0: stand-by
1: Sun acquire
2: Earth acquire
3: Yaw acquire
4: Normal
5: Yaw maneuver
6: Delta-H (Thruster)
7: Delta-V (Thruster)
8: CERES Calibration
The information in spacecraft Attitudecontrol system.
Value: Meaning
0: inaccurate
1: indeterminate
2: accurate
Value: Meaning
0: other mode
1: Observation mode
Bit meaning if bit =1<0>: LOGAMP noise limit error<1>: Noise level limit error<2>: Out of PR dynamic range<3>: Not reach surface position<7>: FCIF mode change (see 1.27)
Bit meaning if bit =1<0> Warning for clutter because of strong
nadir surface echo. (see 1.28)
The fractional part of the orbit at scan time.
(Scan time - Orbit Start Time) /(Orbit End time - Orbit Start Time)

Notes:· bit number

MSB
7 6

5

4

3

2

LSB
1 0

a) PR Status #1 in Scan Status
The flags listed here indicate warnings of PR conditions (noise level,
echo power and echo position, and mode change). In data processing,users should be cautions with the following as a scan with non-zerostatus includes questionable range bins or angle bins.
<1>
<2>
<3>

Noise level limit error: The meaning of this warning is the same as
10 ”System Noise Warning Flag”.
Surface echo is so strong that it exceeds the PR receiver dynamic
range. If this bit is ON, surface echo level may be questionable.
If Surface echo is out of range window, Bin Surface Peak andrelated data become uncertain.

- 19 -

b) PR Status #2 in Scan Status
In some cases, antenna sidelobes are directed to nadir receive surface
echo positions. When the main beam is off nadir, the timing of suchnadir-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 a predetermined threshold. When the flag isON, please be careful about the echoes at all angle bins around the same
logical range bin number as the Bin-surface-peak at nadir (angle binnumber 25).

7. Navigation (pr_navigation)
This is the output of NASA’s geolocation toolkit.
This is recorded each angle.
Table 1-5. Navigation
Name
X component of spacecraft position
Y component of spacecraft position
Z component of spacecraft position
X component of spacecraft velocity
Y component of spacecraft velocity
Z component of spacecraft velocity
Spacecraft geodetic latitude
Spacecraft geodetic longitude
Spacecraft geodetic altitude
Roll of spacecraft attitude
Pitch of spacecraft attitude
Yaw of spacecraft attitude
Sensor Orientation Matrix #1
Sensor Orientation Matrix #2
Sensor Orientation Matrix #3
Sensor Orientation Matrix #4
Sensor Orientation Matrix #5
Sensor Orientation Matrix #6
Sensor Orientation Matrix #7
Sensor Orientation Matrix #8
Sensor Orientation Matrix #9
Greenwich Hour Angle

Formatfloat32 scPosX
float32 scPosY
float32 scPosZ
float32 scVelX
float32 scVelY
float32 scVelZ
float32 scLat
float32 scLon
float32 scAlt
float32 scAttRoll
float32 scAttPitch
float32 scAttYaw
float32 att1
float32 att2
float32 att3
float32 att4
float32 att5
float32 att6
float32 att7
float32 att8
float32 att9
float32 greenHourAng

Noteunit: munit: munit: munit: m/s
unit: m/s
unit: m/s

unit: munit: deg
unit: deg
unit: deg

unit: deg

Notes :a) spacecraft position: The position (in meter) in Geocentric Inertial
Coordinates at the Scan time.
These coordinates will be True of Date, as interpolated from the data inNASA flight dynamics facility ephemeris files.
b) sensor orientation matrix: The rotation matrix from the instrument
coordinate frame to geocentric inertial coordinate.

- 20 -

8. Power (powers)
Power is recorded for each scan and consists of the calibrated PR transmitter
power and the transmitter pulse width.
Table 1-6. PowerName

PR transmitter power
PR transmitter pulse width

Formatint16
radarTransPowerfloat32 transPulseWidthNote
unit: dBm*100
unit: sec

Note: dBm*100: For example, -9436 represents –94.36 dBm

9. System Noise (int16

systemNoise[49][nscan])System Noise is recorded in each angle bin. This is the value estimated byaveraging four noise samples. Unit is 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.
If data is missing, the dummy value (-32734) is recorded.

10. System Noise Warning Flag (int8

sysNoiseWarnFlag[49][nscan])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), thisflag may be neglected. Received power levels in all range bins will increase incases (1) and (2) as much as the increase of the system noise.
PR may receive radio interference in the following areas.
N3.1 E 101.7 (in Malaysia)
N33.8 W118.2 (around Los Angeles)
S34.8 W68.4 (around Santiago)
N10.5 W66.9 (in Chili)
N4.7 E36.9 (around Ethiopia – Kenya border)
S32.8 W63.4 (around Amazon)etc.

- 21 -

11. Minimum Echo Flag (int8

minEchoFlag[49][nscan])This value shows the esistence of the rain echo at each angle bin.
Six values are used in the Minumun Echo Flag: 0, 10, 20, 11, 12, and 13.
0: No rain. (Echoes are very weak.)
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 weakechoes 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 by sidelobe
clutter, see section 1-4.)
Please be careful using the Minimum Echo Flag except when it is 0 or 20.

12. First Echo Height (int16

binStormHeight[2][49][nscan])The First Echo Height (storm height) is represented by the logical range binnumber (1 to 400, 125-m interval). Two types of First Echo Height are estimated,depending on whether the minimum echo flag = 10 or 20. (If the first echo isdetected below the clutter-free bottom, the two types depend on whether the flag
= 11 or 12.)

13. Range Bin Number of Ellipsoid (int16

binEllipsoid[49][nscan])Ellipsoid Height is represented by the logical range bin number (1 to 400).
This is calculated by the following equation.
binEllipsoid[j] = RayStart + (scRange – startBinDist)/rangebinSize x 2(scRange: see 19. spacecraft range)- 22 -

14. Range Bin Number of Clutter-free Bottom(int16 binClutterFreeBottom[2][49][nscan])This is the bottom range-bin number (logical range bin number) in clutter-freerange bins estimated by the algorithm provided by Dr. Awaka (Hokkaido Tokai
Univ., Japan).
binClutterFreeBottom [0][49]: clutter free certain,
binClutterFreeBottom [1][49]: clutter free probable.

15. Range Bin Number of Mean DID (int16

binDIDHmean[49][nscan])binDIDHmean represents the range bin number corresponding to the mean heightof all DID data samples available in a 5 × 5km area that overlaps most with thefootprint.

16. Range Bin Number of Top of DID (int16

binDIDHtop[49][nscan])binDIDHtop[][0] represents the range bin number corresponding to the highest
value (top) of all DID data samples in a 5 × 5km box, and binDIDHtop[][1], therange bin number corresponding to the highest value in a 11 × 11km box.

17. Range Bin Number of Bottom of DID (int16

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

18. Satellite Local Zenith Angle (float32

scLocalZenith[49][nscan])The angle between the local zenith (on the Earth ellipsoid) and the beam centerline.

- 23 -

19. Spacecraft Range (float32

scRange[49][nscan])The distance between the spacecraft and the center of the footprint of the beamon the Earth ellipsoid.

20. Bin start ofoversample (int16

osBinStart[49][nscan])The first byte indicates that logical range bin number of starting theoversample.
The second byte indicates the status of the onboard surface tracker (0, normal; 1,
Lock off).
Oversample only applies to 29 angles (angle 11 to 39).

21. Land/Ocean Flag (int16

landOcenFlag[49][nscan])The land or ocean information from the Digital Terrain Elevation Dataset (DTED)Intermittent Dataset (DID) provided by NASA/JPL.
0 = water (ocean or inland water)
1 = land
2 = coast (not water nor land)
3 = water (surface peak is not correctly detected because of high attenuation)
4 = land /coast (surface peak is not correctly detected because of highattenuation)
In the product version 6, two categolies 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 3 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 4 and thebinSurfPeak is recalculated using data between the binClutterFreeBottom andbinClutterFreeBottom+8 (bins) toward the Earth.

- 24 -

22. Topographic Height (int16

surfWarnFlag[49][nscan])The topographic mean height (m) of all DID samples in a 5 × 5km.

23. Bin Number of Surface Peak (int16

binSurfPeak[49][nscan])The bin surface peak indicates the logical range bin number of the peak surface
echo. The algorithm to detect the surface peak is provided by Dr. Kozu, CRL(presently at Shimane Univ.).
If the surface is not detected, 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 theoversample data.

24. Normal Sample (PR received power) (int16

normalSample[140][49][nscan])The normal sampled PR received powers are recorded (unit: dBm*100).
The data is stored in the array of 49 angles ∗ 140 elements.
Since each angle has a different number of samples, the elements after the end ofsample are filled with a value of -32767.
If a scan is missing, the elements are filled with the value -32734.
Logical range bin number comparable with binSurfPeak, binEllipsoid, etc.
is calculated with rayStart in RAY_HEADER (see 3. Ray Header, Note a ).

25. Surface Oversample (int16

osSurf[5][29][nscan])The PR records theoversampled data in five range bins around the surface peakdetected 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 (unit: dBm*100).
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 other logical range bin, then merge with the interleaving
normal sample data.

- 25 -

26. Rain Oversample (int16

osRain[28][11][nscan])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 (unit: dBm*100).
The 125m interval dataset in heights from 0 km to 7.5 km can be generated byinterleaving the Normal Samples with the Surfaceoversamples and rainoversamples. 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 surfaceoversample follows the rain oversample
continuously. Therfore, the logical range bin number of the Surfaceoversample
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)

1-1.2.2. 1C21 PRODUCT FILE

The main output of the PR Level-1C, 1C21, is the radar “reflectivity factor.”
The file format is exactly the same as that of 1B21 except for the replacement of thereceived power by the radar reflectivity factor and noise (no echo range bin) by adummy value.

- 26 -

Name
Data Granule

Table 1-7. 1C21 products file structure
FormatNote(Data object per granule)

Metadata
Calibration Coefficients72 bytetable 1-2.

Ray Header

60 byte*49

table 1-3.

Swath Data

(Data object per scan =0.6 sec.)

Scan Timefloat64

scantime[nscan]

Geolocation

float32

geolocation[2][49][nscan]latitude, longitude

Scan Status

table

15 byte*[nscan]table 1.-4.

Navigationtable

88 byte*[nscan]table 1-5.

Power

table

6 byte*[nscan]table 1-6.

System Noise

int16

systemNoise[49][nscan]

dBm*100

System Noise Warning Flag

int8

sysNoiseWarnFlag[49][nscan]

Minimum Echo Flag

int8

minEchoFlag[49][nscan]First Echo Height

int16

binStromHeight[49][nscan]

range bin number

Range Bin Number of Ellipsoid

int16

binElliposid[49][nscan]

range bin number

Range Bin Number of Clutter-free

int16

binClutterFreeBottom[2][49][nscan]

range bin number

Range Bin Number of Mean DID

int16

binDIDHmean[49][nscan]

range bin number

Range Bin Number of Top of DID

int16

binDIDHtop[49][nscan]

range bin number

Range Bin Number of Bottom of DID

int16

binDIDHbottom[49][nscan]

range bin number

Satellite Local Zenith Angle

float32

scLocalZenith[49][nscan]degSpacecraft Range

float32

scRange[49][nscan]m

Bin Start ofoversample

int16

osBinStart[2][29][nscan]

Land/Ocean Flag

int16

landOceanFlag[49][nscan]

Topographic Height

int16

surfWarnFlag [49][nscan]m

Bin Number of Surface Peak

int16

binSurfPeak[49][nscan]

range bin number

Normal Sample

int16

normalSample[140][49][nscan]dBZ*100

Surface Oversample

int16

osSurf[5][29][nscan]dBZ*100

Rain Oversample

int16

osRain[28][11][nscan]dBZ*100

Bottom- 27 -

Notes：For example, -9436 represents –94.36 dBZ
The 1C21 product has the same format as 1B-21.
In 1C-21, the normal sample, surfaceoversample and rain oversample containradar reflectivity factors (dBZ, mm6/m3) which are converted from the PR
received powers in the corresponding places in 1B21 output. The radar equation
used isPr(range) =

π3 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 atomospheric attenuation.

- 28 -

1-1. 3.

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
in order 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
the one 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 theobtained data is the result from averaging of 32 pulses, 32 times of P(N) stands forthe total received power.
The estimated correction error is less than 0.2 dB for rain echo and less than 0.3 dB- 29 -

for surface echo.

1-1. 4.

Major changes in 1B21 algorithm for product version 6

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）

1-1. 5.

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. The initialcheckout 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
pattern measurements 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 thoseobserved from previous airborne and satelliteborne scatterometers.

- 30 -

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 thereceiver noise figure. Actually the rain echo power is measured from thesubtraction of the system noise power from the total receiver power (rain echo
power + system noise power). The accuracy of rain echo power can becharacterized 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 Zm can be considered to be about 16-18 dBZ after thedetailed 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
especially in mountainous regions. An algorithm has been implemented whichanalyzes the radar echo range profile very carefully to determine the boundary
between rain and surface 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 a surface echo is treated as a rain echo (and in mountainous
regions, clutter position when it rains can happen to become too high in a veryrare occasion). Please be 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.

- 31 -

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 freerange 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 maybe noise(Some weak echoes above noise exist in clutter free ranges),
20 = rain certain(Some strong echoes above noise exist in clutter free ranges),- 32 -

11 = rain possible but maybe noise or surface clutter(Some weak echoes exist in possibly cluttered ranges), andrain possible but maybe clutter
12 = (Some strong echoes exist in possibly cluttered ranges).
Therefore please be careful in using the Minimum Echo Flag except 0 and 20.

6. Information concerning the surface location in 1B21 and 1C21.
The following variables are newly added in 1B21 and 1C21 products.
a. Range bin number of Ellipsoid (binEllipsoid)b. Range bin number of clutter free bottom (binClutterFreeBottom)
c. Range bin number of mean DID (binDIDHmean)d. Range bin number of top of DID (binDIDHtop)
e. Range bin number of bottom of DID (binDIDHbottom)
As you can imagine from the name of each variable, those represent range binnumbers corresponding to the surface height from the Earth ellipsoid, which may
be useful to analyze a range profile of PR received power or radar reflectivity
factor.

7. 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
the range bin number determined from a Digital Elevation Model (DID). In mostcases, 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 is in error, and theother is a case in which rain echo is so strong so that surface echo is masked by therain echo. We expect those cases are rare, but please keep in mind those may occur
with a small probability.

- 33 -

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

8. 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.

- 34 -

1-1. 6.

Planned Improvements

Routine monitoring of PR performance and periodical ARC calibrations are being
conducted. Depending on the drift of PR system parameters, the calibration
factors and the look-up table may be updated in future.

1-1. 7.

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 data processing
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.

- 35 -

1-2.

DID access routine

1-2. 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.

1-2. 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.

1-2. 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- 36 -

1-2. 4.

Some details of the algorithm(a) Height_mean
A mean of DID elevation over a 5 km * 5km box, Height_mean, is
computed with 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.

1-2. 5.

Input data(a) DID data set.
(b) latitude/longitude- 37 -

1-2. 6.

Output data(a) int Height_mean[49],(b) int Height_max[49][2],(c) int Height_min[49][2],(d) int Hmedian[49],(e) int Hstd[49],(f) int LWflag[49],1-2. 7.

/* Unit in m (5km * 5km)/* 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: mixed

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

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]: Maximum of DID elevation over 11 km * 11 km box.
Unit is in [m].
(c) int Height_min[i][0]: Minimum of DID elevation over 5 km * 5 km box.
Unit is in [m].
int Height_min[i][1]: 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: mixed.

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

- 38 -

1-2. 8.

Interfaces with other algorithms

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

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

- 39 -

===== 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.

where j runs from 1 to 49 and the range bin numbers are those for 125m
intervals.

1-2. 9.

Special notes (caveats)None.

1-2.10.

References

None.

- 40 -

1-3.

Main-lobe clutter rejection routine

1-3. 1.

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.

1-3. 2.

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

1-3. 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 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- 41 -

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 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 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.

1-3. 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 occurs because of an inaccuracy of DID elevation data,(2) Strong attenuation makes the radar echo at and around binSurfPeak verysmall, indistinguishable from noise,(3) The radar echo at and around binSurfPeak is actually very small becauseof a specular reflection over a very flat surface when the antenna 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
elevation, offset is needed when phenomenon A or G occurs.

- 42 -

(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 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
not found, the empirical upper bound obtained by (c) is used as the stating point.
(e) Determination of the clutter free bottom:
First, whether the stating 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.

1-3. 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*/

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

osBinStart[29][2],- 43 -

int binSurfP_in[49],/* L1b21swathdata->binSurfPeak*/

int Height_mean_in[49],/* unit [m]; mean. of DID elev. (5 km box)*/

int Height_max_in[49][2],/* unit [m]; Max. DID elev. [0]: 5 km, [1]: 11 km */int Height_min_in[49][2],/* unit [m]; Min. DID elev. [0]: 5 km, [1]: 11 km */int Hmedian_in[49],/* unit [m]; Median of DID elev. 5 km * 5 km*/

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

*/

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

1-3. 6.

5km * 5km
0:W, 1:L, 2:C*/

Output data

int binClutterFreeBottom[49][2], /* bin number with 125 m resol.

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

*/

/*

*/

int ist[49].

ist[i] = 0: normal,/*/*

1: missing data input and/or */data corruption,*//*

2: bug (please notify author), *//*3: DID elevation doubtful,*//*

4: binSurfPeak doubtful

*/

/*
/*
/*

- 44 -

maybe due to large ATT,
5: binSurfPeak doubtful*/*/

but not so serious as ist=4. */1-3. 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)- 45 -

1-3. 8.

Interfaces with other algorithms

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

1-3. 9.

Special notes (caveats)

Since the DID elevation data contains a large error in some area, in particular inhigh mountain areas, the main-lobe clutter rejection routine has a chance of not
being able to output the correct clutter free bottom. Though some improvements
are achieved in the product-ver. 6, there still remains the chance of occurring bad
clutter free bottom (the occurrence of bad clutter free bottom is estimated to beless than 1 %, but not zero). Tibet and Andes are the most suspicious regions
where bad clutter free bottom would still occur.
Main changes made in the product-ver. 6 are as follows:(a) Oversample data is used,(b) Added ist=4 and 5 to the output status flag so as to make the re-examinationof binSurfPeak more accurately.

1-3.10.

References

None.

- 46 -

1-4.

Redefinition of the Minimum Echo Flag

1-4. 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.

1-4. 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 theminimum requirement, a weak surface echo that is picked up by a sidelobe in thenadir 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.

- 47 -

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,(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
as sidelobe echo. This procedure is included to avoid misidentifying thebright band echo as a sidelobe echo.

1-4. 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.

- 48 -

Appendix. Detail information of the metadata
ECS (EOSDIS Core System) Metadata Elements [Core Metadata]
Defined Names of0bject Name
Parameterin the HDF
in the toolkit

Type

TK_ORBIT_NUMBER

Orbit Number

int

17

Range
Beginning
Date

date

25

Range
Beginning
Time

time

23

The time when the granule coverage
began. See beginning date.

Range Ending
date
Date

22

The date when the granule coverage
ended. See beginning date.

Range Ending
time
Time

20

The time when the granule coverage
ended. See beginning date.

GranulePointerchar

48

Short Name

char

66

Size MB ECS
float
Data Granule

21

Longitude Of
Maximum
Latitudechar

50

SpatialTK_SPAT_COV Spatial
char
Coverage Type _TYPE
Coverage Type33

Metadata
Element

1 Orbit Number

TK_BEGIN_DATE
2 Beginning Date *****.tkyear*****.tkmonth*****.tkday

3

BeginningTime

4 Ending Date

5 Ending Time

6 Granule ID

TK_BEGIN_TIME***** .tkhour***** .tkminute***** .tksecond
TK_END_DATE***** .tkyear***** .tkmonth***** .tkday
TK_END_TIME***** .tkhour***** .trminute***** .tksecond
TK_GRANULE_lD

7

ID of ECS
Data Object

8

Size MB ECSTK_FILE_SIZE
Data Object

Longitude of
9 Maximum
Latitude10

Ellipsoid
Name
Equatorial
12
Radius11

TK_DATA_ID

TK_LON_OF_MAX_LATTK_ELLIPSOID
Ellipsoid Name char
_NAME
Equatorial
TK_EQ_RADIUS
float
Radius- 49 -

Estimated
Description
size

50
51

The orbit number to be used in
calculating the spatial extent of thisdata.
The date when the granule coverage
began. Granule coverage defined as
the orbit for Level-1 and Level-2
satellite data, as the hour of the
granule for Level-1 and Level-2
ground validation data, as the day of
the granule for rain gauge anddisdrometer data, and as the pentad ormonth of the granule for Level-3 data.

ID of granule. Same as input file
name. (ex. 1B12.19990706.1039.1)
The unique identifier of an ECS
collection to which this granulebelongs. (i.e. “Total Power, Noise”,“PR Reflectivity”)
The size attribute will indicate thevolume of data contained in the
granule.
Longitude of the northernmost extent
of the satellite orbit. Decimal degrees
with 6 figures precision after thedecimal point. Positive east, negative
west. A point on the 180th meridian is
assigned to the western hemisphere.
This attribute denotes whether the
locality/coverage requires horizontal,
vertical or both spatial domain andcoordinate system definitions. “both”
Name of the ellipsoid.
“World Geodetic System (WGS) 84”
Equatorial radius of the earth ellipsoid(meters). “6378.137”

13

TK
Denominator of_FLATTENING
Flattening_RATIO

14

Orbit Model
Name

15

Semi Major
Axis

Denominator
Flattening
Ratio

float

51

TK_ORBIT_MODEL_NAME

Orbiit Model
Name

char

98

TK_KEP_SEMI_MAJOR_AXIS

Semi Major
Axis

float

19

16 Mean Anomaly

TK_KEP_MEAN
Mean Anomaly float_ANOMALY

l8

Right
Ascension of
17
Ascending
Node

Right
TK_KEP_RIGHT_ASCEN Ascension
_NODE
Node

float

42

TK_KEP_ARG_OF_PERIGEE

float

28

18

Argument of
PerigeeArgument of
Perigee

TK_KEP
Eccentricity
float_ECCENTRICITY
TK_KEP
20 Inclination
Inclination
float_INCLINAT10N
TK_KEP
21 Epoch date
_EPOCH
Epoch Date
date
_DATE
TK_KEP
22 Epoch time
_EPOCH
Epoch Time
time
_TIME
TK_KEP
Epoch
23_EPOCH
Epoch millisec int
milliseconds_MILLISECTK_WEST
West
West Bounding
24_BOUND
Bounding
float
Coordinate_COORD
Coordinate
TK_EAST
East Bounding
East Bounding
25_BOUND
float
Coordinate
Coordinate_COORDNorth
TK_NORTH
North
Boundingfloat
26 Bounding_BOUND
Coordinate
Coordinate_COORDSouth
TK_SOUTHSouth
27 Bounding_BOUND
Bounding
float
Coordinate_COORD
Coordinate
Center Point
TK_CENTER
28
Center Latitude float
Latitude_POINT_LAT
Center Point
TK_CENTER
Cener
29
float
Longitude_POINT_LON
Longitude
30 Radius
TK_RADIUS
Radius Value float
19 Eccentricity- 50 -

21
20

The reciprocal of the flattening ratio,f,
Where f = 1 – b/a, a = Equatorial
radius of the earth ellipsoid and b =Polar radius of the earth ellipsoid“0.00335281”
The reference name to the orbital
model to be used to calculate thegeolocation of this data to determine
global spatial extent.
“Definitive FDF Ephemeris”
Half of the long axis of the orbit
ellipse (meters).
Used Geometric metadata.
Angle around the orbit at the Epoch
Time about the Ellipse center from theascending node (radians).
Used Geometric metadata.
Right Ascension in Geocentric Inertial
Coordinates of the north boundequator crossing (radians).
Used Geometric metadata.
Angle from the ascending node toperigee (radians). Used Geometricmetadata.
Eccentricity of ellipse (meters).
Used Geometric metadata.
Angle between Orbit plane and Earth
Equatorial plane (radians).

19

Reference date for orbital elements.
Used Geometric metadata.

19

Reference time for orbital elements.
Used Geometric metadata

20

Reference milliseconds for orbital
elements. Used Geometric metadata29

The degree value for the west
longitude of boundary. “-180”

29

The degree value for the east
longitudeof boundary. “180”30

The degree value for the north latitude
of boundary. “40”30

The degree value for the south latitude
of boundary. “-40”52

Latitude of center point of product.

52

Longitude of center point of product.

15

Distance in km from Point. “-9999.9”

Latitude
3l
Resolution

32

Longitude
Resolution

TK_LATITUDE_RES

Latitude
Resolution

float

27

TK_LONGITUDE Longitude_RES
Resolution

float

28

char

112

char

50

char

98

Geographic
33 Coordinate
Units
Temporal
34
Range Type

Geographic
TK_GEO
Coordinate_COORD_UNITS
Units
TK_TEMPOR
Temporal_RNG_TYPE
Range Type
Qualiity
QA Parameter TK_QA_PARAM Assurance
35
Name
_NAME
Parameter
Name
Quality
QA Parameter TK_QA_P^RAM Assurance
36
Value_VALUE
Parameter
Value

37

Reprocessing
StatusBrowse38 Package
Reference

char

99

TK_REPRO_STAT

Reprocessing
Actualchar

40

TK_BROUSE_NAME

Browse Pointer char

105

Science
Contactchar

93

39 Contact Name TK_CONTACT

40 Mean Motion

TK_NUN_ORBITS

Mean Motion float

50

41

Orbit Adjust
Flag

TK_ORBIT_ADJUST

Orbit Adjut
Flag

int

50

42

Attitude Mode TK_ATTITUDE
Flag
_MODE

Attitude Mode
int
Flag

50

Solar Beta
Angle At
float
Beginning Of
Granule50

Solar beta angle TK_BEGIN
43 at beginning of _SOLAR
granule_BETA- 51 -The minimum difference between two
adjacent latitude values expressed in
Geographic Coordinate units ofmeasure. “-9999.9''
The minimum difference between two
adjacent longitude values expressed in
Geographic Coordinate units ofmeasure. “-9999.9''
Units of measure used for the latitude
and longitude resolution values.
“Decimal Degrees"This tells the system how temporal
coverage is specified for the granule
Science Quality Flag
A post processing indication of quality
by the algorithm developer.
The Quality Indicator takes the formof 4 possible ASCII strings:''NOT BEING INVESTIGATED",“BEING INVESTIGATED''.
“FAILED" or ”PASSED”.
This attribute identifies the intent of
the product author to reprocess thedata (i.e. data gaps, geolocation
accuracy, scientist review quality
flags). “NULL”
This attribute will contain asystem-resolvable reference to an
HDF package containing collocationof browse granules. “NULL”
The name of the algorithm developer
related to this granule.The contactname supplied here must exist in the
ECS contact database.
“JAXA Earth Observation Center”.
Number of orbits per day, including
fractions of orbits.
Used Geometric metadata.
Orbit Adjust Flag.
Values are as follows: 0 = no orbit
adjust activity during this orbit. 1 =orbit adjustment control modes
occurred during this orbit.
Attitude Mode flag. Values are as
follows: 0 = forward mode(+X forward) throughout this orbit 1 =backward mode (-X forward)
throughout this orbit 2 = yaw
maneuver during this orbit.
Elevation of sun in the orbit plane at
the orbit start (degrees)/
Used Geometric metadata.

Solar beta angle
Solar Beta
TK_END_SOLAR
44 at end ofAngle At End float_BETA
granuleOf GrnuleElevation of sun in the orbit plane at
the orbit start (degrees).
Used Geometric metadata.
Euler Sequence (3 integers) and Euler
angles for rotation from spacecraft
Sensor
TK_SENSOR
Sensorcoordinates to sensor coordinates in
45
char
100
Alignment_ALGN
Alignment
degrees. (These are to be provided by
the science team) “0.0, 0.0, 0.0, 1.2,
3”
Euler Sequence (3 integers) and Euler
angles for rotation from sensor
coordinates to Channel coordinate in
Sensor
TK_SENSOR
Sensor50*
degrees. (These are to be provided
46 Alignment_ALGN_CHAN Alignment
char number ofby the science team if needed, but they
Channel Offsets _OFFSET
channels
Channel Offset
are not nominally used in TSDIS
processing since geolocation is notdone per channel) “0”Parameters describing the scan path as
used for pixel geolocation.
For a (nominal) conical scan model
the following parameters are used:
Axis of Scan (±1, 2, or 3).
Reference Axis for zero rotation angle(±1, 2, or 3), and Scan cone angularradius in degrees. Starting rotation
Scan Path
TK_SCAN_PATH Scan Path47
char
100 angle relative to the scan axis in
Model_MODELModel
degrees.
Total rotation angle spanned indegrees, Active scan duration time inseconds (between first and last pixel),
and Time Offset between spacecraft
time of the sensor data packet and thefirst pixel time, in seconds.
“1.3, 90.0, -17.0, 34.0, 0.3, 0.0”
Parameters describing the scan path
separately for each channel in degrees.
Scan Path
Scan Path(These are to be provided by the
TK_SCAN_PATH
48 Parameters
Model
char
100 science team if needed, but they are_PARAMPer Channel
Parameter
not nominally used in TSDIS
processing since geolocation is notdone per channel) “0”
TSDIS granule ID for the ephemeris
file. The format is
EPHEM.YYMMDD.nn.,
Ephemeris file TK_EPHEM
Ephemeris
49
char
50
where YY is year,
descriptor_FILE_NAME
File ID
MM is month, DD is day of themonth,and nn is the version number.

- 52 -50

PS (Product Specific) Metadata Elements [Archive Metadata]
Defined Names of
Object Name
Estimate
Parameter
Type
Description
in the HDF
d sizein the Toolkit
l Data Gaps
TK_DATA_GAP DataGap
float
50
The sum of the duration of the data
Duration
gaps in seconds in the orbit (satellitedata) or granule (GV data).
2 Number of
TK_NUM_DATA Number Of
float
50
The number of data gaps in the data in
Data Gaps
Data Gaps
the orbit (satellite data) or_GAP
granule (GV data).
3 Algorithm
TK_ALGORITHM Algorithmchar
50
The version of the science algorithm is
Version_VERSION
Versionwritten as “M.m”, where “M” is an
integer corresponding to majorrevisions of the code. Major revisions
are changes in the science algorithm
which do affect the science, aredelivered to TSDIS in an officialdelivery package, and require
reprocessing. “m” is an integer
corresponding to minor revisions orcorrections. Minor revision or
corrections are made so the sciencealgorithm will function properly in
TSDIS, do not affect the science,
are not delivered to TSDIS, in an
official delivery package, and to not
require reprocessing. “M” is written
without leading zeroes, with a range
from 1 to 99. “m” is written withleading zeroes, with a range from 00
to 99. At launch, the version of allscience algorithm is “1.00”.
4 Product Version TK_PRODUCTProduct
int
50
A single integer indicating the version
Number_VERSION
Versionof the product.
Number
The first Product Version Number is 1.
The Product Version Number isincremented every time the product isreprocessed due to the fact that thealgorithm creating it changes or thealgorithms creating the input to thealgorithm change.
5 Toolkit Version TK_TOOLKIT
Toolkitchar
50
Version of Toolkit used to create this_VERSION
Versiongranule.
6 Calibration
TK_CAL_COEF Calibrationint
50
Version of the calibration coefficients
Coefficient_VERSION
Coefficient(i.e. 1,2,3, etc.)
VersionVersionMissing Data int
50
7 Missing Data TK_MISSING
Number of missing scans in the orbit_DATA(satellite data), missing rays (groundradar data) or missing observations(rain gauge or disdrometer data)
express in percent.
8 Percentage of TK_PERCENT
Percent Of
char
50
List by channel of the percentage of
Bad or Missing _BAD
Badbad or missing pixels in the orbit
Pixels_MISS_PIXCEL Or Missing(satellite data) or granule (GV data).
Pixels
“8.95%”
Metadata
Element- 53 -

9 Maximum
TK_MAX_VALID Maximum
Valid Value of _CHANNEL
Valid Value
Channelof Channel
10 Minimum
TK_MIN_VALID Minimum
Valid Value of _CHANNEL
Valid Value
Channelof Channel

char

50

char

50

11 Min Max Unit TK_MIN_MAX Min Max Unit char
_UNITS
12 Orbit Size
TK_ORBIT_SIZE OrbitSize
int50

13 Radar Wave
length14 Minimum
Reflectivity
Threshold
15 Algorithm ID

TK_RADARRadar Wave float_WAVELENGTH length
TK_MI_REF
Minimum
float_THRESHOLD
Reflectivity
Threshold
TK_ALGORITHM Algorithm ID char_ID
16 Data Accuracy TK_DATA
Data
char
_ACCURACY
Accuracy
17 Input IDs
TK_INPUT
Input Files
char_FILES
18 Data of
TK_GEN_DATE Data Of
char
Generation of _INPUT_FILES Generation Of
Input Files
Input Files
19 Data Center
TK_DATA
Data Center char
Source Of_CENTER_SRC Source Of
Input Files
Input Files
20 Generation
TK_GEN_DATE Generation
int
Date
Date
21 Day/Night
TK_DAY_NIGHT Day Night
float

50
50
50

50
50
300
50

50

List of the generation dates of the input
files. For ingested files, this is the date
TSDIS received the file.
List of the centers generating the input
files. e.g., TSDIS NMC.

50

Date the dataset was generated.

50

Percentage scans during the orbit in
daytime mode. “-9999.9”
Channel 1 Mirror Side A
Channel 1 Mirror Side B
Channel 2 Mirror Side A
Channel 2 Mirror Side B
List of the intercepts and slopes
defining the following correction to thebrightness temperatures for channel:deltaT={A_ch*(tb-250)/50}+B_ch
The entries in the list are as follows:
10GHz Vertical adjustment intercept
10GHz Horizontal adjustment intercept
19GHz Vertical adjustment intercept
19GHz Horizontal adjustment intercept
21GHz Vertical adjustment intercept
37GHz Vertical adjustment intercept
37GHz Horizontal adjustment intercept
85GHz Vertical adjustment intercept
85GHz Horizontal adjustment intercept
10GHz Vertical adjustment slope
10GHz Horizontal adjustment slope
19GHz Vertical adjustment slope
19GHz Horizontal adjustment slope
21GHz Vertical adjustment slope
37GHz Vertical adjustment slope
37GHz Horizontal adjustment slope
85GHz Vertical adjustment slope

22 Solar Channel
Gains

TK_SOLAR_GAIN

Solar Channel float
Gains

50

23 SSM/I
Adjustment
Coefficients

TK_SSMI_ADJUST

SSMI Adjust float
Coef

30

- 54 -

List by channel of the maximum valid
value(value specified by the instrument
scientist). 1B:”-110”, 1C:”20”
List by channel of the minimum valid
value (value specified by the
instrument scientist).
1B:“-20”,1C:“80”Units of the Minimum and Maximum
valid values. 1B: “dBm”, 1C: “dBZ”
Numbers of scans in Orbit. If the
granule is empty, Orbit Size = 0.
Wavelength of the radar (meter).
“0.02178”
The threshold (dBZ) below which
ground based radar reflectivity data is
set to the missing value. “-9999.9”
Name of the algorithm(i.e. 1B21, 1C21)
List by channel of the accuracy of thedata.
List of input granule IDs. “NULL”

85GHz Horizontal adjustment slope
24 Orbit First Scan TK_FIRST_SCAN Orbit FirstUTC Date_UTC_DATEScanUTC Datedate

50

25 Orbit First Scan TK_FIRST_SCAN Orbit FirstUTC Time_UTC_TIMEScan
UTC Timetime

50

26 Orbit First Scan TK_FIRST_SCAN Orbit FirstUTC_UTC_MILLISEC Scan UTC
Milliscconds
Milliseconds

int

50

27 Orbit First
TK_FIRSTSCAN Obit First
Scantime _SC_SECSSCS ecs
Spacecraft clock
28 Orbit First
TK_FIRSTSCAN Orbit First
Scantime _SC_SUBSECS SC Subsecs
spacecraft
Clock
Subseconds
29 Orbit Last Scan TK_LAST_SCAN Orbit Last
_UTC_DATEScanUTC Date
UTC Date
30 Orbit Last Scan TK_LAST_SCAN Orbit Last
UTC Time_UTC_TIMEScan
UTC Time
31 Orbit Last Scan TK_LAST_SCAN Orbit Last
UTC
_UTC_MILLISEC Scan
Milliseconds
UTC
milliseconds
32 Orbit Last
TK_LAST_SCAN Orbit Last
Scantime _SC_SECS
SC Secs
Spacecraft clock
33 Orbit Last
TK_LAST_SCAN Orbit Last
Scantime _SC_SUBSECS SC Subsecs
Spacecraft clock
Subseconds
34 UTCF Seconds TK_UTCF_SECO UTCF
NDS
Seconds
35 UTCFTK_UTCF
UTCF
Subseconds_SUBSECONDS Subscconds

int

50

int

50

The subseconds field of the spacecraft
clock time of the first scan in the orbit.

date

50

Orbit Last Scan UTC Date.
See Orbit First Scan UTC Date.

time

50

int

50

Orbit Last Scan UTC Time. Decidedby L1A file header.
See Orbit First Scan UTC Time
Orbit Last Scan UTC Milliseconds.
See Orbit Last Scan UTC Milliseconds

int

50

The seconds field of the spacecraft
clock time of the last scan in the orbit.

int

50

The subseconds field of the spacecraft
clock time of the last scan in the orbit.

int

50

int

50

The second field of the UTCF
for the granule.
The subscconds field of the UTCF
for the granule.

- 55 -

Orbit First Scan UTC Date.
Date is a 10 character string with thefollowing characters: YYYY/MM/DD,
where YYYY = year, MM = month
number, DD = day of month and “/” isa literal. If the granule is empty, thevalue is ‘0/0/0’. In 2A-52, UTC date isstored as “/” is replaced by “-”. In
1B-11 and 2A-12, UTC date is stored
in separate words for year, month andday of month.
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 is stored in separate
words for hour, minute, and second.
Orbit First Scan UTC Milliseconds.
Milliseconds is a 3 character stringwith the following characters: MMM,
where MMM = the number ofmilliseconds later than the last wholesecond.
The seconds field of the spacecraft
clock time of the first scan in the orbit.

36 UTCF Flag

TK_UTCF_FLAG UTC Fflag

int

50

37 Leap
Second flag

TK_LEAP_SEC
_FLAG

Leap
Seconds Flag

Int

50

Radars Site
Name
Radar City

char

50

char

50

Radar State

char

50

Radar
Country
Number Of
VOS
43 Radar Grid
TK_RADARRadar Grid
Origin Latitude _ORIGIN_LAT
OriginLatitude
44 Radar Grid
TK_RADARRadar Grid
origin_ORIGIN_LON Origin
Longitude
Longitude
45 Radar Grid
TK_RADARRadar Grid
Origin Altitude _ORIGIN_ALT
OriginAltitude46 Radar Grid
TK_RADARRadar Grid
Spacing x_SPACING_X
Spacing X
47 Radar Grid
TK_RADARRadar Grid
Spacing y_SPACING_Y
Spacing Y
48 Radar Grid
TK_RADARRadar Grid
Spacing z_SPACING_Z
Spacing Z
49 Radar Grid
TK_RADARRadar Grid
Size x_GRID_SIZE_X Size X
Radar Grid
50 Radar Grid
TK_RADAR_GRID_SIZE_Y Size Y
Size y5l Radar Grid
TK_RADARRadar Grid
Size z_GRID_SIZE_Z Size Z
52 DZ CalTK_GV_DZCAL DZ Cal

char

50

int

50

int

50

int

50

Longitude (degrees) of the origin.
“-9999.9”

int

50

Altitude (km) of the origin. “-9999.9”

float

50

float

50

float

50

int

50

int

50

int

50

float

50

53 GVL1C_Scale TK_GV_L1C
GV L1C_SCALEScale
54 Alpha
TK_GV_ALPHA Alpha

float

50

float

50

55 Runtime
Optionschar

100

The zonal interval (km) between grid
points. “-9999.9”
The meridional interval (km) between
grid points. “9999.9”
The vertical interval (km) between grid
points. “-9999.9”
The number of grid points in the zonal
grid direction. “-9999”
The number of grid points in themeridional grid direction. "-9999”
The number of grid points in thevertical grid direction. “-9999”
Radar calibration offset (dBZ).
“-9999.9”
Scaling factor for 1C-51 mask
(unitless) “-9999.9”
Correction for gaseous two-way
attenuation (dB/km). “-9999.9”
Runtime options for algorithm
including QC parameters used.
“NULL”.

38 Radar sitename39 Radar city

TK_RADAR_NAME
TK_RADAR_CITY
40 Radar state
TK_RADAR_STATE
4l Radar country TK_RADAR_COUNTRY
42 Number of VOSTK_NUM_VOS

TK_GV
Runtime_RUNTIME_OPT Options- 56 -

Flag that indicates the origin of the
UTCF. 0 = UTCF was derived fromthe first ACS packet in the orbit. 1 = acorrected UTFC was used. “0”Flag that indicates if a leap second
occurred within the granule.
0 = no; 1 = yes.
Name of the GV radar or radar site,whichever is applicable. “NULL”
Nearest city to the radar site. "NULL”.
State or province containing the radarsite, if applicable. “NULL”
Country containing the radar site.
"NULL''The number of volume scans in the
granule. “-9999”
Latitude (degrees) of the origin.
"-9999.9''

56 Anomaly Flag TK_ANOMALY_FLAGAnomaly Flag char

100

57 Software
Version58 Database
Version
59 Total Quality
Code

Softwareint
VersionDatabase
int
VersionTotal Quality char
Code

50

Longitude
On Equator

float

50

TK_UTC_DATE UTC Date
date
_ON_EQUATOR On Equator
TK_UTC_TIME UTC Timetime
_ON_EQUATOR On Equator
TK_UTCUTC
int_MILLSEC_ON Millisecs_EOUATOR
On Equator
TK_CENTER
Center Scan date
_SCAN
UTC Date_UTC_DATE
65 Orbit center
TK_CENTER
Center Scan timescan UTC time _SCAN
UTC Time_UTC_TIME
66 Orbit Center
TK_CENTER
Center Scan
int
scan UTC_SCAN
UTC Millisec.
milliseconds_UTC_MILLISEC
67 Orbit first scan TK_FIRST_SCAN FirstScanLat float
latitude_LAT
68 Orbit first scan TK_FIRST_SCAN First Scan
float
longitude_LON
Lon
69 Orbit last Scan TK_LAST_SCAN Last Scan Lat float
latitude_LAT
70 Orbit last scan TK_LAST_SCAN Last Scan Lon float
longitude_LON
71 Number of
TK_NUM_0F
Number Of
int
Rain Scans
Rain Scans_RAIN_SCAN

50

TK_SOFTWARE_VERSION
TK_DATABASE_VERSION
TK_TOTAL_QUALITV_CODE
60 Longitude
TK_LON_ON
on the Equator _EQUATOR
61 UTC Dateon the Equator
62 UTC Timeon the Equator
63 UTCmilliseconds
on the Equator
64 Orbit centerscan UTC date

- 57 -

50
50

50
50

50

This flag indicates if and why agranule is empty. The possible values
are:“EMPTY: GENERATED AFTERSOFTWARE ERROR” *“EMPTY: NO DATA DUE TO NO
RAIN”“EMPTY: NO DATA RECORDED”“EMPTY: DATA RECORDED BUT
STILL MISSING”“EMPTY: REASON UNKNOWN” *“NOT EMPTY: POSSIBLE
PROBLEM”“NOT EMPTY” *It is expected that satellite data would
use only the three values followed byan asterisk. GV data is expected to use
all seven values.
Version of the Software
Version of PR Database in the PR L1
softwareTotal quality of the PR L1 product.
Range is ‘G’, ‘F’, or ‘P’.
Longitude on the equator from theascending node. Range is -180.000 to
179.999.
UTC date on the equator.
See Orbit First Scan UTC Date.
UTC time on the equator.
See Orbit First Scan UTC Time.
UTC millisecond on the equator.
See Orbit First Scan UTC
Milliseconds.
UTC date at orbit center scan.
See Orbit First Scan UTC Date.

50

UTC time at orbit center scan.
See Orbit First Scan UTC Time.

50

UTC milliseconds at orbit center scan.
See Orbit First Scan UTC
Milliseconds.
Latitude of orbit first scan.
Range is -40.000 to 40.000
Latitude of orbit first scan.
Range is -180.000 to 179.999.
Latitude of orbit last scan.
Range is -40.000 to 40.000.
Longitude of orbit last scan.
Range is -180.000 to 179.999.
Number of rain scan whose
Minimum Echo Flag is 1 or 2.

50
50
50
50
50

2. Level 2
2-1.
1.

2A-21: Surface Cross Section

Objectives and functions of the algorithm

The primary objective is to compute the path-integrated attenuation (PIA) using thesurface reference technique (SRT). The surface reference technique rests on theassumption that the difference between the measurements of the normalized surface crosssection within and outside the rain provides a measure of the PIA.
An estimate of the rain-free normalized radar surface cross section (σ0 or NRCS) is used asa reference value for computing the PIA. The algorithm selects the “best” of four types ofreference estimates that may be computed. The estimates used arez

Along-track Spatial Average. 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 the text below, this estimate is referred to as the spatial average.

z

Temporal Average. An average at each angle bin of the σ0 data at 1°×1°
latitude-longitude cell computed over the month.

z

Global Average. A global mean σ0 classified by surface type and angle bin,computed for a “typical” month.

z

Cross-track Hybrid. A reference data set that results from a quadratic fit of thealong-track spatial average data over the 49 angles bins within the cross-track swath.
This is explained below in more detail.

In addition to the sample mean of the NRCS as a function of angle bin (and in some cases
location or surface type), the reference data sets also include the standard deviation of eachof the sample means. This quantity is used to estimate the stability of the reference
rain-free mean NRCS.
In the spatial surface reference data set, the mean and standard deviation of the NRCS arecalculated 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 -17° to +17° with respect to nadir.
The 2 additional angle bins (making the total 51 rather than 49) are used to take care of
non-zero pitch/roll angles that can shift the incidence angle outside the normal range.
For the temporal surface reference data set, the running mean and standard deviation arecomputed over a 1°×1° (latitude, longitude) grid. Within each 1°×1° cell, the data arefurther categorized into incidence angle categories (26). The number of observations ineach category, Nt, is also recorded.

- 58 -

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 are only 25+1,
where the additional bin is used to store data from angles outside the normal range.
As of version 6, a new method of estimating surface reference values is used for oceanscans. This hybrid method takes the spatial surface reference data set for the entire scanand computes a cross-track fit. The assumption is that the cross-track angular dependenceof the surface cross section can be approximated by a quadratic. As implemented, thismethod applies only to scans that are entirely over ocean. Whenever this condition is met,
and hybrid estimate can be computed, then it will be chosen in preference to the spatial andtemporal estimate. See section 8 for more detail about the hybrid method.
When rain is encountered, the mean and standard deviations of the reference σ0 values are
retrieved from the spatial and temporal surface reference data sets. To determine whichreference measurement is to be used, the algorithm checks whether Nt ≥ Ntmin and Ns ≥ Nsmin,
where Ntmin and Nsmin are the minimum number of samples that are needed to be considereda valid reference estimate for the temporal and spatial reference data sets, respectively.
(Currently, Ntmin=50 and Nsmin=8.) If neither condition is satisfied, no estimate of the PIA ismade and the flags are set accordingly (see below). If only one condition is met, then thesurface reference data that corresponds to this is used. If both conditions are satisfied, thesurface reference data is taken from that set which has a smaller sample standard deviation.
If a valid surface reference data set exists (i.e., either Nt ≥ Ntmin or Ns≥Nsmin or both) thenthe 2-way path attenuation (PIA) is estimated from the equation:
PIA = σ 0 (reference value) − σ 0 (in rain)

where σ0(in rain) is the value of the normalized radar surface cross section over the rain
volume of interest and <σ0(reference_value)> is the mean value obtained from either the
temporal or spatial reference data sets, the choice of which depends on the considerations
discussed above.
The hybrid estimate is computed after the entire scan has been processed as describedabove. If the hybrid estimate is computable (entire scan is over ocean, and spatial estimates
exist for a sufficient number of angle bins, Nh≥Nhmin [currently, Nhmin =5]), then the hybrid
estimate is substituted for the previously selected estimate.
To obtain information as to the reliability of this 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_dev(reference value), then the reliability factor of the PIA estimate is defined as:

reliabFactor =PIA
std_dev(reference value)- 59 -

When this quantity is large, the reliability is considered high and conversely. This is thebasic idea. Specific definitions of the reliability flag and reliability factors are given in thedefinitions of the output variables. Description of the HDF output variables for 2a-21 canbe found in Volume 4 - levels 2 and 3 file specifications available at:<http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4.pdf>

Two comments should be made.
i.

The PIA is often defined as the one-way path attenuation rather than the 2-way
attenuation used here. Note also that the PIA(2-way) is related to the specificattenuation or attenuation coefficient k (dB/km) by the equation:
PIA(2 - way) = 2 ∫ k(s) ds
rs0

where the path integral is taken along the direction of the main beam and where theintegration limits range from the radar to the surface. Since the attenuation from theradar to the storm top is negligible, the integral can also be thought of as going fromthe storm top to the surface.
ii. A case can be made for defining the reliability factor other than that given above. For
example, we can define reliability factors by:Rel =PIA - std_dev(reference value)
PIA

Rel′ = PIA - std_dev(reference value)so that Rel=1 (or Rel’ = PIA) would correspond to a perfect estimate whereas
increasingly smaller values of Rel (including negative values) would correspond tolower reliabilities. Since the numerator and denominator of the expressions for Rel
and Rel’ can be computed from the output data, these quantities can be easily
generated.

- 60 -

2.

Command line arguments:
1B21.inputfile.HDF
2A21.outputfile.HDF
2A21.int_tr.dat
2A21.int_tw.dat
2A21.int_s.dat
2A21.diagthe 1B-21 HDF filethe 2A-21 HDF output file
the read-only temporal intermediate file
the write-only temporal intermediate filethe spatial intermediate filethe verification (diagnostic) file

Note that the verification file is created in the program and should not exist prior to
execution.
3.

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).
rainFlag(49) [integer*2]
Rain/no-rain flag (rain=1; no-rain=0) The rain possible category from 1B-21 is included in
the no-rain category; only the rain-certain category is considered rain.
incAngle(49) [real*4]
Incidence angle with respect to nadir (in degrees); pitch/roll correction is included.
pathAtten(49) [real*4]
Estimated 2-way path-attenuation in (dB) where
rs

pathAtten = 2 ∫ k(s)ds0where k(s) is the attenuation coefficient in dB/km and integral runs from storm top to thesurface. The path attenuation is often designated as the PIA, the path-integrated
attenuation.
reliabFlag(49) [integer*2]
Reliability Flag for the PIA estimate, pathAtten, defined below.
reliabFactor(49) [real*4]
Reliability Factor for the PIA estimate, pathAtten, defined below.

- 61 -

3.1 Definition of reliabFlag

reliabFlag = 10000*iv + 1000*iw + 100*ix + 10*iy + iz

whereiv is a rain/no-rain indicator
iw is an indicator of the reliability of the PIA estimate
ix indicates the type of surface reference used
iy provides information about surface detection
iz gives the background typeiv = 1 (no rain along path)= 2 (rain along path)
iw = 1 (PIA estimate is reliable) - see definitions below=2(
is marginally reliable)=3(
is unreliable)=4(
provides a lower bound to the path-attenuation)= 9 (no-rain case)ix = 1 (spatial surface reference is used to estimate PIA)
= 2 (temporal “““ PIA)= 3 (neither exists — i.e. insufficient number of data points)= 4 (unknown background type)= 5 (no-rain case & low SNR — do not update temporal or spatial SRs)
= 6 (global surface reference)= 7 (cross-track-spatial hybrid surface reference)= 9 (no-rain case)iy = 1 (surface tracker locked - central angle bin)=2(
unlocked - central angle bin)= 3 (peak surface return at normally-sampled gate - outside central swath)=4(
not at normally-sampled gate - outside central swath)iz = 0 (ocean)= 1 (land)= 2 (coast)= 3 (unknown or of a category other than those above or ‘mixed’ type)

Note: for missing data set reliabFlag = -9999- 62 -

3.2 Definition of reliabFactor

reliabFactor = pathAtten/std_dev(reference value)

where PIA is the 2-way path-integrated attenuation (dB), and std_dev(reference value)is the standard deviation as calculated from the no-rain σ0 values. Both quantities are in dB.
In versions 1-4 of the algorithm, the reliabFactor was defined as the difference:
pathAtten - std_dev(reference value)rather than the ratio pathAtten/std_dev(reference value)
The parameter iw (in reliabFlag) is determined from reliabFactor and the SNRof the surface return (in dB).
As currently defined:
iw = 1 (reliable) if ((reliabFactor ≥ 3) and (SNR(dB) > 3))= 2 (marginally reliable) if ((reliabFactor ≥ 1) and (reliabFactor < 3) and(SNR(dB) > 3))= 3 (unreliable) if either (reliabFactor < 1) or((SNR(dB) ≤ 3).and.(reliabFactor < 3))= 4 (lower bound) if ((reliabFactor ≥ 3) and (SNR(dB) ≤ 3))[The iw = 4 case is defined because, while the attenuation estimate will be negatively
biased because of a low signal-to-noise ratio, it may lead to the best rain estimate possible
under the circumstances.][SNR is the signal-to-noise ratio; expressed in dB this is given by the difference between
the noise-corrected radar return power (dBm) and the radar noise power (dBm)]
Note: for missing data, set reliabFactor = -9999.9
Note: pathAtten can assume both positive and negative values. Negative values have anegative reliabFactor, they are marked unreliable (iw=3). Before version 6, negative
pathAtten were set to zero.

- 63 -

4.

Description of the Processing Procedure:At each angle bin, calculate the normalized radar surface cross section, σ0, and check
whether rain is present. Also, find the (1°×1° × angle-bin) element into which themeasurement falls.
If rain is present, retrieve the mean and standard deviations from the temporal and spatialreference data sets (formed from previously measured data under rain-free conditions). If
both temporal and spatial reference data sets satisfy certain conditions, check whichsample mean has the lower variance. Using the sample mean associated with the smaller
variance, compute an estimate of the path-integrated attenuation and an associatedreliability factor. If neither the spatial nor temporal reference data satisfy these conditions,use the global reference.
In version 6, check the following conditions: the entire scan is over ocean and the spatialreference exists in at least Nhmin (Nhmin =5) angles bins (out of a total of 49) within the scan;
if these two conditions hold, then the hybrid reference data is used (section 8).
If rain is absent, update the temporal statistics (mean and mean-square) of σ0 at therelevant (1°×1° × angle-bin) element. Also, update the spatial statistics of σ0.

5.

Interfaces to other algorithms:

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

6.

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 = 2 (rain certain);minEchoFlag = 1 (rain possible) and minEchoFlag = 0 (rain absent) are treatedas no-rain cases. Note that the minEchoFlag variable is read from 1B-21.

- 64 -

e.

Before version 6, images of path attenuation from 2A-21 sometimes showed a striatedor streaky pattern where the attenuation estimates at one or more angles are larger thanthe estimates at adjacent angles. This occurred more often at near-nadir angles wherehigh values of the surface cross section are observed under rain-free conditions.
Where it is used, the cross-track-spatial hybrid method appears to eliminate most ofthese streaky patterns.

f.

The diagnostic file includes attenuation and reliability results from several alternative
methods:“standard” [version 5], cross-track, and hybrid, with 3 alternative
reliabFactor formulas.
Each entry is written on one line with the following fields:
method - A text string identifying the methodscan number
angle bin number
PIA
reliabFactor
reliabFlag
The method ID values are:stdPIA Version-5 standard PIA (spatial or temporal)
xTrack Cross-track method (ocean only)
xtHyb1 Hybrid method, reliabFactor=A/chisqr
xtHyb2 Hybrid method, reliabFactor=A/avg(sd)xtHyb3 Hybrid method, reliabFactor=A/rms(sd)In the reliabFactor formulas above, A is the Hybrid PIA, chisqr is the reduced
Chi-square for the cross-track fit, sd is the standard deviation for the individual
spatial average for the current angle bin, and rms(sd) is the root-mean-square of the
sd’s over all angle bins for the current scan. The value written in the HDF file is
xtHyb3.
The “xTrack” method is another experimental cross-track method that uses non-rain
angle bins in the current scan. It is computed only if the scan includes a mixture ofrain and non-rain angle bins, all over ocean. This method was experimentally
introduced in version 5.
Because each line is labeled with the method ID, the diagnostic file can easily be
divided into separate files for each method. Examples of this are shown in thefollowing Unix commands:
egrep 'stdPIA' 2A21.990913.10321.6.diag | cut -d: -f2 > stdpia
egrep 'xTrack' 2A21.990913.10321.6.diag | cut -d: -f2 > xtrackegrep 'xtHyb1' 2A21.990913.10321.6.diag | cut -d: -f2 > xthy1
egrep 'xtHyb2' 2A21.990913.10321.6.diag | cut -d: -f2 > xthy2
egrep 'xtHyb3' 2A21.990913.10321.6.diag | cut -d: -f2 > xthy3- 65 -

g. In previous versions of the algorithm (versions 1-4) the reliabFactor was definedas the difference: pathAtten - std_dev(reference value). In version 5 and 6,
reliabFactor is defined as the ratio: pathAtten/std_dev(reference value).
h. 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 version 6,
pathAtten is no longer set to zero. Negative values are possible, although they will
always be marked unreliable in the reliabFlag.

7.

Description of Temporal Intermediate File

Two temporal intermediate files are used to store (write-only file) and read (read-only file)
the rain-free statistics of the normalized surface cross sections as a function of incidence
angle (26 categories) and location (1°×1° latitude-longitude grid).
For the first month of data (December, 1997), the read-only and write-only temporalintermediate files are initialized to zero. During the processing of data from this month, therain-free statistics are continuously updated and stored in the write-only file. At the end of
the month, the write-only file for December is used as the read-only file for January andthe write-only file is re-initialized to zero. This means that for the data processed in
January, the statistics compiled in December will be used for the temporal reference data
set. At the end of the processing of the January data, the write-only file, used to store thestatistics for January, is used as the read-only file for the month of February. In general,
the write-only file from the previous month is used as the read-only file (i.e. the reference
data set) for the present month and where the write-only file is re-initialized at the
beginning of each month.
At the beginning of the post-boost data processing, the temporal files are set to zero. In
particular, for the first segment of post-boost data (Aug. 2001), the read-only intermediate
files are zeroed out. For the next month, the read-only files are converted to the write-only
file and used as the temporal reference data for Sept. 2001.

- 66 -

8.

The Cross-track Hybrid Surface Reference Method

2A-21 v5 computes the Path Integrated Attenuation (PIA) for each angle bin using spatial
and temporal averages, selecting the method that gives the largest reliability factor.
Version 6 also implements two alternative “cross-track” methods for ocean scans. The
results of these methods are written in the diagnostic file along with the v5 result. Whenappropriate, the “cross-track hybrid” PIA is chosen as the 2A-21 product.
Both methods perform a cross-track quadratic fit of the reference surface cross sections.
The xtrack method fits a quadratic using data from all rain-free angle bins in the current
scan; the hybrid method fits a quadratic using data from the current along-track spatial
average at each angle bin.
If the rain region is extensive, the xtrack method may have few or no data points to fit; if
enough data are available to fit, the points will always be near the rain observations
because they are taken from the same scan. The hybrid method always (or almost always)
has a full scan worth of data to fit. The 49 spatially-averaged data points have the samepotential problems as the standard spatial average, namely, that in some cases the spatial
average might be computed in a region remote from the current IFOV, so that the rain-freealong-track spatial averages are computed over ocean areas that are far from the rain cell inquestions. (By examining the reference data for an orbit of data processed in reverse order
we find that the spatial averaged reference data can differ significantly particularly incoastal regions.)
The spatial average for each angle bin is computed over the last 8 rain-free observations
over the same background type (i.e., ocean, land, or coast). The standard deviation fromthe spatial average is used as a weight in the fitting procedure. The fitted function is aquadratic 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 = σ NR
(θ i )

and, using “AS” to denote the along-track spatial reference, the standard deviation is0
SAS (θ i ) = var(σ NR(θ i ))

The fit function is the quadraticyfit(θ i ) = a + bθ i + cθ i2- 67 -

We determine the parameters a, b, and c by minimizing
 y − yfit(θ i ) χ = ∑ i
SAS (θ i ) 
i=1 
49

2

2

The (2-way) hybrid PIA is the difference between the Surface Reference value, yfit(θi),
and the apparent (attenuated) surface cross section, σ0i:
Ai = yfit(θ i ) − σ i0

At this point, it is unclear what reliability factor is appropriate for the cross-track hybrid
PIA estimate. Currently, the program computes three candidate values and writes them tothe diagnostic file. The reliability factor is a ratio of the PIA estimate to an estimate of theuncertainty. The difference between the candidate factors is the choice of uncertainty
estimate. For the standard spatial average product, the uncertainty estimate is the standard
deviation of the spatial average. (For the temporal average it is the standard deviation of
the temporal average. The question of whether these choices are the most appropriate, andwhether or not they represent the best criteria for selecting between spatial and temporalestimates is unresolved.) Three alternative reliability factors are described below; the third,
based on the RMS of the spatial averages across the scan, is used in the HDF in version 6.
The first hybrid reliability factor is based on the reduced chi-square for the fit,χ N2 −3 =χ2N−3

N is the number of angle bins, usually N=49. The reliability factor isreliabFactor_1(i) =Ai

χ N2 −3

Two alternate reliability factors are based on the sum of the standard deviations from withthe along-track spatial reference, SAS, and on the RMS of SAS:
reliabFactor_2(i) =

Ai
49

1
∑ SAS (θ j )49 j =1

andreliabFactor_3(i) =Ai
rms(SAS )- 68 -

Whererms(SAS ) =1 49 2∑ SAS (θ j )49 j=1

In version 6, reliabFactor_3 is the value included in the HDF product.

9.

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)∆θ ≤ θ < (angle1−1+ 0.5)∆θ(angle2 − 26 − 0.5)∆θ ≤ θ < (angle2 − 1 + 0.5)∆θ
where θ is the incidence angle and ∆θ is the angle bin size.
These relations can be expressed more simply byθ+ 1 + 0.5angle1 = int

 ∆θ
θ

angle2 = int
+ 26 + 0.5 ∆θrespectively.
There was a problem with the implementation of this algorithm before version 6: ∆θ 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 andsome were over-populated because the angle bins did not correspond with the actual beamspacing.
In version 6 of the 2A-21 algorithm, ∆θ has been set to a constant value of 0.75°.

- 69 -

10.

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.
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.

- 70 -

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 V6 (version 6).
Main changes are as follows:(a) Rain type is expressed by 3-digits number, while in the previous versions by
2-digits number.
(b) Shallow non-isolated (type of rain) is newly detected in addition to theV5-existing shallow isolated.
(c) All the shallow isolated are classified as convective in V6, while in V5 mostof the shallow isolated are stratiform. In contrast to shallow isolated, the rain
type of non-shallow isolated can be stratiform/convective/other depending
on its intensity.

- 71 -

(d) Changed the criteria for other type, which makes a substantial decrease in
the number of other type of rain.
(e) When rain is 'certain' and rain type is 'other', it most probably indicates that
there exists ice cloud only.
(f) When BB is detected, rain type is stratiform. (In the previous versions,however, rain type can be convective even though BB is detected in a very
exceptional case.)(g) Oversample data are used in the detection of BB, and oversample range binnumbers are used for computing heights.
(h) Upper and lower boundaries of BB, and the width of BB are added to the
output.
(i) Improvement in BB detection is made.
(j) Changed a convective threshold in H-method from 40 dBZ to 39 dBZ; theeffect of this change, however, is very small.
(k) Rain probable is introduced. (Internal use in 2A23 only, and the type ofrain probable is other.)

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.
(c) Rain type classification:- Vertical profile method (V-method)[1],- Horizontal pattern method (H-method)[2].

- 72 -

(d) Detection of shallow isolated and shallow non-isolated:- A simple examination of the height of storm top being much lower than theestimated height of freezing level. When an isolation condition is satisfied,
the type is shallow isolated, otherwise shallow non-isolated. Here, theisolated condition means that the shallow area is isolated from thenon- 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,
when corrupted input data are detected.
(f) Estimated height of freezing level:- Temporal and spatial interpolation of a climatological surface temperature
at the sea level, and a use of a constant lapse rate of temperature.
(g) Height of storm top:
- A simple conversion from range bin number to the height above thesea level.

2-2.4.

Processing Flow

(1) Open files.
(2) Read in 1C21 metadata, and copy the metadata to 2A23 HDF file.
(3) Read in a static data for the estimation of the height of freezing level (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.
- 73 -

(g) Classify rain type by H-method.
processing.
(h) Unify rain types.
(i) Set status flag.
(j) Write output to 2A23 HDF file.

Reject sidelobe clutter during this(6) Close files and end the processing.

2-2.5.

Input data(a) From 1C21 HDF file:(1) metadata(2) rayHdr[49].rayStart(3) rayHdr[49].startBinDist(4) scanStatus.missing(5) scanStatus.dataQuality(6) geolocation[49][2](7) minEchoFlag[49](8) binStormHeight[49][2](9) binEllipsoid[49](10) binClutterFreeBottom[49][2](11) binDIDHmean[49](12) scLocalZenith[49](13) scRange[49](14) osBinStart[29][2](15) landOceanFlag[49](16) binSurfPeak[49](17) normalSample[49][140](18) normalSample_scale[49][140](19) osSurf[29][5](20) osRain[11][28](scan header)(scan header)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(L1C_21_SWATHDATA)(b) From sst-hou.grd file (for the estimation of freezH):(1) sstdata[144][91][2]- 74 -

2-2.6.

Output data

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

2-2.7.

Output file specifications

This section describes details of items (6)-(17) 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- 75 -

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
normalconditions, the rain certain case in rainFlag is identical to therain certain
case in minEchoFlag of 1C21.
(b) int16 rainType[49]:
In V6 of 2A23, the flag rainType[i] (i=0 to 48) indicates the unified rain type by
3-digits numbers. (Beware that, in V5 and earlier, rain type is expressed by
2-digits numbers. Also note that the variable type of rainType is changed from
int8 in V5 to int16 in V6.)
rainType[i]= 100: Stratiform.
When R_type_V[i] = T_stra,
and R_type_H[i] = T_stra;(BB detected)

110: Stratiform.
When R_type_V[i] = T_stra,(BB detected)
and R_type_H[i] = T_other;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)

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)- 76 -

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;
220: Convective
When R_type_V[i] = T_conv,
and R_type_H[i] = T_other;
230: Æ this number is not used in V6.
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)- 77 -

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,
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)- 78 -

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)
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.
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.
If sidelobe clutter were not rejected, the type would be 271
or 291.
When R_type_V[i] = T_other,
R_type_H[i] = T_other;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- 79 -

(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 level of
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:
HBB[i] = (L1c21_swath_data->scRange[i] - rangeBB)* cos(zenith[i]);- 80 -

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]:Height of freezing level estimated from the climatological surface temperature
data (sst-hou data).
> 0 : Estimated height of freezing level [m]= -5555 : When error occurred in the estimation of freezH= -9999 : Data missing(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.
Hence, 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 foreach angle bin,binStormHeight[i][0]: possible value,
binStormHeight[i][1]: certain value,
2A23 converts only the certain value of binStormHeight to stormH.

- 81 -

(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 empiricalformula (see item (4) in Appendix). In V6, BBwidth is trustworthy 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.

- 82 -

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 large
range resolution of 250m.
(d) Bright band detection and rain type classification are carried out forrain-certain case only.
(e) Rain type is expressed by 3-digits number inV6, and the variable type of
rainFlag is changed from int8 to int16.
(f) Rain type of all the shallow isolated is convective in V6, though the echo
intensity of most of the shallow isolated is weak (see [3] for details). Since
most of shallow rain is masked by the surface clutter near antenna scan edges,
the count of shallow isolated shows dependence on antenna scan angle. In V6,
the count of convective rain also shows dependence on antenna scan angle
because of the angle bin dependence of shallow isolated, which occupies about
40% of the population of convective rain.
(g) 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.
(h) V6 outputs freezH even when there is ‘no rain’. It should be noted, however,that freezH is derived from climatological surface temperature, hence may not
be reliable in particular over land.

- 83 -

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, pp.143-146, 1998.
[2] 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, pp.1978-2007, 1995.
[3] Schumacher, C. and R.A. Houze, Jr., “The TRMM Precipitation Radar's View of
Shallow, Isolated Rain," J. Appl. Meteor., 42, 1519-1524, 2003.
[4] Fabry, F. and I. Zawadzki, “Long-term radar observations of the melting layerof precipitation and their interpretation," J. Atmos. Sci., 52, 838-851, 1995.
[5] Klaassen, W., “Radar observations and simulation of the melting layer ofprecipitation," J. Atmospheric Sciences, 45, 3741-3753, 1988.

- 84 -

Appendix.

Some details of 2A23

(1) freezH[i] (i=0, ..., 48)
The height of freezing level, freezH[i], is computed as follows from a
climatological surface temperature:
freezH[i] =(sst_interp -273.15) / T_lapse * 1000. [m]where sst_interp is the interpolated surface temperature (interpolation withrespect to space and time), and T_lapse is the lapse rate of the temperature(= 6.0 [deg/km]).

(2) BB detection
In the BB detection, several conditions are imposed on BB, whose heightis designated by HBB. Major conditions for the existence of BB are as follows:(a) BB has a peak,(b) HBB must be close to freezH (within +/-2.5km) and lower than 6.5 km.
(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 satisfies thecondition Z - Z_hbb < 2dB. When Z_hbb < 40 dBZ, a kind of slope of Z
below BB is smaller than a specified value.
(f) When Z at HBB, Z_hbb, exceeds 40 dBZ, Z below HBB should notdecrease rapidly.
Note:

The condition (e) allows Z below BB peak can be greater than Z_hbb.
The condition (f) is to avoid a false peak due to a strong attenuation in
the case of strong convective rain.

The detection of BB is made with several steps:
1st step:

The following two independent methods are applied:(a): Candidates for BB peak are selected, on one vertical plane with 49
angle bin data, using a spatial filter technique[1]. Let the height of BB
candidate as HBB. (This step examines three adjacent angle bins ofdata at one time because of the usage of spatial filter.)- 85 -

(b): Candidates for BB peak are selected, on one vertical plane with 49
angle bin data, by detecting a large slope, which characterizes theupper part of BB profile. Stringent BB must have an upper slope
being greater than 3 dB/0.25 km.
If HBB by (a) and that by (b) are different, the one which is closest to
the median of HBB is selected as HBB.
2nd step: Here computes the median of HBB, which are detected in the firststep. Then it goes on to detect a local peak within the median of HBB+/- 750 m (in range), and to determine if this local peak is a BB peakor not by examining the slope of the upper part of BB profile.
Note that in the 1st step (b), a large slope is detected first and thenexamines a local peak below the large slope, while in the 2nd step,
a local peak is detected first and a test is made if the peak accompanies
a large slope in its upper part.
3rd step:

Similar to the 2nd step, but with a less stringent condition on the
shape of BB profile.

4th step:

Detection of BB which has a weak peak.

5th step:

Detection of smeared 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).
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.

- 86 -

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 [4], and the definition of the upperboundary is the one which is somewhere in between the definition by Fabry and
Zawadzki [4] and that by Klaassen [5].

(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,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)- 87 -

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 height of freezing level.
(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)
Æ shallowRain[i] = 10: maybe shallow isolated,
20: maybe shallow non-isolated,
Hstorm < freezH - 1500 m (1.5 km)
Æ shallowRain[i] = 11: shallow isolated(with higher level of confidence),
21: shallow non-isolated(with higher level of confidence),
where freezH is the height of freezing level (see item (1) of this Appendix).
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 is not trustworthy over land.

- 88 -

(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 39 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
be convective,(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 [2], 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.

- 89 -

(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 39 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).

- 90 -

2-3.

2A25

2-3. 1.

Objectives

The objectives of 2A25 are to correct for the rain attenuation in measured radarreflectivity and to estimate the instantaneous three-dimensional distribution ofrain from the TRMM Precipitation Radar (PR) data. The estimated vertical profilesof attenuation-corrected radar reflectivity factor and rainfall rate are given at eachresolution 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 V5 to V6

The major points of improvement in V6 are as follows:(1) The effects of attenuation due to cloud liquid water, water vapor,and molecular oxygen are considered in the attenuation correction algorithm(2) The attenuation between the nearSurfBin (the lowest range bin that is free fromthe mainlobe surface clutter) and the actual surface is estimated by assuming agiven slope of dBZe and accounted for in the surface reference technique.
(3) The estimates of Ze, R and several other parameters that varies with theadjustment parameter (ε) of α are calculated as the expected values with respect tothe posterior probability distribution function p(ε). In V5, the maximum likelihood
value of ε was used.
(4) The error estimates in the path-integrated attenuation by the surface referencetechnique and from the rain echoes are reevaluated.
(5) The definition of the upper range of the surface clutter is changed for thosecases in which the rain echo is undetected because of large attenuation.
(6) The value of the parameter that defines the height of nearSurfRain waschanged in accordance with the change of clutterFreeBottom in 1B21 and 1C21.

- 91 -

(7) Several new output variables are introduced (See section 2.3-10). Some of themsuch as sigmaZero and freezH are exact copies of frequently used variables in
2A21 and 2A23.
(8) The input parameter files are copied in the 2A25 data file. They are written byusing the following code. Refer to the TSDIS users manual to read them.
TKwriteFileInfo(&granuleHandle2A25,PARAM_FILE_GEN,"Parameters:General");TKwriteFileInfo(&granuleHandle2A25,PARAM_FILE_CONV,"Parameters:Convective");
TKwriteFileInfo(&granuleHandle2A25,PARAM_FILE_STRAT,"Parameters:Stratiform");
TKwriteFileInfo(&granuleHandle2A25,PARAM_FILE_OTHER,"Parameters:Other");
TKwriteFileInfo(&granuleHandle2A25,ERROR_P_FILE,"Parameters:Errors");

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 (∆σ 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.)- 92 -

The bright-band height and climatological freezing height 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 α in the k-Ze relationship
k=αZeβ 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 α. Since α is adjusted, we call thistype of surface reference method the α-adjustment method.
The α-adjustment method assumes that the discrepancy between the PIA estimate
from ∆σ 0and that from the measured Zm-profile can be attributed to the deviationof the initial α 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 ∆σ 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 and 6 of 2A25, the errors in thesemethods are treated in a probabilistic manner. Because the relationship between
the error in α and that in the Hitschfeld-Bordan method changes substantiallywith the 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.

- 93 -

When the PIA estimate from the surface reference (∆σ 0)

is unavailable, it isreplaced by an equivalent ∆σ 0c that would make the attenuation-corrected
Z-profile near the surface nearly constant vertically if the correction by the surface
reference method is applied with this equivalent ∆σ 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 valuesof ∆σ 0c are reset to zero. The use of ∆σ 0c instead of ∆σ 0 from the surface reference
seldom occurs in V6.
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 effect in the attenuation
correction and the conversion from Ze to rainfall rate are not made in V6, although
the non-uniformity of rain distribution, i.e., the low resolution variability of the
PIA for a given angle bin is calculated from the PIAs at the angle bin in question
and the eight surrounding angle bins in V6 as well as in V5.
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 (ε) of α in the k-Ze
relation and adjusted in accordance with the α-adjustment in the attenuation
correction. The final estimate of R is obtained as the expectation of all possible
values of R with the probability p(ε).

- 94 -

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[]- 95 -

Input header data from 1C21 used in 2A-25:
rayHdr[].rayStart
rayHdr[].mainlobeEdge
rayHdr[].sidelobeRange[]

2-3. 6.

Output data

Output files:
2A-25 HDF data fileVI fileData format
The file content description for 2A25 can be found in the Interface Control
Specification (ICS) between the Tropical Rainfall Measuring Mission Science Data andInformation System (TSDIS) and the TSDIS Science User (TSU) Volume 4: File
Specification for TSDIS Products - Level 2 and 3 File Specifications. It is available at:
http://tsdis02.nascom.nasa.gov/tsdis/Documents/ICSVol4.pdf
Output data (in alphabetical order):attenParmAlpha[][]k-Z parameter alpha at 5 nodes
attenParmBeta[]
k-Z parameter betacorrectZFactor[][]attenuation-corrected Z factor in dBZ
epsilon[]correction factor with the hybrid method
epsilon_0[]
correction factor with the SRT
errorRain[]error estimate of rain rate near surface in dB
errorZ[]
error estimate of Z near surface in dB
e_SurfRain[]estimated rain rate at the actual surface
freezH[]freezing height from 2A23
geolocation[][]geolocation
method[]method usednavigatenavigation data
nearSurfRain[]estimated rain rate near surface
nearSurfZ[]
estimated Z near surface
nubfCorrectFactor[][] non-uniform beam filling correction factors
ParmNode[][]bin numbers of 5 nodes for alpha, a and b- 96 -

pia[][]

path-integrated attenuations from final Z,

precipWaterParmA[][]
precipWaterParmB[][]precipWaterSum[]
qualityFlag[]rain[][]
rainAve[][]rainFlag[]rainType[]
rangeBinNum[][]reliab[][]scanStatus
scanTime
scLocalZenith[]sigmaZero[]spare[][]
thickThPIZ[]
weightW[]xi[][]
zeta[][]

in surface clutter, and from 2A21
PWC-Z parameter a in PWC=a*Z^b at 5 nodes
PWC-Z parameter b in PWC=a*Z^b at 5 nodes
sum of PWC from rain top to surface
quality flag
rainfall rate in mm/h.
average rainfall rate between 2 and 4 km
status flag for rainfall estimate
rain type from 2A23
bin numbers of BB, storm top, etc.
reliability of the output
scanStatus
scanTime
spacecraft local zenith angle
surface scattering cross section sigmaZero from 2A21
spare
range bin number where PIZ > threshPIZ
weight for the calculation of epsilonf
normalized standard deviation of PIA
integral of alpha*Zm^beta

zeta_mn[][]zeta_sd[][]zmmax[]ZRParmA[][]
ZRParmB[][]mean of zeta over 3x3 IFOVs
standard deviation of zeta
maximum of Zm
Z-R parameter a in R=a*Z^b at 5 nodes
Z-R parameter b in R=a*Z^b at 5 nodes

For details, see section 2-3. 10.

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.

- 97 -

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'.
In V6, if Zm becomes less than the noise level in the range bins near the surface
with zeta larger than the threshold value, these range bins are regarded as
cluttered bins and the bottom range bin to which the data are processed for rain
profiling is raised from the clutter-free bottom defined in 2A23.
2. The error estimates in 'rain' and 'correctZFactor' are given in 'errorRain[]' and'errorZ[]'. However, these estimates indicate only very crude estimates. (Theestimation method is improved in V6 in which these errors are estimated based on
the standard deviation of the final probability distribution.)
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.
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.

- 98 -

5. 2A25 relies on the output of 1C21 to separate the surface cluttered ranges
from the clutter free ranges. Because the clutter identification routine used in
1B21 is 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, the value of alpha in the k-Z-Relationship (k = alpha * Z^beta) at 5
nodal points are given in attenParmAlpha[][].
The values in attenParmAlpha[][] are the initial values of alpha. To obtain themean values of alpha used in the final attenuation estimation, the initial values
must be multiplied by epsilon[].
8.

The values of a and b given inZ-RParmA[][]and ZRParmB[][] are

the expected values of a and b in the R-Z-Relationship (R = a * Z^b), respectively.
The values of R and Ze are calculated as the expected values, too. Therefore, you
do not obtain the same value of R if you calculate R by using the formula R = a *Z^b with a and b given in Z-RParmA[][]and ZRParmB[][]. In other words, <R>= <a * Z^b> which is not necessarily equal to <a>*<Z_e>^<b>.

- 99 -

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).
T. Kozu 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, pp.147-150, 1998.
T. Iguchi, 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.
R. Meneghini, 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.

- 100 -

2-3.10.

Detailed description of output variables

New Output Variables
float32

epsilon_0[49];float32

e_SurfRain[49];float32

freezH[49];

int16

parmNode[49][5];float32

pia[49][3];float32

precipWaterParmA[49][5];float32

precipWaterParmB[49][5];float32

precipWaterSum[49];

int16

rainType[49];int16

rangeBinNum[49][7];float32

scLocalZenith[49];float32

sigmaZero[49];

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)

float32

rainAve[49][2]; (unit of rainAve[][1])

int16

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

float32

spare[49][2]; p(epsilon)'s area and standard deviation

Obsolete (No data in V6)
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];int16

ZRParmNode[49][5]; moved to parmNode[49][5];- 101 -

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];float32

errorRain[49];float32

errorZ[49];float32

e_SurfRain[49];New

float32

freezH[49];New

float32

geolocation[49][2];int16

method[49];

NAVIGATION

navigate;

float32

nearSurfRain[49];float32

nearSurfZ[49];float32

nubfCorrectFactor[49][2];

int16

parmNode[49][5];New

float32

pia[49][3];New

float32

pia2a25[49];Obsolete

float32

precipWaterParmA[49][5];New

float32

precipWaterParmB[49][5];New

float32

precipWaterSum[49];

New

int16

precipWaterSum_scale[49];

New

int16

qualityFlag[49];float32

rain[49][80];int16

rain_scale[49][80];float32

rainAve[49][2];int16

rainAve_scale[49][2];int16

rainFlag[49];

int16

rainType[49];

New

int16

rangeBinNum[49][7];Partly new

int8

reliab[49][80];ObsoleteNew

PR_SCAN_STATUS scanStatus;- 102 -

float64

scanTime;

float32

scLocalZenith[49];New

float32

sigmaZero[49];New

float32

spare[49][2];int16

thickThPIZ[49];Obsolete

float32

weightW[49];Obsolete

int16

weightW_scale[49];Obsolete

float32xi[49][2];Obsolete

float32

zmmax[49];float32

zeta[49][2];float32

zeta_mn[49][2];float32

zeta_sd[49][2];int16

ZRParmA_scale[49][5];float32

ZRParmA[49][5];int16

ZRParmB_scale[49][5];float32

ZRParmB[49][5];int16

ZRParmNode[49][5];Obsolete

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

Internally this quantity is stored as
int16 attenParmAlpha_scale[49][5] after multiplied (scaled) by 10000000.
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]).

- 103 -

attenParmBeta
float32
REAL*4attenParmBeta[49];attenParmBeta(49)Internally this quantity is stored as
int16 attenParmBeta_scale[49] after multiplied (scaled) by 10000.
Attenuation parameter betak = alpha*Z^beta.
beta is given for each angle bin.
A constant beta is used for all ranges in one angle bin.

attenParmNode (Obsolete. No data in V6)
int16

attenParmNode[49][5];INTEGER*2

attenParmNode(5,49);

This parameter gives the range bin numbers of the nodes where attanParmAlphaand attenParmBeta are given. The numbers are stored in parmNode[49][5] in V6.

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)).

- 104 -

epsilon
float32

epsilon[49];

REAL*4

epsilon(49)The multiplicative correction factor to alpha in the k-Ze relation.
The value is the mean of epsilon with the probability density function (pdf)of epsilon defined by the rain echo, surface echo and their uncertainties.
The standard deviation of the pdf is given in spare[][1] and the area ofthe likelihood function is given in spare[][0].

epsilon_0(New variable)

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.

- 105 -

errorRain
float32

errorRain[49];

REAL*4

errorRain(49)Error estimate of rain rate near the surface expressed in dB.
The error is calculated as the standard deviation of the probability
distribution of rain rate derived from the pdf of epsilon.

errorZ
float32

errorZ[49];

REAL*4

errorZ(49)Error estimate of correctZFactor near the surface expressed in dB.
The error is calculated as the standard deviation of the probability
distribution of correctZFactor derived from the pdf of epsilon.

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)Freezing height expressed in m 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.)- 106 -

Note that the phase transition height used in 2A25 is different fromthe freezing height given in freezH. In fact, when the bright band is detected,
its height is the phase transition height, and in other cases the phasetransition height is 1.2 times the height given in freezH.

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.

method (New definition. bit 4, 5, 6, 7, 8, 9, 10, 11, 12, 13)
int16

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- 107 -

+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
+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 in V6.

navigate
NAVIGATION

navigate;

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

nearSurfRain
float32

nearSurfRain[49];

REAL*4

nearSurfRain(49)Internally this quantity is stored as
int16 nearSurfRain_scale[49][80] after multiplied (scaled) by 100.

- 108 -

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.
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)Internally this quantity is stored as
int16 nearSurfZ_scale[49][80] after multiplied (scaled) by 100.

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)- 109 -

nubfCorrectFactor
float32
REAL*4nubfCorrectFactor[49][2];nubfCorrectFactor(2,49)'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 3.0.
nubfCorrectFactor[][1] is the NUBF correction factor for the Z-R relation andits range is between 0.8 and 1.0.
N.B. No NUBF correction is made in V6. As a result, both nubfCorrectFactor[][0]and nubfCorrectFactor[][1] are always set to 0 in V6.

parmNode (New variable)
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)), andZRParmB[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.

- 110 -

pia

(New variable)
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.

pia2a25(Obsolete, No data in V6)

float32

pia2a25[49];

REAL*4pia2a25(49)moved to pia[49][0] in version 6.

Path-integrated attenuation from the estimated Z profile- 111 -

precipWaterParmA(New variable)

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*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 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*Z^b where a and b from the interpoloted values of precipWaterParmA
and precipWaterParmB does not necessarily agree with precipWaterSum.
The former is <a>*<Z>^<b> where as the latter is <a*Z^b>. precipWaterSum
also includes the precipitation water content in the surface clutter range.

precipWaterParmB(New variable)

float32

precipWaterParmB[49][5];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*Z^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)).

- 112 -

precipWaterSum(New variable)

float32

precipWaterSum[49];

REAL*4

precipWaterSum(49)Internally this quantity is stored as
int16 precipWaterSum_scale[49] after multiplied (scaled) by 1000.
Vertically integrated value of precipitation water content.
The unit is g km/m^3 or equivalently kg/m^2.
“precipWaterSum” give the sum of the precipitation water content calculated
from Ze at each range bin. The summation is from the rain top to the actual
surface. The water content in the surface clutter range is estimated with thesame assumption that is used in the attenuation correction.The sum includes
both liquid and solid phase regions.

qualityFlag (New definition, bit 2, 3, 4, 5, 11, 12, 13)
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+4: NSD of PIA calculated from less than 6 points+8: NUBF for Z-R below lower bound+16: NUBF for PIA above upper bound+32: epsilon not reliable, epsi_sig <= 0.0+64: 2A21 input data not reliable+128: 2A23 input data not reliable+256: range bin error+512: sidelobe clutter removal+1024: probability=0 for all tau+2048: pia_surf_ex <= 0.0- 113 -

+4096: const Z is invalid+8192: reliabFactor in 2A21 is NaN+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.
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.

- 114 -

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.
In V6, this reset is made before the mean of the distribution is calculated
so that the mean never reaches 300 mm/h. If the substantial part ofthe distribution exceeds this threshold, a flag in flagRain is set.
(The rainfall rate that corresponds to the epsilon at which the pdf p(epsilon)
becomes one tenth of the maximum of p(epsilon) is larger than 300 mm/h,
the flag is set.)rainAve (New definition)
float32

rainAve[49][2];

REAL*4

rainAve(2,49)

Internally this quantity is stored as
int16 rainAve_scale[49][2] after multiplied (scaled) by 100.
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 new unit in V6 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.)

- 115 -

rainFlag (New definition)
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) large part of rain rate pdf 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(New variable)

int16

rainType[49];INTEGER*2

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

- 116 -

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)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 for freezH.)

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 the threshold, 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 that isprocessed 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.

- 117 -

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.
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]is different from (rangeBinNum[][1]-1).

The latter case may happen when therain echo 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 the noise level, the data smaller than the noise level are treatedas 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 Z < 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).

- 118 -

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 the version 6, the threshold is chosen that approximately corresponds tothe attenuation of 4 dB.

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.

- 119 -

spare(New definition)

float32

spare[49][2];

REAL*4spare(2,49)

spare[49][0] : area of the likelihood function of epsilon.
spare[49][1] : standard deviation of the probability distribution function(pdf) of epsilon.

thickThPIZ(Obsolete. No data in V6)

int16

thickThPIZ[49];INTEGER*2

thickThPIZ(49)weightW(Obsolete. No data in V6. Can be calculated from epsilon andepsilon_0.)

float32

weightW[49];

REAL*4weightW(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, epsilon_0 is output instead of weightW.
The relationship among epsilon, epsilon_0 and weightW is as follows.
epsilon = 1 + weightW*(epsilon_0 - 1)

- 120 -

xi (Obsolete. No data in V6. Can be calculated from zeta_sd and zeta_mn.)
float32xi[49][2];

REAL*4xi(2,49)

Normalized standard deviation of zeta and PIA_est
xi[][0]: xi = zeta_sd/zeta_mnxi[][1]: nsd_l = normalized standard deviation of pia_est
When zeta_mn is less than 0.01, xi[][0] is set to 0.
When pia_mn is less than 0.1, zi[][1] is set to 0.
xi is unitless.

zeta
float32

zeta[49][2];

REAL*4zeta(2,49)

Integral of 0.2*ln(10)*beta*alpha*Z^beta from rain top to the clutter-freebottom.
zeta[][0]: zeta = Integral of 0.2*ln(10)*beta*alpha*Z^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 is different
from the final estimate of epsilon.).
zeta is always between 0 and 100, typically between 0 and 2.
than 5, the 4th bit of rainFlag is set.
zeta is unitless.

- 121 -

When it is larger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.
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.)

- 122 -ZRParmA
float32

ZRParmA[49][5];REAL*4

ZRParmA(5,49)

Internally this quantity is stored as
int16 ZRParmA_scale[49][5] after multiplied (scaled) by 100000.
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.
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)

Internally this quantity is stored as
int16 ZRParmB_scale[49][5] after multiplied (scaled) by 10000.
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

(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].

- 123 -

storedin

ParmNode[49][5]Appendix 1.

Output data structure defined in the toolkit/****************************************//* Define L2A-25 data structure.
*//****************************************/
typedef struct{
int8
mainlobeEdge;
int8
sidelobeRange[3];} CFLAGS;
typedef struct{
CFLAGS
clutFlag[CLUTFLAG_TBL_SIZE];} CLUTTER_FLAGS;
typedef struct{
float64
scanTime;
float32

geolocation[49][2];PR_SCAN_STATUS scanStatus;
NAVIGATION

navigate;

float32

scLocalZenith[49];

int16

rain_scale[49][80];float32

rain[49][80];int8

reliab[49][80];int16

correctZFactor_scale[49][80];float32

correctZFactor[49][80];int16

attenParmNode[49][5];int16

attenParmAlpha_scale[49][5];float32attenParmAlpha[49][5];int16

attenParmBeta_scale[49];float32attenParmBeta[49];int16

ZRParmNode[49][5];

int16

parmNode[49][5];float32

precipWaterParmA[49][5];float32

precipWaterParmB[49][5];int16

ZRParmA_scale[49][5];float32

ZRParmA[49][5];- 124 -

int16

ZRParmB_scale[49][5];float32

ZRParmB[49][5];float32

zmmax[49];int16

rainFlag[49];int16

rangeBinNum[49][7];int16

rainAve_scale[49][2];float32

rainAve[49][2];

int16

precipWaterSum_scale[49];float32

precipWaterSum[49];int16

weightW_scale[49];float32

weightW[49];float32

epsilon_0[49];int16

method[49];float32

epsilon[49];float32

zeta[49][2];float32

zeta_mn[49][2];float32

zeta_sd[49][2];float32xi[49][2];float32

sigmaZero[49];float32

freezH[49];int16

thickThPIZ[49];float32

nubfCorrectFactor[49][2];

int16

qualityFlag[49];float32

nearSurfRain[49];float32

nearSurfZ[49];float32

pia2a25[49];float32

e_SurfRain[49];float32

pia[49][3];float32

errorRain[49];float32

errorZ[49];float32

spare[49][2];int16

rainType[49];} L2A_25_SWATHDATA;- 125 -

Scale 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_6.61.dat”

1/* parameter file for v6.4 of 2A25. Oct. 9 2002 */2/* Do not delete empty lines. */3/* Do not add or delete lines. Absolute line numbers are important. */41.0000vratio[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 */91.2257

vratio[5]/* Terminal velocity ratio at 5 km */101.2806

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

1.5440vratio[10]/* Terminal velocity ratio at 10 km */15

1.6234

vratio[11]/* Terminal velocity ratio at 11 km */16

1.7283vratio[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

2.2219vratio[16]/* Terminal velocity ratio at 16 km */- 126 -

21

2.3658vratio[17]/* Terminal velocity ratio at 17 km */22

2.5189vratio[18]/* Terminal velocity ratio at 18 km */23

2.6819vratio[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

1.2

fhcf

/* Freezing height correction factor */

27

0.3

nsd_cnv[0]/* Conv. factor of NSD for stratiform: was 0.3 */

28

0.5

nsd_cnv[1]/* Conv. factor of NSD for convective: was 0.5 */

29

0.4

nsd_cnv[2]/* Conv. factor of NSD for default: was 0.4 */30

0.0000

nubf_cf[0]/* Conv. coefficients for nubfCFs: was 1.30 */310.0000

nubf_cf[1]

/*

32

0.00

nubf_cf[2]

/*

33

0.00

nubf_cf[3]/* Conv. coefficients for nubfCFzr: was 0.17 in V5 */

34

0.10

zeta_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 */nubfCFs = 1 + nubf_cf[0]*NSD^2
nubf_cf[1]*NSD^2*PIA_a

*/
*/

*/

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 */

46

1.00

epsi_init[0][2] /* initial offset factor of epsilon for ocean other rain */

47

1.00

epsi_init[1][0] /* initial offset factor of epsilon for land stratiform rain */

48

1.00

epsi_init[1][1] /* initial offset factor of epsilon for land convective rain */

49

1.00

epsi_init[1][2] /* initial offset factor of epsilon for land other rain */

50

0.08

atten_O2_surf/* PIA due to O2 at 0 m from geoid */

51

7.70

scale_h_O2/* scale height of O2 in km */

52

90.0

r_humid_in_rain /* relative humidity inside the raining area */

53

70.0

r_humid_out_rain

54

2.00

scale_h_H2O/* relative humidity outside the raining area *//* scale height of H2O in km */- 127 -

Appendix 3.

Parameters defined in “param_error_6.61.dat”

Note that many of the parameters defined in this file are not used in V6.
The parameters marked with “n” are not used.

01 0.7
d_Zm_typ/* Typical error (offset) in Zm in dB */o
02 0.5d_alpha_typ/* Typical error in alpha in dB */n
03 0.05d_beta_typ/* Typical error in beta in dB */n04 0.6d_zra_typ/* Typical error in a in dB */o
05 0.05
d_zrb_typ/* Typical error in b in dB */o
06 1.5d_surf_typ/* Typical error in sigma^0 in dB */n
07 1.0d_nubfCf_s/* Typical error in NUBF correct. factor for surf.*/ n
08 0.2d_nubfCf_zr/* Typical error in NUBF correct. factor for ZR */o
09 -0.2
dv_dh/* Typical change of velocity per km in dB*/n
10 1.0height_err_0C /* 0C height error in km */o
11 0.3height_err_BB /* BB height error in km when it exists */o
12 -0.07
dalpha_dT/* Change of alpha per 1 degree in dB */n
13 0.01
dbeta_dT/* Change of beta per degree in dB */n
14 0.02
da_dT/* Change of a in ZR per degree in dB */o
15 -0.005 db_dT/* Change of b in ZR per degree in dB */o
16 1.3d_alpha_id/* Error in alpha in dB caused by wrong ident. */n
17 -0.05
d_beta_id/* Error in beta in dB caused by wrong ident. */n
18 2.00
d_zra_id/* Error in a in dB caused by wrong identification */ o
19 0.02d_zrb_id/* Error in b in dB caused by wrong identification */ o
20 0.4
stddev_epsi_strat/* nominal error of epsilon for strat in linear unit */o
21 0.3
stddev_epsi_conv/* nominal error of epsilon for conv in linear unit */o
22 0.7
stddev_SRT_O/* nominal error of SRT over ocean in dB */o
23 2.2
stddev_SRT_L/* nominal error of SRT over land in dB */o
24 5.0stddev_SRT_N/* nominal error of SRT in const-Z method in dB */o- 128 -

Appendix 4.

Parameters defined in “param_strat_1.dat”

1 /* parameter file for v6 of 2A25. June 13, 2001 */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 0.0000861 alpha_init[0][0] /* alpha for low density snow, bb.011, strat */11 0.0001084 alpha_init[0][1] /* alpha for high density snow, bb.017, strat */12 0.0004142 alpha_init[0][2] /* alpha for bright band peak, bb.17, strat */13 0.0002822 alpha_init[0][3] /* alpha for rain (stratiform) 0C */14 0.0002851 alpha_init[0][4] /* alpha for rain (stratiform) 20C */15 0.79230
beta_init[0]/* beta for stratiform column, strat */16 /* R-Ze coefficients */17 -1.8545 zr_a_c0[0][0]/* stratiform, bb.011, a'= 251.0 */18 -1.8985 zr_a_c0[0][1]/* stratiform, bb.017, a'= 304.3 */19 -2.3448 zr_a_c0[0][2]/* stratiform, bb.17,
a'=1648.4 */20 -1.6969 zr_a_c0[0][3]/* stratiform, 0C ,a'= 284.3 */21 -1.6416 zr_a_c0[0][4]/* stratiform, 20C,
a'= 276.1 */22
23 1.6263 zr_a_c1[0][0]/* stratiform, bb.011 */24 1.6041 zr_a_c1[0][1]/* stratiform, bb.017 */25 1.4259 zr_a_c1[0][2]/* stratiform, bb.17 */26 0.9367 zr_a_c1[0][3]/* stratiform, 0C */27 0.9567 zr_a_c1[0][4]/* stratiform, 20C */28
29 -0.2734 zr_a_c2[0][0]/* stratiform, bb.011 */30 -0.2797 zr_a_c2[0][1]/* stratiform, bb.017 */31 -0.4191 zr_a_c2[0][2]/* stratiform, bb.17 */32 -0.7720 zr_a_c2[0][3]/* stratiform, 0C */33 -1.9319 zr_a_c2[0][4]/* stratiform, 20C */34
35 -0.1119 zr_b_c0[0][0]/* stratiform, bb.011, b=0.7729, 1/b=1.294 */36 -0.1167 zr_b_c0[0][1]/* stratiform, bb.017, b=0.7644, 1/b=1.308 */37 -0.1374 zr_b_c0[0][2]/* stratiform, bb.17, b=0.7288, 1/b=1.372 */38 -0.1601 zr_b_c0[0][3]/* stratiform, 0C ,b=0.6917, 1/b=1.446 */39 -0.1722 zr_b_c0[0][4]/* stratiform, 20C,
b=0.6727, 1/b=1.487 */40
41 -0.1040 zr_b_c1[0][0]/* stratiform, bb.011 */42 -0.0907 zr_b_c1[0][1]/* stratiform, bb.017 */- 129 -

43 -0.0235 zr_b_c1[0][2]/* stratiform, bb.17 */44 +0.0996 zr_b_c1[0][3]/* stratiform, 0C */45 +0.1116 zr_b_c1[0][4]/* stratiform, 20C */46
47 0.1327 zr_b_c2[0][0]/* stratiform, bb.011 */48 0.1275 zr_b_c2[0][1]/* stratiform, bb.017 */49 0.1118 zr_b_c2[0][2]/* stratiform, bb.17 */50 0.2811 zr_b_c2[0][3]/* stratiform, 0C */51 0.4095 zr_b_c2[0][4]/* stratiform, 20C */52 /* LWC-Ze coefficients (log10 of a and b in LWC = a Ze^b) */53 -2.4161 zl_a_c0[0][0]/* stratiform, bb.011, a=0.00383613 */54 -2.4881 zl_a_c0[0][1]/* stratiform, bb.02, a=0.00325046 */55 -3.1290 zl_a_c0[0][2]/* stratiform, bb.17, a=0.00074301 */56 -2.6994 zl_a_c0[0][3]/* stratiform, 0C ,a=0.00199806 */57 -2.6502 zl_a_c0[0][4]/* stratiform, 20C ,a=0.00223787 */58
59 1.5422 zl_a_c1[0][0]/* stratiform, bb.011 */60 1.8509 zl_a_c1[0][1]/* stratiform, 0C */61 1.8344 zl_a_c1[0][2]/* stratiform, 0C */62 1.5283 zl_a_c1[0][3]/* stratiform, 0C */63 1.5422 zl_a_c1[0][4]/* stratiform, 20C */64
65 -0.2365 zl_a_c2[0][0]/* stratiform, bb.011 */66 -0.2254 zl_a_c2[0][1]/* stratiform, 0C */67 -0.3571 zl_a_c2[0][2]/* stratiform, 0C */68 -0.5889 zl_a_c2[0][3]/* stratiform, 0C */69 -1.6158 zl_a_c2[0][4]/* stratiform, 20C */70
71 -0.1471 zl_b_c0[0][0]/* stratiform, bb.011, b=0.71266 */72 -0.1520 zl_b_c0[0][1]/* stratiform, bb.02, b=0.70472 */73 -0.1768 zl_b_c0[0][2]/* stratiform, bb.17, b=0.66564 */74 -0.2122 zl_b_c0[0][3]/* stratiform, 0C,
b=0.61342 */75 -0.2243 zl_b_c0[0][4]/* stratiform, 20C,
b=0.59658 */76
77 -0.1056 zl_b_c1[0][0]/* stratiform, bb.011 */78 -0.0915 zl_b_c1[0][1]/* stratiform, 0C */79 -0.0442 zl_b_c1[0][2]/* stratiform, 0C */80 0.0630 zl_b_c1[0][3]/* stratiform, 0C */81 0.0751 zl_b_c1[0][4]/* stratiform, 20C */82
83 0.1453 zl_b_c2[0][0]/* stratiform, bb.011 */84 0.1357 zl_b_c2[0][1]/* stratiform, 0C */85 0.1265 zl_b_c2[0][2]/* stratiform, 0C */86 0.1913 zl_b_c2[0][3]/* stratiform, 0C */87 0.4320 zl_b_c2[0][4]/* stratiform, 20C */- 130 -

Appendix 5.

Parameters defined in “param_conv_1.dat”

1 /* parameter file for v6 of 2A25. June 13, 2001 */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 0.0001273 alpha_init[1][0]/* alpha for low density snow */11 0.0004109 alpha_init[1][1]/* alpha for rain (convective) 0C */12 0.0004109 alpha_init[1][2]/* alpha for rain (convective) 0C */13 0.0004109 alpha_init[1][3]/* alpha for rain (convective) 0C */14 0.0004172 alpha_init[1][4]/* alpha for rain (convective) 20C */15 0.7713
beta_init[1]/* beta for convective column, conv */16 /* R-Ze coefficients */17 -1.6932 zr_a_c0[1][0]/* convective, bb.011, a=0.02027, a'= 174.09 */18 -1.4579 zr_a_c0[1][1]/* convective, 0C ,a=0.03484, a'= 159.44 */19 -1.4579 zr_a_c0[1][2]/* convective, 0C ,a=0.03484, a'= 159.44 */20 -1.4579 zr_a_c0[1][3]/* convective, 0C ,a=0.03484, a'= 159.44 */21 -1.3953 zr_a_c0[1][4]/* convective, 20C ,a=0.04024, a'= 147.43 */22
23 1.8122 zr_a_c1[1][0]/* convective, bb.011 */24 0.8745 zr_a_c1[1][1]/* convective, 0C */25 0.8745 zr_a_c1[1][2]/* convective, 0C */26 0.8745 zr_a_c1[1][3]/* convective, 0C */27 0.9377 zr_a_c1[1][4]/* convective, 20C */28
29 -0.5919 zr_a_c2[1][0]/* convective, bb.011 */30 -1.2688 zr_a_c2[1][1]/* convective, 0C */31 -1.2688 zr_a_c2[1][2]/* convective, 0C */32 -1.2688 zr_a_c2[1][3]/* convective, 0C */33 -2.5559 zr_a_c2[1][4]/* convective, 20C */34
35 -0.1217 zr_b_c0[1][0]/* convective, bb.011, b=0.7556, 1/b=1.3234 */36 -0.1792 zr_b_c0[1][1]/* convective, 0C,
b=0.6619, 1/b=1.5108 */37 -0.1792 zr_b_c0[1][2]/* convective, 0C,
b=0.6619, 1/b=1.5108 */38 -0.1792 zr_b_c0[1][3]/* convective, 0C,
b=141 10.6619, 1/b=1.5108 */39 -0.1915 zr_b_c0[1][4]/* convective, 20C,
b=0.6434, 1/b=1.5542 */40
41 -0.1235 zr_b_c1[1][0]/* convective, bb.011 */42 +0.0977 zr_b_c1[1][1]/* convective, 0C */43 +0.0977 zr_b_c1[1][2]/* convective, 0C */- 131 -

44 +0.0977 zr_b_c1[1][3]/* convective, 0C */45 +0.0986 zr_b_c1[1][4]/* convective, 20C */46
47 0.1535 zr_b_c2[1][0]/* convective, bb.011 */48 0.2375 zr_b_c2[1][1]/* convective, 0C */49 0.2375 zr_b_c2[1][2]/* convective, 0C */50 0.2375 zr_b_c2[1][3]/* convective, 0C */51 0.4773 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
65 -0.5818 zl_a_c2[1][0]/* convective, bb.011 */66 -1.0761 zl_a_c2[1][1]/* convective, 0C */67 -1.0761 zl_a_c2[1][2]/* convective, 0C */68 -1.0761 zl_a_c2[1][3]/* convective, 0C */69 -2.2027 zl_a_c2[1][4]/* convective, 20C */70
71 -0.1618 zl_b_c0[1][0]/* convective, bb.011, b=0.68902 */72 -0.2377 zl_b_c0[1][1]/* convective, 0C,
b=0.57855 */73 -0.2377 zl_b_c0[1][2]/* convective, 0C,
b=0.57855 */74 -0.2377 zl_b_c0[1][3]/* convective, 0C,
b=0.57855 */75 -0.2500 zl_b_c0[1][4]/* convective, 20C,
b=0.56232 */76
77 -0.1259 zl_b_c1[1][0]/* convective, bb.011 */78 0.0533 zl_b_c1[1][1]/* convective, 0C */79 0.0533 zl_b_c1[1][2]/* convective, 0C */80 0.0533 zl_b_c1[1][3]/* convective, 0C */81 0.0545 zl_b_c1[1][4]/* convective, 20C */82
83 0.1724 zl_b_c2[1][0]/* convective, bb.011 */84 0.2681 zl_b_c2[1][1]/* convective, 0C */85 0.2681 zl_b_c2[1][2]/* convective, 0C */86 0.2681 zl_b_c2[1][3]/* convective, 0C */87 0.5077 zl_b_c2[1][4]/* convective, 20C */- 132 -

Appendix 6.

Parameters defined in “param_other_1.dat”

1 /* parameter file for v6 of 2A25. June 13, 2001 */2 /* Do not delete empty lines. */3 /* Do not add or delete lines. Absolute line numbers are important. */4 /* parameters for other type of rain */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 0.0001273 alpha_init[2][0]/* alpha for low density snow, 0.011, conv */11 0.0001598 alpha_init[2][1]/* alpha for low density snow, 0.017, others */12 0.0004109 alpha_init[2][2]/* alpha for rain (others) 0C */13 0.0004109 alpha_init[2][3]/* alpha for rain (others) 0C */14 0.0004172 alpha_init[2][4]/* alpha for rain (others) 20C */15 0.7713
beta_init[2]/* beta for others column, others */16
17 -1.6932 zr_a_c0[2][0]/* others, bb.011 */18 -1.7280 zr_a_c0[2][1]/* others, bb.017 */19 -1.4579 zr_a_c0[2][2]/* others, 0C */20 -1.4579 zr_a_c0[2][3]/* others, 0C */21 -1.3953 zr_a_c0[2][4]/* others, 20C */22
23 1.8122 zr_a_c1[2][0]/* others, bb.011 */24 1.7697 zr_a_c1[2][1]/* others, bb.017 */25 0.8745 zr_a_c1[2][2]/* others, 0C */26 0.8745 zr_a_c1[2][3]/* others, 0C */27 0.9377 zr_a_c1[2][4]/* others, 20C */28
29 -0.5919 zr_a_c2[2][0]/* others, bb.011 */30 -0.6085 zr_a_c2[2][1]/* others, bb.017 */31 -1.2688 zr_a_c2[2][2]/* others, 0C */32 -1.2688 zr_a_c2[2][3]/* others, 0C */33 -2.5559 zr_a_c2[2][4]/* others, 20C */34
35 -0.1217 zr_b_c0[2][0]/* others, bb.011, */36 -0.1274 zr_b_c0[2][1]/* others, bb.017 */37 -0.1792 zr_b_c0[2][2]/* others, 0C */38 -0.1792 zr_b_c0[2][3]/* others, 0C */39 -0.1915 zr_b_c0[2][4]/* others, 20C */40
41 -0.1235 zr_b_c1[2][0]/* others, bb.011 */42 -0.1085 zr_b_c1[2][1]/* others, bb.017 */- 133 -

43 +0.0977 zr_b_c1[2][2]/* others, 0C */44 +0.0977 zr_b_c1[2][3]/* others, 0C */45 +0.0986 zr_b_c1[2][4]/* others, 20C */46
47 0.1535 zr_b_c2[2][0]/* others, bb.011 */48 0.1520 zr_b_c2[2][1]/* others, bb.017 */49 0.2375 zr_b_c2[2][2]/* others, 0C */50 0.2375 zr_b_c2[2][3]/* others, 0C */51 0.4773 zr_b_c2[2][4]/* others, 20C */52 /* LWC-Ze coefficients (log10 of a and b in LWC = a Ze^b) */53 -2.2070 zl_a_c0[2][0]/* others, bb.011, a=0.00620868 */54 -2.2699 zl_a_c0[2][1]/* others, bb.02, a=0.00537114 */55 -2.4070 zl_a_c0[2][2]/* others, 0C ,a=0.00391752 */56 -2.4070 zl_a_c0[2][3]/* others, 0C ,a=0.00391752 */57 -2.3522 zl_a_c0[2][4]/* others, 20C ,a=0.004444 */58
59 2.0441 zl_a_c1[2][0]/* others, bb.011 */60 1.9998 zl_a_c1[2][1]/* others, bb.02 */61 1.5269 zl_a_c1[2][2]/* others, 0C */62 1.5269 zl_a_c1[2][3]/* others, 0C */63 1.5766 zl_a_c1[2][4]/* others, 20C */64
65 -0.5818 zl_a_c2[2][0]/* others, bb.011 */66 -0.5713 zl_a_c2[2][1]/* others, bb.02 */67 -1.0761 zl_a_c2[2][2]/* others, 0C */68 -1.0761 zl_a_c2[2][3]/* others, 0C */69 -2.2027 zl_a_c2[2][4]/* others, 20C */70
71 -0.1618 zl_b_c0[2][0]/* others, bb.011, b=0.68902 */72 -0.1675 zl_b_c0[2][1]/* others, bb.02, b=0.68004 */73 -0.2377 zl_b_c0[2][2]/* others, 0C,
b=0.57855 */74 -0.2377 zl_b_c0[2][3]/* others, 0C,
b=0.57855 */75 -0.2500 zl_b_c0[2][4]/* others, 20C,
b=0.56232 */76
77 -0.1259 zl_b_c1[2][0]/* others, bb.011 */78 -0.1099 zl_b_c1[2][1]/* others, bb.02 */79 +0.0533 zl_b_c1[2][2]/* others, 0C */80 +0.0533 zl_b_c1[2][3]/* others, 0C */81 +0.0545 zl_b_c1[2][4]/* others, 20C */82
83 0.1724 zl_b_c2[2][0]/* others, bb .011 */84 0.1662 zl_b_c2[2][1]/* others, bb .017 */85 0.2681 zl_b_c2[2][2]/* others, 0C */86 0.2681 zl_b_c2[2][3]/* others, 0C */87 0.5077 zl_b_c2[2][4]/* others, 20C */- 134 -

3. Level 3
3-1.
1.

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

Objective of the algorithm

The objective of the algorithm is to calculate various statistics over a month from the level2 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
such as the presence of stratiform rain or the presence of a bright-band. For example, tocompute the unconditioned mean rain rate, the conditional mean must be multiplied by theprobability of rain which, in turn is calculated from the ratio of rain counts to the total
number of observations 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
other dimensions, as noted, for height, rain type, etc. Histograms are dimensioned(16,72,30,*) with 30 categories.
The 0.5×0.5-degree statistics are dimensioned (148,720,*), and have a product nameending with “2”. There are 148 latitude cells and 720 longitude cells.

- 135 -

2.

Output Variables

2.1 Variable naming convention

Variable names consist of a word or several words strung together describing thegeophysical quantity, 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)- 136 -

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
are computed at 3 heights + path-averaged, 2, 4, 6-km and full path.
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- 137 -

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

real
real
integer
integer*2
real
real
integer

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

real
real
integer
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
integer- 138 -

Convective raine_surfRainConvMean1(16,72)
e_surfRainConvDev1(16,72)
e_surfRainConvPix1(16,72)
e_surfRainConvH(16,72,30)
e_surfRainConvMean2(148,720)
e_surfRainConvDev2(148,720)
e_surfRainConvPix2(148,720)

real
real
integer
integer*2
real
real
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.
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)
shallowIsoRainDev1(16,72)
shallowIsoRainPix1(16,72)
shallowIsoRainH(16,72,30)
shallowIsoRainMean2(148,720)
shallowIsoRainDev2(148,720)
shallowIsoRainPix2(148,720)

real
real
integer
integer*2
real
real
integer- 139 -

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

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
real- 140 -

Stratiform 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 thepath attenuation from Hitschfeld-Bordan estimate is equal to that from the surface
reference technique (SRT). For small values of attenuation it is approximately equal to theratio of the path 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
marginally reliable (see 2A-21) and when bit 8 of the method flag from 2A-25 is set toone.

Epsilon is the multiplicative factor of α for the hybrid method of 2A-25. For small valuesof attenuation it is approximately equal to the ratio of the path attenuation from 2A-25 tothat of the Hitschfeld-Bordan path attenuation. The epsilon values are stored only under
the conditions for which the epsilon_0 data are stored. The number of counts for epsilonand epsilon_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
path attenuation (see 2a25).
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- 141 -

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)

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

- 142 -

Nadir bright-band statistics
Height and width (meters) and maximum reflectivity (dBZ). The statistics are computed at
the nadir 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)

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 datafrom one side only). Also note that the convention differs from that in 2A-21 where the
2-way path attenuation is used.

- 143 -

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 bereliable or marginally reliable.
‘Hb’ denotes the Hitschfeld-Bordan path attenuation from 2A-25. In some cases, theestimate 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.
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- 144 -

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
no longer 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 is assumed to have failed, and both a and b are set to -999.0.

All rain types
rzA1(16,72,2)
rzB1(16,72,2)
rzPix1(16,72,2)
rzA2(148,720,2)
rzB2(148,720,2)
rzPix2(148,720,2)

real
real
integerreal
realinteger- 145 -

Convective 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- 146 -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- 147 -

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
bin boundaries are (mm/h):
0.01
0.2050482 0.2734362 0.3646330 0.4862459 0.6484194
0.8646811 1.153071 1.537645
2.050482
2.734362
3.646330
4.862459 6.484194
8.646811 11.53071
15.37645
20.50482
27.34362 36.46331
48.62460
64.84194
86.46812 115.3071 153.7645
205.0482
273.4362
364.6331
486.2460 648.4194
864.6812
For bright band height histogram, HHBB, the 31 bin boundaries [km] are:
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), the31 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 height histogram, snowIceLH,
bbNadirWidthH, 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- 148 -

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[dimensionless] are:
1.00
1.05 1.10 1.15 1.20
1.55 1.60 1.65 1.70
2.10 2.20 2.30 2.40

factor histogram, nubfH, the 31 bin boundaries
1.25 1.30 1.35 1.40 1.45 1.50
1.75 1.80 1.85 1.90 1.95 2.00
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

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).

- 149 -

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 (40 S to 30 S)
2 -35 to -30 (35 S to 30 S)…
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 toa 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)- 150 -

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.

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 definedin 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 of version 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 the observations‘below the surface’ will be counted as ‘no-rain’ events. This will introduce a negative
bias into the mean rain rate at the (lat,long) box in question.

- 151 -

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 forindividual 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) arebeing 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’ areincluded in the statistics (that is, the statistics conditioned on rain being present).
Although some rain events will be missed, the advantage of this selection is that theset 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 (seecomment i.).
vii. The quantity ‘minEchoFlag’ (from 1B-21 and 1C-21) provides information on thepresence/absence of rain along each of the 49 angle bins that comprise the cross-track
scan. To test whether rain is present at a particular range bin or height above theellipsoid, a threshold value must be used. Presently, this threshold is dBZt > 0.01 dB
so that if minEchoFlag indicates the certainty of rain along the beam and if dBZt >0.01 dB at a particular range bin or height level, then the data (e.g., rain rate, dBZm,
dBZt, etc) are used in the calculation of the statistics (mean and standard deviation).
A difficulty arises in defining the histograms for the rain rates. The lowest histogram
bin for dBZt and dBZm is taken from 0.01 dB to 12 dB; the subsequent bins are taken
equal to 2 dB so that the bin boundaries are 14 dB, 16 dB,…, 70 dB. Since the Z-R
relationship that is used in 2A-25 can change depending on the storm type and verticalstructure, and because the histogram bins must be fixed, the bins for the quantity 10
log R (where R is the rain rate in mm/h) are determined from the nominal relationshipZ = 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 boundaryof the first bin) is 0.625×0.01-14.38 = -14.32 dB. It is possible, however, for dBR to
be less than this because the actual Z-R relationship used in 2A-25 differs from thenominal relationship. In order to count all non-zero rain rates (under ‘rain-certain’
conditions), the lower boundary of the first dBR histogram bin is set to -20 dB rather
than -14.32 dB. The reason for doing this is to ensure that the number of data points
that are categorized in the rain rate histogram are equal to the number of data points
used in the calculation of the mean and standard deviation of this quantity.

- 152 -

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 thevalues 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 that intersect
the height: to estimate dBZm, dBZt and rain rate at that height, a gaussian weighting isdone in dB space for the reflectivity factors and in linear space for the rain rates. This
resampling lowers the minimum detectable threshold that, in turn, affects thehistogram counts in the 2 lowest bins. In other words, the histogram counts at thelowest 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.
ix. As noted in comment v., the rain rate statistics over mountainous regions at the heightlevels of 2 and 4 km will tend to underestimate the actual values; for these cases, thenear-surface rain rate statistics (under ‘rain-certain’ conditions) should be a morereliable 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 probabilities ofthe 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, amultiplication of Rm by N would be used. For example, the accumulation in mm in a
30 day month N = 720.

- 153 -

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 rainrain) =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 rainrain) =rainPix1(i, j,6)
stratRainPix1(i, j,6)Pr′′(stratiform rainrain)=rainPix1(i, j,6)
Pr (stratiform rainrain) =Pr'' corresponds to what is the most common definition of the probability of stratiform rain:
given that rain is present, what is the probability that it is stratiform. Pr is the probability
that, given rain is present at a particular height level (denoted by the index k), that the rainis 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.

- 154 -

5.

Changed Variables in Version 6

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
epsilonConvPix1
epsilonConvMean1
epsilonConvDev1
epsilonConvH
epsilonConvPix2
epsilonConvMean2
epsilonConvDev2
epsilonStratPix1
epsilonStratMean1
epsilonStratDev1
epsilonStratH
epsilonStratPix2
epsilonStratMean2
epsilonStratDev2- 155 -

pia0Pix
pia2a25Pix
piaHbPix
piaSrtPix
piaCCoefPix
piaSrtssPix
piaSrtssMean
piaSrsstDev
piaSrtssH
piaHbssPix
piaHbssMean
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

5.2

shallowRainPix1
shallowRainMean1
shallowRainDev1
shallowRainH
shallowRainPix2
shallowRainMean2
shallowRainDev2

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

Deleted Variables

bbwidthMean1
bbwidthDev1
epsilonPix1
epsilonMean1
epsilonDev1
epsilonH

5.3

shallowIsoRainPix1
shallowIsoRainMean1
shallowIsoRainDev1
shallowIsoRainH
shallowIsoRainPix2
shallowIsoRainMean2
shallowIsoRainDev2

stormHtZmCCoef
wrainPix1
wrainPix2
xiZmCCoefzmGradH
zpzmH

Spelling Correction

stratZtH; was “startZtH”- 156 -

surfRainAllPix1
surfRainAllMean1
surfRainAllDev1
surfRainAllH
surfRainAllPix2
surfRainAllMean2
surfRainAllDev2

3-2. 3A-26: Estimation of Space-Time Rain Rate Statistics
Using a Multiple Thresholding Technique1.

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 the estimated values of the probability distribution function of thespace-time rain rates at 4 “levels” (2 km, 4 km, 6 km and path-averaged) and themean, standard deviation, and probability 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. (Fitsbased 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 teambelieves that a statistical 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.

2.

Description of the Method

A general understanding of the method can be gained by noting that the amountof attenuation in the TRMM radar signal depends on the 2-way path attenuation
down to the range gate of interest. This attenuation increases as the range gate istaken deeper into the storm (closer to the surface) and as the rain rate increases.
Although some general features of the rain are used in 2a-25, the rain rateestimates 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 datafrom 3a-25 and not the data from 3a-26.

- 157 -

Algorithm 3a-26 serves as an alternative way of estimating the space-time rainstatistics. 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 anintermediate region over which the rain rate estimates are most accurate. Using
only these estimates and an assumption as to the form of the probability
distribution function (log-normal), the parameters of the distribution can be foundby minimizing the rms difference between the hypothetical distribution and thevalues of the distribution obtained directly from the measurements. Once the
distribution is estimated, the mean and standard deviation of the distribution canbe calculated [Refs. 1-2, Ref. 6].
Useful by-products from the calculation of the probability distribution of rain rates
are the fractional 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 havebeen 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 ofthreshold as well as the method that is used to determine the high-resolution rain
rates. There are 3 methods that are 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 thesurface reference method, is implemented in the code but the results are output
only to a diagnostic file for evaluation. For the 3 estimates of rain rate (Z-R, HB
and 2a-25), Q (or zeta as defined in 2a-25) is used as the threshold parameter.
What this means is that if the threshold is set to a particular value, Q*, then if themeasured value of Q is less than Q*, the corresponding rain rate is accepted - thatis, it is used to update the distribution function of 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 increased a 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
distribution function. It should be noted that Q is a proxy for the attenuation andusually assumes a value between 0 and 1.

- 158 -

If the Z-R method (without attenuation correction) of estimating the highresolution rain rates is considered, the corresponding output files include the rain
rate distribution function, zeroOrderpDf, and the mean, standard deviation, andprobability 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 threshold should 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 theZ-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 ofsmaller threshold values (Q = 0.2) may lead to better estimates of the mean
space-time rain rate. In the case 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 casenearly all of the Z-R rain rate estimates are accepted so that the method reduces tofitting 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)

- 159 -

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 isconsidered, nominally, as the optimum choice of threshold, the variable,
rainMeanTH, has been defined to store these values. In particular:
rainMeanTH(lat,long,ih) = zeroOrderFit(lat,long,ih,1,3)
The accuracy of the results at other Q thresholds and the statistics derived fromthe Hitschfeld-Bordan (hbFit) and rain rates from 2a-25 (fit2A25) will be
evaluated as additional data from the TRMM radar become available.

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 sets that 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 aparticular type of rain (stratiform or convective). For the 3a-26 products the means
and standard deviations derived from the zeroOrderFit, 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 asubset 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:hlevelHeightellipsoid

1
2
3
4

2 km
4 km
6 km
Path-averageabove- 160 -

For 3a-25 products, the height levels relative to the ellipsoid are:hlevelHeightellipsoid

1
2
3
4
5
6

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

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 greater) all
heights are measured relative to the 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 the rain rates measured at aheight level given by hlevel.
From 3a-25, the mean rain rate (mm/hr), conditioned on rain being present atheight level, ih, is given by:
rainMean1(lat, long, ih).
To convert this to an unconditioned mean rain rate the quantity is first multipliedby the probability of rain. This can be approximated by the ratio of the number ofrain 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 ismultiplied 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- 161 -

wherePrRain(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 the same 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

4. Relationship between 3a-26 and the fractional areas above particularthresholds
The single threshold technique (ATI) uses the fractional area above a particularrain rate threshold as a linear estimator for the area-average rain rate. Estimates ofthe fractional areas above a threshold can be obtained from the estimateddistribution functions described above.
As noted above, the counts, which are proportional to the probability distributionfunctions of rain rate, are stored in the arrays:
zeroOrderFit(16, 72, 4, 3, 6)
hbFit(16, 72, 4, 3, 6)
fit2A25(16, 72, 4, 3, 6)- 162 -

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 (standard deviation of log-normal distribution)= 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 thetotal 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 thenumber of rain counts above the rain rate threshold corresponding to the 'ir'
indice. Denote this rain rate by RR(ir). The fractional area below the rain rate
threshold RR(ir) at height level ih at the Q 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)- 163 -

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 terms of the HDF outputs:
zeroOrderpDf(lat,long,ir=9,ih=1,iq=6)
nrain(lat,long,ih=1)
ntot(lat,long)- 164 -

5.

Reliability estimates

The reliability is defined as the rms difference between experimentally determinedvalues of the pDf and the fitted values of the pDf at those values for which theexperimentally-determined pDf increases monontonically.
reliabZeroOrder(16,72,4,6)
reliabHB(16,72,4,6)
reliabSRT(16,72,4,6)
if the number of data points is too few or an error occurs in the fitting procedure,
the following default values for reliab* and *Fit will be used:
if too few rain occurrences lat-long box, (nrain <200 .and. nrain ≠ 0) then*Fit and reliab* will be set to -999.
if number of data points < 2× number of unknowns or
if the number of threshold levels is too few or
if warning or fatal error occurs in the fitting then*Fit and reliab* will be set to -777.
if unconditioned mean rain rate > 3 mm/h
and distribution at R = 0.1 mm/h is concave (positive 2nd derivative)thenreliab* set to -888 but *Fit parameters are output in normal fashion
if unconditioned mean rain rate > 3 mm/h
and distribution at R = 0.1 mm/h is convex (negative 2nd derivative)thenreliab* set to -555 and *Fit parameters are output in normal
fashionif distribution at R = 0.1 mm/h is convex (negative 2nd derivative)
and unconditioned mean ≤ 3 see section 11.vi.

- 165 -

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 from40 S to 35 S and box 36 covers from 35 N to 40 N. The longitude boxes are labeledfrom 1 to 72 where box 1 runs from 180 W to 175 W and box 72 runs from 175 E to179.999 E.

7.

Notes on the processing procedure
1. Assume that 1 granule of data corresponds to 1 orbit.
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 monthspace-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 temporarystorage, and then overwritten once the updated statistics are completed.
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 based on the quantity zeta (as defined in 2a-25) or Q (as defined in 3a-26),
where:r

Q = ζ = 0.2ln β ∫ αZ mβ0where Zm is the measured or apparent reflectivity factor, k = αZ β , and k is theattenuation coefficient or specific attenuation (dB/km), and Z is the actualreflectivity 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 the center of which is closest to the surface drawn 2 km
above the ellipsoid.

- 166 -

6. 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 quantity that 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 for thismethod. On the other hand, Q (or ζ) is a monotonic function of thepath-integrated rain rate and is appropriate for the 0th order and HB
estimates of RR.
7. For the path-integrated attenuation (PIA) as derived from the surface
reference technique (and the corresponding rain rate), an appropriate proxyvariable is the SRT estimate of PIA itself. Results based on the SRT are
output only to diagnostic file.
8. The motivating principle of the multiple threshold method is that forarea-wide estimates of the rain rate it is more accurate to extrapolate to the
low and high regions of rain rate than to attempt to measure the
distribution of these values directly. Reasons for the 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
9. 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 have the highest accuracy (where thesignal-to-noise ratio is high and attenuation is low).
10. Currently, the maximum number of thresholds within the EDR is taken to
be 25 (the optimum number is still an issue and will depend upon thenumber of samples and the range of the variable).
11. 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 somenumber, iqqmin. Presently, iqqmin = 200.

- 167 -

8.

Input Parameters (initialized in 3a-26)

Thresholds:
data QUthres0th /0.1,0.2,0.3,0.5,0.75,0.9999/ ! Q-thresholds for Z-R and 2a-25
data QUthresHB/0.1,0.2,0.3,0.5,0.75,0.9999/ ! Q-thresholds for HB

data QLsrt/1.5,1.,0.8,0.6,0.4,0.1/! PIA-thresholds for SRT

The rain rate distribution functions consist of the count values in the following 25
rain rate categories
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 ismade only when the following condition is satisfied:
iqqmin = 200 ! Minimum number of valid rain occurrences needed forfitting to be done.
In identifying the number of valid thresholds, we require that the count value
increase by a certain amount from between successive rain rates thresholds; in fact,
the upper rain rate threshold can be identified as that threshold beyond which thecount value does not increase by at least nfu counts, where:
nfu = 30

- 168 -

9.

Output Variables

Arrays for the calculation of probabilities [int*4].
ttlCount(16,72)
Number of observations at each 5×5-degree box overthe month.
rainCount(16,72,4)
Number of rain observations at each 5×5-degree box
over the month. Note that all height levels aremeasured relative to the ellipsoid.
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 distributionfunction (25 categories) using 0th order (Z-R) rain rateestimate 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 estimatesfrom 2a-25.

- 169 -

Convention for zeroOrderpDf(16,72,25,4,6),
hbpDf(16,72,25,4,6), and pDf2A25(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 as derived 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
rate estimates.
fit2A25(16,72,4,3,6)Same as above except data from 2a-25 are used for rain rates
estimates.
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.

- 170 -

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 arealigned 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 the fitting parameters, calculate the mean, standard
deviation and probability of rain for each distribution.

vii.

Re- initialize the intermediate file11.

Comments and Issuesi.

It is assumed in the program that the verification file does not exist; if italready exists 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 andthe path-average while for 3a-26 the levels are [2, 4, 6] km and thepath-average.

iii.

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

- 171 -

iv.

Resampling of the radar data from the range direction to the vertical isdone differently in 3a-25 and 3a-26. In 3a-25, the estimate of thereflectivity factor at a particular height is done by a gaussian weightingof the range gates that intersect that height. 3a-26 uses only a single
value of Z and R - that gate, the center of which intersects the height ofinterest.

v.

The Z-R or 0th method refers to the zeroth order solution of thereflectivity factor from the basic weather radar equation. In thisapproximation, no compensation is made for attenuation so thereflectivity factor is directly proportional to the measured radar return
power. This approximate reflectivity factor is sometimes called theapparent or measured reflectivity factor. In converting any estimate of
the reflectivity 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, isobtained by using 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 this algorithm.

vi.

In version 5 of the algorithm, additional error flags have been addedthat are used to specify the behavior of the second derivative of theestimated distribution function, F, at a rain rate of 0.01 mm/h. Since F isassumed 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

π 0

ln R − µu=s 2

The sign of the second derivative can be determined by:
d dF
>0
dR dR
d dF
<0
if (µ - lnR) < s2, thendR dR

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

- 172 -

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
dR dR
d dF
< 0,
accept the parameters of this distribution. However, if
dR dR
d dF
again; continue this until a Q is foundincrease Q and evaluate
dR dR
d dF
for which> 0 at which point accept the correspondingdR dR
distribution.

Begin with Q = 0.3 and evaluate

12.

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.

- 173 -

PR Team Members
PR Team Leader:
Ken'ichi Okamoto
Department of Aerospace Engineering
Graduate School
Osaka Prefecture University
1-1 Gakuen-cho, Sakai, Osaka 599-8531 Japan
Phone: +81-72-254-9241 Fax: +81-72-254-9241
e-mail: okamoto@aero.osakafu-u.ac.jp

1B21, 1C21 Algorithm Developers:
Nobuhiro Takahashi
National Institute of Information and Communications Technology
4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795 Japan
Phone: +81-42-327-6179 Fax: +81-42-327-6666e-mail: ntaka@nict.go.jp

Shuji Shimizu
JAXA Earth Observation Research and application Center
Harumi-Island Triton Square Office tower-X 22F,
1-8-10 Harumi, Chuo-ku, Tokyo 104-6023 Japan
Phone: +81-3-6221-9049 Fax: +81-3-6221-9192
e-mail: shimizu@eorc.jaxa.jp

Jun Awaka
Hokkaido Tokai University
5-1-1-1, Minami-sawa, Minami-ku, Sapporo 005-0825 Japan
Phone: +81-11-571-5111 Fax: +81-11-571-7879
e-mail: awaka@de.htokai.ac.jp

Toshio Iguchi
National Institute of Information and Communications Technology
4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795 Japan
Phone: +81-42-327-7543 Fax: +81-42-327-6666e-mail: iguchi@nict.go.jp- 174 -

2A21, 3A25, 3A26 Algorithm Developer:
Robert Meneghini
NASA Goddard Space Flight Center
Code 975, Greenbelt, Maryland 20771 USA
Phone: +1-301-286-9128 Fax: +1-301-286-0294
e-mail: bob@meneg.gsfc.nasa.gov

2A23 Algorithm Developer:
Jun Awaka
Hokkaido Tokai University
5-1-1-1, Minami-sawa, Minami-ku, Sapporo 005-0825 Japan
Phone: +81-11-571-5111 Fax: +81-11-571-7879
e-mail: awaka@de.htokai.ac.jp

2A25 Algorithm Developer:
Toshio Iguchi
National Institute of Information and Communications Technology
4-2-1 Nukui-Kitamachi, Koganei, Tokyo 184-8795 Japan
Phone: +81-42-327-7543 Fax: +81-42-327-6666e-mail: iguchi@nict.go.jp- 175 -