Algorithm theoretical basis document (ATBD) of the algorithm
to derive total water vapor content from ADEOS-II/AMSR
Yoshiaki Takeuchi
Numerical Prediction Division / Japan Meteorological Agency
1. Introduction
An algorithm for the physical-statistical retrieval of total water vapor content (PWA) from satellite-based
microwave radiometers named AMSR has been described. Input data are brightness temperature (T BB) of 6channels, i.e.19 GHz V/H, 24 GHz V/H, 37 GHz V/H, observation time, latitude and longitude. Ancillary data
are land/open sea/sea ice map data, sea surface temperature data, sea surface wind speed data, temperature data at
850 hPa, and a few look-up tables. Sea surface temperature (SST), sea surface wind speed (Vs), and temperature
at 850hPa (T85) is given by global analysis, forecast data or another standard product by AMSR etc.. Several flags,
which are related to success/failure and accuracy, are added to each result by the algorithm.
The characteristics of this algorithm are the follows:- One retrieval is carried out by measurement in a field of view.
- The algorithm is applicable over open sea region.
- The algorithm is based on single-layer atmosphere model.
- Complicated radiative transfer calculation and detailed temperature and water vapor profile as a first guess areunnecessary.
- An iteration calculation is included to obtain atmospheric transmittance and vertical mean atmospherictemperature. The iteration is stable.
- Dependencies of surface emissivity to SST and Vs are considered statistically.
- Ancillary data such as land/open sea/sea ice map, surface temperature, and sea surface wind speed andtemperature at 850 hPa are needed.
- The dynamic range of the algorithm is 0-70 Kg/m2 for PWA.
- The algorithm assures that the probability of retrieved PWA is equivalent to that of radio sonde of match-up
data set.
- Flag related to success/failure and accuracy is added to each result.
2. Background and forward modelThis algorithm is based on a model consists of single-layer atmosphere and sea surface as shown in Fig.2.1.
The atmosphere includes water vapor and cloud liquid water as absorber and emitter at microwave region. Sea
surface is assumed to be Fresnel reflection surface.
Tr is square of atmospheric transmittance at a frequency
AMSR
and a satellite zenith angle (θs) , namely microwave emitting
direction. Ta is vertical mean temperature of atmosphere at
the frequency andθs . Tr and Ta depend on vertical profile ofθStemperature, water vapor, and cloud liquid water. We
ignore the dependency of Tr and Ta to polarization since theTr
Ta Atmospheredependency can be detected only in heavy rain region byεS
Ts Sea Surface
measurements of higher frequency.
To be exact, Ta also depends slightly the direction ofradiation transfer, i.e. upward or downward, due toFig.2.1 RT model for AMSR
inhomogeneity of temperature and water vapor. In ouralgorithm, we define Ta as the average of upward Ta anddownward Ta.
ε SV andε SH are sea surface emissivity for vertical and horizontal polarization, respectively. ε SV andε SHdepend on frequency, SST, Vs and θs.
By using the model, the difference between brightness temperature of vertical polarization TV and that ofhorizontal polarization T H at a frequency is given by
T V - TH = Tr*(ε SV -ε SH )*T,

(2.1)

whereT ≡ Ta + (SST-Ta)/Tr1/2.
Brightness temperature T BB at a frequency is related to Tr andε S as
T BB = α*{1-Tr*(1-ε S)},
where vertical mean temperature of atmosphere-sea surface system α is defined by
α ≡ Ta+(SST-Ta)*Tr1/2 *ε S /{1-(1-ε S )*Tr}.

(2.4)

From (2.3) and (2.4), Tr and Ta can be calculated by the following manner. For 19 GHz V/H, 24 GHz V and37 GHz V/H,
1) ε S is calculated from frequency, SST, Vs, andθ s.
2) Initial value of Tr is set.
Tr = exp(-0.2)(2.5)3) Ta can be approximated as a function of Tr and T85. Ta is determined from a two dimensional look-up table.
Ta = Ta(Tr,T85)(2.6)4) α is calculated by (2.4).
5) Tr is calculated using the formula derived from (2.3).
Tr = (1-T BB/α)/(1-ε S )(2.7)6) From 5), two Tr value can be calculated both for vertical polarization channel and horizontal polarization
channel, then calculate new Tr by taking square root of the product of TrV and TrH.
Tr = (TrV*TrH) 1/2(2.8)

7) Step 3) to 6) are repeated until Tr value is converged. Usually, this iteration calculation is stable andconverges within a few iterations.
When Tr is obtained, optical depth of atmosphere τ is calculated from Tr.
τ = -0.5*ln(Tr)τ is summation of optical depth of water vapor and optical depth of cloud liquid water.
τ = (kv*PWA + kl*LWC)/cos(θ s),(2.9)(2.10)

where PWA is total water vapor content, LWC is total cloud liquid water content, kv is vertical mean absorption
coefficient of water vapor, kl is vertical mean absorption coefficient of cloud liquid water. kv and kl depend
vertical profile of temperature, water vapor and cloud liquid water and frequency. Tr at 19GHz is denoted as
Tr19. Tr at 24GHz is denoted as Tr24. From (2.9) and (2.10), PWA can be calculated by the following
formula:PWA = 0.5*cos(θ s )*{kl24*ln(Tr19)-kl19*ln(Tr24)} /(kv24*kl19-kv19*kl24). (2.11)

However, it is difficult to calculate kv and kl theoretically because kv and kl depend vertical profile oftemperature, water vapor and liquid water. Instead of the theoretical calculation, we construct water vapor
content index (PWI) as a linear combination of ln(Tr19) and ln(Tr24). In addition, we introduce a cloud liquidwater index CWI, which is deduced from (2.1) and (2.2) for 19GHz and 37GHz.
CWI = ln{(T19V-T19H)/(ε S 19V-ε S 19H)/T19} -ln{(T37V-T37H)/(ε S 37V-ε S 37H)/T37}(2.12)

where T19 and T37 are given by
T19 = Ta19+(SST-Ta19)/Tr191/2,
T37 = Ta37+(SST-Ta37)/Tr371/2.

(2.13)(2.14)PWI = β*ln(Tr19)-ln(Tr24)+γ*CWI(2.15)

In conclusion, PWI is calculated bywhere β and a constant γ is determined so that we can get the maximum correlation between PWI and PWA fromradio sonde in the match-up data set described later. Since it is found that β strongly depends SST, we give β asa function of SST. β is given at SST of 0°C , 16°C , 24°C , 28°C , 30°C and β at any SST is given byinterpolating these values.
3 Detail description of the algorithm
This section describes the detail of the algorithm. Input data of these programs are shown in Table 3.1 andflags added by the algorithm are summarized in Table 3.2.
3.1 Land and sea ice mask
Land and sea ice is masked by using land/ocean flag and sea ice data. Sea ice data will be revised once a day
by using the latest data such as AMSR sea ice level-3 products. If a FOV of AMSR is judged as land or sea ice,then the flag 'land/sea ice' is set and the retrieval is quit.
3.2 Quality check of AMSR brightness temperature data
1) Brightness temperatures T19V, T19H, T24V, T24H, T37V and T37H are within the range from 90 K to 300 K,
2) T19V-T19H is positive,3) T24V-T24H is positive,4) T37V-T37H is positive, and
5) T24V-T19V is less than TBD K.
If above conditions are false, then the flag 'bad TBB' is added and the retrieval is quit.
3.3 Quality check of ancillary data
If sea surface wind speed (Vs) of ancillary data set is out of the range from 0 to 60 m/s, a default value Vs = 5
m/s is set.
If sea surface temperature (SST) of ancillary data set is out of the range from 0 to 35 °C, the flag 'others' isadded and the retrieval is quit.
If temperature at 850 hPa (T85) of ancillary data set is out of the range from 200 K to 300 K, a default value
T85 = SST - 10 K is set.
3.4 Calculation of index of cloudiness and its quality check
Sea surface emissivities (ε S ) at 19 GHz V/H, 24 GHz V/H, and 37 GHz V/H are calculated from frequency,
SST, and θ S theoretically, and then corrected with SST and Vs. λ is given by look-up table and δ is a constant.
ε SH = 1-(1-ε SH)λδ , ε SV = 1-(1-ε SV)λδ -1(3.1)

The index of cloudiness is calculated by the formula:
CCI = ln{(T19V-T19H)/(ε S19V-ε S 19H) /(T37V-T37H)*(ε S 37V-ε S 37H)}.

(3.2)

If the CCI is less than -0.05, the flag 'bad TBB' is added and the retrieval is quit.
3.5 Decision of clear, cloudy, or rain category
If T19V is larger than 240 K, it is assumed to be rainy condition.
If T19V is less than 240 K and CCI is larger than 0.2, it is assumed to be cloudy condition.
If T19V is less than 240 K and CCI is less than 0.2, it is assumed to be clear condition.
3.6 Calculation of vertical mean temperature of atmosphere and square of atmospheric transmittance andtheir quality check
For each channel, i.e. 19GHz V/H, 24GHz V/H, 37GHz V/H, square of atmospheric transmittance (Tr) andvertical mean temperature of atmosphere (Ta) are calculated from temperature at 850hPa (T85), sea surface
emissivity (ε S ), sea surface temperature (SST) and brightness temperature iteratively. The details are described at
section 2. In the case that Ta cannot be obtained or α is less than T BB, the flag 'bad TBB' is added and theretrieval is quit.
3.7 Calculations of water vapor content index and cloud liquid water index
Water vapor content index (PWI) is calculated from (2.15) and (2.12).
3.8 Conversion PWI to water vapor content
PWI is converted to total water vapor content (PWA, kg/m2) using a look-up table. If PWI is out of range oflook-up table, the flag 'low accuracy' is added.

flag
description
availability
normalnormal (clear condition)
available
cloudynormal (cloudy condition)
available
rainy
normal (rainy condition)
available
inavailable
land/sea ice land or sea ice region
low accuracy accuracy may be low
available
bad TBBbrightness temperature is illegal inavailable
othersno sea surface temperature
inavailable
failure of sea surface emissivity
estimation
Table 3.1 List of input data for PWA retrievals

availability
flag
description
normalnormal (clear condition)
available
cloudynormal (cloudy condition)
available
rainy
normal (rainy condition)
available
land/sea ice land or sea ice region
inavailable
low accuracy accuracy may be low
available
bad TBBbrightness temperature is illegal inavailable
othersno sea surface temperature
inavailable
failure of sea surface emissivity
estimation
Table 3.2 Summary of flags added by the algorithm

3.9 Heavy rain correction to water vapor content
In the case of rainy category, PWA is corrected by T19H/T19V.
If T19H/T19V is less than 0.884, PWA = PWA-1.51.
If T19H/T19V is more than 0.884, PWA = PWA+(T19H/T19V-0.884)/(0.960-0.884)*16.5-1.51.
4. How to construct look-up tables and to decide retrieval coefficients
This section describes the procedure for determination of several coefficients used in the algorithm,
proposal for a match-up data set, from which the coefficients are determined. The scheme of coefficient decision
should be in automated processing appropriate for operational retrievals.

Look-up tables and several coefficients for the retrieval are derived from a match-up data set between AMSR
observation and in-situ observation, i.e., radio sonde data of international radio sonde network. The GANAL
analysis provided by JMA and AMSR level3 products should be included in the match-up data set.
Table 4.1 shows proposed list of elements to be included in the match-up data set. The data set is also used invalidation.
4.1 Look-up table of sea surface emissivity
correction on sea surface temperature and sea
surface wind
A coefficientλ defined as (4.1) is calculated withthe match-up data set between radio sonde, sea surface
temperature, sea surface wind and AMSR TBB. Thenthe results are compiled into two dimensional tablewith axis of SST and Vs.
λ = {(1-T BBH/αH)/(1-T BBV/αV)}/{(1-ε SH)/(1-ε SV)}

(4.1)

4.2 Look-up table to calculate Ta from T85 and Tr
Ta and Tr is calculated theoretically fromtemperature and water vapor profile observed by radio
sonde in the match-up data set. The results arecompiled as a look-up table to get Ta from T85 and Tr.
Optical parameters used in the radiative transfer
calculation are refered to Janssen (1993).
4.3 Coefficients to construct PWI from linear
combination of atmospheric optical depth at
24GHz and that at 19GHz.

Radio sonde at island or coastal area
Sonde ID
Observation time (min)Pressure (hPa), Temperature (K), Relative humidity(%) at all level2
PWA from sonde profile (kg/m )2
PWA from GANAL at sonde station (kg/m )AMSR observation within 150km from sonde station
Observation time (min)Latitude, Longitude (deg)Time lag between sonde obs. & AMSR obs. (min)Distance between sonde station & AMSR FOV (km)Granule number, Line number, Swath number
AMSR Land /Ocean flag
AMSR incidence angle (deg)AMSR sun azimuth/ elevation (deg)AMSR brightness temperature (K)2
PWA from AMSR observation (kg/m )GANAL interpolated at AMSR FOV
SST (K), Surface wind U,V (m/s)
Temperature (K), Relative humidity (%)
2
PWA from GANAL at AMSR FOV (kg/m )AMSR level3 interpolated at AMSR FOV
SST (K), Sea Ice
Sea Winds level3 interpolated at AMSR FOV
Surface wind U,V (m/s)
Table 4.1 Proposed list of coefficients for retrieval

It is estimated with a match-up data set between and validation
radio sonde data and TBB so that the correlation between PWI and PWA accomplish maximum. The β(Ts) andconstants γ and δ will be determined after launch of AMSR.
4.4 Look-up table from PWI to PWA
The look-up table is designed as the provability of PWA with AMSR retrievals is equivalent to that of PWA
with radio sonde.
4.5 Coefficients for heavy precipitation correction for water vapor content
It is estimated with a match-up data set between PWA sonde and PWA AMSRnocor and T19H/T19V.
Finally, It is noted that careful treatment of producing match-up data set is essential to attain the accuracy
require-ment of AMSR total water vapor amount. Well checked radio sonde data, brightness temperature data,and good collocation data should be selected. Consistency between the match-up data set and a validation data
set is also essential to evaluate the algorithm correctly.
Reference
Janssen, M.A. Ed.(1993) Atmospheric Remote Sensing by Microwave Radiomeroty,
Jhon Wiley & Sons, Inc., 572pp.