Foreword

The Advanced Microwave Scanning Radiometer (AMSR) is a multi-frequency, dual-polarized microwave
radiometer that detects microwave emissions from the Earth's surface and atmosphere.

Various geophysicalparameters, particularly those related to water (H2O), can be estimated from AMSR data.

In addition to theproven parameters such as water vapor, precipitation, and sea surface wind speed, novel geophysical parameters,
including sea surface temperature and soil moisture, are expected to be retrieved by using new frequency channels.
The largest ever microwave radiometer antenna enables us to perform continuous global observation with highspatial resolution.

Long-term record of AMSR measurements will play an important role in climate changemonitoring as well as in providing indispensable information for understanding the Earth's climate system,
including water and energy circulation.

Near real-time products will be used for investigating satellite data

assimilation into weather forecasting models and will contribute to improving forecast accuracy.

AMSR is scheduled to be launched on board the Advanced Earth Observing Satellite-II (ADEOS-II) in 2002.
ADEOS-II is an integrated observing platform with multiple sensors covering the spectrum from visible tomicrowave frequencies.

In addition to AMSR, a combination of these sensors will provide a means of

examining the Earth's phenomena from various aspects.
model of the AMSR on ADEOS-II.

AMSR-E on the NASA EOS Aqua is an enhanced

AMSR-E also will be launched in 2002. I hope that these papers will be

helpful to utilize the AMSR and AMSR-E data of which will be available soon.

March 2002

Dr. Akira Shibata
AMSR lead scientist

EORC Bulletin/Technical Report-Special Issue on AMSR Retrieval Algorithms-

Contents

Page No

Development of AMSR and AMSR-E retrieval algorithms at EORC
Keiji Imaoka
Algorithm theoretical basis document (ATBD) of the algorithm
to derive total water vapor content from ADEOS-II/AMSR
Yoshiaki Takeuchi
AMSR Ocean Algorithm
Frank J. Wentz
AMSR Precipitation Rate Retrieval Algorithm-- Theoretical Basis and Operation
Grant W. Petty

Description of Precipitation Retrieval Algorithm For ADEOS II AMSRGuosheng Liu
AMSR/AMSR-E Sea Surface Wind Speed Algorithm
Akira Shibata
AMSR/AMSR-E Sea Surface Temperature Algorithm
Akira Shibata
Algorithm Theoretical Basis Document (ATBD)
For the ADEOS/AMSR Sea Ice Algorithm

Josefino C. Comiso

Description of Snow Depth Retrieval Algorithm for ADEOS II AMSR
Alfred Chang and Richard Kelly
AMSR Snow Algorithm Development and Validation in the Eurasian continent
Toshio Koike
AMSR soil moisture algorithm development and validation
Toshio Koike
Description of Soil Moisture Retrieval Algorithm for ADEOS II AMSR
Thomas J. Jackson
The IROE algorithm
Simonetta Paloscia
ADEOS-II AMSR Soil Moisture Algorithm
Eni G. Njoku

Development of AMSR and AMSR-E retrieval algorithms at EORC
Keiji Imaoka
Earth Observation Research Center / NASDA
1. Introduction
The Advanced Microwave Scanning Radiometer (AMSR) is a multi-frequency, dual-polarized microwave
radiometer that detects microwave emissions from the Earth's surface and atmosphere. Various geophysicalparameters, particularly those related to water (H2 O), can be estimated from AMSR data. In addition to theproven parameters such as water vapor, precipitation, and sea surface wind speed, novel geophysical parameters,
including sea surface temperature and soil moisture, are expected to be retrieved by using new frequency channels.
The largest ever microwave radiometer antenna enables us to perform continuous global observation with highspatial resolution. Long-term records of AMSR measurements will play an important role in climate changemonitoring as well as in providing indispensable information for understanding the Earth's climate system,
including water and energy circulation. Near-real-time products will be used for investigating satellite data
assimilation into weather forecasting models and will contribute to improving forecast accuracy. In thistechnical report, we will summarize the theoretical basis and descriptions of an each retrieval algorithm.
2. Algorithm Development
NASDA issued the first Research Announcement (RA) in October 1995 to solicit standard algorithms for
ADEOS-II AMSR and GLI. Standard algorithms will be installed at the Earth Observation Center (EOC) to
operationally produce Level 2 and 3 geophysical products. The AMSR sensor team was organized based on thisannouncement. After the decision of providing AMSR-E to the EOS PM-1 satellite, the team has also been
responsible for AMSR-E standard algorithms. Retrieval algorithms for AMSR standard products have been
evaluated and selected through an algorithm inter-comparison proces s by the AMSR sensor team. Theinter-comparison procedure was mainly based on a comparison between in-situ or aircraft data and retrieved
geophysical parameters from brightness temperatures of existing space-borne sensors such as the Special Sensor
Microwave/Imager (SSM/I). Although the comparison showed little differences in the performance ofalgorithms, the day-1 algorithms (i.e. the algorithms at launch phase) and supporting PIs were selected based on
this result (e.g. whether he or she could meet report and program deadlines). The AMSR algorithm selection
board was held at EORC in May 2000. As a result of this board, the soil moisture product was re-defined as a
research product at the launch phase due to the difficulties of accurate retrieval. For geophysical parameters with
two algorithm candidates, one algorithm was selected as standard and the other one was positioned as a researchalgorithm. Current day-1 algorithm investigators are listed in Table 1. These day-1 algorithms will be used at
EOC during the first six-months after launch. After the real AMSR brightness temperatures are obtained, thisselection will be re-shuffled, and one algorithm will be selected based on its real performance. Through the 2nd
Research Announcement, several PIs have joined the project as research algorithm investigators. These PIs will
be added to the list at the next opportunity.
Table 1. Day-1 algorithms for AMSR and AMSR-E
Geophysical products
Integrated water vapor
Integrated cloud liquid water
Precipitation
Sea surface wind speed
Sea surface temperature
Sea ice concentration
Snow depth
Soil moistureStandard
Takeuchi
Wentz
Petty
Shibata
Shibata
ComisoChang-

Research
Liu
Wentz
Koike
Njoku, Jackson,
Paloscia, Koike

3. Algorithm integration testing
EORC is responsible for proto-typing and testing the AMSR data retrieval system. We asked the algorithm
PIs to submit their source codes for retrieval algorithms. Prior to this request, NASDA distributed the “common
library,” that is a kind of interfacing toolkit between the PI environment and the NASDA processing system. We
can easily integrate PI source codes written using this common library into our processing system. During fiscal
year 2000, we were provided the algorithms twice, corresponding to the distributions of different version of thecommon library. Since the AMSR has not flown yet, no real brightness temperatures are available to check thecondition and performance of each algorithm. As the input data for the testing, we generated AMSR simulated
brightness temperatures by using existing microwave radiometer data such as SSM/I and SMMR with slightcorrections for incident angle and center frequencies. Radiative transfer calculations were also used fornonexistent frequency channels. Through the algorithm integration testing, we have confirmed that most of thealgorithms functioned properly. Since the AMSR simulated data are not ideal, we have to wait for the real
AMSR data to investigate algorithm performance. Sample browse images of the retrieval results are shown in Fig.
1.

Fig. 1. Global images generated by AMSR processing system at EORC. Images of sea surface wind speed (left)
and sea surface temperature (right) are shown as examples. Input data are AMSR simulated ascending passes onJune 24, 1998.

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.

AMSR Ocean Algorithm
Frank J. Wentz
Remote Sensing Systems

1. Overview and Background Information
1.1. Introduction
With the advent of well-calibrated satellite microwave radiometers, it is now possible to obtain long time series of geophysical parameters that are important for studying the global hydrologic cycle and the Earth's radiationbudget. Over the world's oceans, these radiometers simultaneously measure profiles of air temperature and thethree phases of atmospheric water (vapor, liquid, and ice). In addition, surface parameters such as the nearsurface wind speed, the sea-surface temperature, and the sea ice type and concentration can be retrieved. A wide
variety of hydrological and radiative processes can be studied with these measurements, including air-sea and airice interactions (i.e., the latent and sens ible heat fluxes, fresh water flux, and surface stress) and the effect ofclouds on radiative fluxes. The microwave radiometer is truly a unique and valuable tool for studying our planet.
This Algorithm Theoretical Basis Document (ATBD) focuses on the Advanced Microwave Scanning Radiometer (AMSR) that is scheduled to fly in December 2000 on the NASA EOS-PM1 platform. AMSR will measure the Earth’s radiation over the spectral range from 7 to 90 GHz. Over the world’s oceans, it will be possible toretrieve the four important geophysical parameters listed in Table 1. The rms accuracies given in Table 1 comefrom past investigations and on-going simulations that will be discussed. Rainfall can also be retrieved, which is
discussed in a separate AMSR ATBD.
We are confident that the expected retrieval accuracies for wind, vapor, and cloud will be achieved. The Special Sensor Microwave Image (SSM/I) and the TRMM microwave imager (TMI) have already demonstrated thatthese accuracies can be obtained. The AMSR wind retrievals will probably be more accurate than that of SSM/I
and less affected by atmospheric moisture. A comparison between sea surface temperatures (SST) from TMI withbuoy measurements indicate an rms accuracy between 0.5 and 0.7 K. One should keep in mind that part of theerror arises from the temporal and spatial mismatch between the buoy measurement and the 50 km satellite footprint. Furthermore, the satellite is measuring the temperature at the surface the ocean (about 1 mm deep) whereas
the buoy is measuring the bulk temperature near 1 m below the surface. There are still some concerns with regards to the sea-surface temperature retrieval, which are discussed in Section 1.5.
This document is version 2 of the AMSR Ocean Algorithm ATBD. The primary difference between this version
and the earlier version is that the emissivity model for the 10.7 GHz has been updated using data from TMI. In
addition, there are several small updates to the radiative transfer model (RTM).
Table 1. Expected Retrieval Accuracy for the Ocean Products
Geophysical Parameter
Rms Accuracy
Sea-surface temperature TS
0.5 K
Near-surface wind speed W
1.0 m/s
Vertically integrated (i.e., columnar) water vapor V
1.0 mm
Vertically integrated cloud liquid water L
0.02 mm1.2. Objectives of Investigation
There are two major objectives of this investigation. The first is to develop an ocean retrieval algorithm thatwill retrieve TS, W, V, and L to the accuracies specified in Table 1. These products will be of great value to the
Earth science community. The second objective is to improve the radiative transfer model (RTM) for the ocean
surface and non-raining atmosphere. The 6.9 and 10.7 GHz channels on AMSR will provide new information on
the RTM at low frequencies. Experience has shown that these two objectives are closely linked. A better understanding of the RTM leads to more accurate retrievals. A better understanding of the RTM also leads to new remote sensing techniques such as using radiometers to measure the ocean wind vector.
1.3. Approach to Algorithm Development
Radiative transfer theory provides the relationship between the Earth’s brightness temperature TB (K) as
measured by AMSR and the geophysical parameters TS, W, V, and L. This ATBD addresses the inversion problem of finding TS, W, V, and L given TB. We place a great deal of emphasis on developing a highly accurate
RTM. Most of our AMSR work thus far has been the development and refinement of the RTM. This work is now
completed, and Section 2 describes the RTM in considerable detail.

The importance of the RTM is underscored by the fact that AMSR frequency, polarization, and incidence angle selection is not the same as previous satellite radiometers. Table 2 compares AMSR with other radiometersystems. Albeit some of the differences are small, they are still significant enough to preclude developing AMSR
algorithms by simply using existing radiometer measurements. The differences in frequencies and incidence angle must be taken into account when developing AMSR algorithms.
2. Geophysical Model for the Ocean and Atmosphere2.1. Introduction
The key component of the ocean parameter retrieval algorithm is the geophysical model for the ocean andatmosphere. It is this model that relates the observed brightness temperature (TB) to the relevant geophysical parameters. In remote sensing, the specification of the geophysical model is sometimes referred to as the forward
problem in contrast to the inverse problem of inverting the model to retrieve parameters. An accurate specific ation of the geophysical model is the crucial first step in developing the retrieval algorithm.
2.2. Radiative Transfer Equation
We begin by deriving the radiative transfer model for the atmosphere bounded on the bottom by the Earth’s
surface and on the top by cold space. The derivation is greatly simplified by using the absorption-emission approximation in which radiative scattering from large rain drops and ice particles is not included. Over the spectral
range from 6 to 37 GHz, the absorption-emission approximation is valid for clear and cloudy skies and for lightrain up to about 2 mm/h. The results of Wentz and Spencer [1997] indicate that only 3% of the SSM/I observations over the oceans viewed rain rates exceeding 2 mm/h. Thus, the absorption-emission model to be presented
will be applicable to about 97% of the AMSR ocean observations.
In the microwave region, the radiative transfer equation is generally given in terms of the radiation brightness
temperature (TB), rather than radiation intensity. So we first give a brief discussion on the relationship between
radiation intensity and TB. Let Pλ denote the power within the wavelength range dλ, coming from a surface area
dA, and propagating into the solid angle dΩ. The specific intensity of radiation Iλ is then defined by
Pλ = I λ cos θi d λ dA d Ω(1)
The specific intensity is in units of erg/s-cm3 -steradian. The angle θi is the incidence angle defined as the angle
between the surface normal and the propagation direction. For a black body, Iλ is given by Planck’s law to be[Reif, 1965]

Iλ =

2hc 2
λ5 [exp (hc λkT ) − 1](2)

where c is the speed of light (2.998×1010 cm/s), h is Planck’s constant (6.626×10−27 erg-s), k is Boltzmann’s constant (1.381×10−16 erg/K), λ (cm) is the radiation wavelength, and T (K) is the temperature of the black body.
Consider a surface that is emitting radiation with a specific intensity Iλ. Then the brightness temperature TB for
this surface is defined as the temperature at which a black body would emit the radiation having specific intensity
Iλ. In the microwave region, the exponent in (2) is small compared to unity, and (2) can be easily inverted to giveT B in terms of Iν.
λ4 I λ
TB =
(3)
2 kc
This approximation is the well known Rayleigh Jeans approximation for λ >> hc/kT.
In terms of TB, the differential equation governing the radiative transfer through the atmosphere is∂T B= −α ( s ) T B ( s ) − T ( s )(4)∂swhere the variable s is the distance along some specified path through the atmosphere. The terms α(s) and T(s)are the absorption coefficient and the atmospheric temperature at position s. Equation (4) is simply stating thatthe change in TB is due to (1) the absorption of radiation arriving at s and (2) to emission of radiation emanatingfrom s. We let s = 0 denote the Earth’s surface, and let s = S denote the top of the atmosphere (i.e., the elevation
above which α(s) is essentially zero).
Two boundary conditions that correspond to the Earth’s surface at the bottom and cold space at the top are
applied to equation (4). The surface boundary conditions states that the upwelling brightness temperature at thesurface TB↑ is the sum of the direct surface emission and the downwelling radiation that is scattered upward by therough surface [Peake, 1959].

π 2

2π
sec θiT B ↑ (k i ,0) = E( k i )TS +sin θs dθs ∫ dϕs TB ↓ (k s ,0)[σo , c (k s , k i ) + σo ,× (k s , k i )]
4π ∫0
0

(5)

where the first TB argument denotes the propagation direction of the radiation and the second argument denotes
the path length s. The unit propagation vectors k i and k s denote the direction of the upwelling and downwellingradiation, respectively. In terms of polar angles in a coordinate system having the z-axis normal to the Earth’s
surface, these propagation vectors are given by
k i = cos ϕ i sin θ i , sin ϕi sin θ i , cos θ i(6a)k s = − cos ϕs sin θ s , sin ϕs sin θ s , cos θs(6b)
The first term in (5) is the emission from the surface, which is the product of the surface temperature TS and thesurface emissivity E(k i ). The second term is the integral of downwelling radiation TB↓(k s) that is scattered in direction ki . The integral is over the 2π steradian of the upper hemisphere. The rough surface scattering is characterized by the bistatic normalized radar cross sections (NRCS) σo,c(θs ,θi) and σ o,×(θs,θi ). These cross sections
specify what fraction of power coming from ks is scattered into k i. The subscripts c and × denote co-polarization(i.e., incoming and outgoing polarization are the same) and cross-polarization (i.e., incoming and outgoing polarizations are orthogonal), respectively. The cross sections also determine the surface reflectivity R(k i) via the following integral.
π 2

2π
sec θiR(k i ) =sin θs dθ s ∫ dϕs [σo ,c (k s , k i ) + σ o ,× (k s , k i )]
4π ∫0
0

(7)

The surface emissivity E(k i ) is given by Kirchhoff’s law to beE(k i ) = 1 − R(k i )(8)
It is important to note that equations (5) an (7) provide the link between passive microwave radiometry and active
microwave scatterometry. The scatterometer measures the radar backscatter coefficient, which is simply σ o,c(k i ,k i ).
The upper boundary condition for cold space isT B ↓ (k s , S ) = TC
(9)This simply states that the radiation coming from cold space is isotropic and has a magnitude of TC = 2.7 K.
The differential equation (4) is readily solved by integrating and applying the two boundary conditions (5)and (9). The result for the upwelling brightness temperature at the top of the atmosphere (i.e., the value observedby Earth-orbiting satellites) is
TB ↑ (k i , S ) = TBU + τ[ETS + TBΩ ](10)
where TBU is the contribution of the upwelling atmospheric emission, τ is the total transmittance from the surface
to the top of the atmosphere, E is the Earth surface emissivity given by (8), and TBΩ is the surface scattering integral in (5). The atmospheric terms can be expressed in terms of the transmittance function τ(s 1 ,s 2 ) s2τ(s1 , s 2 ) = exp  − ∫ ds α( s) 
 s

 1


(11)

which is the transmittance between points s1 and s2 along the propagation path k s or ki. The total transmittance τin (10) is given byτ = τ(0, S )(12)and the upwelling and downwelling atmosphere emissions are given byS

T BU = ∫ ds α( s ) T ( s ) τ( s , S )

(13a)

0
S

T BD = ∫ ds α( s ) T ( s ) τ (0, s )

(13b)

0

The sky radiation scattering integral is
π 22π
sec θi
TB Ω =sin θs dθs ∫ dϕs (TBD + τTC )[σo , c (k s , k i ) + σo ,× (k s , k i )]
4π ∫0
0

(14)

Thus, given the temperature TS and absorption coefficient α at all points in the atmosphere and given the surface bistatic cross sections, T B can be rigorously calculated. However, in practice, the 3-dimensional specificationof TS and α over the entire volume of the atmosphere is not feasible, and to simplify the problem, the assumptionof horizontal uniformity is made. That is to say, the absorption is assumed to only be a function of the altitude habove the Earth’s surface, i.e., α(s) = α(h). To change the integration variable from ds to dh, we note that for the
spherical Earth
∂s
1+δ
=
(15)
∂h
cos 2 θ + δ(2 + δ)
where θ is either θi or θs , δ = h/RE , and RE is the radius of the Earth. In the troposphere δ << 1, and an excellent
approximation for θ < 60° is,∂s= sec θ(16)∂hWith this approximation and the assumption of horizontal uniformity, the above equations reduce to the following
expressions.
h2τ(h1 , h2 ,θ ) = exp − sec θ ∫ dh α( h) 


h1


τ = τ(0, H ,θi )

(17)
(18)

H

T BU = secθi ∫ dh α( h) T ( h) τ (h, H ,θi )

(19a)

0

H

TBD = sec θ s ∫ dh α( h) T ( h) τ( 0, h,θs )

(19b)

0

Thus, the brightness temperature computation now only requires the vertical profiles of T(h) and α(h) along withthe surface cross sections. The following two sections discuss the atmospheric model for α(h) and the sea-surface
model for the cross sections, respectively. In closing, we note that the AMSR incidence angle is 55° and hence
approximation (16) is quite valid, with one exception. In the scattering integral, θs goes out to 90°, and in thiscase we use (15) to evaluate the integral.
2.3. Model for the Atmosphere
In the microwave spectrum below 100 GHz, atmospheric absorption is due to three components: oxygen, water vapor, and liquid water in the form of clouds and rain [Waters, 1976]. The sum of these three components
gives the total absorption coefficient (napers/cm).
α( h ) = α O ( h ) + α V ( h ) + α L ( h )(20)
Numerous investigators have studied the dependence of the oxygen and water vapor coefficients on frequency ν(GHz), temperature T (K), pressure P (mb), and water vapor density ρV (g/cm3 ) [Becker and Autler, 1946; Rozenkranz, 1975; Waters, 1976; Liebe, 1985]. To specify α O and α V as a function of (ν,T,P,ρV) we use the Liebe[1985] expressions with one modification. The self-broadening component of the water vapor continuum is reduced by a factor of 0.52 (see below). The liquid water coefficient αL comes directly from the Rayleigh approximation to Mie scattering and is a function of T and the liquid water density ρL (g/cm2 ) (see below). Figure 3
shows the total atmospheric absorption for each component. Results for three water vapor cases (10, 30, and 60mm) are shown. The cloud water content is 0.2 mm. This corresponds to a moderately heavy non-raining cloudlayer.
Let AI denote the vertically integrated absorption coefficient.
H

AI = ∫ dh αI ( h)

(21)

0

where h is the height (cm) above the Earth’s surface and subscript I equals O, V, or L. Equations (17) and (18)then give the total transmittance to beτ = exp [− secθi ( AO + AV + AL )](22)
Assuming for the moment that the atmospheric temperature is constant, i.e., T(h) = T, then the integrals in equations (19) can be exactly evaluated in closed form to yield

TBU = TBD = (1 − τ )T(23)
In reality, the atmospheric temperature does vary with h, typically decreasing at a lapse rate of about -5.5 C/km in
the lower to mid troposphere. In view of (23), we find it convenient to parameterize the atmospheric model interms of the following upwelling and downwelling effective air temperatures:
T U = TB U / (1 − τ )(24a)
T D = TBD / (1 − τ )(24b)These effective temperatures are indicative of the air temperature averaged over the lower to mid troposphere.
Note that in the absence of significant rain, TU and TD are very similar in value, with TU being 1 to 2 K colder.
100.

Total Atmosphere Attenuation (naper)

10.

1.0

0.1

0.01

LegendOxygenWater Vapor, 10 mm
Water Vapor, 30 mm
Water Vapor, 60 mm
Cloud, 0.20 mm

0.001

0.0001

0

10

20

30

40

50

60

70

80

90

100

Frequency (GHz)
Fig. 3. The atmospheric absorption spectrum for oxygen, water vapor, and cloud water. Results for three water vapor cases (10,30, and 60 mm) are shown. The cloud water content is 0.2 mm which corresponds to a moderately heavy non-raining cloud layer.

In view of the above equations, one sees that the atmospheric model can be parameterized in terms of the following 5 parameters:
1. Upwelling effective temperature TU
2. Downwelling effective temperature TD
3. Vertically integrated oxygen absorption AO
4. Vertically integrated water vapor absorption AV
5. Vertically integrated liquid water absorption AL
To study the properties of the first four parameters, we use a large set of 42,195 radiosonde flights launched fromsmall islands [Wentz, 1997]. These radiosonde reports provide air temperature T(h), air pressure p(h), and watervapor density ρV(h) at a number of levels in the troposphere. From these data, the coefficients α O and α V are
computed from the Liebe [1985] expressions, except that the water vapor continuum term is modified as discussed
in the next paragraph. Performing the numerical integrations as indicated above, TU , TD, AO , and AV are found foreach radiosonde flight. In addition, the vertically integrated water vapor V is also computed.
H

V = 10 ∫ dh ρV ( h)

(25)

0

where ρV(h) is in units of g/cm3 , and the leading factor of 10 converts from g/cm2 to mm.
Wentz [1997] computed AV directly from collocated SSM/I and radiosonde observations. At 19, 22, and 37
GHz, the Liebe AV was found to be 4%, 3%, and 20% higher than the SSM/I-derived value, respectively. To
quote Liebe [1985]: ‘Water vapor continuum absorption has been a major source of uncertainty in predicting millimeter wave attenuation rates, especially in the window ranges.’ The frequency of 37 GHz is in a water vapor
window and is most affected by the continuum. It should be noted that Liebe also needed to rely on combined
radiometer-radiosonde measurements to infer the continuum in the 6 to 37 GHz region. Liebe’s data set in thisspectral region is rather limited and does not contain any 37 GHz observations. We believe the SSM/I method ofderiving AV is more accurate than Liebe’s method, and hence adjust the Liebe [1985] water vapor spectrum so that
it will agree with the SSM/I results. We find that very good agreement is obtained by reducing the selfbroadening component of the water vapor continuum by a factor of 0.52. After this adjustment, the agreement at
all three frequencies is within ± 1%.
Figure 4 shows the T D values computed from the 42,195 radiosondes plotted versus V. Three frequencies areshown (19, 22, and 37 GHz), and the curves are quite similar. The solid lines in the figure show equation (26),and vertical bars show the ± one standard deviation of TD derived from the radiosondes. For low to moderate values of V (0 to 40 mm), TD increases with V, and above 40 mm, TD reaches a relatively constant value of 287 K.
The TU versus V curves (not shown) are very similar except that TU is 1 to 2 K colder. The following least-square
regressions are found to be a good approximation of the TD , T U versus V relationship:(26a)
T U = TD + b 6 + b 7 V
(26b)
where
T V = 273 .16 + 0. 8337 V − 3. 029 × 10 −5 V 3 . 3 3
V ≤ 48(27a)
T V = 301.16
V > 48(27b)andς(TS − TV ) = 1.05 ⋅ TS − TV ⋅ 1 −(TS − TV ) 2

1200
ς (TS − TV ) = sign(TS − TV ) ⋅ 14K| TS − TV | ≤ 20K(27c)| TS − TV | > 20K(27d)

V is in units of millimeters and all temperatures are in units of Kelvin. When evaluating (26a), the expression islinearly extrapolated when V is greater than 58 mm. We have included a small additional term that is a functionof the difference between the sea-surface temperature TS and TV, which represents the sea-surface temperaturethat is typical for water vapor V. The term ς ( TS − TV ) accounts for the fact that the effective air temperature istypically higher (lower) for the case of unusually warm (cold) water. The TV versus V relationship was obtainedby regressing the climatology sea-surface temperature at the radiosonde site to V derived from the radiosondes.
Over the full range of V, the rms error in approximation (26) is typically about 3 K. Table 4 gives the b0 throughb7 coefficients for all 8 AMSR frequencies.
The vertically integrated oxygen absorption AO is nearly constant over the globe, with a small dependence on the
air temperature. We find the following expression to be a very good approximation for AO :AO = aO 1 + aO 2 (TD − 270 )(28)
Table 4 gives the aO coefficients for the 8 AMSR frequencies, and Table 5 gives the rms error in this approximation for the 8 frequencies. At 23.8 GHz and below, the error is negligible, being 0.0003 napers or less. At 36.5
GHz, the error is still quite small, being 0.0008 napers. Note that 0.001 napers roughly corresponds to a T B errorof 0.5 K. For the 50.3 and 52.8 GHz oxygen band channels, the error is considerably larger, but (28) is not used
for the oxygen band channels. Rather the oxygen band channels can be used to retrieve TD .

Table 4. Model Coefficients for the Atmosphere
Freq. (GHz)

6.93E+010.65E+0

18.70E+023.80E+036.50E+050.30E+052.80E+0

89.00E+0b0 (K)

239.50E+0239.51E+0240.24E+0241.69E+0239.45E+0242.10E+0245.87E+0

242.58E+0

b1 (K mm −1 )b2 (K mm−2 )213.92E−2−460.60E−4

225.19E−2−446.86E−4

298.88E−2−725.93E−4

310.32E−2−814.29E−4

254.41E−2−512.84E−4

229.17E−2−508.05E−4

250.61E−2−627.89E−4

302.33E−2−749.76E−4

b3 (K mm−3 )457.11E−6

391.82E−6

814.50E−6

998.93E−6

452.02E−6

536.90E−6

759.62E−6

880.66E−6

b4 (K mm−4 )−16.84E−7−12.20E−7−36.07E−7−48.37E−7−14.36E−7−22.07E−7−36.06E−7−40.88E−7

b5

0.50E+0

0.54E+0

0.61E+0

0.20E+0

0.58E+0

0.52E+00.53E+0

0.62E+0

b6 (K)−0.11E+0−0.12E+0−0.16E+0−0.20E+0−0.57E+0−4.59E+0−12.52E+0−0.57E+0

b7 (K mm−1 )−0.21E−2−0.34E−2−1.69E−2−5.21E−2−2.38E−2−8.78E−2−23.26E−2−8.07E−2

aO1

8.34E−3

9.08E−3

12.15E−3

15.75E−3

40.06E−3

353.72E−3

1131.76E−3

53.35E−3

aO2 (K )−0.48E−4−0.47E−4−0.61E−4−0.87E−4−2.00E−4−13.79E−4−2.26E−4−1.18E−4

aV1 (mm −1 )0.07E−3

0.18E−3

1.73E−3

5.14E−3

1.88E−3

2.91E−3

3.17E−3

8.78E−3

0.00E−5

0.00E−5−0.05E−5

0.19E−5

0.09E−5

0.24E−5

0.27E−5

0.80E−5−1−2

aV2 (mm )Table 5. RMS Error in Oxygen and Water Vapor Absorption Approximation
Freq. (GHz)

6.93

10.65

18.70

23.80

36.50

50.30

52.80

89.00

Oxygen, AO

0.00020.00020.00030.00030.00080.00620.01630.0009Vapor, AV

0.00010.00020.00110.00130.00250.00420.00460.0129

290
280
270
260
250

19 GHz

240

290

e

280
270

v

260
22 GHz

240

e

290

f

280

f

270

E

c

t

i

250

260
250

37 GHz

240
0

10

20

30

40

50

60

70

Columnar Water Vapor (mm)Fig. 4. The effective air temperature T D for downwelling radiation plotted versus the RAOB columnar water vapor. The solid
curve is the model value, and the vertical bars are the ± one standard deviation of T D derived from radiosondes.

The vapor absorption AV is primarily a linear function of V, although there is a small second order term. We
find the following expression is a good approximation for AV:
AV = aV1 V + aV2 V2(29)
Table 4 gives the aV coefficients for the 8 AMSR frequencies, and Table 5 gives the rms error in this approximation for the 8 frequencies. For the 6.9 and 10.7 AMSR channels, the rms error in this approximation is negligible,
being 0.0002 napers or less. In the 18.7 to 36.5 range, the error remains relatively small (0.001 to 0.0025 napers),
but not negligible.
The final atmospheric parameter to be specified is the vertically integrated liquid water absorption AL . Whenthe liquid water drop radius is small relative to the radiation wavelength, the absorption coefficient α L (cm−1 ) is
given by the Rayleigh scattering approximation [Goldstein, 1951]:

αL =6πρL (h )  1 − ε 
Im 

λρo
2 + ε(30)

where λ is the radiation wavelength (cm), ρL(h) is the density (g/cm3) of cloud water in the atmosphere given as afunction of h, ρo is the density of water (ρo ≈ 1 g/cm3), and ε is the complex dielectric constant of water. Notethat the dielectric constant varies with temperature and hence is also a function of h. Substituting (30) into (21)
gives

AL =

0.6πL  1 − ε Im λ2 + ε(31)

where L is the vertically integrated liquid water (mm) given byH

L = 10 ∫ dh ρL (h )

(32)

0

The leading factor of 10 converts from g/cm2 to mm. In deriving (31), we have assumed the cloud is at a constanttemperature. For the more realistic case of the temperature varying with height, ε should be evaluated at somemean effective temperature for the cloud. The specification of ε as a function of temperature and frequency isgiven in Section 2.4. An excellent approximation for (31) is found to be
A L = a L 1 1 − a L 2 ( T L − 283 ) L(33)
where TL is the mean temperature of the cloud, and the aL coefficients are given in Table 6 for the 8 AMSR frequencies. The error in this approximation is ≤ 1% over the range of TL from 273 to 288 K, which is negligible
compared to other errors such as the uncertainty in specifying the cloud temperature TL . Note that in the retrieval
algorithm, the error in specifying TL only effects the retrieved value of L. The retrieval of the other parameters
only requires the spectral ratio of AL , which is essentially independent of TL due to the fact that aL2 is spectrallyflat.
In the absence of rain, the cloud droplets are much smaller than the radiation wavelengths being considered,and equations (31) and (33) are valid. When rain is present, Mie scattering theory must be used to compute AL .
For light rain not exceeding 2 mm/h and for frequencies between 6 and 37 GHz, the Mie scattering computations
give the following approximation [Wentz and Spencer, 1998]:

Freq
(GHz)
aL1
aL2
aL3
aL4
aL5

Table 6. Coefficients for Rayleigh Absorption and Mie Scattering.
6.93
10.65
18.70
23.80
36.50
50.30
52.80
0.00780.03030.00070.00001.22160.01830.02980.00270.00601.17950.05560.02880.01130.00401.06360.08910.02810.01880.00201.02200.20270.0261
0.0425-0.00200.9546

0.36820.0236
0.0731-0.00200.89830.40210.02310.0786-0.00200.894389.00
0.96930.01460.1506-0.0020
0.7961A R = a L3 ⋅ 1 + a L4 ⋅ ( TL − 283) ⋅ H ⋅ Ra L5(34a)

The rain column height H (in km) can be approximated by:

H = 1+ 0.14 ⋅ (TS − 273) − 0.0025 ⋅ (TS − 273)2
H = 2.96

if
if

TS < 301
TS ≥ 301,

(34b)
(34c)

where TS denotes the sea surface temperature (in K). The rain rate R (in mm/h) is related to the liquid cloud water
density L by

L = 0.18 ⋅ 1 + HR .
In deriving (34a) we have used a Marshall and Palmer [1948] drop size distribution.

(34d)

2.4. Dielectric Constant of Sea-Water and the Specular Sea Surface
A key component of the sea-surface model is the dielectric constant ε of sea water. The parameter is a complex number that depends on frequency ν, water temperature TS, and water salinity s. The dielectric constant isgiven by [Debye,1929; Cole and Cole, 1941] asεS − ε∞2 j σλε = ε∞ +
−
(35)
1− η
c
1 + jλ R λwhere j = −1 , λ (cm) is the radiation wavelength, ε∞ is the dielectric constant at infinite frequency, εS is thedielectric constant for zero frequency (i.e., the static dielectric constant), and λR (cm) is the relaxation wavelength.
The spread factor η is an empirical parameter that describes the distribution of relaxation wavelengths. The lastterm accounts for the conductivity of salt water. In this term, σ (sec −1, Gaussian units) is the ionic conductivity
and c is the speed of light.
Several investigators have developed models for the dielectric constant of sea water. In the Stogryn [1971]
model the salinity dependence of εS and λR was based on the Lane and Saxton [1952] laboratory measurements ofsaline solutions. Stogryn noted that the Lane- Saxton measurements for distilled water did not agree with those ofother investigators. The Klein and Swift [1977] model is very similar to Stogryn model except that the salinity
dependence of εS was based on more recent 1.4 GHz measurements [Ho and Hall, 1973; Ho et al., 1974]. KleinSwift noted that their εS was significantly different from that derived from the Lane and Saxton measurements. It
appears that there may be a problem with Lane-Saxton measurements. However, in the Klein-Swift model, thesalinity dependence of λR was still based on the Lane-Saxton measurements. We analyzed all the measurements
used by Stogryn and Klein-Swift and concluded that the Lane-Saxton measurements of ε for both distilled waterand salt water were inconsistent with the results reported by all other investigators. Therefore, we completely exclude the Lane-Saxton measurements from our model derivation.
The model to be presented is very similar to the Klein-Swift model, with two exceptions. First, since we excluded Lane-Saxton measurements, the salinity dependence of λR is different. For cold water (0 to 10 C), our λR
is about 5% lower than the Klein-Swift value and for warm water (30 C), it is about 1% higher. Second, our valuefor ε∞ is 4.44 and the Klein-Swift value is 4.9, which was the value used by Stogryn. In the Stogryn model, η = 0,
whereas in the Klein-Swift model, η = 0.02. Grant et al. [1957] pointed out that the choice of ε∞ depends on the
choice for η, where η = 0 → ε∞ = 4.9 and η = 0.02 → ε∞ = 4.5. Thus the Klein-Swift value of ε∞ = 4.9 is probably
too high. In terms of brightness temperatures, these λR and ε∞ differences are most significant at the higher frequencies. For example, at 37 GHz and θi = 55°, the difference in specular brightness temperatures produced byour model and the Klein-Swift model differ by about ± 2 K. Analyses of SSM/I observations show that our newmodel, as compared to the Klein-Swift model, produces more consistent retrievals of ocean parameters. For example, using the Klein-Swift model resulted in an abundance of negative cloud water retrievals in cold water.
This problem no longer occurs with the new model. (The negative cloud water problem was the original motivation for doing this reanalysis of the ε model.)We first describe the die lectric constant model for distilled water, and then extend the model to the more general case of a saline solution. The static dielectric constant εS0 for distilled water has been measured by many investigators. The more recent measurements [Malmberg and Maryott, 1956; Archer and Wang, 1990] are in very
good agreement (0.2%). The Archer and Wang [1990] values for εS0, which are reported in the Handbook ofChemistry and Physics [Lide,1993], are regressed to the following expression:ε S 0 = 87. 90 exp( −0. 004585 t S )(36)
where tS is the water temperature in Celsius units. The accuracy of the regression relative to the point values for
εS0 is 0.01% over the range from 0 to 40 C.
The other three parameters for the dielectric constant of distilled water are the relaxation wavelength λR0 , thespread factor η, and ε∞. We determine these parameters by a least-squares fit of (35) to laboratory measurements
εmea of the dielectric constant for the range from 1 to 40 GHz. A literature search yielded ten papers reporting εmea
for distilled water. Values for λR0 , η, and ε∞ are found so as to minimize the following quantity:
Q = Re( ε − ε m e a )2+ I m (ε − ε m e a )

2

(37)

The relaxation wavelength is a function of temperature [Grant et al., 1957], but it is generally assumed that η andε∞ are independent of temperature. The least squares fit yields η = 0.012, ε∞= 4.44, andλ R 0 = 3.30 exp( −0. 0346 t S + 0 .00017 t 2S )(38)
These values are in good agreement with those obtained by other investigators. Our λR0 agrees with the expression derived by Stogryn [1971] to within 1%. The values for η (ε∞) reported in the literature vary from 0 to 0.02
(4 to 5). Note that using a larger value for η necessitates using a smaller value for ε∞.
The presence of salt in the water produces ionic conductivity σ and modifies εS and λR. It is generally assumed that η and ε∞ are not affected by salinity. Weyl [1964] found the following regression for the conductivityof sea water.
σ = 3.39 × 109 C 0 .892 exp (− ∆ t ζ )
(39)

(

)

ζ = 2.03× 10−2 + 1.27 × 10−4 ∆t + 2.46 ×10 −6 ∆2t − C 3.34 × 10−5 − 4.60 × 10−7 ∆t + 4.60 × 10−8 ∆2t (40)C = 0 .5536 s(41)∆ t = 25 − t S(42)
where s and C are salinity and chlorinity in units of parts/thousand. Note that we have converted the Weyl conductivity to Gaussian units of sec −1 .
To determine the effect of salinity on εS, we use low frequency (1.43 and 2.65 GHz) measurements of ε forsea water and saline solutions [Ho and Hall, 1973; Ho et al., 1974]. For the Ho-Hall data, only the real part of thedielectric constant is used in the fit. Klein and Swift reported that the measurements of the imaginary part were inerror. To determine the effect of salinity on λR, we use higher frequency (3 to 24 GHz) measurements of ε for
saline solutions [Haggis et al., 1952; Hasted and Sabeh, 1953; Hasted and Roderick, 1958]. A least-squares fit tothese data shows that the salinity dependence of εS and λR can be modeled as(

εS = εS 0 exp − 3.45 × 10 −3 s + 4.69 × 10 −6 s 2 + 1.36 × 10 −5 st S()

λR = λR 0 − 6.54 × 10 −3 1 − 3.06 ×10 −2 t S + 2.0 × 10 −4 t S2 s

)

(43)
(44)

The accuracy of the dielectric constant model is characterized in terms of its corresponding specular brightness temperature TB. For each laboratory measurement of ε, we compute the specular TB for an incidence angle of
55° using the Fresnel equation (45) below. Two T B’s are computed: one using εmea and the other using the model
ε coming from the above equations. For the low frequency Ho-Hall data, the rms difference between the ‘measurement’ TB and the ‘model’ TB is about 0.1 K for v-pol and 0.2 K for h-pol. For the higher frequency data set,
the rms difference is 0.8 K for v-pol and 0.5 K for h-pol.
Once the dielectric constant is known, the v-pol and h-pol reflectivity coefficients ρV and ρH for a specular(i.e., perfectly flat) sea surface are calculated from the well-known Fresnel equations

ρv =
ρh =

ε cos θ i − ε − sin 2 θ iε cos θ i + ε − sin 2 θ icos θ i − ε − sin 2 θ icos θ i + ε − sin 2 θ iwhere θI is the incidence angle. The power reflectivity R is then given by
R 0 p = ρp

(45a)

(45b)

2

(46)

where subscript 0 denotes that this is the specular reflectivity and subscript p denotes polarization.
An analysis using TMI data indicates small deviations from the model function for the dielectric constant of sea
water as discussed above. The effect is mainly noted in the v-pol reflectivity. In order to account for these small
differences a correction term of∆R 0 V = 4.887 ⋅ 10 −8 − 6.108 ⋅ 10 −8 ⋅ TS − 273 3
is added to the v-pol reflectivity R 0v in (46). The resulting changes in the brightness temperature range fromabout +0.14K in cold water to about –0.36K in warm water.
2.5. The Wind-Roughened Sea Surface
It is well known that the microwave emission from the ocean depends on surface roughness. A calm sea surface is characterized by a highly polarized emission. When the surface becomes rough, the emission increases

and becomes less polarized (except at incidence angles above 55º for which the vertically polarized emission decreases). There are three mechanisms that are responsible for this variation in the emissivity. First, surface waves
with wavelengths that are long compared to the radiation wavelength mix the horizontal and vertical polarization
states and change the local incidence angle. This phenomenon can be modeled as a collection of tilted facets,
each acting as an independent specular surface [Stogryn, 1967]. The second mechanism is sea foam. This mixture of air and water increases the emissivity for both polarizations. Sea foam models have been developed by
Stogryn [1972] and Smith [1988]. The third roughness effect is the diffraction of microwaves by surface waves
that are small compared to the radiation wavelength. Rice [1951] provided the basic formulation for computing
the scattering from a slightly rough surface. Wu and Fung [1972] and Wentz [1975] applied this scattering formulation to the problem of computing the emissivity of a wind-roughened sea surface.
These three effects can be parameterized in terms of the rms slope of the large-scale roughness, the fractionalfoam coverage, and the rms height of the small-scale waves. Each of these parameters depends on wind speed.
Cox and Munk [1954], Monahan and O'Muircheartaigh [1980], and Mitsuyasu and Honda [1982] derived windspeed relationships for the three parameters, respectively. These wind speed relationships in conjunction with thetilt+foam+diffraction model provide the means to compute the sea-surface emissivity. Computations of this typehave been done by Wentz [1975, 1983] and are in general agreement with microwave observations.
In addition to depending on wind speed, the large-scale rms slope and the small-scale rms height depend on
wind direction. The probability density function of the sea-surface slope is skewed in the alongwind axis and has
a larger alongwind variance than crosswind variance [Cox and Munk , 1954]. The rms height of capillary waves isvery anisotropic [Mitsuyasu and Honda, 1982]. The capillary waves traveling in the alongwind direction have agreater amplitude than those traveling in the crosswind direction. Another type of directional dependence occurs
because the foam and capillary waves are not uniformly distributed over the underlying structure of large-scale
waves. Smith's [1988] aircraft radiometer measurements show that the forward plunging side of a breaking wave
exhibits distinctly warmer microwave emissions than does the back side. In addition, the capillary waves tend tocluster on the downwind side of the larger gravity waves [Cox, 1958; Keller and Wright, 1975]. The dependenceof foam and capillary waves on the underlying structure produces an upwind-downwind asymmetry in the seasurface emissivity.
The anisotropy of capillary waves is responsible for the observed dependence of radar backscattering on winddirection [Jones et al., 1977]. The upwind radar return is considerably higher than the crosswind return. Also, themodulation of the capillary waves by the underlying gravity waves causes the upwind return to be generally
higher than the downwind return. These directional characteristics of the radar return have provided the means tosense wind direction from aircraft and satellite scatterometers [Jones et al., 1979].
To model the rough sea surface, we begin by assuming the surface can be partitioned into foam-free areas andfoam-covered areas within the radiometer footprint. The fraction of the total area that is covered by foam is denoted by f. The composite reflectivity is then given by
R = ( 1 − f ) R c l e a r + f κR c l e a r(47)
where Rclear is the reflectivity of the rough sea surface clear of foam, and the factor κ accounts for the way inwhich foam modifies the reflectivity. As discussed above, foam tends to decrease the reflectivity, and hence κ < 1.
The reflectivity of the clear, rough sea surface is modeled by the following equation:
R c l e a r = (1 − β) R g e o(48)
where Rgeo is the reflectivity given by the standard geometric optics model (see below) and the factor 1 − β accounts for the way in which diffraction modifies the geometric-optics reflectivity. Wentz [1975] showed that theinclusion of diffraction effects is a relatively small effect and hence β small compared to unity.
Combining the above two equations gives
R = (1 − F )R g e o(49)
F = f + β − fβ − f κ + fκβ(50)where F is a ‘catch-all’ term that accounts for both foam and diffraction effects. All of the terms that makeup F
are small compared to unity, and the results to be presented show that F < 10%. The reason we lump foam anddiffraction effects together is that they both are difficult to model theoretically. Hence, rather than trying to compute F theoretically, we let F be a model parameter that is derived empirically from various radiometer experiments. However, the Rgeo term is theoretically computed from the geometric optics. Thus, the F term is a measure of that portion of the wind-induced reflectivity that is not explained by the geometric optics.
The geometric optics model assumes the surface is represented by a collection of tilted facets, each acting as
an independent reflector. The distribution of facets is statistically characterized in terms of the probability density
function P(Su ,Sc) for the slope of the facets, where Su and Sc are the upwind and crosswind slopes respectively.

Given this model, the reflectivity can be computed from equation (7). To do this, the integration variables θs ,φs in(7) are transformed to the surface slope variables. The two equations governing this transformation are
k s = k i − 2(k i ⋅ n )n(51)

− S u , − Sc , 1

n =

(52)
1 + S 2u + S 2cwhere n is the unit normal vector for a given facet. Transforming (7) to the Su ,Sc integration variables yields

Rgeo∫ dS ∫ dS P(S , S ) 1 + S + S (k ⋅ n) (p ⋅ h )ρ h + (p ⋅ v )ρ v [χ(k )(1 − R ) + R ] (53)=∫ dS ∫ dS P(S , S ) 1 + S + S (k ⋅ n)
u

c

u

c

2
u

2

2
c

u

i

c

i

u

h

s

i

2
u

c

2
c

v

s

s

×

×

i

where p is the unit vector specifying the reflectivity polarization. The unit vectors hi and vi (hs and vs ) are thehorizontal and vertical polarization vectors associated with the propagation vector k i (k s) as measured in the tilted
facet reference frame. These polarization vectors in the tilted frame of reference are given by
hj =

kj ×n

(54a)

kj ×n

vj = kj ×hj(54b)

where subscript j = i or s. The terms ρv and ρh are the v-pol and h-pol Fresnel reflection coefficients given above.
The last factor in (53) accounts for multiple reflection (i.e., radiation reflecting off of one facet and then intersec ting another). χ(ks ) is the shadowing function given by Wentz [1975], and R× is the reflectivity of the secondaryintersection. The shadowing function χ(ks ) essentially equals unity except when ks approaches surface grazing
angles.
The interpretation of (53) is straightforward. The integration is over the ensemble of tilted facets having aslope probability of P(Su,Sc). The term 1 + S u2 + S c2 (k i ⋅ n ) is proportional to the solid angle subtended by
the tilted facet as seen from the observation direction specified by ki . The term (p ⋅ h i ) ρ h h s + (p ⋅ v i )ρ v v s is2

the reflectivity of the tilted facet. And, the denominator in (53) properly normalizes the integral.
To specify the slope probability we use a Gaussian distribution as suggested by Cox and Munk [1954], and weassume that the upwind and crosswind slope variances are the same. Wind direction effects are considered in Section 2.7. Then, the slope probability is given by(

P( S u , S c ) = π∆S 2) exp  − S − S 
2
u

−1



∆S 2

2
c



(55)

where ∆S2 is the total slope variance defined as the sum of the upwind and crosswind slope variances. Ocean
waves with wavelengths shorter than the radiation wavelength do not contribute to the tilting of facets and hence
should not be included in the ensemble specified by P(Su ,Sc). For this reason, the effective slope variance ∆S2increases with frequency, reaching a maximum value referred to as the optical limit. The results of Wilheit andChang [1980] and Wentz [1983] indicate that the optical limit is reached near ν = 37 GHz. Hence, for ν ≥ 37 GHz,
we use the Cox and Munk [1954] expression for optical slope variance. For lower frequencies, a reduction factor
is applied to the Cox and Munk expression. This reduction factor is based on ∆S2 values derived from the SeaSat
SMMR observations [Wentz, 1983].
∆S 2 = 5 .22 × 10 −3 Wν ≥ 37 GHz
(56a)
2
−3
1 .3
∆S = 5 .22 × 10 1 − 0 . 00748( 37 − ν ) W
ν < 37 GHz(56b)where W is the wind speed (m/s) measured 10 m above the surface. Note the Cox and Munk wind speed wasmeasured at a 12.5 m elevation. Hence, their coefficient of 5.12×10−3 is increased by 2% to account for our wind
being referenced to a 10 m elevation.
The sea-surface reflectivity Rgeo is computed for a range of winds varying from 0 to 20 m/s, for a range ofsea-surface temperatures varying from 273 to 303 K, and for a range of incidence angles varying from 49° to 57°.
These computations require the numerical evaluation of the integral in equation (53). The integration is done over
the range S2u + S 2c ≤ 4 . 5 ∆S 2 . Facets with slopes exceeding this range contribute little to the integral, and it is notclear if a Gaussian slope distribution is even applicable for such large slopes. Analysis shows that the computed
ensemble of Rgeo is well approximated by the following regression:

R geo = R 0 − [r0 + r1 θ i − 53 + r2 TS − 288 + r3 θ i − 53TS − 288]W(57)

where the first term R0 is the specular power reflectivity given by (46) and the second term is the wind-induced
component of the sea-surface reflectivity. The r coefficients are given in Table 7 for all AMSR channels. Equation(57) is valid over the incidence angle from 49° to 57°. It approximates the θi and TS variation of Rgeo with anequivalent accuracy of 0.1 K. The approximation error in the wind dependence is larger. In the geometric optics
computations, the variation of Rgeo with wind is not exactly linear. In terms of TB, the non-linear component of
Rgeo is about 0.1 K at the lower frequencies and 0.5 K at the higher frequencies. However, in view of the general
uncertainty in the geometric optics model, we will use the simple linear expression for Rgeo, and let the empirical
F term account for any residual non-linear wind variations, as is discussed in the next paragraph.
In the case of the coefficients r2 we do not use the geometric optics model coefficients (Table 7) but rather use thefollowing empirically derived forms (units are s/m-K):
r 2 V− pol = −2.1 ⋅ 10 −5(58)

r 2 h −pol = −5.5 ⋅ 10 −5 + 0.989 ⋅ 10 −6 ⋅ 37 − vifν ≤ 37(59a)r 2 h −pol = −5.5 ⋅ 10 −5

ifν > 37 .

(59b)This accounts for the observations that the wind induced emissivity is less in warm water. This effect was observed during the monsoons in the Arabian sea.

Freq. (GHz)v-pol r0h-pol r0v-pol r1

Table 7. Model Coefficients for Geometric Optics
10.65E+0
18.70E+023.80E+036.50E+050.30E+052.80E+0

89.00E+0−0.27E−03
0.54E−03−0.32E−03
0.72E−03−0.49E−03 −0.63E−03
1.13E−03
1.39E−03−1.01E−03
1.91E−03−1.20E−03
1.97E−03−1.23E−03
1.97E−03−1.53E−03
2.02E−03−0.21E−04−0.29E−04
0.44E−04−0.53E−04 −0.70E−04
0.70E−04
0.85E−04−1.05E−04
1.12E−04−1.12E−04
1.18E−04−1.13E−04
1.19E−04−1.16E−04
1.30E−04

0.75E−05

1.27E−05

1.39E−05

1.40E−05

1.15E−05−0.15E−05 −0.23E−05
0.31E−06
0.41E−06−0.36E−05
0.45E−06−0.32E−05
0.35E−06−0.30E−05
0.32E−06

6.93E+0h-pol r1
0.32E−04v-pol r2

0.11E−05

0.48E−05

0.01E−05h-pol r2
0.00E−05v-pol r3
0.00E−06h-pol r3

−0.03E−05
0.08E−06

0.00E−05−0.09E−06

0.00E−06 −0.02E−06 −0.12E−06 −0.20E−06 −0.36E−06 −0.43E−06 −0.44E−06 −0.46E−06
r0 in units of s/m, r1 in units of s/m-deg, r2 in units of s/m-K, r3 in units of s/m-deg-K

In the 10-37 GHz band, the F term is found from collocated SSM/I-buoy and TMI-buoy observations. The
procedure for finding F is essentially the same as described by Wentz [1997] for finding the wind-induced emissivity, but in this case we first remove the geometric optics contribution to R. The F term is found to be a monotonic function of wind speed described by
F = m1W
W < W1(60a)
F = m 1 W + 12 ( m 2 − m 1 )( W − W 1 ) 2 ( W 2 − W1 )W1 ≤ W ≤ W2
(60b)
F = m 2 W − 12 ( m 2 − m 1 )( W 2 + W1 )W > W2(60c)
This equation represents two linear segments connected by a quadratic spline such that the function and its first
derivative are continuous. The spline points are W1 = 3 m s and W2 = 12 m s for the v-pol and W1 = 7 m s
and W2 = 12 m s for the h-pol , respectively. The m coefficients are found so that the TB model matches the
SSM/I observations in the and TMI observations when the buoy wind is used to specify W. For the lowest channel ν = 6.9 GHz no data exist yet and we have simply used the same values as for the ν = 10.65 GHz channel.
This will be updated as soon as AMSR data become available. Table 8 summarizes the results for m 1 and m 2 at
the 8 AMSR frequencies for v and h polarizations. Both coefficients flatten out and reach a maximum forν ≥ 37 GHz.

Table 8. The coefficients m1 and m2 . Units are s/m.
Freq. (GHz) 6.93
10.65
18.70
23.80
v-pol m1
0.00020 0.00020 0.00140 0.00178
h-pol m1
0.00200 0.00200 0.00293 0.00308
v-pol m2
0.00690 0.00690 0.00736 0.00730
h-pol m2
0.00600 0.00600 0.00656 0.00660

36.50
0.00257
0.003290.00701
0.0066050.30
0.00260
0.00330
0.00700
0.00660

52.80
0.00260
0.00330
0.00700
0.00660

89.00
0.00260
0.00330
0.00700
0.00660

These results indicate that diffraction plays a significant role in modifying the sea-surface reflectivity. If diffraction
were not important, β would be 0 in equation (50), and F would be proportional to the fractional foam coverage f.
Since f is essentially zero for W < 7 m/s, m1 would be 0. This is not the case, and we interpret the m1 coefficient as anindicator of diffraction.
2.6. Atmospheric Radiation Scattered by the Sea Surface
The downwelling atmospheric radiation incident on the rough sea surface is scattered in all directions. The
scattering process is governed by the radar cross section coefficients σ o as indicated by equation (14). For a perfectly flat sea surface, the scattering process reduces to simple specular reflection, for which radiation comingfrom the zenith angle θs is reflected into zenith angle θi , where θs = θi. In this case, the reflected sky radiation is
simply RT BD . However, for a rough sea surface, the tilted surface facets reflect radiation for other parts of the sky
into the direction of zenith angle θi . Because the downwelling radiation TBD increases as the secant of the zenith
angle, the total radiation scattered from the sea surface is greater than that given by simple specular reflection.
The sea-surface reflectivity model discussed in the previous section is used to compute the scattered sky radiation
TBΩ . These computations show that TBΩ can be approximated byT B Ω = [(1 + Ω)(1 − τ )( T D − T C ) + TC ] R(61)
where R is the sea-surface reflectivity given by (49), TBD is the downwelling brightness temperature from zenith
angle θi given by (24), and Ω is the fit parameter. The second term in the brackets is the isotropic component of
the cold space radiation. This constant factor can be removed from the integral. The fit parameter for v-pol andh-pol is found to beΩ V = [ 2 .5 + 0. 018 (37 − ν) ][ ∆S 2 − 70. 0 ∆S 6 ] τ3 . 4(62a)Ω H = [ 6 .2 − 0 .001( 37 − ν )2 ][ ∆S 2 − 70 . 0 ∆S 6 ] τ 2 .0

(62b)where ν is frequency (GHz) and ∆S2 is the effective slope variance given by (56). The term ∆S 2 − 70 . 0 ∆S 6
reaches a maximum at ∆S2 = 0.069. For ∆S2 > 0.069, the term is held at its maximum value of 0.046. Ω V has alinear dependence on frequency, whereas ΩH has a quadratic dependence, reaching a maximum value at ν = 37
GHz. For ν > 37 GHz, both Ω V and Ω H are held constant at their maximum values. Approximation (62) is valid
for the range of incidence angles from 52° to 56°. For moderately high winds (12 m/s) and a moist atmosphere(high vapor and/or heavy clouds), the scattering process increases the reflected 37 GHz radiation by about 1 K forv-pol and 5 K for h-pol. At 7 GHz, the increase is much less, being about 0.2 K for v-pol and 0.8 K for h-pol.
The accuracy of the above approximation as compared to the theoretical computation is about 0.03 K and 0.2 K at
7 and 37 GHz, respectively. Note that when the atmospheric absorption becomes very large (i.e., τ is small), Ω
tends to zero because the sky radiation for a completely opaque atmosphere is isotropic.

2.7. Wind Direction Effects
The anisotropy of the sea-surface roughness produces a variation of the brightness temperature versus winddirection, as discussed in Section 2.5. In the 19 to 37 GHz band, Wentz [1992] determined this wind direction
signal using collocated SSM/I TB’s and buoy wind vectors. At an incidence angle near 53°, the wind direction
signal exhibits the following second-order harmonic variation with wind direction:∆E 1 9 − 3 7 = γ 1 cos φ + γ 2 cos 2 φ(63)
where ∆E is the change in the sea-surface emissivity and φ is the wind-direction angle relative to the azimuth-lookangle. When φ = 0° (180°), the observation is upwind (downwind). The subscript 19-37 denotes that the results
are for the 19-37 GHz band. The amplitude coefficients γ1 and γ2 are found to be essentially the same for both 19
and 37 GHz. The coefficients are different for the two polarizations and do vary with wind speed as given below
γ 1 V = 7.83 × 10 −4 W − 2 .18 × 10 −5 W 2(64a)

γ 2 V = −4 .46 × 10 −4 W + 3.00 × 10 −5 W 2(64b)

γ 1 H = 1. 20 × 10 −3 W − 8. 57 × 10 −5 W 2γ 2 H = − 8. 93 × 10 −4 W + 3. 76 × 10 −5 W 2

(65a)

(65b)
In Wentz [1992], the wind direction signal was expressed in terms of a brightness temperature change rather thanan emissivity change, and the wind speed was referenced to a 19.5 m anemometer height. In the above equations,
we have converted the Wentz [1992] expressions from ∆T B to ∆E and use a 10 m reference height for W.
Little is known about the wind direction signal for frequencies below 19 GHz. Some very preliminary datafrom the Japanese AMSR aircraft simulations suggests that the signal decreases with decreasing frequency. Other
than this, there are no experimental data on the variation of TB versus φ at 6.9 and 10.7 GHz. As an educatedguess on what will be observed at these lower frequencies we reduce the wind direction signal from its value at 19
GHz by a factor of 0.82 at 10.7 GHz and by a factor of 0.62 at 6.9 GHz.
The result for the wind direction signal from (64) and (65) should be regarded as preliminary. Recent aircraft
data Yueh et al. [1999] as well as a first analysis of TMI measurements suggest that at wind speeds below 8 m/s
the wind direction signal is noticeably smaller than the one obtained from (64) and (65), especially for the h-pol.
A reanalysis of the directional signal using data from 5 SSM/I satellites between 1987 and 1999 as well as recent
TMI data is currently under way.
3. The Ocean Retrieval Algorithm
3.1 Introduction
In general, there are three types of ocean retrieval algorithms:
1. Multiple linear regression algorithms
2. Non-linear, iterative algorithms
3. Post-launch in-situ regression algorithms
The first two types are physical algorithms in the sense that radiative transfer theory is used in their derivation.
The third type is purely statistical with little or no consideration of the underlying physics. We now describe eachof these algorithms and discuss their strengths and weaknesses.
3.2 Multiple Linear Regression Algorithm
Consider a linear process in which a set of inputs denoted by the column vector X is transformed to a set of
outputs denoted by the column vector Y. The linear process is then characterized by the matrix A that relates Y toX.
Y = AX(66)
The measurement of Y usually contains some noise ε and is denoted by~
Y = Y + e = AX + e(67)
The retrieval problem is then to estimate X given Y . The most commonly used criteria for estimating X is to find~
X such that the variance between Y and Y is minimized. Using this criteria, one finds the well known leastsquares solution:~∃ = (A TΞ − 1 A)− 1 A T Ξ − 1YX
(68)
where Ξ is the correlation matrix for the error vector ε . If the errors are uncorrelated, then Ξ is diagonal.
~
For our application, the system input vector X is the set of geophysical parameters P and the output vector Y
is the set of TB measurements. Note that X and Y can be non-linear functions of P and TB, respectively without
violating the requirement for linearity between X and Y. For example, the relationship between TB and atmospheric parameters V and L can be approximated by
TB ≈ TE 1 − R exp[− 2 sec θi ( AO + aV V + a L L )]
(69)
~

{

}

where TE is an effective temperature of the ocean-atmosphere system which is relatively constant. Then,ln( TE − TB ) = ln( RT E ) − 2 sec θi ( AO + aV V + a L L )(70)
From this we see that the relationship between TB and V, L can be linearized by transforming from Y = T B to Y =ln(TE − T B). Wilheit and Chang [1980] followed this approach and used a value of 280 K for TE . As a further
extension, Y can also include higher order terms such as TB2 and TB37V T B23H.
Likewise, the input X can be a nonlinear transformation of the geophysical parameters P. For example, thewind speed dependence of TB (i.e., ∂T B/∂W) increases with wind speed, and the relationship can be made linear
by the following transformation

W′ = W
W < W1(71a)
W ′ = W + M 1 ( W − W1 ) 2
W1 ≤ W ≤ W2(71b)
W ′ = M 2W − M 3
W > W2(71c)
This transformation represents two linear segments connected by a quadratic spline such that the function and its
first derivative are continuous.
Thus the requirement of linearity is not as constraining as it might first appear, and a generalized linear statistical regression algorithm can be represented byI
Pj = ℜ c0 j + ∑ cij ℑ(TBi ) 
i =1



(72)

where ℑ and ℜ are linearizing functions. Subscript i denotes the AMSR channel (1 = 6.9V, 2 = 6.9H, etc.), andsubscript j denotes the parameter to be retrieved (1 = TS, 2 = W, 3 = V, 4 = L). For AMSR, our initial design forthe linear regression algorithm discussed in the next section uses the following linearizing functions:ℑ( TB ) = TB
ν = 6.9 and 10.7 GHz(73a)ℑ( TB ) = − ln( 290 − TB )
ν = 18.7, 23.8, and 36.5 GHz(73b)ℜ( X ) = X(74)
After testing the initial algorithm, we will experiment with additional linearizing functions, such as the wind speed
linearization given by (71).
In principle, the cij coefficients can be found from (68) given the A matrix and the error correlation matrix Ξ .
However, even after the linearizing functions are applied, the relationship of Y versus X is not strictly linear, andthe elements of A matrix are not constant, but rather vary with P. One could find a linear approximation for the Y
versus X relationship, and then derive the cij coefficients from (68). However, we prefer the more direct approachsuggested by Wilheit and Chang [1980] in whichbrightness temperatures are computed for an ensemEnvironmental Scenes
ble of environmental scenes and then multiple linear
42,195 Radiosondes
regression is used to derive the cij coefficients, as is
5 Cloud Models
discussed in the following section.
SST Randomly Varied for 0 to 30 C
Wind Speed Randomly Varied from 0 to 20 m/s
Wind Direction Randomly Varied from 0 to 360
3.3. Derivation and Testing of the Linear Regression Algorithm
The derivation of the c ij coefficients in the
Truth: Ts, W, V, L
AMSR linear regression algorithm is shown in Figure 5. A large ensemble of ocean-atmosphere
Complete Radiative Transfer Model
scenes are first assembled. The specification of theatmospheres comes from 42,195 quality-controlled
radiosonde flights launched
Simulated AMSR TB's
from small islands during the 1987 to 1990 time
period [Wentz, 1997]. One half of these radiosonde
Gaussian Noise Added
flights are used for deriving the cij coefficients, andWithheld Data Set
the other half is withheld for testing the algorithm.
A cloud layer of various columnar water densities
Derive Coefficients for Multiple
ranging from 0 to 0.3 mm is superimposed on the
Linear Regression Algorithm
radiosonde profiles.
Underneath these simulated
atmospheres, we place a rough ocean surface. The
Algorithm Coefficientssea-surface temperature TS is randomly varied from0 to 30 C, the wind speed W is randomly varied
from 0 to 20 m/s, and the wind direction φ is ranRun Algorithm
domly varied from 0 to 360°. About 400,000 scenes
are generated in this manner.
Retrieved values for Ts, W, V, L
In nature, there is a strong correlation between
T S and W. We could have incorporated this correlaEvalulate Algorithm Peformancetion into the ensemble of the scene. For example,
we could have discarded cases of very cold waterand very high water vapor, which never occur in
Performance and Cross Talk Statistics
nature. However, for now we include these unrealistic cases in order to determine if the algorithm is Fig. 5. Derivation and testing of the linear regression algorithm

truly capable of separating the T S signal from the V signal.
Atmospheric brightness temperatures T BU and TBD and transmittance τ are computed from the radiosonde +cloud profiles of T(h), p(h), ρV(h), and ρL(h) using equations (17), (18) and (19). The reflectivity R of the roughsea surface is computed according to the equations given in Section 2.5, and the atmospheric radiation scatteredfrom the sea surface T BΩ is computed from (61). Wind direction effects are included as described in Section 2.7.
Finally, the brightness temperature T B as seen by AMSR is found by combining the atmospheric and sea-surface
components, as is expressed by (10).
Noise is added to the simulated AMSR T B’s. This noise represents the measurement error in the AMSR T B’s.
The measurement error depends on the spatial resolution. At a 60-km resolution, which is commensurate with the
6.9 GHz footprint, the measurement error is 0.1 K. A random number generator is used to produce Gaussian
noise having a standard deviation of 0.1 K. This noise is added to the simulated T B’s. At this point in the simulation, we could also add modeling error to the T B’s. Modeling error accounts for the difference between the modeland nature. It is a very difficult parameter to determine since it involves physical processes which are not sufficiently understood to be included in the current model. For now, we are not including any modeling error in thesimulations, but we will be investigating this problem in the future.
Given the noise-added simulated T B’s, the standard multiple linear regression technique is used to find the cijcoefficients. The coefficients are found such that the rms difference between Pj and the true value for the specified environmental scene is minimized. For the initial set of simulations, we use all 10 lower frequency channels(i.e., 6.9, 10.7, 18.7, 23.8 and 36.5 GHz, dual polarization). Later on, we will investigate the utility of using a
reduced set of channels.
The algorithm is tested by repeating the above process, only this time using the withheld environmental
scenes. The geophysical parameters T S, W, V, and L are computed from the noise-added T B’s using equation (72).
Statistics on the error in Pi are accumulated. The results are shown in Figure 6. The solid line in the figure shows
the mean retrieval error, and the dashed lines show the one standard deviation envelope. The retrieval error foreach of the four parameters is plotted versus the four parameters in order to show the crosstalk error matrix. The
diagonal in the crosstalk matrix verifies that the dynamic range of a given parameter is correct, and the offdiagonal plots verify that there is no crosstalk error in the retrieval.
The results look quite good. There is a little crosstalk, but it is quite small. Table 9 gives the overall rms error forthe retrievals. Wind direction variability is a major source of error in the T S retrieval. When wind direction variability is removed from the simulations, the T S retrieval error decreases to 0.3 C. The wind direction problem isfurther discussed in Sections 1.5 and 4.3.
We again emphasize that these results are very preliminary. There is much more work to do. For example,
the cloud models need to be more variable and the performance of the relatively simple LSR algorithm needs tobe compared with the non-linear algorithm discussed in the next section.
Table 9. Preliminary Estimate of Retrieval Error
Ocean Parameter
Rms Error
Sea-Surface Temperature
0.58 CWind Speed
0.86 m/s
Columnar Water Vapor
0.57 mm
Columnar Cloud Water
0.017 mm
3.4. Non-Linear, Iterative Algorithm
The major shortcoming of the multiple linear regression algorithm is that the non-linearities in the T B versus P
relationship are handled in an ad hoc manner. The linearization functions are only approximations, and the inclusion of second order terms such as T B2 and T B37V T B23H do not really describe the inverse of the T B versus P relationship. A more rigorous treatment of the non-linearity problem is to express the TB versus P relationship interms of a non-linear model function F(P), and then invert the following set of equations
TBi = Fi (P ) + ε i(75)
where subscript i denotes the observation number and ε i is the measurement noise. The number of observations
must be equal to or greater than the number of unknown parameters (i.e., the number of elements in P). For each
set of AMSR observations, equations (75) are inverted to yield P. This method is much more numerically intensive than the linear regression algorithm in which there is a fixed relationship between P and T B. However, given
today’s computers, the computational burden is no longer a problem.

Equation (75) is solved using an extension of Newton’s iterative method. In Newton’s method, the model function is expressed as a Taylor expansion:

T Bi = Fi ( P) + ∑ (Pj − Pj )4

j =1

SST DIF (C)WIND DIF (M/S)

VAPOR DIF (MM)

CLOUD DIF (MM)

0

30 0

∂Fi
∂Pj

+ O 2 + εi

(76)

P

20 0

70 0

.3

.1

.1

0

0

-.1

-.1

3

3

0

0

-3

-3

2

2

0

0

-2

-2

2

2

0

0

-2

-2
0

30 0
SST (C)

20 0
WIND (M/S)

70 0
VAPOR (MM).3
CLOUD (MM)Fig 6. Preliminary results for the linear statistical regression algorithm for AMSR. The solid line in the figure shows the mean retrieval error, and the dashed lines show the one standard deviation envelope. The retrieval error for each of the four parameters isplotted versus the four parameters in order to show the crosstalk error matrix. The diagonal in the crosstalk matrix verifies that the
dynamic range of a given parameter is correct, and the off-diagonal plots verifies that there is no crosstalk error in the retrieval.

where P is a first guess value for P and O2 represents the higher order terms in the expansion. This system ofsimultaneous equations is written in matrix form as∆TB = A ∆P + O 2 + e(77)
where A is a matrix of i × j elements and ∆ TB , ∆ P, and ε are column vectors. The elements of A, ∆ TB, and ∆ P
are

Aij =

∂Fi
∂Pj

(78)
P

∆TB i = TB i − Fi ( P )∆Pj = Pj − Pj

(79)
(80)

Equation (77) is solved by ignoring the higher order terms (i.e., by setting O2 to zero), and the solution is

P = P + (A TΞ − 1 A) − 1 ATΞ − 1 ∆ TB

(81)

where Ξ is the error correlation matrix. This procedure is then repeated with P from (81) replacing P , and several
such iterations are performed. For the no-noise case ( ε = 0), Ξ drops out of the formulation and an exact solution
is obtained when ∆ TB goes to zero. For the noise case, a solution is found when ∆ TB reaches some constant
minimum value.
The solution of P can be constrained by the inclusion of a priori information. This is accomplished by including additional equations in (77). For example, if ancillary information on wind direction were available, then thefollowing equation could be added to (77)φ = φ∃ + ε φ(82)
where φ∃ is the a priori estimate of φ and ε φ is the rms uncertainty in that estimate. Similar constraining equations
can be included for other types of information such as the vertical distribution of water vapor and air temperature.
In general, there is no guarantee that a solution will be found using this method. Furthermore, if a solution isfound, there is no guarantee that it is an unique solution. However for the case of AMSR, the relationships between P and TB are quasi-linear in that ∂T B/∂P > 0 for all channels except 36.5 GHz in cold water, for which∂T B/∂T S is < 0. Experience has shown that a solution is nearly always found. It also appears that this solution is
unique, but this needs to be verified.
We have been assuming that the TB versus P relationship can be exactly described by a non-linear model
function F. In this case, the non-linear, iterative algorithm has the distinct advantage of finding the exact solution.
In comparison, the P found by the linear regression algorithm would be in error by some degree due to the nonlinearities. However, in practice it is not possible to exactly represent the TB versus P relationship in terms amodel function F(P). For example, the TB not only depends on the columnar content of water vapor but also on
vertical distribution of the vapor. Thus, some approximations need to be made when going from the integral
equations of radiative transfer to a simplified model function F(P). These assumptions were discussed in length in
Section 2. In the derivation of the linear regression algorithm, the complete integral formulation of the radiativetransfer theory is used, and there is no need for the simplifying assumptions.
In comparing the two types of algorithms, there is a tradeoff between errors due to non-linearities in the linear regression algorithm and errors due to simplifying assumptions in the non-linear, iterative algorithm. Our plan
is to develop and test both types of algorithms in parallel, compare their relative performance, and then select one
or the other.
3.5. Post-Launch In-Situ Regression Algorithm
After AMSR is launched, purely statistical algorithms can be developed by collocating the AMSR TB’s withselected in-situ sites. A simple least-squares regression is then found that relates the in situ parameter to the T B’s.
The mathematical form of this type of algorithm is identical to the linear regression algorithm given by (72). The
difference is that the cij coefficients are not derived from radiative transfer theory, but rather from the regression to
the in situ data. Examples of this type of algorithm are the Goodberlet et al. [1989] SSM/I wind algorithm and theAlishouse et al. [1990] SSM/I water vapor algorithm.
The strength of the purely statistical algorithm is that it does not require a radiative transfer model, and hence
it is not affected by modeling errors. The weaknesses are:
1. The algorithm for AMSR cannot be developed until after launch.
2. Large in situ data sets covering the full range of global conditions must be assembled and collocated with the
AMSR observations.

3. The purely statistical algorithm is keyed to specific sensor parameters such as frequency and incidence angle.
For example, none of the algorithms developed for SSM/I can be applied to AMSR. In contrast, SSM/I algorithms based on radiative transfer theory can be interpolated to the new AMSR frequencies and incidence angle.
4. Cross-talk among the various geophysical parameters is a problem for the statistical algorithm. For example,
consider sea-surface temperature TS and water vapor V which are highly correlated on a global scale. A purely
statistical algorithm will mimic this correlation and will generate a TS product that is always highly correlatedwith V. In nature, when the true V changes and T S remains constant (i.e., a weather system passing by), the statistical algorithm will erroneously report a change in TS.
5. For the case of cloud water retrieval, for which there is no reliable in situ data, this type of algorithm cannot beused.
We think it is a mistake to ignore the physics when developing an algorithm. It may be the case that relatively simple regressions can be used to retrieve some of the parameters. However, it is important that these regressions be understood in the context of radiative transfer theory. Thus, after AMSR is launched and the collocated in situ data are available, we will calibrate the pre-launch algorithm by making small adjustments to the radiative transfer model rather than developing purely statistical algorithms. This calibration activity is discussed in
the Section 5.
3.6. Incidence Angle Variations
The retrieval of sea-surface temperature and wind speed are sensitive to incidence angle variations. A 1° error in specifying θi produces a 6 C error in TS and a 5 m/s error in W. Thus, it is crucial that the incidence angle
be accurately known and that the retrieval algorithm accounts for incidence angle variations.
The pointing knowledge for the PM platform is specified to be 0.03°/axis. This figure is the 3-standard deviation error in the know ledge of the roll, pitch, and yaw. Yaw variations do not affect the incidence angle, but rolland pitch do. The corresponding 3-standard deviation error in incidence angle is approximately 0.05°. The retrieval accuracy for the geophysical parameters are in terms of a 1-standard deviation error, so we convert the incidence angle error to a 1-standard deviation error of 0.016°, and this results in a 0.1 C error in the TS retrieval anda 0.1 m/s error in the W retrieval. The specification of pointing knowledge for the PM platform is, therefore, sufficient. However, the pointing knowledge of the AMSR instrument is yet to be specified. We will be paying
close attention to this instrument specific ation.
In the non-linear, iterative algorithm, incidence angle is an explicit parameter in the model function, andhence θi variations are easily handled by simply assigning a value to θi before doing the inversion process. There
are two possible methods for handling incidence angle variation in the linear regression algorithm. First, include
incidence angle as an additional term in the regression or second, normalize the TB’s to some constant incidence
angle, say 55°, before applying the regression. This normalization is expressed by
TB 55° = TB (θ i ) + µ ⋅ θ i − 55°(83)
where µ represents the derivative ∂T B/∂θi , which depends on the TS, W, V, and L. We find that µ can be accurately approximated by a TB regression of the type given by (73). This method works well when the incidence
angle variations are ± 1° or less, which should be the case for AMSR.

( )6. References
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AMSR Precipitation Rate Retrieval Algorithm-Theoretical Basis and Operation
Grant W. Petty
Atmospheric and Oceanic Sciences
University of Wisconsin-Madison
1. Introduction
The Standard (pre-launch) Algorithm selected for over-ocean precipitation retrieval for the Advanced
Microwave Scanning Radiometer (AMSR) is an adaptation of the algorithm developed for the Special Sensor
Microwave/Imager (SSM/I) by Petty (1994a,b). The principle features that distinguish this algorithm from otherrain rate algorithms include the following:•

Physical information concerning surface rain rate is supplied by the polarization difference at each frequency
utilized in the inversion. As shown by Petty (1994a), a simple monotonic relationship exists between thelocal polarization difference and the total optical transmittance of the rain cloud at the frequency in question.
The polarization difference is normalized with respect to a hypothetical cloud-free value under similar
background conditions, thus eliminating variable water vapor and surface wind speed as important sources ofsystematic error in the retrieval.

•

Scattering information at 89 GHz, as embodied by the S index of Petty (1994b), is postulated to contain only
indirect information about surface rain intensity and it is therefore utilized only to generate the “first guess”
rain rate field at high resolution. The first guess value at a local is modified only to the degree necessary toeliminate inconsistencies between calculated and observed polarization differences at the lower frequencies.

•

The algorithm undertakes a spatial inversion of the polarization differences at the various frequencies utilized
in the retrieval. That is, it iteratively seeks a high-resolution (5 km) rain rate field which is simultaneously
consistent, to within specified tolerances, with the low-resolution fields of polarization difference observed at
multiple frequencies. The disparate channel resolutions are explicitly accounted for in this inversion.

2. Algorithm Operation
2.1 Theoretical Basis
A number of factors make the optimal estimation of rain rate more difficult than the retrieval of many otherparameters, such as column water vapor, column cloud water, etc. Examples include: (1) much larger optical
thicknesses of precipitation and thus a high degree of non-linearity in both the forward and inverse problems; (2)the complexity of the interactions of microwave radiation (including scattering) with diverse liquid and frozenhydrometeors, whose physical and optical properties are highly variable in space and time; (3) the relative
indirectness of the relationship between path-integrated cloud properties observable from space and surface
precipitation rate; (4) the relatively poor spatial resolution of microwave radiometers compared with thehorizontal scale of variability of rainfall; and (5) the highly 3-dimensional structure of many rain clouds. The lastof these problems is further complicated by the oblique (55°) viewing angle of the AMSR, since it will often be
emission from the sides and surface reflections of rain clouds, rather than their tops, that play a dominant role in
FOV-averaged microwave radiances (Petty, 1994a; Petty et al., 1994).
In view of the numerous physical and structural variables determining radiometer-observed brightness
temperatures in any given pixel containing precipitation, it is important to make use of complementary
information from as many channels as possible. It is further advisable to avoid attributing too great of precision
to theoretically derived relationships, since such relationships generally do not allow for large departures of realrain clouds from common ideal assumptions, such as plane-parallel geometry.
The multichannel spatial inversion approach developed by Petty (1994b) attempts to achieve a balance between
excessive reliance on uncertain physical models and excessive dependence on ad hoc statistical relationships andassumptions about beamfilling, etc. It attempts to maximize the use of the available information, but does so
primarily by reference to observed path attenuation, rather than emission or scattering, so as to reduce the impact

of uncertainties in the properties of frozen hydrometeors aloft.
This method is unusual in explicitly solving for a high-resolution rain field which is simultaneously consistent
with the observed low-resolution polarizations at all frequencies, after allowing for the overlap and varying size ofthe effective fields of view (EFOVs). It also makes generous allowance for uncertainties in the highly simplified
forward model and for geophysical noise of other types; thus, forward calculations are not forced to exactly agreewith the observations but rather are considered consistent if they fall within a specified range of the observed
values for each relevant microwave frequency.
In order to adapt the Petty (1994b) rain rate algorithm to the AMSR, two major revisions were necessary: (1)modification of the assumed antenna pattern and overlap coefficients utilized in the spatial inversion, and (2)development of a simple forward model for predicting brightness temperatures and polarizations specifically at
AMSR frequencies and viewing angles. Furthermore, because the original SSM/I version of the algorithm wasdesigned to operate within a much larger specialized display and analysis program for that sensor, considerable
rewriting and reorganization of the C-language code was necessary in order to repackage the algorithm as aself-contained subroutine (currently about 4000 lines of C and Fortran code).
2.1.1 P AND S INDICESThe foundation of the Petty (1994b) ocean rain rate algorithm lies in the use of polarization information todecouple scattering and attenuation information at a given microwave frequency. This information can then be
utilized separately in the retrieval, weighted according to its relative directness as a measure of surface
precipitation intensity.
As observed by the satellite, polarized brightness temperatures respond to uniform rainfall in the mannerindicated by Fig. 1. For all frequencies, brightness temperatures first increase due to emission by rainfall as seen
against a radiometrically cold ocean background. With increasing rain rate, saturation occurs first at the highest
frequencies. At higher rain rates, scattering due primarily to large ice particles above the melting level begins todepresses brightness temperatures again. This effect is most pronounced at the highest frequencies, and its
magnitude and spectral dependence is strongly dependent on assumptions about ice particle size and concentration
above the melting level.

Figure 1: Idealized relationship between brightness temperature and surface rain rate for selected AMSR frequencies.

From this general behavior, it is clear that single-channel brightness temperatures from the AMSR yield anambiguous measure of rain intensity, since it cannot be determined from the single brightness temperature
whether one is on the left or right side of the peak for a given curve. Theoretically, one could resolve theambiguity by using multiple frequencies at a single polarization, but this requires possibly unwarranted
assumptions about the uniformity of rainfall within the widely differing FOVs of the respective channels.
When one considers the difference between the vertical and horizontal polarizations observed at a given
frequency, the double-valuedness of the relationship disappears. The observed polarization difference ∆T=T V-TH

is essentially a monotonic measure of the visibility of polarized ocean surface emission through and between
clouds and rain (this relationship breaks down somewhat in optically thick rain, owing to subtle effects byoriented ice particles). However, ∆T depends on other environmental properties as well, most notably total
column water vapor V and surface wind speed U. It is therefore advantageous to define a so-called normalized
polarization P asP=

∆T
∆T0 (U ,V ,...)(1)

where ∆T0 is the estimated cloud-free polarization difference at the time and location in question. The utility ofthis definition of P depends on one being able to make a reasonable estimate of U and V in locations of rainfall.
This is accomplished either by direct retrieval from the AMSR data if the rain intensity is not too great or byinterpolation into the rainy pixels from surrounding pixels.
Once P has been calculated for a given AMSR frequency, it serves as a physically direct index of total
FOV-averaged path attenuation at that frequency due to clouds and rain only. It can be shown that, to areasonable approximation (in view of many other unavoidable sources of error),P ≈ τα(2)in the case of horizontal uniform coverage by rain and cloud, where τ is the oblique-path microwave transmittancethrough the rain layer, and α ≈ 1.7 is approximately independent of frequency. Although a minor modification isrequired to account for the polarizing effects of ice particles in optically thick rain clouds, the above relationshipserves as the primary basis for inferring rain intensity in a given FOV. Fig. 2 depicts P as derived from thedual-polarization brightness temperature curves appearing in the left panel of the same figure.

Figure 2: Idealized relationship between normalized polarization P and rain rate for selected AMSR frequencies.

Once a rain cloud becomes optically thick, the normalized polarization P saturates at a value near zero andyields no further information about surface intensity. Beyond that point, only the magnitude of the brightness
temperature depression due to scattering by ice yields qualitative information about rain intensity. This
information is indirect, because there is no unique relationship between the concentration and size of ice particles
aloft and the intensity of surface precipitation. The so-called scattering signature is therefore weighted lightly inthe algorithm, determining the surface rain rate only in cases where the estimate is not contradicted by evidence
from the more physically direct P. In practice, this is accomplished by using the scattering information to
specify the “first guess” rain rate and then modifying this rain rate estimate as necessary so as to eliminate
inconsistencies with the observed P from the lower frequency channels.

As noted above, single channel brightness temperatures are ambiguous in that low values may imply either very
light rain (and hence weak attenuation of the “cold” ocean surface emission or else heavy rain accompanied bymuch ice aloft. This ambiguity is again removed when one considers polarization in addition to brightness
temperature: the unobscured ocean is “cold” but strongly polarized, whereas intense rainfall appears “cold” andonly weakly polarized. The scattering index S for a given frequency is given by a linear combination of thevertical and horizontal polarized brightness temperatures. This index in effect compares the brightness
temperature expected from a non-scattering, isothermal (TC=273 K) cloud layer having the observed value of P
with the observed brightness temperature. Thus,

S = P ⋅ TV 0 + (1 − P ) ⋅ TC − TV .

(3)

Fig. 3 depicts S as derived from the dual-polarization brightness temperature curves in Fig. 1.

Figure 3: Idealized relationship between scattering index S and rain rate for selected AMSR frequencies.

Although all three frequencies show some scattering response to precipitation, only 89 GHz has a large enoughresponse at modest rain rates to be routinely useful. Hence, S89 provides the first-guess rain rate R 0 , based on theempirically determined linear relationshipS89 = CS R0(4)

A preliminary value of CS is 2.9~K/(mm/h).
2.1.2 FORWARD MODEL
Although the relationship between P and total rain cloud transmittance τ is simple and relatively robust (for thehorizontally homogeneous case), still needed is a model for the dependence of τ on rain rate R. We use thefollowing expressionPν = Aν exp (− Cν Z l RνB )(4)

where Zl is an effective rain layer depth (e.g. freezing level), and A ν, Bν, and Cν are frequency-dependent
coefficients derived from theoretical calculations for a uniform Marshall-Palmer rain layer accompanied by anassumed 0.5 kg/m2 of non-precipitating cloud water.
In the current version, Zl is estimated empirically from the retrieved total column water vapor in the vicinity of

the raining pixel. The justification for this method, and the actual relationship, is given by Petty (1994b). In
future versions, we may instead utilize either NWP model-analyzed freezing level or else lower tropospherictemperature estimates derived from the 50-53 GHz channels of the ADEOS-2 AMSR.
Because the above model relationship for P ν is based on highly simplified assumptions, it is treated as an
approximation with fairly generous uncertainties. Only pixels whose forwarded-calculated P ν differs by morethan a specified tolerance ∆P ν from the observed value are considered “inconsistent,” thus requiring iterative
modification of the retrieved rain rate field. However, when observed values of P from multiple channels arebrought to bear, the requirement that the rain rate be consistent (to within tolerances) with all channels
simultaneously constrains the retrieved rain rate rather effectively over a fairly wide range of intensities.
2.1.3 SPATIAL INVERSION
Not addressed so far is the problem of spatial inhomogeneity of rainfall within the respective fields-of-view(FOVs) of the channels used in the retrieval. Since each channel has a different resolution, one cannot assume
that the same rain rate, or even that similar frequency distributions of rain rate, are present within each channel'sFOV. Moreover, lower frequency channels have larger dynamic range (see Fig. 1) but lower sensitivity and alsocoarser spatial resolution than their higher-frequency counterparts. On the other hand, the coarser resolution
FOVs overlap to a significant degree (i.e., are oversampled), suggesting the possibility of inverting the smoothed
low-frequency polarization fields to obtain high-resolution rain fields. Such spatial deconvolution must be
undertaken with care and with due consideration of the inherent ill-posedness of this kind of inverse problem inthe presence of all forms of noise (instrument, geophysical, and that due to model errors).
The method developed by Petty (1994b) assumes that the rain rate is to be retrieved on a grid whose elements
correspond to the positions of the high-resolution (89 GHz) channels' pixels. Unlike the 89 GHz FOVs, however,these grid elements, or retrieval cells, are contiguous and non-overlapping. Fig. 4 depicts the relationshipbetween the fine-resolution rain rate retrieval grid and the effective FOVs of each relevant AMSR channel.
The observed P89 values are used to make an initial determination of whether rainfall is possible within a given
high-resolution retrieval cell. If P 89 is greater than a specified threshold, the pixel is deemed rain-free; otherwise
it is flagged as “rain possible.” The observed S89 value is then used to assign a first-guess rain rate to each cell
identified as “rain possible,” according to (4).
The next step is to forward-calculate the normalized polarization (P) field from the first-guess rain rate. Thisis accomplished by first computing local values P i for each high resolution retrieval cell using (5), and then taking
a weighted sum of these values within each FOV to derive an estimate of the low-resolution value of P
corresponding to a given image pixel:

Pj = ∑ w i , j Pj .
i

(6)Figure 4: Relationship between rain rate retrieval cells and the FOVs corresponding to a single A-scan.

Because the spatial relationship and degree of overlap between sensor pixels and retrieval cells is fixed at any
point in a scan line, the coefficients wi,j are pre-computed for all channels and stored in arrays which are accessedby the algorithm during both the forward and inverse calculations.
For each sensor pixel for which the forward-computed P differs from the observed P by more than thespecified tolerance ∆P, an adjustment is undertaken of the rain rates in the retrieval cells covered by that sensor
FOV. Only retrieval cells identified as “rain possible” are candidates for adjustment. The magnitude of theadjustment is largest for the retrieval cells having the largest potential influence on the forward-calculated
polarizations. Thus, where two different FOVs overlap a given retrieval cell, the one with the greatest sensitivity
to changes in the rain rate in that cell will have the greatest control over the adjustment. Low sensitivity tochanges in a given rain retrieval cell can be due either to saturation at the current-guess rain rate or else theposition of the cell in the FOV.
The above adjustment is performed for all pixels flagged as “inconsistent” and this adjustment is performed inturn for each frequency utilized in the inversion (currently 18.7 and 36.5 GHz). The process is repeated a fixed
number N times, after which it is assumed that no further improvement can be expected. Because of thediffering resolutions and sensitivities of the different channels, it is rare that convergence, or near convergence, is
not obtained at most locations, provided only that the tolerances are not set too tight. Optimal tolerances anditeration counts are best determined empirically, using real data where possible. For the SSM/I, ∆P = 0.1 and N= 8 yielded good results, but we are testing new values using the synthetic swath data supplied by
NASDA/EORC.
3. Testing
Previous experience with this algorithm was based on the SSM/I version of the Petty (1994b) algorithm, which
has been extensively intercompared with ground validation data in AIP-1, AIP-2, AIP-3, PIP-1, PIP-2, and PIP-3,
as well as several “private” intercomparison studies. In the most recent two organized intercomparisons (AIP-3
and PIP-3), the results for the SSM/I version were very satisfactory by some measures. In particular, thisalgorithm had by far the highest instantaneous correlation with radar at 0.5° resolution in AIP-3. In PIP-3, it was
one of the very few algorithms that simultaneously yielded good rms errors against monthly atoll rainfall amounts
and also a high global time-space correlation with a ship-derived climatology of fractional-time-precipitating(Adler et al., 2000).
Future testing plans include validation of the algorithm using data from the TRMM Microwave Imager (TMI),
which is already flying and has many similar channels to AMSR. While the adaptation of the algorithm to TMIfrom AMSR will be much less arduous than was the adaptation from SSM/I to AMSR (since the previous
adaptation was undertaken with future flexibility in mind), it is still a non-trivial task, owing to the need to derive
yet another set of FOV overlap coefficients wi,j and other sensor-specific coefficients.
4. Known Issues and Future work
4.1 Scan geometry
A quantitative description of FOV overlap between adjacent pixels and between different channels of the AMSR
was recently provided by EORC but has still not been incorporated into the algorithm. Antenna pattern overlap
coefficients provided with current version are based on the assumption of Gaussian effective antenna weighting
patterns.
4.2 Channel Usage
The present version utilizes only 18.7 and 36.5 GHz channels, corresponding to the original SSM/I channels of
19.35 and 37.0 GHz. Future versions may utilize 6.9 and 10.7 GHz channels as well, but the tradeoffs between
computational effort, inversion stability, and retrieval performance improvement must be studied first.
4.3 Cloud free brightness temperatures
A prerequisite for the transformation of the raw polarized brightness temperatures into the P and S variables
utilized in the physical inversion is a reasonably accurate estimate of the cloud-free brightness temperature in bothvertical and horizontal polarization. Currently, this is achieved by first retrieving column water vapor V andsurface wind speed
Figure 5 (left): Validation results over 12 months (1992) of monthly rainfall products submitted to PIP-3. Only “pure SSM/I”
algorithms are indicated in this figure. The horizontal axis indicates the RMS difference from atoll gauges. The vertical axis
indicates the global correlation with ship-derived fractional-time-raining between 60S and 60N. Both sets of statistics wereobtained from the PIP-3 Intercomparison Results volume. Only algorithms for which both statistics were available are included.
The Petty (Purdue U.) physical algorithm is denoted “pur” in this intercomparison.
Figure 6 (right): Instantaneous validation results for SSM/I algorithms submitted to AIP-3, at 0.5 degree resolution. The horizontal
axis depicts the mean ratio over the entire intercomparison period of the algorithm rainfall to the radar rainfall. The vertical axis
depicts the correlation coefficient. Note that there is some uncertainty concerning the absolute calibration of the radar data – mostalgorithms (both SSM/I and IR) clustered around a ratio of approximately 1.5 to 2.5. The Petty physical algorithm was denoted“PE1” in this intercomparison.

U outside of areas of significant precipitation. These retrieved values are then interpolated into areas ofprecipitation and used to estimate cloud free brightness temperatures based on a simple empirical model which
has again been adapted from the SSM/I.
For the pre-launch versions of the algorithm, it is necessary to extrapolate empirical relationship derived for the
SSM/I to the slightly different frequencies and viewing angle of the AMSR. This extrapolation unavoidably
depends on physical models whose absolute accuracy is imperfect. Consequently, we expect some systematic
biases in the determination of cloud free radiances. This biases could in turn introduce errors or inconsistencies
into the rain rate retrievals until the biases are corrected post-launch.
For the post-launch version of the algorithm, actual AMSR observations will be available in order to fine-tune
both the U and V retrievals and the prediction of cloud-free TB from U and V. Alternatively, the U and V values
obtained from the Standard Algorithm for those variables may be utilized.
References
Adler, R., C. Kidd, G. Petty, M. Morrissey, and M. Goodman, 2001: Intercomparison of global precipitation
products: The third precipitation intercomparison project (PIP-3). Bull. Amer. Meteor. Soc. (in press).
Petty, G., A. Mugnai, and E. Smith, 1994: Reverse Monte Carlo simulations of microwave radiative transfer inrealistic 3-D rain clouds. In 7th Conference on Satellite Meteorology and Oceanography, Monterey,
California, 6-10 June.
Petty, G. W., 1994a: Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I:
Theoretical characteristics of normalized polarization and scattering indices. Meteorology and AtmosphericPhysics, 54(1-4), 79-100.
Petty, G. W., 1994b: Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part II:
Algorithm implementation. Meteorology and Atmospheric Physics, 54(1-4), 101-121.

Description of Precipitation Retrieval Algorithm For ADEOS II AMSRGuosheng Liu
Florida State University

1. Basic Concepts of the Algorithm
This algorithm is based on Liu and Curry (1992, 1996), in which the rainfall rate is calculated from the
combination of emission and scattering signatures. Beam-filling correction is embedded in the algorithm.
Radiative transfer model tests show that it is not sensitive to the height of freezing level. This algorithm wastested in GPCP AIP-1, AIP-3, WetNet PIP-2 and PIP-3. The algorithm can retrieve rainfall over both ocean andland although slightly different formulations are used for the different surface types.
The AMSR algorithm is built on the SSM/I algorithm with conversions from AMSR brightness temperatures to
SSM/I brightness temperatures.
Ocean Algorithm:
In this updated version, the combination function is defined by Liu et al. (1995) as following:f = (1 −DD0) + 2 (1 −

PCT
PCT 0

)

(1)

where D is the depolarization of 18.7 GHz and D0 is D at the threshold of rain onset; PCT is the polarization
corrected brightness temperature defined by (Spencer et al., 1989): PCT = 1.818T B89V - 0.818TB89H, and PCT 0 is
PCT at the threshold of rain onset. PCT and D for AMSR channels are then converted to SSM/I PCT and D by
the following equations:

PCTSSM / I = 2.2 + 0.996PCTAMSRDSSM / I = −0.14 + 0.903 * DAMSR(2)These equations are derived by radiative transfer simulations for various atmospheric and surface conditions.
Then rainfall rate are calculated based on the equations originally derived from SSM/I channels.
D0 and P0 are determined monthly for every 3° (latitude) x 6° (longitude) box based on 37 GHz depolarization andsea surface temperature, and are saved in a file as a look-up table. The relationship between f and rainfall rate isdetermined by radiative transfer calculation result with consideration of beam-filling effect, and can be expressedby

R = αf β(3)where α and β are spatial scale-dependent coefficients. The dependence of α and β on spatial scale is due to thespatial dependence of beam-filling effect. For SSM/I in which the spatial resolution of 19 GHz is ~ 50 km,
α=10.6 and β=1.621. For AMSR and TMI, the spatial resolution for 19 GHz is about half of that in SSM/I. The
values for α and β are determined by an empirical equation based on radiative transfer model simulation and TMI
data: α=8.25, and β=1.88. Test results show that these coefficients produce satisfactory rain rates from TMI datawhen compared to TRMM PR rain rates and GPCP climatology. Detailed discussion is given in section 2 on thescale-dependent parameters, α and β.
Land Algorithm:
The land portion of our algorithm uses 18.7 and 89 GHz brightness temperatures. It is expressed by

R = a ( DT B − DT B 0 )(4)

where a=0.2 is a coefficient derived from radiative transfer model simulations; DTB =TB18.7 -TB89.
convert DT B for AMSR to DT B for SSM/I by

DTBSSM / I = −0.6 + 0.9558DT BAMSR

Again, we first(5)

Then the rainfall algorithm originally developed for SSM/I is used.
DTB0 is DTB at the threshold of rain onset that is determined monthly for every 3° (latitude) x 6° (longitude) box
based on Liu and Curry (1992) and is saved in a file as a look-up table.
The algorithm is deterministic (non-iterative) and all threshold parameters (D0 , PCT 0 , and DTB0) are available as alook-up table. Therefore, the retrieval is extremely fast.
2. Determination of the Scale-Dependent Parameters
Results of earlier studies (e.g., Liu and Curry, 1992, Spencer et al., 1989) showed that the beam-filling effect tends
to make the R-T B relation closer to “linear” than that indicated by radiative transfer models assuming aplane-parallel rain layer. Liu and Curry (1992) tried to explain this behavior of R-T B relation. The determinationof α and β in this algorithm is based on this consideration. First, we assume the parameter β in (3) varies withspatial scale, x ( in km), asβ = β∞ − A[1 − exp( − Bx κ )],(6)

where β∞ =2.792 is β for plain parallel rain layer determined by our radiative transfer simulations. κ is anadjustable parameter used to vary the strength of scale dependence. For now we use κ=0.7 which seems to work
well for our algorithm for TMI and SSM/I data. A and B are determined as following. First, when scale, x,
becomes infinite large, β is 1, implying that for infinitely large spatial resolution the R-T B relation is linear (notethe argument mentioned earlier). Then, it is determined that A = β∞ − 1 . The constant B is then determinedby applying (6) to our SSM/I algorithm used in Liu and Curry (1996), which gives βSSMI =10.6 for a scale of 50km.

In the studies of Liu and Curry (1992), it is also found that when rainfall rate is as high as 50 mm/hr, the ratio
between observed TB and plane-parallel model generated TB should be close to 1. Based on this argument, we
determine α by letting
1

1

 R50  β AMSR  R50  β SSMI



= 
 αAMSR  αSSMI (7)where R50 =50 mm/h.
It is noted that the development of the parameters of α and β are based on the algorithm we developed for SSM/I.
Figure 1 shows the f-R relations derived from the aforementioned approach for different spatial resolutions. Forvery high resolution, we may believe the rainfall within the FOV is homogenous. For very low resolution, thef-R relation is assumed to be linear. Actual satellite measurements (AMSR, TMI, SSM/I) will have an f-R
relation curve between the two extremes.

2.8

2.4

2
Homogeneous(Very Hi-Res)
TMI/

1.6

AMSR

SSM/I
1.2

Very Low-Res

0.8

SSMI
0.4

TMI
linear[low]Homo[high]

0
0

5

10

15

20

25

30

35

40

45

50

RAIN (mm/hr)

Fig. 1 Relations between f and rainfall rate for different spatial resolutions.

3. Validation -- Comparison with Other Datasets
Figure 2 shows the comparison of this algorithm using SSM/I data with GPCP satellite-raingauge combinedmonthly rainfall product (Huffman, et al., 1997) for the year of 1992. The two retrievals are generally agreed
with each other although some discrepancies can also be found; such our retrievals are general lower, particularly
for latitudes where precipitation peaks. This disagreement can partially be attributed to the low temporal
coverage of SSM/I data.
Figure 3 shows the comparison with TRMM TMI-PR combined (3B31) product and GPCP satellite-raingauge
combined product for 1998. Our retrievals seem to compare well with these products. We are still working on
this comparison for other years to investigate whether there are discrepancies for those years. Further
investigation may lead modification of the tuning parameter, κ, given in (6). Figure 4 shows the comparison
with product derived from TRMM PR alone. The latitudinal variation of the two estimates agrees well although
our estimates are slightly larger than the PR estimates. It is noted that PR estimates are also smaller than TRMM
TMI and TRMM Combined products.

The following table lists the bias, correlation coefficient and rms difference when of our algorithm whencompared to TRMM combined and GPCP products. The statistics are calculated using 1998 monthly 5° x 5°
datasets.

Statistics When Compared to TRMM Combined and GPCP Data
Bias in %Correlation

rms Diff in %

GPCP

1%

0.78

69%

TRMM Combined

6%

0.82

61%

4. References
Huffman, G. J., R. F. Adler, P.A. Arkin, A. Chang, R. Ferraro, A. Gruber, J. Janowiak, R.J. Joyce, A. McNab, B.
Rudolf, U. Schneider, and P. Xie, 1997: The Global Precipitation Climatology Project (GPCP)
Combined Precipitation Data Set. Bull. Amer. Meteor. Soc., 78, 5-20.
Liu, G., and J. A. Curry, 1992: Retrieval of precipitation from satellite microwave measurements using bothemission and scattering. J. Geophys. Res., 97, 9959-9974.
Liu, G., and J. A. Curry, 1996: Large-scale cloud features during January 1993 in the North Atlantic Ocean asdetermined from SSM/I and SSM/T-2 observations. J. Geophys. Res., 101,7019-7032.
Liu, G., J. A. Curry and R. -S. Sheu, 1995: Classification of clouds over the western equatorial Pacific Ocean using
combined infrared and microwave satellite data. J. Geophys. Res., 100, 13,811-13,826.
Spencer, R. W., H. M. Goodman, and R. E. Hood, 1989: Precipitation retrieval over land and ocean with SSM/I:
Identification and characteristics of the scattering signal. J. Atmos. Oceanic Technol., 6, 254-273

90
APR

JUL

OCT

FEB

MAY

AUG

NOV

MAR

J JUUNN

SEP

DEC

JAN
60
30
0
-30

SSM/I

-60

GPCP 1992 V1C

90
60
30
0
-30
-60

90
60
30
0
-30
-60
-90
0

1

2

3

4

5

6

7

8 0

1

2

3

4

5

6

7

8 0

1

2

3

4

5

6

7

8

0

1

2

3

4

RAIN (mm/day)Fig. 2 Comparison with GPCP satellite-raingauge combined rainfall(blue).

5

6

7

8

40
FEB

MAR

APR

MAY

JUN

JUL

AUG

SEP

OCT

NOV

DEC

JAN

30
20
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0
-10
-20
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40
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0
-10
-20
-30
40
30
20
10
0
-10
-20
-30
40
30
20
10
0
-10
-20

LIU
GPCP
TRMM

-30
-40
0 1

2 3

4 5 6 7 8 0

1 2 3 4 5 6 7
RAIN (mm/day)

8 0 1 2

3 4

5 6

Fig.3 Comparison with TRMM combined (red) and GPCP (green) products for 1998.

7 8

40
30

FEB

MAR

APR

MAY

JUN

JUL

AUG

SEP

OCT

NOV

DEC

JAN

20
10
0
-10
-20
-30

LIU
TRMM PR

40
30
20
10
0
-10
-20
-30
40
30
20
10
0
-10
-20
-30
40
30
20
10
0
-10
-20
-30
-40

0 1 2 3 4 5 6 7 8

0

1 2

3 4

5 6

7 8 0

1 2 3

4 5

RAIN (mm/day)Fig. 4 Comparison with TRMM Precipitation Radar (red) product for 1998.

6 7

8

AMSR/AMSR-E Sea Surface Wind Speed Algorithm
Akira SHIBATA
Meteorological Research Institute
1. Abstract
Sea surface wind speed (SSW) is retrieved mainly from 37 GHz vertical (V) and horizontal (H) brightness
temperature of AMSR/AMSR-E by a graphical method. The retrieval is restricted to no rain condition, since thebrightness temperature of 37 GHz is saturated under rainy condition, SSW obtained from 37 GHz has a large
anisotropic feature depending on an angle difference between antenna direction and wind direction. Its
anisotropic feature is corrected by using two data from 37 and 10 GHz, since 10 GHz data are less anisotropic.
Even under rainy condition, 10 and 6 GHz data are not saturated, so wind speed will be able to be retrieved byusing those horizontal data. Retrieval accuracy of wind speed using 10 and 6 GHz will become worse than using
37 GHz, since a sensitivity of 10 and 6 GHz to wind speed is not so strong.
2. Wind speed from 37 GHz
The brightness temperature of vertical (V) polarization does not change under condition of sea surface windspeed less than 7 - 8 m/s. But, the one of horizontal (H) polarization increases monotonically with wind speed. At
37 GHz, the sensitivity is about 1K/(m/s). Above 7 - 8 m/s of wind speed, both V and H temperature increase.
Fig. 1 shows a thematic method of calculating wind speed. A line shown by “A” represents a calm sea state, andline “B” represents a roughened sea state. SSW is calculated from a horizontal length of “C” shown in Fig. 1.
When atmospheric opaque due to water vapor and cloud liquid water increase, both V and H temperature increase.
The atmospheric opaque is corrected by a convergence made by two lines of A and B. A position of the line A ischanged in accordance with SST change, and coefficients of slope and intercept defining the line A are alsochanged. Those coefficients given at 5 °C interval of SST from 0 to 35 °C.
The brightness temperature of 37 GHz is saturated under rainy condition, i.e., the ocean surface can not be seen
by 37 GHz data. A judge whether 37 GHz data can be used is made by using the value defined in Fig.1 in the
AMSR/AMSR-E SST algorithm.

Fig. 1 Retrieval of wind speed from the vertical and horizontal polarization data
3. Correction of anisotropic wind speed
SSW obtained by the method described in § 2 has a large anisotropic feature depending on an angle between theantenna direction and wind direction. Airborne Microwave Radiometer (AMR) experiments of NASDA suggestthat at about 9 m/s of wind speed, a difference of the length C defined in Fig. 1 reaches about 4K between the
downwind and upwind case. In such a condition of wind speed, the brightness temperature of V polarization of the
upwind direction is larger by about 2K than one of the downwind direction, and the difference of H polarization isabout 1K. At lower frequencies such as 10 or 6 GHz, the anisotropic features become weaker. Even at 13 - 14
m/s of wind speed, the difference is less than 1 K at 10 GHz.
In the current algorithm, the anisotropic feature is corrected by a combination of two lengths C from 37 and 10
GHz. Fig. 2 shows a thematic method to correct the anisotropic feature. C from 37 GHz has the larger
anisotropic feature than one from 10 GHz. Above 7 - 8 m/s of wind speed, two lengths C calculated from 37 and
10 GHz take different values between the downwind and upwind cases as shown in Fig. 2. The anistropic feature
is corrected by taking a middle position.

Fig. 2 Correction of anisotropic feature by using 37 and 10 GHz data

4. Wind speed from 6 and 10 GHz under rainy condition
The brightness temperature of 37 GHz is saturated under rainy condition, but ones of 10 or 6 GHz are notsaturated in almost cases. The sensitivity of H polarization at 37 GHz to wind speed is about 1K/(m/s) as
mentioned above, and ones of 10 and 6 GHz H are about 0.6K/(m/s). A retrieval accuracy using the former data
is much better than the latter data, but 10 and 6 GHz H data can be used in retrieval of wind speed under rainy
condition. The brightness temperature due to water vapor, liquid water (totally they are called as atmosphericopaque) increases as different behavior between 6 and 10 GHz. The brightness temperature change due to windeffect is almost same between 6 and 10 GHz. So, wind speed will be separated from the atmospheric opaque fromtwo data of 6 and 10 GHz H.
5. Reference
Shibata A. (1996) :Remote sensing on ocean surface by passive microwave radiometer , Kishou Kenkyu Note, no.
187, pp. 53-63.

AMSR/AMSR-E Sea Surface Temperature Algorithm
Akira SHIBATA
Meteorological Research Institute
1. Abstract
Sea Surface Temperature (SST) is retrieved mainly from AMSR/AMSR-E 6GHz and 10 GHz verticalpolarization (V) data, by using 37 GHz V and H (horizontal), 23 V, 6H, and 10H data as supplements. The
current SST algorithm includes following nine procedures.
(a) Incident angle correction(b) Atmospheric (water vapor, cloud liquid water) correction(c) Surface wind correction(d) Land contamination correction(e) Removal of sunglitter area(f) Salinity correction(g) Removal of sea ice area(h) Conversion to SST(i) Spatial running mean
A target of retrieved SST accuracy is within 0.5 - 0.7°C when compared with buoy SST.
2. Detailed data processing procedures(a) Incident angle correction
Correction of the brightness temperature, dA, due to incident angle variation is given by the following
equations;dA= - 2.9*(A - 55.0) 6 GHz V
dA= - 2.7*(A - 55.0) 10 GHz V,
where A is the incident angle. The horizontal polarization data are also corrected by similar equations.
(b) Atmospheric correction
Correction for atmospheric opaque is obtained from a pair of two temperatures of 23 GHz V and 37 GHz V.
Fig. 1 shows an example of getting the correction value for TMI 10 GHz which reads 37V and 21V to give thecorrection value for 10V. Because brightness temperatures of 23V and 37V are changed with SST, the table ismade with 5°C interval of SST from 0 to 35 °C. It is necessary to omit data contaminated by rain, since SST
accuracy becomes worse in rainy areas. Its judge is made by counting the number of pixels within 6 GHz or 10
GHz spatial resolution, in which the correction value shown in Fig. 1 is out of specified range. If the number ofpixels with out of range is larger than a threshold, SST is missing.
(c) Surface wind correction
Correction for sea surface wind is made independently from two frequencies ;6V and 6H, and 10V and 10H,
which are already corrected for atmospheric opaque. Fig. 2 shows a thematic map to make the wind correction.
Brightness temperature of V polarization is almost constant under a condition of sea surface wind speed less than
7 - 8 m/s. But, the one of H polarization increases uniformly. Above 7 - 8 m/s, both brightness temperature of
V and H polarization increase with wind speed, whose ratio is about 1 /1.7. This ratio may depend on a relative
angle between the wind direction and antenna direction, and also on a difference between SST and airtemperature.

Fig. 1 Effect of atmospheric opaque for 10 GHz V

Fig. 2 Effects of surface wind for 10 GHz V and H(d) Land contamination correction
Contamination by land emission increases drastically when the pixel approaches a shoreline, or the pixel includes
an island. Here, land contamination is corrected for pixels that the increment is less than 2 K. For pixels ofcontamination larger than 2 K, SST is missing.
(e) Removal of sunglitter area
Sunglitter is checked by using a relative angle between the antenna beam direction and sun direction, which is
given by L1B. SST is missing for pixels of the relative angle larger than 30°.
(f) Salinity correction

Salinity effect can not be neglected when SST is high as 30 °C, and the correction value is an order of 0.1 or 0.3
K. Its effect is calculated in advance by using the climate salinity, and a data set of correcting salinity effect isprepared with spatial resolution of 1 degree. This data set is not modified even after the launch.
(g) Removal of sea ice area
Sea ice will be detected by checking the value obtained from the atmospheric correction. If its value exceeds
5.5 K in the latitude larger than 65°, it is judged that the pixel is contaminated by sea ice. SST is missing when
the number of pixels with sea ice contamination exceeds a specified value.
(h) Conversion to SST
The relationship between 6V (or 10V) and SST is calculated by using the complex relative dielectric constantgiven by Klein and Swift (1977). Fig. 3 shows its the relationship.

Fig. 3

Relation between SST and 6 V ( or 10V)(i) Spatial running mean
The temperature resolution at 6 GHz is about 0.3 K for one pixel, which is corresponding to about 0.6°C of
SST. It is necessary to reduce its noise. A current method is a spatial running mean with 5 pixels by 5 pixels(50 km by 50 km area). The simulation indicates the reduced noise becomes less than 0.1 K after applying 5 by
5 running mean.
3. References
Shibata A., K. Imaoka, M. Kachi, and H. Murakami (1999) :SST Observation by TRMM Microwave Imager
aboard Tropical Rainfall Measuring Mission, Umi no Kenkyu, vol.8, no.2, pp. 135 to 139 (in Japanese)

ALGORITHM THEORETICAL BASIS DOCUMENT (ATBD)FOR THEADEOS/AMSR SEA ICE ALGORITHM
Josefino C. Comiso
Laboratory for Hydrospheric Processes
NASA Goddard Space Flight Center

1. Introduction
During the last century, the average global temperature has been increasing at the rate of 0.05K per decade(Jones, 1999). Because of feedback effects associated with the high albedo of ice and snow, such increases intemperature are expected to be amplified in polar regions (Budyko, 1966). Recent observations suggest that the
Arctic environment may indeed be changing. Limited submarine sonar data indicate that the Arctic sea ice coverhas been thinning by more than one meter in the last few decades (Rothrock et al., 1999; Wadhams and Davis,
2000, and Tucker et al., 2001) while sea ice extent in the same region has declined by about 5 to 6% in the lasttwo decades (Bjorgo et al., 1997; Parkinson et al, 1999). Even more intriguing is the observation that theperennial sea ice cover is retreating at the much faster rate of 7-8% per decade (Johannessen et al., 1999; Comiso,
2001). The implication of the latter if the rate persists is that in a matter of a little more than a century, theperennial sea ice cover may disappear completely, causing profound changes in the characteristics, climate, andecology of the Arctic system. To get this phenomena in proper perspective, more in depth studies of the changes
in the global sea ice cover and associated changes in the environment are needed.
Sea ice covers a significant fraction of the global oceans (about 5 to 8%) and is one of the most seasonalparameter on the Earth’s surface. Its high albedo, which ranges from about 80% (Grenfell, 1983) to 98%(Vowinckel and Orvig, 1970), compared to that of the open ocean (10% to 15%) minimizes heat absorbed by thesurface and results in a sharp contrast in energy flux between ice free and ice covered oceans. This abruptchange in energy exchange can, under appropriate conditions, affect atmospheric circulation and give rise toviolent weather systems known as polar lows (Carleton, 1985; Businger and Reed, 1989; Gloersen et al., 1989).
Sea ice with its snow cover is also an effective insulator that limits the exchange of energy and momentum
between the ocean and atmosphere. For example, in winter, the heat flux in an open lead exceeds by two ordersof magnitude the heat flux through an adjacent thick ice cover (Badgley, 1966; Maykut, 1978). A large fractionof world’s deep and bottom water is believed to be formed at polar latitudes (Stommel, 1962; Gordon, 1978;
Killworth, 1983). Coastal polynyas near shelves around the Antarctic continent have been noted as ice factories
and principal sources of bottom water (Zwally et al., 1985; Comiso and Gordon, 1998). The cold, dense water
formed from sea ice growth in Arctic coastal polynyas helps maintain the Arctic Ocean halocline (Aagaard et al.,
1981; Cavalieri and Martin, 1994). This dense water can also induce convection and deepen the mixed layer.
Similar phenomenon is observed in the Odden, which is an ice tongue formation in Greenland Sea (Shuchman etal., 1996; Comiso et al., 2001) regarded as one of only four regions where open ocean convection occurs with thedirect generation of deep water.
Because of its vast extent, large scale studies of the sea ice cover can be done most effectively through the useof satellite data. The later is available through various frequency channels from visible through infrared tomicrowave frequencies. Visible and infrared satellite data (e.g., AVHRR) have been used for mesoscale studies
but the coverage of sea ice provided by the data is limited because of the persistence of cloud cover in polar
regions. Detailed characterization of sea ice under all weather conditions has recently been provided bysynthetic aperture radar (SAR) data (e.g., ERS-1, JERS-1, and Radarsat) but only a small fraction of the entire ice
cover can be monitored at a time because of operational and data acquisition constraints and a narrow swath width(100 km to 500 km) that limits spatial and temporal resolution. These data sets have nonetheless been usefulfor regional studies and provide information that have been used to improve the interpretation of other satellite
data.
The most comprehensive and consistent source of global sea ice data has been satellite passive microwave
sensors (Zwally et al., 1983; Parkinson et al., 1987; Gloersen et al., 1992). Microwave sensors, not limited byweather conditions or light levels, are particularly well suited for monitoring sea ice, because of the strong

contrast in thermal microwave emission between areas of ice-free ocean and ice-covered waters. The firstpassive microwave sensor used extensively for studying the global distribution of sea ice was the Electrically
Scanning Microwave Radiometer (ESMR) on board the NASA Nimbus 5 satellite (Gloersen et al., 1974; Zwally
et al., 1983). The single channel ESMR, operating at 19.35 GHz, provided daily coverage of the polar regions
and allowed for the first time synoptic observations of sea ice concentration needed for undertaking a detailed
study of global sea ice variability. The ESMR sea ice algorithm was based on a linear relationship between theradiometric brightness temperatures of ice-free water and consolidated sea ice. Temperature variability effects
were reduced using climatological data. At the ESMR frequency the contrast between ice and water is ~100 K.
Although the estimated accuracy was only 15% (Comiso and Zwally, 1982), these data were used successfully to
document sea ice changes in both hemispheres (Zwally et al.,1983; Parkinson et al., 1987).
The Scanning Multichannel Microwave Radiometer (SMMR) was launched on the SeaSat and Nimbus-7
research satellites in July 1978 and October 1978, respectively (Gloersen and Barath, 1977). With its
multichannel capability, SMMR provided more information about the ice cover than ESMR. Multichannel
SMMR algorithms extended the calculation of ice concentration to include the discrimination of two ice types,
first-year and multiyear in the Arctic (Svendsen et al., 1983; Cavalieri et al., 1984; Swift et al., 1985) and sea ice
temperature (Gloersen et al., 1992). Errors in the retrieval of multiyear ice concentration are, however, reported
to be large (Kwok et al., 1996) because of the large variability in the emissivity of multiyear ice. A multichannel
SMMR algorithm to obtain sea ice concentration only was also developed (Comiso and Sullivan, 1986; Comiso,1986). The various algorithms take advantage of two or more channels to reduce errors associated with physicaltemperature variability, emissivity anomalies, and weather effects. In 1987, the first in a new series of passive
microwave radiometers was launched as part of the Defense Meteorological Satellite Program (DMSP). Thissensor, called the Special Sensor Microwave/Imager (SSM/I), operates at frequencies ranging from 19.4 GHz to85.5 GHz. The SSM/I measures both horizontally and vertically polarized components at all frequencies except
at 22.2 GHz for which only a vertically polarized component is obtained.
The advent of the Advanced Microwave Scanning Radiometer (AMSR) sensor, will mark a significant
improvement in the capability for monitoring the sea ice cover. The new sensor will be basically a combinationof both SMMR and SSM/I systems but with much better resolution. This means improvements in the ability toremove ambiguities in sea ice concentration through the use of the 6 and 10 GHz channels which have muchbetter contrast in the signature of sea ice and open water than SSM/I channels. These channels also allow for thedetermination of ice temperature, which is an important polar parameter, and can be used to minimize
uncertainties in the derived ice parameters that are associated with the spatial variability of ice temperatures.
The high resolution data provided by the 85 GHz will also be useful in discriminating different surface types that
may be associated with different emissivities.
2. Scientific Objectives
The specific objectives of this document are (a) to provide the theoretical basis of the algorithm that will be
used to generate sea ice data sets from AMSR brightness temperatures; (b) to assess the accuracy of theseproducts; and (c) to evaluate the range of applicability and the limitations of the derived data. Although passive
microwave satellite data have been around for a while, AMSR will be a new high performing instrument that
requires algorithms designed to take advantage of its added capabilities. AMSR data are expected to provide thebaseline for new polar climate data sets and the means to evaluate the quality and consistency of historical satellite
data. High quality and consistently derived sea ice parameters are needed to ensure that the time series data aresuitable for climate change research (e.g., trend and mass balance studies).
Accurate and consistent data on sea ice cover are needed to fulfill some of the scientific goals of NASDA’s
ADEOS-II project. Among the objectives is to acquire data sets needed for climate change studies andmeteorology research. More specifically for the polar regions is to study processes associated with sea ice, toimprove and verify global circulation models (GCM), and to gain insights into the changing global climate asreflected in the polar regions. For process studies, it is important to detect and quantify the small but physicallysignificant changes in the physical characteristics of the ice cover, especially in polynya and divergence areas andin the marginal ice zones. Accurate quantification of these polynyas and divergence areas are important in thatthey are the primary source of global bottom water (Gordon and Comiso, 1988; Martin et al., 1992). There
should also be a good match of the sea ice cover as observed by satellites with those derived from GCMs. Thiswill ensure that the physical and mathematical formulation of these models as well as the assumptions made arebased on solid foundations. Furthermore, studies of the changing ice cover and its future requires high standards
in the quality and accuracy of retrieved satellite data (Bjorgo et al., 1997; Cavalieri et al., 1999; Comiso andSteffen, 2001). A fully validated algorithm for generating such a data set will go a long way towards fulfilling
this goal.
3. AMSR Instrument Characteristics
The AMSR is a fourteen channel, eight-frequency total power passive microwave radiometer system that will
be launched aboard the ADEOS-II satellite in 2002. It measures vertically and horizontally polarized radiances
at 6.925, 10.65, 18.7, 23.8, 36.5, 50.3, 52.8, and 89.0 GHz. A second instrument, called AMSR-E, is a slightly
modified version which will be launched on board EOS-Aqua satellite also in 2000. The ADEOS-II is amorning satellite while the EOS-Aqua is an afternoon satellite. Data from the two systems thus complement
each other and will all be acquired and processed by NASDA’s Earth Observation Center. AMSR consists of an
offset parabolic reflector 2 m in diameter, fed by an array of seven feedhorns. The AMSR rotates continuously at
40 rpm about an axis parallel to the local spacecraft vertical. At an altitude of 802.9 km, it measures the
upwelling scene brightness temperatures over an angular sector of + 61o about the sub-satellite track, resulting in aswath width of 1600 km. During a period of 1.5 seconds the spacecraft sub-satellite point travels 10 km. Even
though the instantaneous field-of-view (IFOV) for each channel is different, active scene measurements arerecorded at equal intervals of 10 km (5 km for the 89 GHz channels) along the scan. The half-cone angle atwhich the reflector is fixed is 47.4 o which results in an Earth incidence angle of 55.0 o . Table 1 lists the pertinent
performance characteristics
The radiometer calibration error, exclusive of antenna pattern correction effects, is composed of three major
contributors: warm load reference error, cold load reference error, radiometer electronics nonlinearities and errors.
An estimate of the warm load reference error is ~0.5 K, based on the RSS of the various components. The error
in the cold reference measurement is mainly produced by the error in coupling between the cold sky reflector andthe feedhorn. This is estimated to be ~0.5 K. The radiometer electronics nonlinearity results in an error thatcan be estimated during the thermal vacuum calibration testing (on SSM/I this error is ~0.4 K). A source of error
in the receiver electronics is the gain drift resulting from temperature variations over one orbit. This error
depends on the design of the receiver and overall design of the sensor. The gain drift can be as much as ~0.24 K
for a temperature variation of less than 10 K over one orbit. Accounting for all errors, the total sensor bias error
is 0.66 K at 100 K increasing with temperature to 0.68 K at 250 K.

Table 1. ADEOS AMSR SENSOR PERFORMANCE CHARACTERISTICS___________________________________________________________________________________________
CHARACTERISTICS
CENTER FREQUENCIES (GHz)
6.9
10.7
18.7
23.8
36.5
89.0
50.3
52.8
___________________________________________________________________________________________BANDWIDTH (MHz)
350
100
200
400
1000
3000
200
400
SENSITIVITY (K)
0.3
0.6
0.6
0.6
0.6
1.1
IFOV (km x km)
76x44
49x28
28x16
31x18
14x8
6x4
12x8
12x8
SAMPLING RATE (km x km)
10x10
10x10
10x10
10x10
10x10
5x5
INTEGRATION TIME (ms)
2.6
2.6
2.6
2.6
2.6
1.3
BEAM EFFICIENCY (%)
95.3
95.0
96.3
96.4
95.3
96.0
BEAMWIDTH (degrees)
2.2
1.4
0.8
0.9
0.4
0.18

4. Standard and Research Products
The standard product for sea ice is sea ice concentration which is deemed essential to meet the overall scientificobjectives of the ADEOS program. Ice temperature is also derived by the same algorithm and will be generated
as a research product (Table 2). These products will be mapped to a standard polar grid currently used for the
SSM/I (NSIDC, 1992). The grid resolutions for the AMSR brightness temperatures and sea ice concentrations
were selected to take advantage of the full spatial resolution of the AMSR, while still providing continuity with

similar data from SMMR and SSM/I. Accuracies of the derived sea ice data will be determined with the aid of
a comprehensive validation program described in section 5. In addition to the sea ice parameters, gridded
brightness temperatures will also be provided at grid resolutions commensurate with the Level 2A
spatially-averaged data (Table 2). Note that the 6.9 and 10.7 GHz data are gridded at a finer resolution thanactual resolutions of about 58 and 37 km, respectively. The reason is to be able to use these channels in
combination with higher frequency channels without losing too much on the resolution in the latter which are theprimary channels for the algorithm. Further justification for using this gridding procedure will be presented later.
It should be pointed out the sampling rate is 10x10 km for the 6.9GHz to 36.5 GHz channels and is 5x5 km for the
89 GHz channels. Also, observations at 6.9 and 10.7 GHz are produced at a spatial interval of approximately
20-km and at the sensor sampling rate for the other frequencies. Level 2A brightness temperature data will be
convolved using the Backus-Gilbert method to provide the spatial averaging that is especially useful in thegridding the 6.9 and 10.7 GHz data at a finer resolution than actual resolution.

Table 2. AMSR Level 3 Tb and Sea Ice Data Sets________________________________________________________________________________________PARAMETERAPPROX.
GRIDTEMPORAL FOOTPRINTRESOL.
RESOL. SIZE________________________________________________________________________________________
6.9
58 km
25.0 km
10.7
37 km
25.0 kmDaily Ascend., Decend., & Combined
18.7
21 km
25.0, 12.5 km
Daily Ascend., Decend., & Combined
23.8
21 km
25.0, 12.5 km
Daily Ascend., Decend., & Combined
36.5
11 km
25.0, 12.5 km
Daily Ascend., Decend., & Combined
89.0
5 km
25.0, 12.5, 6.25 km
Daily Ascend., Decend., & Combined
Sea Ice Conc.
25.0, 12.5 km
Daily Ascend., Decend., & Combined
Sea Ice Temp.
25.0 kmDaily Ascend., Decend., & Combined________________________________________________________________________________________
Sea ice concentration has been the parameter that is produced routinely from satellite passive microwave datafor both global change research and operational requirements. It is the parameter that is used to quantify theextent of sea ice cover, the location of ice edges, the area of open water within leads and polynyas in the ice pack,and the amount of ice that survives the melt season. It is, however, a quantity that is difficult to define becauseof the ever changing nature, and therefore signature, of the ice cover. For example, as ice evolves from open
water through grease ice, nilas, young ice and then thick first year ice with snow cover, the emissivity of thesurface also changes constantly from that of open water to that of thick first year ice cover. Thus, in areas of
predominantly new ice cover, the retrieved ice concentration can be less that those of thick ice cover, even if thefraction of true open water in both regions are the same. The change is similar to that of the reflectivity of thesurface as observed in visible channel data and provide the means to identify areas of interest such as those ofpolynyas and divergence regions.
Ice temperature, which is a research product, is of great importance for polar studies especially in energybalance calculations. Direct measurement of ice surface temperature is particularly valuable for sea ice coverprediction models (Preller et al., 1992). When combined with ice concentration measurements, ice temperature
data would considerably reduce current uncertainties in the estimates of polar energy budgets. The monitoring of
long-term changes in ice temperature may also provide valuable information about changes in the thickness of theice and its snow cover. While AVHRR ice surface temperature algorithms have been developed (e.g., Schluessel
and Grassl, 1990; Yamanouchi and Seko, 1992; Comiso, 2000), spatial and temporal coverage is limited by thepresence of clouds as noted earlier. On the other hand, passive microwave would provide continuous coverage atgood spatial and temporal resolution. It should be pointed out that the parameter retrieved from AMSR
represents the snow/ice interface temperature in the seasonal regions and the average temperature of the freeboard
layer of the ice in the perennial ice regions.
5.0 Algorithm Description and Theoretical Basis

The basic radiative transfer equation that applies to the brightness temperature, (TB) observed by satellites at agiven wavelength isTB =εT S e-ττ+T(z) ζ(z) e-τ +τ ’(z) dτ’(z)0+(1-ε)κ e-ττ

T(z) ζ(z) e-τ ’(z) dτ’(z)0(1)

where ε is the emissivity of the surface, TS is the physical temperature of the surface, τ’(z) and τ are theatmospheric opacities from the surface to a height z and from the surface to the satellite height, respectively, κ isan estimate of the diffusiveness of the surface reflection, and ζ(z) is the emittance at z. In equation (1), the firstterm represents radiation directly from the earth’s surface which is the dominant contribution. The second term
represents satellite observed radiation directly from the atmosphere, while the third term represents downwellingradiation from the atmosphere but reflected from the surface of the earth. A fourth term that takes into accountthe reflected contribution of radiation from free space, which is a negligible additive contribution, is not includedin equation (1).
Within the ice pack, the radiation observed by the passive microwave satellite sensor comes from ice covered
surface, open water, or a combination of both. The observed brightness temperature, TB, is expressed in terms of
the relative contribution from each surface by a linear mixing formulation given by
T B = TO CO + TICI

(2)

where TO and TI are the brightness temperatures of ice-free ocean and sea ice, respectively. CO and CI are thecorresponding fractions of each of the two ocean surface components within the field-of-view of the instrument
and add to unity (e.g., CO = 1-CI). Equation (2) forms the basis for sea ice concentration algorithms. The
challenge is how to take into account temporal and spatial changes in TO and TI which are both functions ofemissivity (ε), temperature (T S), and atmospheric opacities (τ, and τ’), as indicated in equation (1). Suchchanges can be taken into account or at least minimized through the utilization of several AMSR channels as will
be described below.
5.1

Basic Bootstrap Algorithm

Passive microwave data have been especially useful for sea ice studies because of the relatively high contrast in
the emissivity of open water and sea ice (Zwally et al., 1983). The contrast is frequency dependent and is higher
with the low frequency channels than with the high frequency channels. Thus, if resolution is not an issue, the
6.9 GHz data from AMSR would be best suited for ice retrievals since it provides the best contrast between ice
and open water. The radiation at this frequency is also less vulnerable to atmospheric and surface effects thanthat of the other channels making the frequency channel especially useful for retrieving ice temperatures. The
additional use of the 10.7 GHz data is also promising because of better resolution than the 6.9 GHz data and may
be utilized to improve the accuracy of the ice concentration retrievals.
Assuming a linear relationship between the brightness temperature and the fraction of ice cover, as in equation(2), the ice concentration, CI, corresponding to an observed brightness temperature, TB, over a sea ice covered
region can be derived from the equation
CI = (TB - T O )/(TI - T O ).

(3)

T O , TI , and T B all include contributions from the intervening atmosphere, as described in Zwally et al. (1983). T I
varies spatially mainly because of spatial changes in the emissivity and temperature of the ice, while TO isapproximately constant for open water surfaces within the ice pack. Thus, the success of an ice concentration
algorithm depends on how accurately the value of TI is determined. Equation (3) can be used without correcting
each data element for atmospheric effects as long as the atmospheric opacity is relatively uniform spatially for theset of frequency channels that are used in the algorithm. At the frequencies utilized, any advantage provided by
an atmospheric correction through a radiative transfer model is usually negated by errors in the model due to thepaucity of radiosonde atmospheric data. As will be shown later, the impact of the variability of atmosphericeffects on the accuracy of derived sea ice parameters appears to be negligible.

The Basic Bootstrap Algorithm (BBA) is based on the original Bootstrap Algorithm that is currently used forprocessing SMMR and SSM/I data (Comiso, 1986; Comiso, 1995; Comiso et al., 1997) in which TI and TO inequation (3) are determined through the use of multichannel data. Data from three sets of channels have beenfound to be especially useful: (a) 19 GHz and 37 GHz brightness temperatures, both vertically polarized (called
V1937); (b) vertically and horizontally polarized 37 GHz brightness temperatures (called HV37); and (c) 19 GHz
and 37 GHz brightness temperatures, both horizontally polarized (called H1937). Scatter plots in 2-dimensional
space using the HV37 and V1937 combinations are shown in Figures 1a and 1b, respectively. The data points
were collected by a set of P3a aircraft radiometers flown over nearly 100% ice cover in the Arctic in May 1987
(Comiso et al., 1991). In both plots, the data points are mostly along the line AD and form a compact andelongated cluster of points similar in characteristics to those of satellite data (Comiso, 1986). The linearity of thedata points along AD is the key information that is utilized by the Bootstrap Algorithm to identify the proper
value of TI in equation (3). In the scatter plot shown in Figure 1a, data points of open water within the packwould fall near the location labeled O. Thus, for an observation corresponding to any data point, B, in this 2-D
space, TI is a data point along the line AD and its value is inferred from the intercept of the lines AD and OB.
Ice concentration is determined basically from an equivalent form of equation (3), which in this case is the ratio of
OB to OI, as described in Comiso (1995). The complete formulation is given in Comiso (1995) and explicitly inthe next section but with brightness temperature data replaced by emissivity data. The existence of consolidated
ice clusters such as those along AD in Figure 1 have been confirmed by ship radiometer data over the Antarctic(Comiso et al., 1989; Grenfell et al., 1994) and over locally grown sea ice at CRREL (Grenfell and Comiso, 1986).
The variability of the data points across the consolidated ice cluster defined by the line AD in the similar scatterplots that make use of satellite data is a measure of the variability of TI and includes temperature, emissivity, andatmospheric effects.
In the Arctic, a combined used of the HV37 and V1937 sets is desirable because of spatial inhomogeneity andcomplexity in the physical characteristics of the ice cover (Comiso, 1986). The use of the HV37 set is especiallyadvantageous in the perennial ice region in winter, because the slope of data points in this set is close to unity andhence the temperature effects are minimal. Also, the standard deviation of data points about the line AD is close
to 2K which is equivalent to 2.5% error in the estimates of ice concentration. This reflects how well sea ice
concentration can be derived in the region. The V1937 set is a good complement of the HV37 set and has theadvantage that it uses vertical channel data only which are observed to be less affected by layering andinhomogeneities in the ice (Matzler, 1984; Grenfell et al., 1994) than the horizontal channels. This set has beenfound to be especially suitable in seasonal sea ice regions as in the peripheral seas of the Arctic and most part of
the Antarctic (Comiso et al., 1984; Comiso and Sullivan, 1986) where snow cover is known to have layering and avery complex texture (Massom et al., 1998; Worby and Massom 1995).
Although the V1937 set is more sensitive to fluctuations in ice temperature than the HV37 set (Comiso, 1995),
the spatial variations in surface ice temperature (i.e., snow ice interface temperature), as observed from limited
data in the Antarctic, has been observed to be relatively small and have a standard deviation of about 2K.
Sensitivity studies and analysis of the distribution of the consolidated ice cluster indicate that the error fromtemperature effects is indeed small compared to other sources of error. In the Antarctic, the HV37 set is not as
useful as in the Arctic because consolidated ice data in this set are close to or almost along the line OA. The useof this set would lead to the retrieval of erroneously large fraction of open water in some consolidated ice regions.
The V1937 set has thus been the primary set used to retrieve ice concentrations from SMMR and SSM/I data.
Recent studies, however, indicate that the accuracy of the retrieved product in the Antarctic can be further
improved with the use of a formulation similar to that of the Arctic but with the H1937 set used instead of the
HV37 set. The additional use of the H1937 set has been observed to be especially useful in young ice regions
and enables a better characterization of the sea ice cover near coastal and polynya areas. The use of the latter is a
new and is currently part of the Basic Bootstrap Algorithm.
Typical monthly sea ice concentration maps derived using BBA for the Northern and Southern Hemispheres
during summer and winter are shown in Figure 2. The large seasonal change in the extent of the ice cover inboth hemispheres are apparent. Also apparent are relatively lower concentrations than average along coastlines,
which are sites of coastal polynyas, near islands and big icebergs, and along the ice edges. These regions aresites of open water and new ice. The maps thus represent what is generally expected as ice distributions in bothhemispheres.

5.2 The AMSR Bootstrap Algorithm
The AMSR algorithm for sea ice is a modified version of the Basic Bootstrap Algorithm and is called the
AMSR Bootstrap Algorithm (ABA). The modified version will provide the means to estimate surface ice
temperature and at the same time use the latter to further reduce errors in the determination of ice concentration.
In particular, it makes use of 6.9 GHz data to reduce if not eliminate temperature effects when the V1937 andH1937 data sets are utilized. The algorithm has been successfully tested using SMMR data which have the basic
channels required. However, some adjustments would be needed after launch when real AMSR data becomes
available since SMMR is known to have problems with calibration and the resolution of the 6 GHz channels iscoarse at 150 km, compared to 58 km for AMSR.
The schematic of the procedure for estimating of ice concentration and ice temperature, is shown in Figure 3.
The technique which was reported in Comiso and Zwally (1997) is similar to that of the Basic Bootstrap
Algorithm, as described in Comiso (1995), with TB replaced by ε, the latter basically independent of temperaturefluctuations. The effective emissivity of the surface within each data element can be estimated from
εB = εI CI + εO (1-CI)(4)

where CI is initially obtained from equation (3) through the use of a combination of 6 and 37 GHz channels at
vertical polarization, while εI and ε0 are emissivities of ice and open water, respectively, which can be derived
from histograms of data within the pack and assumed constant. Unlike equation (2), equation (4) is not the exact
formulation for the observed satellite data but sensitivity studies indicate that the associated error is very small(<1%) and is highest when the concentration is 50%. The physical temperature of the ice surface within eachdata element is then given by
Tp = TB (6V)/εB(6V)
where TB(6V) is the observed brightness temperature of the surface at 6 GHz (vertical polarization).
emissivity of the surface at 19 and 37 GHz can then be derived from

(5)
The

εB(19V) = TB(19V)/Tp(6)

ε B(19H) = TB(19H)/Tp(7)

ε B(37V) = TB(37V)/Tp(8)

ε B(37H) = TB (37H)/Tp

(9)

and

with the assumption that the temperature of the layer of ice from which radiation emanates is approximately
frequency independent between 6 and 37 GHz and is equal to Tp. The use of emissivity instead of brightness
temperature for estimating ice concentration is justified by the matching of reference data points of bothconsolidated ice (100% IC) and open water (0% IC) as discussed in Comiso and Zwally (1997). As in Comiso(1995) which makes use of brightness temperatures, the tie points for a datapoint at B are represented by theintercept points (ε1I,ε2I ) along the 100% ice line AD which are calculated using the equations
ε1I = ( ε1A - ε1O - εA2 SAD + ε2O SOB )SOB /(SOB -SAD )+ ε1O - SOBε2O(10)

ε2I = (ε1A - ε1O - ε2A SAD + ε2O SOB )/(SOB -SAD )(11)

where SAD and SOB are slopes of the lines AD and OB, respectively, (ε1A , ε2A) represents any point along the line
AD, and (ε1O , ε2O) represents the open water reference emissivity. The ice concentration for the data point at B
is derived from the ratio of the distances OB and OI (see Figure 1) and given by the equation
C = [{(ε1B - ε1O )2 +(ε2B - ε2O )2 }/{(ε2I - ε2O )2 + ( ε1I - ε1O )2 }]1/2(12)

In the formulation, it is convenient to choose ε2A =0 at point A along AD with ε1A the resulting offset.
Additional details, including the assumptions in the determination of the line AD and the point O, are discussed inComiso (1995). Since the initial calculation of the emissivity at 6.9 GHz makes use of ice concentration that has
not been temperature corrected, the emissivity is recalculated using the more accurate result from equation (12)and a second iteration follows, starting with equation (4) as indicated in Figure 2, to obtain the final ice
concentration estimate. Also, the final value of Tp is then used to calculate the average physical temperature ofice surfaces in each data element, TS, using the equation
T S = [TP – T O (1-CI)]/CI .

(13)

To illustrate the effectiveness of ABA, we make use of SSM/I data in conjunction with skin surface
temperatures derived from AVHRR data (Comiso, 2000) since the former do not have a 6.9 GHz channel.
Figures 4a-4d show examples of skin surface temperature maps for a summer (March) and a winter (September)month in 1992 in both hemispheres. The images show temperature distributions over the open water, sea ice,and the continent and illustrate how surface temperature changes spatially at various latitudes. As expected, thecoldest temperatures are located in the continent while intermediate but still subfreezing temperatures are over sea
ice with the temperatures increasing progressively towards the north. Areas of polynya formation are usually
warmer than adjacent regions. These temperature data are then converted to snow/ice temperature data, thatwould represent TP in the above formulation, using regression parameters derived by Comiso et al. (1989) using
data in the Antarctic region.
To illustrate the difference between the use of brightness temperatures alone compared with the use ofemissivity, Figures 5 show scatter plots using the HV37 and V1937 sets for both variables in the Arctic region
during winter. The distributions for brightness temperatures are shown to be very similar to those of emissivities.
The cluster along the consolidated ice (AD) are also shown tobe equally compact. Although there are large
spatial variations in surface temperature as indicated in Figure 4, the net effect on the distribution of the data
points in the HV37 and V1937 sets appears to be small.
In the consolidated ice regions, the data points are apparently redistributed such that the net variability about thecluster AD in the emissivity plots is essentially the same as in the brightness temperature plots. This implies
very similar errors for both systems. Similar plots are shown in Figure 6 for the Antarctic. Again thebrightness temperature plots are very similar to those of the emissivity plots.
Ice concentrations were derived using TP from AVHRR and ABA for the same summer and winter months of1992 (as in Figure 2) and the results are presented in Figures 7a-7d. The maps for each season look very similar
with the areas of high ice concentrations and reduced concentrations confined in the same general locations. The
ice concentration maps for September 1992 in the Antarctic have been shown to be consistent with Landsat and
OLS satellite observations (Comiso and Steffen, 2001), and with the expected behavior of the ice cover in coastaland some deep ocean regions (e.g., near the Maud Rise and the Cosmonaut Sea) where polynyas have been
observed. Difference maps between the BBA and ABA ice concentrations for each season are shown in Figures
8a-8d. Generally, the two maps are basically identical within errors. Relatively higher concentrations (by lessthan 4%) are observed with the ABA in the Central Arctic and near the continent in the Antarctic region where thedifference are likely due to much colder temperatures than average. It is interesting to note, however, thatalternating positive and negative differences are observed around the periphery of the Antarctic ice cover. Thisis coherent with the effect of the Antarctic Circumpolar Wave (ACW) as described by White and Peterson (1996)
in which alternating high and low temperature anomalies are observed. The advantage with ABA, is that it
enables the retrieval of surface ice temperatures , and has the potential of obtaining more accurate retrievals incoastal polynyas and in regions where the surface ice temperatures are abnormally cold. The difference from thetwo retrievals may be small but for some regions, like polynya regions, the impact may be significant.
Since low frequency channels are not available in the SSM/I system, ABA was also developed and tested using
Nimbus-7 SMMR data. The SMMR system, which has a 6.6 GHz channel, provided the means to put together aworking version of ABA that has the right input parameters. However, the effectiveness of ABA, especially in
retrieving ice temperatures, could not be fully tested because of very large footprints for SMMR and instrumental
problems associated with polarization mixing. This made it difficult to evaluate discrepancies between BBA andABA results. The advent of AMSR data and the validation program will provide the means to test and refine theprogram and validate the results.
5.3

Masking Algorithms

Since the polar maps include land areas, a land mask is used to ensure that the algorithm is applied on data inthe ocean regions only. Previous versions of such land mask have been based on existing maps put together
through collaborative efforts of many agencies and foreign countries but the accuracy in some areas have beenquestionable because of the lack of direct measurements in these areas. Such mask has been updated using datafrom a dedicated RADARSAT mission in the Antarctic in 1998. Significant differences between the old and the
new maps are apparent, reflecting some errors in the previous data and a constantly changing continental
boundary due to surges and iceberg calving. The comparison indicates that surges at the Ross Ice Shelf andRonne Ice Shelf have been going on in the last few decades. If the previous land mask currently used for SSM/I
data is used on recent data, it would produce erroneous coastal polynyas of about 50 km wide. It is apparent thatthe location of the continental margin is not constant and that regular updates in the land mask for sea ice
retrievals is needed.
At the ice-free land/ocean boundaries, there are also erroneous ice concentrations in the ocean part adjacent toland because the brightness temperatures are similar to those of ice covered regions. To illustrate this problem,
an ice concentration map in the Ross Sea region is shown in Figure 9a during the summer when the Ross Sea Ice
Shelf boundary has a minimum of sea ice. Along the continental boundary, significant ice cover is retrieved by
the algorithm. The result for applying an algorithm developed by Cho et al. (1996) is shown in Figure 9b. The
technique uses a running 3 by 3 matrix with the middle pixel in consideration. If there is a land pixel in thematrix, the middle pixel value is replaced by the minimum value within the 3 by 3 matrix. The technique iseffective in removing some of the pixels with non-zero ice concentration in the north and western side but overall,
improvements appeared to be needed. An improved version of this technique is currently used for the Bootstrap
algorithm and when applied, the result is shown in Figure 9c. This later technique which searches one or two
pixels further to find open water generally better results than the Cho et al. technique, as indicated, but at the frontof the ice shelf, there is still significant ice. Generally, it works better in other regions but for this particular case,it did not work very well because of aforementioned problem with the land/ocean mask. The ice covered area infront of the shelf is more than should be the case because the actual front of the shelf is further north than
indicated by the land mask (white). The latter technique is more effective when there is less contamination along
the coastline, as is usually the case, and also when AVHRR climatological temperature data are used to mask out
areas in relatively warmer oceans.
The retrieved ice concentrations also show erroneous data in areas of open ocean where the signature is similar
to those of ice covered ocean. This usually happen in areas of abnormal weather and/or wind conditions. A
masking technique to automatically eliminate such bad data in the open ocean has been developed,as described inComiso (1995), but such technique is not 100% efficient, especially with SSM/I because the lowest channel isclose to the water vapor line. The use of the AVHRR climatological data in conjunction with the ocean masking
technique provide significant improvements but not near the sea ice margin. The use of low frequency AMSR
data, which are less sensitive to weather effects (e.g., 6.9 and 10.7 GHz) and show better contrast between sea ice
and open water are expected to significantly reduce errors in the marginal ice region.
5.4 Error Analysis and Sensitivity Studies
The physical basis of and assumptions in the Bootstrap algorithm have been confirmed using ship based
radiometer experiments in the Antarctic (Comiso et al., 1989; Grenfell et al., 1994), an aircraft experiment in the
Arctic (Comiso et al., 1991) and a controlled sea ice experiments at the Cold Regions Research Laboratory(Grenfell and Comiso 1986). Comparative studies of ice concentrations derived from SSM/I using the Bootstrap
Algorithm with those derived from aircraft, SAR, Landsat, and helicopter data have indicated consistencies within
an average of 5 to 15% in winter and 10 to 20% in the summer (Comiso et al., 1984; Comiso, 1986; Comiso et al.,
1991; Comiso and Kwok, 1996; Comiso and Steffens, 2001). Good validation data sets for much of the
Antarctic region, however, have been difficult to come by and hence the need for a coordinated aircraft and in situ
validation program in the region, especially for a new and more versatile system like AMSR.

Errors associated with the estimate of ice concentration are caused primarily by spatial and temporal changes insurface temperatures, emissivity, and atmospheric opacity. Other sources of errors include the retrieval oferroneous ice concentrations in the open ocean and at the land/ocean boundaries as discussed in the previous
section. The impact of surface temperature has been examined and discussed previously. It is apparent that themaps generated with BBA and with ABA, provide results that are almost identical within errors. Sensitivity
studies for errors due to variations in temperature has also been reported previously (Comiso, 1995; Comiso et al.,1997). Because the snow cover is such a good insulating material, the spatial fluctuation of the snow/ice
temperature has been found to be relatively small (with σ being about 2.5 K). The Antarctic sea ice cover is very
seldom without a snow cover not only because of frequent snow precipitation but also because of drifting snow.
However, katabatic and geostropic wind can be persistent in some areas, depleting the snow cover and causing thetemperature of the emitting sea ice surface to be abnormally low in some regions of Antarctica. The difference
maps in Figure 4 show that in these regions, the average bias due to temperature is about 2 to 4%. This
discrepancy is small but if verified to be indeed a bias associated with temperature, the use of ABA provides
enhanced ability to characterize more accurately small features of scientific interest, such as coastal polynyas, thesizes of which are sometimes comparatively small.
The large variability in the emissivity of the sea ice cover (Grenfell et al., 1994) is likely the main source oferror in the determination of sea ice concentration. The success of the algorithm depends on the ability toestablish the right tie-point (TI) for each data element. Cluster analysis results indicate that most of the data
points representing 100% ice cover tend to cluster along the line AD in Figure 1. This information enables thealgorithm to account for the large variability in emissivity (and also in temperature and atmospheric opacity).
The algorithm assumes that the cluster is approximately linear. Any significant deviation of an ice data pointfrom this linearity and the location of the AD line produces an error. Also, the accuracy in the retrieval depends
on the compactness of this cluster along the line AD.
In the Arctic, the distribution of the data points in the HV37 and V1937 sets are shown in Figure 5a and 5b forbrightness temperatures and Figures 5c and 5d for emissivities. In the Central Arctic, the data points have astandard deviation of about 2 K about this line for the HV37 set which is the main set used in the region. In the
Antarctic, the scatter plots for H1937 and V1937 are shown in Figure 6 and indicate less defined distributions
along AD than those in the Arctic. The standard deviation about the cluster line is higher at about 5K for theV1937 set which is previously the only set used in the region. The error in the determination of ice
concentration is thus higher in the Antarctic than in the Arctic.
Polarization and gradient ratios have been used in the NASA Team Algorithm to overcome spatial variations insurface ice temperature. The use of this technique, is apparently not so effective in the seasonal ice region,
especially in the Antarctic, because of possible differences in the response of the vertically and horizontally
polarized radiation to different surface and subsurface conditions within the ice pack can be very different(Markus and Cavalieri, 2000; Comiso and Steffen, 2001). The results is also an indication that variability inemissivity is indeed a much bigger source of error than variability in ice temperatue.
Depending on frequency, the emissivity of first year sea ice can be very different from that of multiyear ice.
This is especially the case in the Arctic because of the presence of an extensive perennial ice cover. In the
Antarctic, the signature of multiyear ice is more difficult to establish. At the end of the summer, the region withthe largest area of sea ice cover is located in the Western Weddell Sea. However, the signature of ice in thisperennial ice region is similar to that of most other Antarctic regions (Zwally et al., 1983). The reason for this isthat the summer ice is actually advected to the northeast during the subsequent winter following the direction of
the Weddell Gyre and causing the ice cover in the Western Weddell region to be eventually replaced by seasonalsea ice during the year. However, in other areas like the Bellingshausen/ Amundsen (B/A) Seas, the signature ofice in the winter is different from those of other regions. This was most apparent in the 1980s when the region
was consistently covered by perennial ice during the summer. Unlike the ice cover in the Western Weddell
region, the perennial sea ice at B/A are more confined and could remain basically in the same general location forseveral years and therefore acquires a multiyear ice signature as in the Arctic. To minimize the error in the
retrieval of ice concentration in the region, a different tie point for consolidated ice (i.e., different slope and offset
for AD) is used to better match the different distribution of ice clusters in the region. Such correction isnecessary since otherwise, large areas of the region would be mistaken as a divergence or polynya regions. Since
1989, however, drastic retreats in the summer ice cover was observed (Jacobs and Comiso, 1994), due to apossible change in the climate of the region (King and Harangozo, 1998). In 1989 and later dates, it became
evident that the signature of ice in the B/A region is more and more similar to those of the rest of the Antarctic
region likely because of gradual disappearance of thick multiyear ice cover. While not a serious problem atpresent, AMSR data will be examined for changes in the ice distribution patterns that may cause multiyear ice
signatures in some areas to reappear again.
The signature of sea ice in the spring and summer also becomes very different from that of autumn and winter.
This happens as a result of wetness in the snow cover due to above freezing temperatures during the period.
When the snow cover has about 3% liquid water, as in early spring, the dielectric property of the surface becomesvery high and the snow surface becomes opaque. The resulting emissivity of the surface approaches that of a
blackbody and the observed brightness temperature of sea ice at all frequencies increases considerably. As
spring progresses, the snow gets melted and the surface of the ice is covered by slush or liquid causing an effectthat is opposite to that of early spring. The emissivity of ice during this period is thus not as well defined as
during the winter period. Errors in the retrieval of ice concentration are therefore larger and adjustments in thetie points are desired to account for the changing character of the surface and to optimize accuracy.
The ocean mask can also be a source of error if it does not provide consistent lower threshold for ice concentration.
This threshold is established for some average conditions but algorithms for the ocean mask may not be able toadjust to big fluctuations in weather and wind conditions. At some low concentration levels, it is difficult todiscriminate between sea ice covered area and open water because the brightness temperatures for these two typesof surfaces are almost identical. The lowest (threshold) ice concentration in which discrimination is possible iswhat normally defines the ice edge location. For SSM/I, the discrimination is done through the use of a cut-off
in the V1937 and V1922 sets, as described in Comiso (1995). While this may improve with AMSR data, thethreshold concentration currently used is approximately 10% but for better consistency, a 15% cutoff is usuallyused for long term ice extent studies. The cut-off technique is basically effective, as illustrated in the comparisonof an ice concentration map derived using the Bootstrap algorithm and a SAR image for the region indicated by arectangular box in the ice concentration map (Figure 10a). Features at the ice edge shown by the high-resolution
SAR image are basically reproduced in the passive microwave image. The open water features within the ice
pack are also coherent in the two images if the changing SAR backscatter for open water within the ice pack istaken into account. It is also apparent in Figure 10b that the character of the ice cover changes significantly fromthe marginal ice zone, where loosely connected pancakes, new ice, and ice bands are located, to the inner zone,
where thicker and more consolidated ice are found.
A more quantitative characterization of the ice edge by satellite data is depicted in the plots in Figure 11. The
plots in Figures 11a and 11b represent brightness temperatures at 6 SSM/I channels along a transect at
approximately 148 o E longitude from open water through the marginal ice zone and into the pack. As indicated,the brightness temperature increases with latitude at all frequencies except at 85 GHz (vertical polarization) in themarginal ice zone. The approximate location of the ice edge along this particular transect has been provided
through direct observations from the Australian ship, R.V. Aurora Borealis, and is represented by the vertical dashline. The ice concentrations derived from the Bootstrap and Team algorithms are indicated in Figure 11c andshown to increase with brightness temperatures and have values of about 25% at the ship observed ice edge.
Ship observations are usually dependable but difficult to interpret in terms of large scale characteristics in the ice
cover because of limited field of view. Complications in the observation of the ice edge can be seen in the SAR
image (Figure 10b) in which ice bands form and grease ice can form several kilometers beyond (to the north of)
the ice bands.
While the specific case shown in Figure 11 indicates good agreement, some other cases, reported in Worby andComiso (2001), show large discrepancies. Sometimes, the ice edge identified from ship is several km to thenorth of the SSM/I ice edge. This is especially the case in spring and summer, when ice floes breaks up and thesurface of the ice is covered by liquid. Also, sometimes the opposite is true, and this is usually the case when theship misses some ice fronts to the north, as in the SAR image. Furthermore, the ice edge location, as identified
by the Bootstrap algorithm, is sometimes several km to the north of that identified by the Team algorithm. For
long term time series studies, consistency in the determination of ice extent is important and this can happen only
if the ice edge is identified in a consistent manner for each season and independent of weather, and satellite sensor.
Errors associated with the spatial and temporal variability in the opacity of the atmosphere are expected to besmall at microwave frequencies used by the algorithm and are often neglected [Comiso and Zwally, 1982; Massom,
1991]. However, some sensitivity studies using a radiative transfer model have indicated that such errors can beas large as 10% when the Team Algorithm is used [Oelke, 1997]. Not knowing how accurately the models
represent actual conditions and what the effect is on the Bootstrap algorithm, actual data are used to investigate
the impact of the passage of a low pressure system in the Ross Sea region on derived daily ice concentrations.
Figures 12a and 12b show ECMWF mean surface pressure maps and synoptic winds during two periods (June 13
and June 20) when there were large changes in the pressure fields. Figures 12c and 12d are scatter plots of 19
GHz(V) versus 37 GHz(V) data in the region shown in the other images while Figures 12e and 12f showcorresponding ice concentration maps. Comparing ice concentrations in the rectangular box shown in the images,
which includes the low pressure field in June 20th , the Bootstrap algorithm yielded an average ice concentration of
97% with a standard deviation of 2.7% on June 13 and an average ice concentration of 98% with a standard
deviation of 2.1% on June 20. For comparison, the Team algorithm yielded an average ice concentration of 90%
with a standard deviation of 5.5% on June 13 and an average ice concentration of 86% with a standard deviationof 3.4% on June 20. These results indicate that the impact of the passage of a low pressure system on the daily
ice concentration in relatively consolidated ice regions was relatively minor, especially for the Bootstrap
algorithm. In the scatter plots, data points within the rectangular study area are shown as red and it is apparent
that the occurrence of the low pressure system caused the brightness temperatures to increase slightly (suggestingenhanced emission in the atmosphere) but proportionately at the 19 and 37 GHz channels. The ice
concentrations did not change much because the increases caused the data points to shift along the line AD, whichcorrespond to the tie points for consolidated ice in the Bootstrap Algorithm. It should be noted that winds wererelatively steady during the two periods in the study area but a much stronger change occurred at the Ross Sea
shelf region (at about 77o S, 180o E) likely causing the observed reductions in concentrations in the region from
June 13 to June 20. A seven-day separation was chosen to ensure that atmospheric conditions over the pack ice
were different. A similar study with 3-day separation (June 17 and 20) yielded very similar results.
5.5. Validation Issues and Validation Program
The validation criterion is that the derived AMSR-E sea ice products agree on average with the corresponding
validation data set to within the estimated accuracy of the validation data set. The validation data sets will bederived from any or a combination of field, aircraft, submarine and high-resolution visible and infrared satellite
data and are expected to provide a more accurate measure of the standard sea ice products than the AMSR
retrieved products. The underlying philosophy of this approach is that confidence in the sea ice products derived
from the AMSR will be achieved by showing consistency of such products with independently derived data thatare spatially and almost temporally coincident (Comiso and Sullivan, 1986; Cavalieri, 1991; Cavalieri et al., 1991;
Steffen and Schweiger, 1991; Grenfell et al., 1994). Operating within this paradigm, the following is a summaryof validation methods for each of the AMSR standard products.
The cornerstone of the validation program is the acquisition of a comprehensive data set after the launch of
ADEOS-II and EOS-Aqua satellites. The data set will consist primarily of concurrent aircraft, in situ, andsatellite data to be collected during the winter 2003 and spring 2004 periods in both hemispheres. One suchdedicated program is the Antarctic AMSR Validation Program sponsored by NASA. A P-3 aircraft equippedwith a scanning microwave radiometer which has all AMSR frequencies, an infrared radiometer, a laser altimeterand a snow radar will be used on a mission based in Punta Arenas, Chile in August 2003. A sample track for theaircraft over ice covered ocean is shown in Figure 13. Cruises that are expected to provide in situ data during thevalidation period include those for the US/Nathaniel Palmer, the UK/HMS Endurance, the German/RV Polarsternand other international vessels. Among the polar scientists who had expressed interests in this validation
endeavor are Dr. F. Nishio of Japan, Dr. Doug Martinson and Stan Jacob of Lamont Earth Science Observatory,
Prof. Koni Steffen of the University of Colorado, Dr. Miles McPhee of the University of Washington, Prof. Ray
Smith of the University of California at Santa Barbara, Dr. Peter Wadhams of the University of Cambridge and Dr.
Martin Jeffries of the University of Alaska. The validation program will be coordinated with related projects,
especially activities of other scientists whose proposals were approved under a general validation program for the
ADEOS-II and EOS/AGUA project and under various Announcements of Opportunities in the Earth Science
Enterprise Program. The strategy is to take advantage of in situ and other data sets that will be available for thistime period. Similar projects will be undertaken with ships of opportunities that will be in the Arctic andAntarctic region during the validation period. Issues and strategies for validating sea ice concentration and ice
temperature are discussed below.

Sea Ice Concentration: Sea ice concentration is defined as the areal percentage of sea ice observed within thefield of view of the satellite sensor. The primary approach for the validation of retrieved AMSR ice
concentrations is to utilized data from the dedicated aircraft campaigns in conjunction with high resolution
satellite data, including those from Landsat 7, Terra and Aqua MODIS, NOAA-AVHRR, DMSP-OLS,
RADARSAT. The aircraft data will provide the means to assess the absolute accuracy of the retrieval at someplaces and some seasons while the satellite data provides better spatial and temporal coverage. High-resolution
active microwave satellite data such as the Radarsat SAR, are most useful during persistent cloud cover conditions
and during darkness. Data from microwave scatterometers, such as those from QuickSCAT, will be utilized for
identifying areas of divergence and where significant reductions of ice concentration is expected. However, datafrom active systems are more difficult to interpret than those from passive and visible systems, because of
unpredictable backscatter from different ice types, from open water within the ice pack, and from wind-roughened
seas. Such data are valuable but require validation.
Aircraft campaigns are planned for both Arctic and the Antarctic regions and for dry and wet seasons. Suchprogram will provide multi-channel passive microwave data similar to AMSR but at a much better resolution.
The high resolution will provide the means to test the effectiveness of the mixing formulation in different ice
regimes and conditions. The aircraft will also be equipped with digital and film camera system for thecharacterization of small features of the ice cover, a laser ranging system for surface topography studies and ice
thickness estimates, and a multi-frequency radar for snow cover studies. The strategy is to apply the algorithm
on co-registered and coincident aircraft and spacecraft data and evaluate how the results matches each otherquantitatively and how they compare with similar analysis from high resolution visible and infrared data.
Discrepancies will be analyzed and explained through the use of ancillary data and further examination of the highresolution data. Data at the ice edge, open ocean, and land/ocean boundaries will also be analyzed to validate theeffectiveness and consistency of the masking algorithms.
The validation program will take into consideration the large changes in physical and radiative characteristics of
sea ice during an ice season. During early ice growth period, the ice cover consists mainly of new ice, pancakes,
young ice, and relatively undeformed first year ice. On the other hand, during late winter, the ice cover consistsof predominantly thick and vast ice floes with relatively thick snow cover. During the melt season, the vast ice
floes get broken up to smaller units and the surface gets covered by slush or liquid. For at least two periods (dryand wet periods) the changes in the radiative signature will be quantified as accurately as possible andrelationships with the accuracy of the retrieved sea ice parameters will be evaluated.
As a complementary approach, time series of images will be analyzed to check AMSR retrievals for temporalconsistency. The growth and decay of sea ice are limited by physical laws and environmental conditions andsuch time series data can provide the means to establish how well the expected time development of the ice coveris reproduced by the satellite data. This effort will help identify weaknesses in the technique that are not obvious
from examination of individual images.
Atmospheric effects can be estimated using radiative transfer modeling to account for the effects indicated byequation (1). The results from the latter can be used to correct the brightness temperatures observed by theaircraft and satellite and results are used to derive the geophysical parameters that are used in the validation. As
indicated earlier, the choice of channel is important and with the set of channels used in the ABA algorithm, theeffect appears to be negligible. Further confirmation that this is indeed the case will be done through radiativetransfer modeling studies of atmospheric effects using actual atmospheric profile measurements during thevalidation period.
Radiative transfer modeling of the microwave radiation emanating from the sea ice cover will also be
undertaken because it allows for a better understanding of the emission characteristics of different sea ice surfaces
at the different AMSR frequencies and polarizations. Such procedure has been conducted previously (e.g.,
Tjuatja et al., 1993; Grenfell et al., 1994; Tjuatja et al., 1995) but results were of limited value because of the lackof needed atmospheric and surface data. Some refinements will be implemented and data acquired during thevalidation program will be used to obtain improved results that will be used to better interpret spatial and temporalchanges in the microwave signatures as observed in the aircraft, field, and satellite data sets.

Sea Ice Temperature: The ice temperature derived from the vertically polarized 6.9 GHz channel represents thetemperature of the sea ice layer that emits much of the signal observed by the radiometer. For first year ice, it is
the temperature of the snow/ice interface because at this frequency the snow cover is transparent to the radiationand the surface is opaque due to relatively high salinity. For multiyear ice, the derived sea ice temperature
represents a weighted-average of the freeboard portion of the ice. During previous Antarctic cruises, thephysical characterization of the ice cover made on a regular basis included quantitative measurements oftemperature profiles through the snow and ice. Such data were taken during the Weddell Sea winter and spring
cruises of 1982, 1983, 1986, and 1989. These data were used to obtain empirical relationships between the snow
skin-depth temperatures and the snow/ice surface temperature. The snow skin-depth temperature is routinely
measured by infrared (IR) satellite instruments (e.g., AVHRR, ATSR, and MODIS). The primary technique forthe validation of AMSR ice temperature data is to make use of this empirical relationship that converts IR satellite
data to ice temperature data and use the latter for comparative analysis with AMSR data. The aircraft IR data
will be converted to surface ice temperatures that in turn will be compared with ship measurements to assess
errors associated with the use of empirical parameters. Further refinements of the empirical parameters will bemade through the use of more field data and a thermodynamic model of sea ice and snow.
The retrieved ice temperatures will be further validated using surface temperature data from buoys, ships, icecamps, and other platforms. While these are only point measurements, the horizontal variability of the snow/ice
interface temperature is not expected to be large over a few km. Also, there exist some arrays of buoys thatprovide continuous measurements and could be used to check the temporal consistency of the derived AMSR
temperature data.
6.
6.1

Computer Requirements and Coordination
Software and Data Storage Requirements

The Basic Bootstrap algorithm (BBA) has been tested without problems at the NASDA Earth Observation
Center data facility and is ready for routine processing. An enhanced version of this algorithm has beenenhanced to better account for spatial variations in surface ice temperature as described in this document. The
new algorithm is called AMSR Bootstrap Algorithm (ABA). This algorithm has been tested using SMMR data
but AMSR data is expected to be much better calibrated and has much higher resolution than SMMR. Further
testing is thus necessary once AMSR data becomes available. In the meantime, BBA can be used since resultsfrom the two are very similar and the differences where they occur are within errors. Both algorithms haveworking versions currently running on SGI UNIX workstations at Goddard. ABA is only a slightly bigger
program than BBA and there should not be any problem installing it in the NASDA system. An estimate ofprocessing time for one month of SSM/I Level-3 daily average data is of the order of 1.2 minutes and 2.1 minutes
on an SGI Octane workstation using BBA and ABA, respectively.
Input to the AMSR-E sea ice algorithms will consist of Level 2A AMSR brightness temperatures, latitude,
longitude, time and a land/ocean flag. The output sea ice products will consist of sea ice concentration and sea
ice temperature and will include latitude, longitude, and a time stamp. The algorithms are coded in C. As soon
as AMSR data is available, ABA will be tested and a final version including documentation will be delivered to
NASDA within a few months.
6.2

Data Management, Quality Control and Archival

The NASDA/Earth Observation management is primarily responsible in the acquisition and management of
AMSR data. During the first year of operation, AMSR data will also be processed by the PI, using his own
computer system, for comparative analysis with other data sets and for quality control. Enhanced techniques andprocedures developed during this time will be delivered to NASDA for implementation and generation of the sea
ice data sets.
Quality control of brightness temperatures will be done during the generation of the Level 2A products. The
first step in the quality control of the sea ice products will consist of checking whether or not the retrieved sea ice
products fall within reasonable limits. Diagnostics will be based in part on satellite sea ice climatology
developed since the launch of the Nimbus 7 SMMR in 1978. These data will provide a useful measure of theseasonal and regional values for sea ice concentration and to some extent sea ice temperature.

Exception handling will consist of flagging missing data, land, and unreasonable retrievals. Missing
brightness temperatures will result in setting a missing flag for the sea ice retrieval. The sea ice algorithm will
not be run over land. It is presumed that out-of-range brightness temperatures will be handled in the generationof Level 2A products. Out-of-range retrievals will be handled within the algorithm. Diagnostics for checking
out-of-range data will be used in the algorithms to determine whether the output should be flagged as
unreasonable. In some cases, for example, sea ice concentrations greater than 100% will be set to 100% and sea
ice concentrations less than 0 will be set to zero. Much larger discrepancies will be flagged as unreasonable.
6.3

Consistency Checks and Coordination with Other Projects

Sea ice concentration and ice temperature are two parameters that are obtainable using other satellite sensors.
For example, one of the data products that are supposed to be generated from ADEOS-II/GLI andEOS-Agua/MODIS is sea ice concentration using visible channel data. There may be differences in sampling
rate, resolution and sensitivity to clouds and weather but where there is good cloud free data available from GLI
and MODIS, the retrieved product should agree with that of AMSR. Also, GLI and MODIS sensors havethermal infrared channels that provide surface skin temperatures. After a normalization is applied to the latter, toobtain ice temperature, as discussed earlier, the results should be compatible with ice temperatures derived from
AMSR. If not, the reason for the discrepancies should be evaluated in terms of different resolution, different
emissivities and reflectivities, and different types of surfaces. Retrieved geophysical parameters should besensor independent but if the results from different sensors are different, users of the products should be advise
about such differences and why.
Validation data are oftentimes very expensive to acquire and should be shared with other projects which mightneed them. Among the key validation data sets that will be used for AMSR data are the aircraft and Landsat data
as described earlier. The same data sets could also be used for validating GLI and MODIS products. Similarly,
validation data sets accumulated for GLI and MODIS may be useful for AMSR data validation.
Activities of the scientists and engineers involved in different projects should also be coordinated such that thesame set of standards are applied to different sensors, especially those that are similar. For example, AMSR datafrom both ADEOS-II and EOS-Aqua should be processed with the same quality checks and calibration standards.
Similarly for aircraft radiometer AMSR simulator data that need to be compared with satellite data. This will
guarantee that data sets from different sensors are consistent and can be used interchangeably and/or in
combination for scientific research.
7.

Summary

The theoretical basis and description of the algorithm that will be used to derive sea ice parameters from AMSR
data has been discussed. Two techniques with almost equal performance are presented. One is called the Basic
Bootstrap Algorithm (BBA), which is the original algorithm that was proposed to NASDA for evaluation and waschosen to be used as the standard algorithm for AMSR. An enhanced technique has been developed in themeantime and called AMSR Bootstrap Algorithm (ABA) which is expected to provide more accurate results.
The two algorithms, as tested, are currently providing very similar results but ABA has the advantage ofaccounting for abnormally cold ice surface temperatures and in providing an ice temperature product. The latter
is a research product but could provide very valuable information needed for polar process studies that cannot be
obtained otherwise. The error in the determination of ice concentration is estimated at about 5 to 15% during
winter and 10 to 20 % during the summer using SSM/I data. This significantly improves when AMSR data isused since the latter have much better resolution and greater spectral range. The error in the determination of ice
temperature is yet to be determined but is expected to be less than 4K.
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Use T B(6V, 37V) to generate initial ice
concentration data, C i using the Bootstrap
techniqueCalculate surface emissivity using a mixing
algorithm:
ε = εi C i + εO (1-Ci)

Iterate Once with
Ci = CI

Calculate the overall temperature of thesurface within the pixel
TP = TB(6V)/ε

Calculate surface emissivities at 18 GHz and 37 GHzε(18V) = T B(18V)/TPε(18H) = T B(18H)/TPε( 3 7 V ) = TB(37V)/TPε(3 7 H ) = TB(37H)/TP

Calculate ice Concentration, CI, from ε (18V),
ε (18H), ε (37H) and ε (37V)
using the Bootstrap TechniqueCalculate Ice Temperature using
TS = [T P – TO(1-CI)]/C I
where TO = 271 K

Figure 3. Schematics of the AMSR Bootstrap Algorithm

Figure 1. Scatter plots from aircraft data in consolidated
ice regions in the Arctic for (a) 37H vs 37V; and (b) 19V
vs 37V.

Figure 2. Color-coded monthly ice concentration from
SSM/I using BBA for March 1992 and September 1992
in the Northern and Southern Hemispheres.

Figure 4. Monthly surface temperatures in the Antarctic
derived from AVHRR thermal infrared data for March
1992 and September 1992 in the two hemispheres

Figure 5. Scatter plots for the sets (a) HV37 and (b)V1937 using brightness temperature data, and (c) HV37
and (d) V1937 using emissivity data in the Northern
HemisphereFigure 6. Scatter plots for the sets (a) H1937 and (b)V1937 using brightness temperature data, and (c) H1937
and (d) V1937 using emissivity data in the Southern
Hemisphere

Figure 8. Color-coded ice concentration difference
between BBA and ABA for March 1992 andSeptember 1992 for the two hemispheres

Figure 7. Color-coded monthly ice concentration from
SSM/I using ABA for March 1992 and September 1992
in the Northern and Southern Hemispheres

Figure 9. (a) Original ice concentration map at the Ross
Sea/Ross Ice Shelf region; (b) Ice concentration map withthe land/ocean mask of Cho et al. (1996) applied; and (c)Ice concentration map with the Bootstrap land/oceanmask applied.

Figure 11. Transects of (a) vertically polarized
brightness temperatures, (b) horizontally polarized
brightness temperatures, and (c) ice concentrations
derived from the Bootstrap and Team Algorithms on
April 21, 1995 from the open ocean into the ice pack.

Figure 13. Transect of a typical aircraft tract during theWinter AMSR Antarctic Validation Program in August
2003.

Figure 10. (a) Ice concentration map derived using the
BBA for May 6, 1998. (b) Radarsat SAR image on May 6,
1998 over the rectangular region shown at 180o E in (a).

Figure 12. ECMWF pressure and wind fields in the Ross
Sea on (a) June 13, 1988 and (b) June 20, 1988. Scatterplots of 19 GHz (V) versus 37 GHz(V) on (c) June 13,
1988 and (d) June 20, 1988. Data from the box in (a)and (b) are indicated as red data points in (c) and (d). Ice
concentration maps derived from SSM/I data using the
Bootstrap Algorithm are shown with wind field data on (e)June 13, 1988 and (f) June 30, 1988.

Description of Snow Depth Retrieval Algorithm for ADEOS II AMSR
Dr. Alfred Chang and Dr. Richard Kelly
NASA/GSFC
1. Introduction
The development of a snow depth retrieval algorithm for ADEOS II AMSR has been developed from current
applications of snow depth retrievals from the Special Sensor Microwave Imager (SSM/I). While the SSM/I is
not exactly identical in spatial and waveband configuration to the planned ADEOS II AMSR, it is sufficiently
comparable over its four frequencies to be a useful instrument with which to develop a snow retrieval algorithm
that is based on the microwave emission properties of snow. The AMSR will have an improved spatial
resolution and expanded waveband range compared with the SSM/I and it is expected, therefore, that algorithm
development will continue post launch.
2. Underlying principles for snow depth retrieval
There are two aspects to successful snow cover retrieval from space using passive microwave radiometers. First,
the snowpack must be detected and second it must be quantified in terms of its snow depth. Fresh of dry snow
(containing a negligible amount of liquid water) is a forward scatter of naturally upwelling radiation. Comparedwith non-snow surfaces, therefore, a snowpack has a distinctive electromagnetic signature at frequencies above 25
GHz. When viewed using passive microwave radiometers from above the snowpack, the scattering of upwellingradiation depresses the brightness temperature of the snow at increasingly high frequencies. This scattering
behavior of snow can be exploited to detect the presence of snow on the ground. Having detected the snow, it isthen possible to estimate the snow depth of the pack using the degree of scattering. Chang et al. (1987) proposeda scheme to estimate the snow depth of a dry, homogeneous, single layer snowpack using radiative transfer theory
and the difference between two horizontally-polarized brightness temperature channels at high and low
frequencies such that:
SD = a ∆TB)+ b [cm],(1)

where b is generally regarded as zero and a = 1.59 cm K-1 and the assumption is made that the snow grain radius
is 0.3 mm and snow density is 300 kg m-3 . The ∆TB term is the difference in brightness temperature between 19
GHz and 37 GHz channels (horizontal polarization). This model works well under the non-complex snow
conditions (flat land, no significant forest cover, single layer dry snow) and has been the basis for several SD or
snow water equivalent (SWE) retrieval algorithms (e.g. Goodison and Walker, 1994, Foster et al., 1997).
However, for global applications there are several additional factors that need to be taken into consideration andincorporated into a retrieval scheme for successful snow depth estimation. These are described in the following
section.
3. Confounding factors
Snowpack properties
It is known that at passive microwave wavelengths, shallow snow (less than 10 cm) is transparent to naturally
upwelling microwave wavelengths (Armstrong and Brodzik, 1999). This factor can lead to non-detection of thesnowpack and hence underestimation of the snow volume. This factor will be most prominent in the early andlate parts of the winter season. Use of a high frequency channel (e.g. 89 GHz on AMSR) will assist with thisdetection although great care must be exerted when using this channel on account of potential atmosphericcontamination.
Wet snow can confound snow depth retrievals by depressing the scattering behaviour of the snow. Ultimately,
this leads to underestimation of the pack. Unfortunately, at present there is little that can be done to overcome
this problem directly although at least the detection of wet snow is possible by using a combination of information
about the surface temperature (Sun et al., 1996), polarization difference at 37 GHz (Walker and Goodison, 1994)
and immediate snow cover history.

Equation (1) above indicates a static parameterization based on radiative transfer properties of a snowpack (0.3mm radius grains and 300 Kg m-3 density). While this can be applied in some areas around the world at certain
times, the nature of snow is such that it can be temporally and spatially dynamic in evolution (Colbeck, 1986).
To retain the a coefficient in (1) suggests that globally, snow covers are homogeneous in character which clearly is
not the case. Although Josberger et al. (1995) found that snowpack properties can be homogeneous at regional
scales, for continental applications this will not be the case. The a coefficient should, therefore, be varied both
spatially and temporally and so we have computed a set of coefficients for each month of the year. The spatial
distribution of the coefficients is achieved using the seasonal snowpack classification of Sturm et al. (1995) which
divides the northern hemisphere into 6 dominant regional snow types: taiga, tundra, alpine, maritime, ephemeraland prairie. The a coefficients are re-computed for each of these regions based on dominant snowpack
characteristics thought to dominate in each region.
False scatterers
Precipitation acts as a confounding effect on snowpack retrievals. This is because precipitation clouds consist ofhydrometeors that act like a snowpack on the ground and scatter upwelling microwave radiation away from theradiometer’s field of view. Currently it is not possible to detect the presence of snow or retrieve snow depth
from beneath precipitating clouds but it is possible to detect precipitation and therefore flag the presence ofrainfall. The method used was developed by Grody and Basist (1996).
Forest cover
A major problem in large areas of the globe is the effect that forest cover has on the retrieval of snow depth frompassive microwave radiometers (Chang et al., 1996). Dense coniferous (and perhaps deciduous forest at
early/late times in the season) depress the microwave scattering signal from snow within the forest causing an
under-retrieval of the snow depth. Attempts have been made to overcome the problem (e.g. Foster et al., 1997)
but the problem is not easily resolvable at the moment. The Robinson and Kukla (1985) global albedo data set
has been used to estimate forest cover through the following relationship:
ff = -150albedo + 120

[%]

(2)

where ff is the forest fraction in percent and the two coefficients describe a straight line. This linear relationshipis based in the fact that for land surfaces that are not water bodies, low albedos (<0.5) are likely to be indicative ofdense forest whilst higher albedos (>0.5) are probably indicative of low stand or no vegetation. The range offorest cover is calibrated to between 0 % and 90 %and is then re-scaled linearly to 0 to 1 where 1 represents
100 % and 0 represents 0 % such that the data can be incorporated into (1):SD = a ∆TB) / (1-ff) + b

[cm].

(3)

A full account of this relationship can be found in Foster et al. (1997). This relationship is currently underfurther refinement since the Robinson and Kukla (1985) data set is at 1.0º spatial resolution which is coarser than
the scale used in this project (9.28 km equal area grid). In addition, there are better products available andbecoming available to provide more up-to date information about the global distribution of forest cover. For
example, direct forest cover data are available through the International Geosphere and Biosphere Project (IGBP)(although these are derived from annual average land cover data sets based on the reflective properties of the land
surface from AVHRR data). It is expected that in the future, more dynamic forest cover information will beavailable through MODIS reflectance or land category products that are produced every 16 days. This will
provide a better characterization of the forest cover plus it will give improved information about stem volume(rather than percentage cover in a pixel) which is thought to be the key effect on microwave retrievals of snow inforested areas (Kurvonen et al., 1998).
Mountainous terrain
Retrieval of snow depth from complex mountain topography is a challenge for low spatial resolution passive
microwave radiometers. This is because within a given footprint in a mountain zone, the variability of snow
depth is much greater than in flat terrain. Consequently, to avoid underestimation and overestimation, suchterrain is flagged and avoided in the current version of the algorithm.
used to flag mountain topography.

The GTOPO30 product from the USGS is

4. Implementation of the algorithm
The algorithm, coded in C, is currently implemented from a Unix Bourne Shell. The procedure is shown by theflow chart in Figure 1 below. The first step is to determine the kind of surface present (flat land, water body onland, ice, ocean, mountainous terrain, snow climatologically (im)possible, forest cover). The climatologicalpossibility of snow cover presence is obtained from Dewey and Heim (1981 and 1983). Unless the surface is flat
land without heavy forest cover, the procedure flags the surface type and does not attempt to compute the snow
depth. For flat land without heavy forest cover, the algorithm proceeds to Step 2, which reads, in AMSR channelbrightness temperatures.
Step 3 determines that the AMSR data are within a reasonable range and that there are no gross data errors in thebrightness temperature. Step 4 obtained the surface temperature estimate based global circulation model
estimates from the Japanese Meteorological Agency. This step is used to determine whether or not the surface islikely to be too warm and, therefore, the probability is low for the presence of snow. Step 5 screens for
precipitation and Step 6 determines whether there is wet or dry snow present and Step 7 estimates the snow depth.
If the snow is dry, the algorithm computes the snow depth using equation (3) above. The applied a coefficient in(3) dependent on whether or not the underlying soil is dry or wet, the Sturm et al. (1995) seasonal snow class andalso on the time of year.
5. Validation of algorithm
Two data sets were assembled to validate the algorithm developed for ADEOS II AMSR snow depth estimation.
First, a four-year record from 1992 – 1995 of daily GTS meteorological station snow depth measurements andcoincident SSM/I brightness temperatures prepared by NASDA, Japan were reanalyzed (see Chang and Koike,
2000). The second data set used was a month of daily global WMO meteorological station snow depth data for
January 2001.
1992-1994 data set validation
This data set comprises 86 GTS meteorological stations distributed in the northern hemisphere and quality
controlled (originally there were 100 but anomalous and erroneous readings were screened). The data comprisefour years of gauged daily snow depth measurements from January 1992 to December 1995. Coincident SSM/I
brightness temperatures at each station are also stored in the data set.
Snow depth was estimated using the simple algorithm from equation 1 (hereafter referred to as the “1.59”
algorithm) and also using the spatially and temporally dynamic algorithm from equation 3 (hereafter referred to as
the Chang algorithm). The estimated snow depths from both algorithms were compared with the gauge data andthe mean absolute error (an indicator of the magnitude of algorithm error) and the mean error (a measure ofalgorithm bias) for both algorithms for the entire four-year period was computed. Figure 1 shows two
histograms of the results. The mean absolute error (MAE) histogram shows that both algorithms perform
similarly well at the global scale. The average MAE for the Chang algorithm is 16.6 cm while for the “1.59”
algorithm it is 16.1 cm. This would suggest that the errors are similar in magnitude for each station over the four
years. However, inspection of the bias in the adjacent histogram demonstrates that the Chang algorithm bias ismuch closer to 0 cm than the “1.59” algorithm (-5.9 cm and –0.3 cm for Chang and “1.59” respectively). Thissuggests that although the absolute errors are similar, the underestimation of snow depth traditionally found in thepassive microwave estimates, is reduced in the new algorithm. The reason for this could be on account of thefact that the new Chang algorithm incorporates the “forest effect” in its estimates thus reducing the bias
(underestimation) commonly found in retrievals. Figure 2 shows the MAE and ME for sites where the forest
fraction is greater than 30%. Again a similar situation emerges with similar average MAE estimates for bothalgorithms (19.6 cm and 21.3 cm for the “1.59” and Chang algorithms respectively). However, the average bias
in the Chang algorithm is much less under high forest fractions with an average ME of –13.7 cm and 1.3 cm forthe “1.59” and Chang algorithm respectively.

Figure 1
AMSR Snow depth
algorithm logic

Preliminaries

Get Ancillary Data:•Land/sea/ice•Topography•Snow class (Sturm et al., 1995)•Snow (Im)possible
Locate AMSR data and read in one scan line of AMSR data.

Step 1 (For each AMSR sample)
Test for:•Ocean, land water body, ice•Snow Impossible•Mountain•Otherwise continue to Step 2

FLAG
FLAG
FLAG

Step 2 Obtain AMSR brightness temperatures
Continue to Step 3
Step 3 Do range check of brightness temperatures in all channels•Bad data•Good data continue to Step 4

FLAG

Step 4 Obtain surface temperature from Japan Meteorological
Agency global circulation model data:•If T ≥ 275 K, surface too warm
•If T < 275 K continue to Step 5

FLAG

Step 5 Precipitation screen (Grody and Basist (1996)):

Scat = max(Tb18V-Tb36V -3, Tb23V-Tb89V -3, Tb36V-Tb89V - 1)
•If (Tb23V > 258) or (Tb23V > 254 and Scat < 2) or(Tb23V > (165+0.49Tb89V) then rainfall is present•Otherwise continue to Step 6

FLAG

Step 6 Wet or dry snow screen (Walker and Goddison, 1994)•If (Tb36V – Tb36H > 10) and (T ≥ 270 K) wet snow
•Otherwise continue to Step 7

FLAG

Step 7 Wet or dry soil screen and Snow Depth (SD) Estimate•If {[(Tb36V – Tb18V)/18] ≥ -0.3} and (T ≥ 270 K) and(T ≤ 273 K) Wet soil snow depth estimate:[cm]
SD = 1.66(Tb18V-Tb36V)•Otherwise dry soil snow depth estimate:SD = a(Tb18V-Tb36V-5) / (1 – ff)•Goto Step 1 for next sample[cm]January 2001 data set validation
A similar exercise was conducted for a relatively constrained (temporally) data set but which contained many
more gauged snow depth measurements. Data were obtained from the WMO’s network of approximately 600
stations (many in the GTS network) in the northern hemisphere. MAE and ME calculations were made at four
distinct spatial scales to determine whether the Chang and “1.59” algorithms might perform differently.
Computations were made at a global scale, North America data, Canadian data and Northern Great Plains data.
The results are shown in the time plots in Figure 3. It is clear that the MAE values are, again, similar for boththe “1.59” and Chang algorithms. However, the bias in the Chang algorithm is reduced significantly in the
Chang algorithm estimates. This is the case at all spatial scales with the anomalous exception of the ME for the
Northern Great Plains where the “1.59” algorithm does marginally better.
Again, it was suggested that the reason for the improved bias revealed in the Chang results is due to the fact thatthe forest effect is incorporated in the algorithm. Figure 4 is similar to Figure 3 except that again, computationsof MAE and ME were performed only for pixels with forest fraction greater than 30%. The results support theargument that the Chang algorithm does reduce the overall bias in the estimates caused by forest cover.
Figure 5 Shows visually representation of the two algorithms for 1 January 2001. The left panel is the result ofapplying the “1.59” algorithm and the right panel is a representation of the Chang algorithm. The same screens(rainfall, mountains etc.) are applied in both algorithms so that the differences between the two retrievals are thespatial variation in snow depth.

1992-1995 GTS-SSM/I Daily Data
Mean Absolute Error

1992-1995 GTS-SSM/I daily data
Mean Error (Bias)

30

18
1.59
Chang

20
15
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frequency

frequency

25

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-10

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Error (cm)Figure 1. Global validation (mean absolute error and bias) of AMSR (chang) algorithm compared with standard‘static’ algorithm (see equation 1) for 86 global GTS snow depth gauge stations.

1992-1995 GTS-SSM/I Daily Data
Mean Absolute Error

1992-1995 GTS-SSM/I Daily Data
Mean Error (bias)

14

8
159
chang

12

7
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frequency

1.59
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6

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20

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Figure 2. Global validation (mean absolute error and bias) of AMSR (chang) algorithm compared with standard‘static 1.59’ algorithm (see equation 1) for 86 global GTS snow depth gauge stations where forest fraction isgreater than 30%.

Global25
20

MAE-159
ME-159MAE-changME-chang

1050Error (cm)Error (cm)

15

-5
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Canada

30
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MAE-159

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25

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50Error (cm)15
Error (cm)

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ME-159MAE-changME-chang

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1

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January 2001 (day)10 13 16 19 22 25 28 31
January 2001 (day)Figure 3. Comparison of ‘Chang’ and ‘1.59’ snow depth algorithm validation. MAE is the mean absolute error
and ME is the mean error (bias). The comparison is for applications of the algorithms in January 2001 and fromall stations at global, North America, Canada and Northern Great Plains scales.
Global3030

10MAE-159
ME-Chang
MAE-159
ME-Chang

0-10Error (cm)20
Error (cm)Canada40

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40

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MAE-159
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January 2001 (day)Error (cm)Error (cm)30
20

10 13 16 19 22 25 28 31

30
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N. Great PlainsMAE-159
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MAE-159
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47

10 13 16 19 22 25 28 31
January 2001 (day)Figure 4. Comparison of ‘Chang’ and ‘1.59’ snow depth algorithm validation. MAE is the mean absolute error
and ME is the mean error (bias). The comparison is for applications of the algorithms in January 2001 for EASE
grid pixels that are characterized with forest cover greater than 30% and from all stations at global, North America,
Canada and Northern Great Plains scales.

Figure 5. Visualisation of the “1.59” snow depth algorithm (left) and the Chang snow depth algorithm (right) for 1
January 2001. The colour scale units are in cm.

6. Future developments
Results from the work to date are very encouraging and suggests that the new algorithm development should
improve the old static coefficient methodology described by equation 1. However, the retrieval residuals or
errors still need further constraint. Despite a retrieved error (MAE) of 16.6 cm globally, translating this into a
SWE produces a value of 1.6 mm for fresh snow (with a density of 100 kg m-3 ) and more for seasonal snow withhigher density. It is clear, however, that the spatial distribution of the coefficient a in equation 3 is important forsuccessful snow depth retrievals. While the Sturm et al. (1995) seasonal snow classification is undoubtedly an
invaluable global descriptor that can help, newer, more sensitive descriptors are needed that can provide higher
spatial resolution for coefficient spatial extrapolation. This is one area that we are currently developing using
geostatistics and land cover data sets and results to date are promising (with further reduced ME and reduced
MAE values). In addition, it is clear that successful estimation of daily local snow depth variability will benefit
from a dynamic temporal component that could be included in the algorithm to determine variations in snowpack
properties. While problematic, this aspect is the subject of current development activities.
An important future development that will assist with the algorithm validation and development is ourparticipation in the Cold Land Processes Field Experiment (CLPX) in North American planned for the 2002-2003
winter season in Colorado. This experiment is part of the NASA Global Water and Energy Cycle (GEWEC)
initiative, the Global Energy and Water Cycle Experiment (GEWEX) and the GEWEX Americas Prediction
Project (GAPP). The broad objectives of the CLPX are to develop our understanding of cold land processes by
increasing our ability to characterize the spatial and temporal variability of snow, ice and frozen ground in thenatural environment, and to identify and quantify the various uncertainties associated with remote sensing
observations and models of cold land processes, thereby improving our abilities to predict the behavior of various
cold land processes (NASA, 2001). As part of this, a significant number of field experiments are planned for
February and March 2002 and 2003 to measure snowpack parameters intensively in three 25 km x 25 km and 1
km x 1 km cells in Colorado. The measurement suite will include snow depth, SWE, and surface wetness androughness and various snow descriptors obtained from snow pits. It is planned that this experiment will also
have access to ground-based and airborne radiometers plus a suite of satellite observations. The aircraft flightlines will cover several the AMSR foot-prints (25 km x 25 km). Consequently, it is anticipated that several of theoutstanding uncertainties associated with snow depth and SWE retrieval form microwave radiometry will beaddressed. This information will assist directly with out efforts for the development of ADEOS II AMSR snow
depth retrieval algorithm.
References
Armstrong, R.L. and M.J. Brodzik, (1999) A twenty year record of global snow cover fluctuations derived frompassive microwave remote sensing data, 5th Conference on Polar Meteorology and Oceanography, American
Meteorological Society. Dallas, TX, 113-117.
Chang, A.T.C., J.L. Foster and D.K. Hall, (1987) Nimbus-7 derived global snow cover parameters, Annals of
Glaciology, 9, 39-44.
Chang, A.T.C., J.L. Foster and D.K. Hall, (1996) Effects of forest on the snow parameters derived frommicrowave measurements during the BOREAS winter field experiment. Hydrological Processes, 10:1565-1574.
Chang, A.T.C. and T. Koike (2000) Progress in AMSR snow algorithm development, in Pampaloni, P. and S.
Paloscia (Eds), Microwave Radiometry and Remote Sensing of the Earth’s Surface and Atmosphere, VSP,
p515-523.
Colbeck, S.C. 1986 Classification of seasonal snow cover crystals, Water Resources Research, 22(29): 59S-70S.
Dewey, K.F. and R.Heim, Jr. (1981) Satellite observations of variation in Northern Hemisphere seasonal snow
cover, NOAA Technical Report NESS 87, 83 pp.
Dewey K.F. and R. Heim, Jr. (1983) Satellite observations of variations in Southern Hemisphere snow cover,
NOAA Technical Report NESDIS 1, 20 pp.
Foster, J.L, A.T.C. Chang and D.K. Hall, (1997) Comparison of snow mass estimates from a prototype passive
microwave snow algorithm, a revised algorithm and snow depth climatology, Remote Sensing ofEnvironment, 62: 132-142.
Goodison, B. and A. Walker, (1994) Canadian development and use of snow cover information from passive
microwave satellite data, In Choudhury, B., Kerr, Y., Njoku, E., and Pampaloni, P. (eds) Passive Microwave
Remote Sensing of Land-Atmosphere Interactions, Utrecht: VSP BV, 245-62.
Grody, N.C. and A.N. Basist (1996) Global identification of snowcover using SSM/I measurements, IEEE
Transactions on Geoscience and Remote Sensing, 34(1): 237-249.
Josberger, E., P. Gloersen, A. Chang and A. Rango, (1995) Snowpack grain size variations in the upper Colorado
River basin for 1984-1992. Journal of Geophysical Research, 101, 6679-6688.
Kurvonen, L., J. Pulliainen, M. Hallikainen (1998) Monitoring of boreal forests with multitemporal special sensor
microwave imager data, Radio Science, 33(3): 731-744.
NASA, (2001) NASA Cold Land Proccesses Field Experiment Plan 2002-2004, Cold Land Processes Working
Group, NASA/ESE/LSHP, http://lshp.gsfc.nasa.gov.
Robinson, D.A. and G. Kukla, (1985) Maximum surface albedo of seasonally snow covered lands in the Northern
Hemisphere. Journal of Climate and Applied Meteorology 24: 402-411.
Sturm, M., J. Holmgren and G.E. Liston, (1995): A seasonal snow cover classification system for local to global
applications. Journal of Climate, 8, 1261-1283.
Sun, C.Y, C.M.U. Neale and J.J. McDonnell, (1996): Snow wetness estimates of vegetated terrain from satellitepassive microwave data. Hydrological Processes, 10: 1619-1628.
Walker, A., and B. Goodison, (1993) Discrimination of a wet snow cover using passive microwave satellite data,
Annals of Glaciology, 17: 307-311.

AMSR Snow Algorithm Development and Validation in the Eurasian continent
Toshio Koike
Department of Civil Engineering, University of Tokyo
The wavelength in the microwave region has sensitivity to the scattering effect of snow grains and leaves.
Microwave remote sensing has potential of the measurement of snow water equivalent and water content ofvegetation. The longer wavelength is one of the advantages of microwaves. It is long enough to reduce thescattering effect of cloud particles and to make microwave sensors useful all-weather ones. In this study, a newalgorithm for snow depth and snow physical temperature by considering the effects of vegetation is developed
based on the microwave radiative transfer theory. It is applied to the SSM/I and TMI data and validated by using
the in-situ data in Russia and the Tibetan Plateau.
The microwave brightness temperature observed by satellites is expressed by the radiative transfer equation
which consists of the soil surface radiation attenuated by snow and vegetation layers and their. A passive
microwave sensor algorithm for snow is proposed based on the radiative transfer theory by introducing the effects
of vegetation. The relationship between the land surface radiation and snow properties is obtained by theradiative transfer theory based on a scattering dielectric layer over a homogeneous half-space. The total land
surface brightness temperature is the sum of the direct component and the diffuse component which corresponds
to the reflected sky radiation and the thermal radio emission from snowpack and soil, and the radiation scatteredfrom the direct and diffuse fields, respectively. By assuming snow grain size, snow density and radiation form
soil-snow interface, brightness temperatures at two different frequencies are calculated by the radiative transfer
equation by inputting snow depth and physical temperature. This forward model calculation was validated
through the aircraft experiment in Japan. To evaluate the vegetation effects on microwave radiative transfer,
three relationships among optical thickness in microwave region, water content of vegetation, LAI and NDVI. In
microwave region, vegetation layer is characterized only by optical thickness, which is expressed by water content
of vegetation. Water content of vegetation is related with LAI by using an empirical equation. According to thevisible and infrared remote sensing, several relationships between LAI and NDVI were proposed. Based on
those three relationships, the effects of vegetation on the microwave radiative transfer can be estimated by NDVI
derived from visible and infrared radiometers.
By assuming constant values of snow grain size, snow density and soil surface emissivity, brightness
temperatures at two different frequencies are calculated for each snow depth, snow physical temperature and
NDVI. By applying a numerical inversion technique to the result of the forward model calculation, we canobtain a look-up table, which calculates snow depth and snow physical temperature by inputting observedbrightness temperature at two different frequencies. In this paper, the proposed algorithm is applied to the data at
19GHz and 37GHz of DMSP SSM/I and TRMM TMI. NDVI is derived from NOAA AVHRR data.
A four years (1992-1995) data set based on in-situ measurements and SSM/I data was complied by Earth
Observation Research Center (EORC) of National Space Development Agency (NASDA) of Japan. Snow
parameters and climatology data from one hundred observational stations spread over the Northern Hemisphere
were involved in the data set. Five closest SSM/I footprints were extracted from the swath data to form thecoincide data set. A statistical analysis of the proposed algorithm was performed for the period of January 20 to25, 1993. The algorithm retrieved snow depth at 69 stations from 100 and the mean absolute difference between
the observations and estimations is 24.5cm. The algorithm was not able to infer accuracy the snow informationfrom deep snowpacks. This is probably due to the limited penetration of 37GHz radiation.
The Tibetan Plateau has been suggested to play an important role in the variation of the Asian summer monsoon
through its atmospheric heating processes. The Intensive Observing Period (IOP) was implemented in 1998 forthe purposes of establishing the satellite-based observing systems and clarifying the interactions between the land
surface and atmosphere over the Tibetan Plateau. The closest footprints of TMI to the Automatic Weather
Stations (AWSs) were used to make a match-up data set. The estimated snow physical temperature is in good
agreement with the observed surface temperature by using the infrared thermometer as shown in Fig. 3, although
the snow depth has not been validated because the lack of the ground-based snow depth data.

AMSR soil moisture algorithm development and validation
Toshio Koike
Department of Civil Engineering, University of Tokyo
Microwave remote sensing can directly measure the dielectric properties which are strongly dependent on theliquid water content. The longer wavelength is one of the advantages of microwaves. It is long enough toreduce the scattering effect of cloud particles and to make microwave sensors useful all-weather ones. The
wavelength in the microwave region has sensitivity to the scattering effect of leaves. Microwave remote sensing
has potential of the measurement of water content of vegetation. The independence of sun as a source of
illumination is also one of the important reasons for using microwaves. We can obtain the data even in night.
This advantage is more important in the case of non-sunsynchronous observation.
Advanced Microwave Scanning Radiaometer (AMSR) is a passive microwave radiometer with frequency
ranges from 6.9 GHz to 89 GHz. It will be flown on-board of the United States Earth Observation System (EOS)
PM-1, “AQUA”, by National Aeronautics and Space Administration (NASA) of the United States and theAdvanced Earth Observing Satellite-II (ADEOS-II) by National Space Development Agency (NASDA) of Japan.
With a large antenna, AMSR will provide the best spatial resolution of multi-frequency radiometer from space.
The spatial resolution of the ADEOS-II AMSR varies from approximately 50km at 6.9 GHz to 5 km at 89 GHz.
The AQUA AMSR-E has slightly coarser spatial resolution due to its 1.6m antenna aperture instead of the 2m one
for ADEOS-II AMSR. The antenna beams scan by continuous rotation along a conical surface, which intersects
the earth’s surface at an angle of 55 degree.
Currently, NASDA is developing an AMSR standard algorithm for soil moisture. The proposed algorithms by
the selected principle investigators (PIs) are now being carefully tested and evaluated using the SMMR and
SMM/I data. There are basically four candidate algorithms. At the time of the test, all algorithms are still underdevelopment and subject to changes. Jackson proposes two types of regression algorithms in addition to hisbasic one. Paloscia adopts two ways for estimation of one parameter, a simple liner regression method andvegetation biomass classification one based on the polarization information. Njoke proposes both empirical andphysically- based algorithms.
The match-up data between SMMR and in-situ soil moisture at 79 Former Soviet Union (FSU) agricultural
fields were provided by NASDA Earth Observation Research Center (EORC). The soil moisture measurements
were conducted at 8th, 18th, and 28th of each month. The algorithm inter-comparison was implemented under
the three typical vegetation conditions, which are indicated by the histograms of NDVI distribution in the area
corresponding to the SMMR foot print. Paloscia’s algorithm works well in three cases due to the effect ofregression adjustment. In the case of not so dense vegetation with heterogeneity, the estimated values by Njoke’s
and Koike’s algorithms scatter around the observed ones. Under the uniform and dense vegetation, those twoshow under estimation or scatter and Jackson’s algorithm can not retrieve soil moisture. To evaluate algorithm
performance, it is necessary to obtain ground truth data in uniform areas or spatially distributed information inheterogeneous areas.
Heterogeneity is one of the critical issues of passive microwave remote sensing of soil moisture due to largefoot print of microwave radiometers, especially at low frequency. A ground-based microwave radiometer(GBMR) was deployed in the SGP99 to respond this scientific requirement.
The GBMR with three frequencies and dual polarization was operated during the SGP99 to provide wellcontrolled observations to enhance algorithm development and aircraft and satellite data validation. Every
morning, the radiometer was calibrated by using liquid nitrogen and the ambient hot load just before the operation.
It was kept working until the end of operation of the day. Incident angle was 55 degree. 100 samples weretaken at each rotation angle by rotating the antenna from –10 degree to + 10 degree with 5 degree interval. Total
number of samples is 500 at each point. After ground surface measurement, sky reference was also collected.
The gravimetric soil moisture samples of 0 – 2.5cm and 2.5 – 5.0 cm layers were collected at three points whichcorrespond to the centers of foot prints at the rotation angle, -10, 0 and +10 degree at each site. The horizontal
soil moisture measurement at 1.0cm, 2.5cm and 5.0cm in depth and the vertical measurement were carried out by
using the TDR system at the same points. The infrared thermometer was used for the measurement of surface
temperature at the points where the soil samples were collected. The soil temperature profiles were measured at
1.0cm, 5.0cm and 10.0cm in depth at the same points. A spectrometer which covers from 380nm – 2500nm with
1 nm sample interval was used. Seven samples were collected along the soil measurement course in addition to
three white board measurements. Two portable surface roughness indicators were used. Two samples, one
along north-south direction and the other along east-west, were collected at each site.

The observation shows that the apparent emissivity, Tb/Ts at 6.9 GHz increases as soil moisture increases. It
is considered that the soil temperature gradient affect the observed brightness temperature significantly in the drysoil cases. The soil temperature difference between the observed values and the estimated effective values
decreases as soil moisture increases. By the simple numerical simulation, the effect of scattering extinction
under dry condition causes the brightness temperature increase as soil moisture increase. This means thattemperature gradient should be considered in dry case.

Description of Soil Moisture Retrieval Algorithm for ADEOS II AMSR
Thomas J. Jackson
USDA ARS Hydrology and Remote Sensing Lab

1. ALGORITHM DESCRIPTION
To a large degree, the research in microwave remote sensing of soil moisture has focused on the forward modelingproblem. This is the process of predicting the brightness temperature from soil properties using radiative transfer
theory. When measuring soil moisture we must be concerned with inversion of this model. This is moredifficult than forward modeling. There are five steps involved in extracting soil moisture using passive
microwave remote sensing. These are; normalizing brightness temperature to emissivity, removing the effects ofvegetation, accounting for the effects of soil surface roughness, relating the emissivity measurement to soil
dielectric properties, and finally relating the dielectric properties to soil moisture.
In our approach, soil moisture retrieval is based upon an algorithm developed by Jackson (1993). Brightness
temperature for a single AMSR channel (6.9 GHz H) is converted to emissivity using a surrogate for the physicaltemperature of the emitting layer. This emissivity is corrected for vegetation and surface roughness to obtain thesoil emissivity. The Fresnel equation is then used to determine the dielectric constant. Finally, a dielectric
mixing model is used to obtain the soil moisture. The theory describing this follows.
Fundamental basis for a smooth bare soil. The measurement provided is the brightness temperature, TB, that
includes contributions from the atmosphere, reflected sky radiation, and the land surface. Atmosphericcontributions are negligible at frequencies <6 GHz. Galactic and cosmic radiation contribute to sky radiationand have a known value that varies very little in the frequency range used for soil water content observations (Tsky~4 K). The brightness temperature of a surface is equal to its emissivity (e) multiplied by its physicaltemperature (T).
Based upon the above, the equation for TB is

TB = eT + [1 − e ]Tsky(1)

The second term of equation 1 will be on the order of 2 K and will be dropped for computational purposes. For
inversion equation 1 is rearranged as follows

e=

TB
T

(2)

If the physical temperature is estimated independently, emissivity can be determined. This can be done using
surrogates based on satellite surface temperature, air temperature observations, or forecast model predictions.
There are two important relationships that must be utilized to relate the sensor measurement to soil water content.
In the first it is necessary to link the sensor measurement to a basic property of the soil that changes with watercontent. By assuming that the target being observed is a plane surface with surface geometric variations andvolume discontinuities much less than the frequency, only refraction and absorption of the media need to beconsidered at low frequencies such as L band (at higher frequencies scattering must be included). This permits
the use of the Fresnel reflection equations (Ulaby et al., 1986). These equations predict the surface microwave
reflectivity as a function of dielectric constant (relative permittivity) of the target (εr) and the viewing angle (Θ)
based on the polarization of the sensor, horizontal (H) or vertic al (V). At these frequencies the reflectivity isequal to 1 minus the emissivity. The Fresnel equations can be simplified by including only the real part of thecomplex dielectric constant (the imaginary part of the complex dielectric constant is relatively small and often
ignored). This simplification makes it possible to invert the Fresnel equations to solve for εr’ given the measured
emissivity.

e H (Θ) = 1 −eV (Θ) = 1 −cos Θ − εr − sin 2 Θ2(3)

cos Θ + εr − sin 2 Θεr cos Θ − εr − sin 2 Θ2εr cos Θ + εr − sin 2 Θ(4)

For a bare soil surface, the target consists of an interface of air and soil plus a shallow contributing layer at the topof the soil column. Since the dielectric constant of air is a known value (~1), the reflectivity provides ameasurement of the dielectric constant of the soil. The Fresnel equations apply when the two media at theinterface each have uniform dielectric properties within the contributing depth. Although this is certainly valid
for air, however, for a soil surface this is not always a valid assumption. It should also be noted that the basic
formulations in equations 3 and 4 result in a larger dynamic range or sensitivity of emissivity to changes in the
dielectric constant for H polarization. It is possible to invert equation 3 to solve for the dielectric constant given
the measured emissivity.
The next critical relationship involves relating this derived dielectric constant to volumetric soil water content.
The dielectric constant of soil is a composite of the values of its components: air, soil and water. Although thedielectric constant is a complex number, for soil mixtures the real part is much more important and variable.
Values of the real part of the dielectric constant for air and soil particles are approximately 1 and 5, respectively.
For water the value of the dielectric constant varies with frequency and is about 80 at the lower frequencies
considered here (<6 GHz) (Ulaby et al., 1986).
The basic reason microwave remote sensing is capable of providing soil water content information is this large
dielectric difference between water and the other soil components. Since the dielectric constant is a volume
property, the volumetric fraction of each component must be considered. The computation of the mixture
dielectric constant (soil, air and water) has been the subject of several studies and there are different theories as tothe exact form of the mixing equation (Schmugge, 1980 and Dobson et al., 1985). A simple linear weighting
function is typically used.
The dielectric constant of water referred to above is that of free water in which the molecules are free to rotate andalign with an electrical field. It has been recognized for some time that not all the water in soil satisfies thiscondition. Schmugge (1980) suggested that some water in the soil had different properties. He proposed thatfor a given soil this could be estimated using soil texture in much the same way that pedo-transfer functions areused to estimate 15 bar and 1/3 bar water contents based on texture (Rawls et al., 1993). He proposed that theinitial water added to dry soil below a "transition" water content were held more tightly by the soil particles andhad the dielectric properties of frozen water (~3).
Vegetation and Surface Roughness. For natural conditions, varying degrees of vegetation will be encountered.
The presence of vegetation will have a major impact on the microwave measurement. Vegetation reduces thesensitivity of the retrieval algorithm to soil water content changes by attenuating the soil signal and by adding a
microwave emission of its own to the microwave measurement. The attenuation increases as frequency
increases. This is an important reason for using lower frequencies. As described in Jackson and Schmugge(1991), at lower frequencies it is possible to correct for vegetation using a vegetation water content-relatedparameter.
When there is vegetation, the observed emissivity is a composite of the soil and vegetation. To retrieve soil
water content it is necessary to isolate the soil surface emissivity (esurf). Following Jackson and Schmugge(1991), the equation describing this ise p = [1 − αp , f , v ][1 − γ p , f ,v ][1 + [1 − e surf
]γ p , f , v ] + e surfp
p γ p , f ,v(5)

Both the single scattering albedo (α) and the one-way transmissivity of the canopy (γ) are dependent upon thevegetation structure (v), polarization (p) and frequency (f).
The transmissivity is a function of the optical depth (τ) as described by the following equation

γ p , f ,v = exp[ −τ p , f , v sec Θ](6)At low frequencies the single scattering albedo can be assumed to be negligible, then substituting equation 6 into
equation 5 and rearranging yields

e surf= 1 + [ e p − 1] exp[ −2τ p , f , v sec Θ]p(7)

The vegetation optical depth is also dependent upon water content (W). In studies reported in Jackson et al.
(1982) and Jackson and Schmugge (1991), it was found that the following functional relationship between the
optical depth and vegetation water content could be appliedτ p , f ,v = b p , f ,vW(8)

There is a limited database of values of b available. The vegetation water content can be estimated using avariety of ancillary data sources. One approach is to establish a relationship between w and a satellite based
vegetation index such as the Normalized Difference Vegetation Index (NDVI) as described in Jackson et al.
(1999).
The emissivity that results from the vegetation correction is that of the soil surface. This includes the effects ofsurface roughness. These effects must be removed in order to determine the soil emissivity (esoil ) which is
required for the Fresnel equation inversion. One approach to removing this effect is a model described in
Choudhury et al. (1979) that yields the bare smooth soil emissivity

e soil= 1 − [1 − e surf
] exp[ −h p , f , g cos 2 Θ]
p
p

(9)

The parameter h is dependent upon the polarization, frequency and geometric properties (g) of the soil surface.
Typically, values are assigned based upon land use and tillage (Choudhury et al., 1979 and Jackson et al., 1999).

2. OPERATIONAL IMPLEMENTATIONN
For each AMSR pixel, the latitude and longitude (from the input file) are used to cross reference to the land coverand NDVI ancillary data files. The third set of ancillary data files representing soil texture and porosity, is not
mapped to any projection and the resolution is 0.083 degrees. The AMSR footprint is readily located in the soil
texture file and its latitude and longitude are retrieved from the input file.
Land cover is first used to screen the data for the selected number of categories that can be inverted for soil
moisture. This also removes water pixels. The next step is another screening to check for anomalous TB values.
Following this, an index developed by Ferraro et al. (1994) is used to screen out pixels with active rainfall. The
final screening is a check of the surface air temperature from the AMSR files versus TB.
Having passed all of the tests above, the footprint data is used to compute soil moisture. T B is divided by anadjusted surface air temperature to estimate emissivity.
Vegetation correction is performed using the pixel NDVI to compute the vegetation water content.
roughness effects are removed utilizing a single roughness parameter, fixed at 0.1 at this time.

Surface

The net result of these corrections is the soil emissivity. From this the dielectric constant of the soil is computed.
The value of the dielectric constant is then used with the dielectric mixing model and the soil texture and porosity
to compute the volumetric soil moisture.

3. ANCILLARY DATA SOURCES
Land Cover
The University of Maryland Geography Department produced a global land cover data base at a resolution of 8
km which is available at http://glcf.umiacs.umd.edu/. The codes for the land covers are as follows;
1
2
3
4
5
6
7
8
9
10
11
12
13

Evergreen Needleleaf Forests
Evergreen Broadleaf Forests
Deciduous Needleleaf Forests
Deciduous Broadleaf Forests
Mixed Forests
Woodlands
Wooded Grasslands/Shrubs
Closed Bushlands or Shrublands
Open Shrublands
Grasses
Croplands
Bare
Mosses and Lichens

AMSR data over areas covered by cover types 1 – 6 cannot be used for retrieving soil moisture due to the effects
of forests. Data over cover types 7 – 10 and 12 – 13 can be used for retrieval. Croplands are considered for soil
moisture retrieval if the NDVI is less than 0.5. Thus, the new land cover types are:
0
1
2
3
4
5

ocean and inland water – more than 20% of footprint covered by ocean or by inland water
good for retrieval – more than 60% of footprint covered by wooded grasslands/shrubs, closed
bushlands or shrublands, open shrublands, grasses, bare, mosses and lichensreasonable for retrieval – categories listed in 1. occupied more than 30% of footprint andcroplands less than 30%
conditional for retrieval – categories listed in 1. occupied less than 30% of footprint andcroplands over 30%
limited for retrieval – more than 60% of footprint covered by croplands
unable for retrieval – more than 30% of footprint covered by evergreen needleleaf, evergreen
broadleaf, deciduous needleleaf, deciduous broadleaf, and mixed forests and woodlands

NDVI
The technique used to incorporate vegetation effects requires NDVI information. These products are available
from various sources and can be acquired and updated to reflect current conditions. The GLI team may generate
data products that can be used for this purpose. However, since this is a research algorithm and arrangements toimport ancillary data sets such as NDVI are not in our control, we are providing an alternative that should be
adequate for most conditions in soil moisture retrieval.
We are providing a series of NDVI data sets that represent the historical averages for each 10 day period
throughout the year. The algorithm will retrieve the NDVI data set that is closest in time (day of the year) to theobservation date for the AMSR data. This NDVI data set then represents the average condition expected for thisdate. The quality of the estimate will depend upon how the current year deviates from the average. It might bepossible in the future to adjust these values for the current conditions by tracking climatological information andcomparing this to the year to year conditions in the records.
To develop the historical averages we used the Pathfinder AVHRR Land data sets. These are global, land surface
data derived from the Advanced Very High Resolution Radiometers (AVHRR) on the NOAA/TIROS operational
meteorological satellites (NOAA-7, -9, and –11) that have provided continuous daily and composite data set from
July 1981 through the present. The daily and composite products include 12 data layers, (NDVI, CLAVR flag,

QC flag, Scan Angle, Solar Zenith Angle, Relative Azimuth Angle, Ch 1 Reflectance, Ch 2 Reflectance, Ch 3
Brightness Temperatures, Ch 4 Brightness Temperatures, Ch 5 Brightness Temperatures, and Day of Year). The
composite is generated by comparing the NDVI values for each 8 km bin from 10 consecutive Daily Data Sets.
Because data at the edge of a scan may contain distortion and bi-directional effect biases, only data within 42
degrees of nadir are used in the composite. For each 8 km pixel, the day with the highest NDVI during a 10 day
period is chosen as the date for inclusion in the composite, and all 12 data layers are updated with data from that
date. This composite process is effective for removing most of the clouds and atmospheric contaminants, thus
providing as close to a cloud free field in each of the data layers as is possible (Holben, 1986). There are threecomposites per month. The first composite of each month is for days 1 to 10, the second composite is for days
11 to 20, and the third composite is for the remaining days.
The NOAA/NASA Pathfinder Land data team has completed their software development and data reproc essing.
Their data are distributed by the Goddard Distributed Active Archive Center (DAAC)(ftp://daac.gsfc.nasa.gov/data/avhrr/global_8km). Data are available from July 13, 1981 to the present. For thisanalysis, we only used data from 1982 to 1999. The NDVI composite is mapped in a global 8 km equal area gridusing the Goode Interrupted Homolosine projection. There are (36*18) data sets. The original AVHRR
Pathfinder NDVI 8 km 10-day composite data from 1982 to 1999 that were used in our processing are on
CDROMs (18 of them).
For each pixel in a 10-day composite data set which is not ocean, inland water or filler, all data points that fall in a
7x7 box centered at that pixel were averaged. In the averaging process, if there were any ocean, inland water orfiller pixels in the 7x7 box, these were not included in the average computation. After this process wascompleted for each individual NDVI data set, the values for each 10 day interval were averaged over the 18 year
record to produce the average annual time series 10-day composite.
Soil Texture
The soil texture and porosity data sets are a result of a study to estimate global soil water-holding capacities bylinking the Food and Agriculture Organization (FAO) soil map of the world with global pedon databases andcontinuous pedotransfer functions (PTF) (Reynolds et al., 2000). The FAO-UNESCO Soil Map of the World(SMW) at 1:5,000,000 is the most comprehensive soil map with global coverage. Great efforts have been madeto relate the FAO soil units to physical soil characteristics by statistically analyzing global pedon databases toestimate soil texture, bulk density and organic matter content. The data set images produced by Reynolds et al.
(2000) have a 5-min spatial resolution to preserve the spatial integrity of the SMW, which is equivalent to a 9 km
x 9 km cell size at equator. Soil properties were estimated at two depths, i.e., 0-30 cm and 30-100 cm. Only
the 0-30 cm depth is needed here. Three of these soil properties were placed in the ancillary directory; clay
content, sand content and porosity.
4. REFERENCES
Choudhury, B. J., Schmugge, T. J., Chang, A. T. C., and Newton, R. W. 1979. Effect of surface roughness on
the microwave emission of soils. J. Geophysical Research, 84:5699-5705.
Dobson, M. C., Ulaby, F. T., Hallikainen, M. T., and El-Rayes, M. A. 1985. Microwave dielectric behavior of
wet soil, II, Dielectric mixing models. IEEE Trans. Geoscience and Remote Sensing, GE-23:35-46.
Ferraro, R. R., Grody, N. C., and Marks, G. F. 1994. Effects of surface conditions on rain identification using the
DMSP-SSM/I. Remote Sensing Reviews, 11:195-209.
Holben, B. N. 1986. Characteristics of maximum-value composite images from temporal AVHRR data.
International Journal of Remote Sensing, 7:1417-1434.
Jackson, T. J. 1993. Measuring surface soil moisture using passive microwave remote sensing. Hydrological
Processes, 7:139-152.
Jackson, T. J. and Schmugge, T. J. 1991. Vegetation effects on the microwave emission from soils. Remote
Sensing of Environ., 36:203-212.
Jackson, T. J., Schmugge, T. J., and Wang, J. R. 1982. Passive microwave remote sensing of soil moistureunder vegetation canopies. Water Resources Research, 18:1137-1142.
Jackson, T. J., Le Vine, D. M., Hsu, A. Y., Oldak, A., Starks, P. J., Swift, C. T., Isham, J. and Haken, M. 1999.
Soil moisture mapping at regional scales using microwave radiometry: the Southern Great Plains hydrology

experiment. IEEE Trans. On Geoscience and Remote Sensing, 37: 2136-2151.
fRawls, W. J., Gish, T. J., and Brakensiek, D. L. 1993. Estimating soil water retention from soil physicalproperties and characteristics. Advances in Soil Sciences, 16:213-234.
Reynolds, C. A., Jackson, T. J., and Rawls, W. J. 2000. Estimating soil water-holding capacities by linking theFood and Agriculture Organization soil map of the world with global pedon databases and continuous
pedotransfer functions. Water Resources Research, 36:3653-3662.
Schmugge, T. J. 1980. Effect of texture on microwave emission from soils. IEEE Trans. on Geoscience andRemote Sensing GE-18:353-361.
Ulaby, F. T., Moore, R. K., and Fung, A. K. 1986. Microwave remote sensing: active and passive, Vol. III,
from theory to application. Artech House, Dedham, MA.

The IROE algorithm
Simonetta Paloscia
Consiglio Nazionale delle Ricerche,Istituto di Ricerca sulle Onde Elettromagnetiche
On the basis of experimental results, obtained in past years by IROE Microwave Remote Sensing Group, it has beenstated that the brightness temperature (Tb) of microwave emission measured at C-band (6.8 GHz) is able to estimate
soil moisture content (SMC) in different conditions of roughness and vegetation biomass, provided that a correction
for the presence of vegetation is introduced. An algorithm has been proposed for computing SMC and correcting theeffects of vegetation by using the sensitivity of Polarization Index (PI=TbV-TbH /TbV+TbH ) at X-band (10 GHz) tobiomass.
The relation between the brightness temperature (Tb) at C-band and the soil moisture of bare soils has the following
generic form:
SMC = M + N ∗ TbC
When the soil is covered by vegetation, the slope (N) of the regression line decreases and the intercept (M) may alsochange. On the other hand, the (PI) at higher frequencies and in particular at X-band is more sensitive to thevegetation biomass, and can discriminate between several levels of Leaf Area Index (LAI) [Paloscia and Pampaloni
1988]. We can therefore assume that PI at X-band could be related to the slope (N) and intercept (M) of theregression line between PI at C-band and SMC, according to equations of the following type:
M = a + b ∗ PIX

and

N = a’ + b’ ∗ PIX

Substituting these relationships in equation (3), we can choose more adequate coefficients for the regression line of
SMC retrieval, which becomes:
SMC= [a + b ∗ PIX] – [a’+ b’ ∗ PIX] ∗ TbC
This procedure can be summarized in the flow-chart of Fig.1.
This algorithm was first tested on microwave data sets collected on agricultural area using IROE airborne radiometers
at C and X band. A comparison of SMC retrieved from radiometric measurements with SMC measured on the
ground, is shown in Fig. 2, which refers to experimental data collected in the agricultural area of “Les Alpilles” inSouthern France [Macelloni et al, 2000]. The resulting correlation coefficient is R=0.78 and the standard error of
estimate is SE=4.31.
The algorithm was subsequently validated to a larger scale by using satellite data from SMMR. NASDA kindly
provided us with a data set of SMMR collected over 79 Russian agro-meteorological stations during a period of about
3 years (from October 1978 to December 1981), together with the corresponding ground-measured values ofgravimetric SMC. The latter data, archived by Dr. K. Masuda and Dr. V. Savelin, represented the average value ofthe first 10-cm layer: they were obtained, with a time interval of 10 days, from April to October. Five SMMR data
were picked up within an area around the target station.
From the analysis of these data sets, the slope and the intercept of the regression line SMC=M+ N*TbC were related tothe corresponding values of PI at X-band (PIX). In this case, we found that:
M= 60.5+7∗ (PIX)And
N= 0.0008 – 0.2156∗Ln(PIX)

The final equation for the retrieval of SMC therefore becomes:
SMC = [60.5+7∗ (PIX)] + [0.0008 – 0.2156∗Ln(PIX)] ∗TbC
The results of this algorithm is shown in the diagram of Fig. 3, where SMC measured on the ground was comparedwith SMC computed from SMMR data with the algorithm. Although the dispersion of experimental data is rather
high, we see that, at least for some ground stations, the algorithm is able to retrieve reasonable data of SMC with R on
the order of 0.70 and SE ranging between 3 and 9 [Paloscia et al. 2001]. The main problem of this validation lies on
the considerable coarse ground resolution of the SMMR at C-band. The retrieval of SMC can work only in the caseof highly homogeneous areas, for which the SMC values measured at the agro-meteorological station can be assumed
to be representative of the entire surrounding zone. Other problems were due to the poor calibration accuracy
between the two polarization channels.

References
G. Macelloni, S. Paloscia, P. Pampaloni, R. Ruisi, C. Susini, 2000, “Airborne Microwave Radiometer
Measurements on Agricultural Fields”, in ‘Microwave Radiometry of Earth’s Surface and Atmosphere’,(Pampaloni & Paloscia Eds), pp. 59-69, VSP press, Utrecht, The Netherlands
Paloscia S. and P. Pampaloni, , "Microwave Polarization Index for Monitoring Vegetation Growth", IEEE Trans. on
Geoscience and Remote Sensing, GE-26, n. 5, pp. 617-621, 1988
S. Paloscia, G. Macelloni, E. Santi, and Toshio Koike, 2001, “A Multifrequency Algorithm for the Retrieval of Soil
Moisture on a Large Scale using Microwave Data from SMMR and SSM/I Satellites, IEEE Trans.on Geosci. andRemote Sensing, Special Issue on Soil Moisture, vol.39, 8, pp. 1655-1661

MW DATAPI
X -b a n d

Tb
C -b a n d

PWC/LAIM = a + b PI X
N =a’ + b’ PI XS M C = M + N ∗T b C

SMC= (a + b ∗ PIX) + [(a’ + b’ ∗ PIX) ∗ TbC]

SMC

Fig. 1 – The proposed algorithm

45
40
SMC comp (%)

35
30
25
20
15
10
5
0
0

5

10 15 20 25 30 35 40 45
SMC meas (%)

Fig. 2 - SMC % estimated with the algorithm as a function of SMC % of the first 5 cm layer measured
on ground. The line represents the 1:1 line. Symbols refer to different crop types: = alfalfa, •= baresoil, x = sunflower, ♦ = wheat.

40

SMCcomp

30

20

10

0
0

10

20

30

40

SMCmeasFig. 3 - SMC% estimated from SMMR data of Tb at C-band vs. SMC% measured on ground. Different
symbols refer to different Russian stations.

ADEOS-II AMSR Soil Moisture Algorithm
E. Njoku
Jet Propulsion Laboratory

The soil moisture algorithm involves a series of steps beginning with quality control of the input data followed byre-sampling of the data, surface type classification, screening of the data for retrieval, and inversion of the brightness
temperatures to obtain soil moisture. A flowchart of the algorithm is shown in Figure 1.
Re-sampling of the data to an Earth-fixed grid is done to facilitate the surface type classification and retrieval steps.
These steps use external data bases to identify water bodies, mountainous areas, soil texture, and other surface features.
The surface type classification includes generation of flags that indicate snow, frozen ground, dense vegetation, or
precipitation, where retrievals are either not possible or are likely to be of degraded quality.
1. Algorithm
control

2. TB
quality-control

3. Earth grid
registration

4. Surface typeclassification

5. Datascreening

6. Regression
retrieval(mod=1)7. Iterative
retrieval(mod=2)

8. Output
processing

Fig. 1 Flowchart of the algorithm

The surface type flags are qualitative and are generated primarily to assist in screening the data and interpreting thesoil moisture retrievals.

The algorithm is a model-based iterative retrieval using the model and approach described in Njoku and Li (1999).
This model expresses the brightness temperature observed by AMSR at a particular frequency as:

TBp = Te { (1 - rsp ) exp (-τc) + (1 - ωp) [ 1 - exp (-τc) ] [ 1 + rsp exp (-τc) ] }where, Te is the surface temperature; rsp is the surface reflectivity, which is related to the volumetric soil moisture mv
through the Fresnel equations; ωp is the vegetation single scattering albedo, and τc is the vegetation opacity, which ismodeled as linearly related to the vegetation water content wc. Fixed values are used for ωp and surface roughness
height (which affects rsp ). The algorithm provides internal corrections for Te and τc in deriving mv , through the useof information contained in the multichannel estimation. At each retrieval point the algorithm finds the set of Te, τcand mv that minimize the weighted sum of squared differences between observed and model-computed multichannelbrightness temperatures. Weights are used to select among the lowest six channels (6.9, 10.6, & 18 GHz; V & H).
A backup algorithm mode uses a regression equation that is empirically based and is implemented as an alternatemeans for evaluating anomalous situations, such as where the iterative algorithm fails to converge. This mode uses a
combination of the six lowest frequency AMSR channels with coefficients derived from Nimbus-7 SMMR data.

Njoku, E. and L. Li, “Retrieval of land surface parameters using passive microwave measurements at 6–18 GHz,”IEEE Trans. Geosci. Rem. Sens., 37, 79–93, 1999