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Latent heat flux at the
sea surface retrieved from
combined TMI and VIRS
measurements of TRMM
P. SchlÜssel a & A. Albert a
a Meteorologisches Institut , Ludwig-Maximilians-
UniversitÄ
Published online: 25 Nov 2010.
To cite this article: P. SchlÜssel & A. Albert (2001) Latent heat flux at the
sea surface retrieved from combined TMI and VIRS measurements of TRMM,
International Journal of Remote Sensing, 22:10, 1975-1998
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int. j. remote sensing, 2001, vol. 22, no. 10, 1975–1998
Latent heat  ux at the sea surface retrieved from combined TMI and
VIRS measurements of TRMM
¨
P. SCHLUSSEL†‡ and A. ALBERT†§
†Meteorologisches Institut, Ludwig-Maximilians-Universitat Munchen
¨
¨
Theresienstraße 37, D-80333 Munich, Germany
‡EUMETSAT, Am Kavalleriesand 31, D-64295 Darmstadt, Germany
§Institut fur Methodik der Fernerkundung, DLR, D-82230 Weßling, Germany
¨
(Received 4 June 1999; in Ž nal form 25 January 2000)
Abstract. Two radiometers ofthe Tropical Rainfall Measuring Mission (TRMM)
were used to retrieve parameters that were necessary to determine the latent heat
 ux density at the sea surface. The Visible and Infrared Radiometer System
(VIRS) was used to measure sea surface temperature. The TRMM Microwave
Imager (TMI) measured near-surface wind speed and air-speciŽ c humidity. The
retrieval schemes for these parameters were derived theoretically by means of
radiative transfer simulations and were validated by TRMM data matched with
buoy measurements. The validation study revealed deŽ ciencies in the description
of the infrared water vapour absorption continuum and in the TMI calibration.
Both eVects were corrected for so that the desired parameters could be retrieved
with adequate accuracy. A global application of the retrieval method to TRMM
data for April 1998 is shown.
1. Introduction
The evaporation of the sea surface constitutes a part of the freshwater  ux
between ocean and atmosphere. The diVerence between precipitation and evaporation
over sea is one of the most important parts of the global hydrological cycle. By the
latent heat of evaporation it also accounts for a substantial part of the air–sea energy
 ux. Direct measurements of the surface evaporation are only possible by means of
eddy correlation techniques. These are conŽ ned to surface observations and are not
possible from satellites. The turbulent water vapour  ux at the sea surface is the
correlation product
E
rw q
(1)
=
ê ê
where w and q are the  uctuations of vertical wind velocity and speciŽ c humidity
ê
ê
above the sea surface, respectively, and r is the air density. The  uctuations have to
be resolved at a temporal scale of about 10 Hz and averaged over time periods of
about 10 minutes to obtain meaningful values of the evaporation (Hasse 1993).
Equation (1) is commonly parametrized with the so-called bulk aerodynamic for-
mula, assuming that the evaporation at the surface is driven by the air–sea humidity
gradient and that the air–sea exchange increases with wind speed. A recent
International Journal of Remote Sensing
ISSN 0143-1161 print ISSN 1366-5901 online © 2001 Taylor & Francis Ltd
/
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//
/

1976
P. Schlussel and A. Albert
¨
formulation of the bulk formula is given by (Fairall et al. 1996)
CE (S, hv T0 )rS(q0 q)
E
(2)
where CE is an exchange coeYcient (also known as Dalton number) depending non-
linearly on wind speed and stability, hv is the virtual potential air temperature, T0
is the sea surface skin temperature, q0 is the sea surface speciŽ c humidity, q is the
air-speciŽ c humidity, and
S
u2 wg
where u is the near-surface wind speed and
b( zi gu* T* /Ta )1 /3
(3)
w
(4)
is the gustiness factor that accounts for evaporation in calm situations, driven by
free convection. Ta is the near-surface air temperature, zi is the atmospheric bound-
ary-layer height, g is the gravitational acceleration, u* is the friction velocity above
the sea surface, b 1.2, and
T*
H/(cp ru* )
(5)
is a scaling temperature following the Monin–Obukhov similarity (MOS) where H
is the sensible heat  ux and cp is the speciŽ c heat of air at constant pressure. The
latent heat- ux density is obtained from (2) by multiplying E with the latent heat
of evaporation, L, which in turn is a function of the temperature.
The functional dependence of C on S and hv
T is described by the MOS
surface-layer theory (e.g. Panofsky anEd Dutton 1984). Su0mmarizing the dependencies
in (2)–(5) and similar ones for the turbulent  ux of momentum leads to mainly three
variables that are needed to calculate the evaporation: T0 , u and q. Further knowledge
is necessary about the air pressure, p, and temperature as well as the planetary
boundary-layer height.
While p and zi are suYciently represented by their mean values, the air temper-
ature must be known more precisely. Liu et al. (1994) suggest to retrieve the surface
air temperature from the air speciŽ c humidity (that is retrieved from the satellite
measurements) and the assumption of a constant relative humidity of 80% in the
marine atmosphere. The usefulness of this coarse parametrization was conŽ rmed by
Taurat (1996) for tropical and subtropical situations. The air temperature derived
by this method is also entered into the calculation of the sensible heat  ux which is
needed in (5). The sensible heat  ux is calculated with a bulk aerodynamic formula
similar to (2).
The use of satellite data to retrieve T , u and q for the use with the bulk formula
(2) has been elaborated for the sensor co0mbination Advanced Very High Resolution
Radiometer (AVHRR) and Special Sensor Microwave/Imager (SSM/I) (Schlussel
¨
et al. 1995, Schlussel 1996). An evaluation of the method has been presented by
¨
Schulz et al. (1996). The validation studies show that the latent heat  ux, derived
from instantaneous satellite measurements agree within a standard deviation of
30 W m (corresponds to an evaporation of 1 mm dayÕ1 ) with co-located ship and
Õ2
buoy measurements. Recently, the combined retrieval method has been successfully
applied in an air–sea interaction study of the Indian Ocean (Ramesh Kumar and
Schlussel 1998), demonstrating the usefulness of this remote sensing method in
¨
climate studies.
The aim of this study is to seek for improvements in the developed remote sensing

Latent heat  ux at the sea surface
1977
methods for tropical and subtropical regions by transferring the techniques for the
use with infrared and microwave radiometers carried by the Tropical Rainfall
Measuring Mission (TRMM ) that is  own as joint US–Japanese satellite mission
since November 1997 (Kummerow et al. 1998). In the following sections we describe
the satellite data as well as the in situ measurements employed for radiative transfer
calculations and validation studies. Subsequently, the development of the retrieval
schemes for T0 , u and q is described. In further sections the validation by means of
buoy measurements is shown and the correction of the calibration of the microwave
radiometer is discussed. Finally, the derived methods are applied to global TRMM
data and Ž elds of the boundary layer parameters as well as the surface latent heat
 ux are presented.
2. Data
DiVerent datasets are used in this study originating from various sources:
1. TRMM satellite data including measurements from the TRMM microwave
Imager (TMI) and the Visible and Infrared Radiometer System (VIRS) for
the time period January to June 1998.
2. Atmospheric data entered into the radiative transfer calculations for the
theoretical development of the retrieval schemes
3. In situ measurements from moored buoys for the validation of the
satellite-retrieved boundary-layer parameters.
2.1. The satellite and its instruments
TRMM is a satellite dedicated to the observation of tropical precipitation in the
latitude band between 38.5 S and 38.5 N. The orbit of TRMM has been chosen to
be non sun-synchronous and drifting in order to avoid diurnal signals in long-
periodical averages of the retrieved rainfall. The nominal height of the satellite is
333 km; about 16 orbits are completed every day. Besides a precipitation radar and
a lightning detector which are not considered in this study TRMM carries two
radiometers, TMI and VIRS. Their spectral characteristics are listed in table 1.
TMI and VIRS are used together for the retrieval of the boundary-layer
Table 1. Spectral characteristics of TMI and VIRS.
TMI
VIRS
Frequency (GHz) IFOV (km)
IFOV at
Wavelength (mm) nadir (km) NE T (K)
/
D
D
polarization
AT CT
NE T (K )
/
10.65 v
10.65 h
19.35 v
19.35 h
21.30 v
37.00 v
37.00 h
85.50 v
85.50 h
63.2 38.2
0.63
0.64
0.50
0.47
0.71
0.36
0.31
0.52
0.93
0.63
1.6
3.75
10.8
12.0
2
2
2
2
2
—
—
0.07
0.08
0.09
/
63.2 38.2
/
30.4 18.4
/
30.4 18.4
/
27.2 16.5
/
16.0 9.7
/
16.0 9.7
/
7.2 4.4
/
7.2 4.4
D
IFOV, Instantaneous Ž eld of view; NE T, noise equivalent temperature diVerence; AT,
along-track; CT, cross-track; v, vertical; h, horizontal.

1978
P. Schlussel and A. Albert
¨
parameters. TMI is a modiŽ ed SSM/I instrument. Other than SSM/I it has an
additional spectral channel at 10.65GHz and a channel at 21.3 GHz instead of a
22.235 GHz channel. While the 10.65 GHz channel will allow for better wind-speed
retrievals in precipitating situations than SSM/I, the 21.3 GHz channel oVers better
retrievals of the water-vapour column in tropical situations than the 22.235 GHz
channel of SSM/I. Owing to the low orbit of TRMM the horizontal resolution of
TMI ranges from 4.4 km 7.2 km (along-track versus cross-track) at 85.5 GHz to
38 km 63.2 km at 10.65 GHz. TMI scans conically with a local incidence angle near
52.8 (nominal value) resolving 208 samples per scan at 85.5 GHz and 104 samples
per scan at the lower frequencies, covering a swath of 758.5 km. Although the TMI
is thought to scan conically with a constant viewing angle of 49 (corresponding to
a zenith angle of 52.8 ) the local incidence angle is not constant due to deviations
of the satellite’s yaw axis from the local vertical and due to the oblateness of the
Earth. Analysis of the true incidence angle which is reported with the data shows a
variation of the incidence angle between 46 and 54 in extreme cases. For most
measurements, however, the TMI incidence angle varies only within 52.5 and 53.0 .
To cover most possible incidence angles all simulations are carried out for 12 diVerent
zenith angles selected from normally distributed random numbers with a mean of
52.1 and a standard deviation of 1.1 . The radiometric noise of the measurements
varies among the channels and corresponds to temperature diVerences between 0.3
and 0.9 K.
VIRS is an optical imager similar to AVHRR with spectral channels located in
visible, near-infrared and thermal infrared atmospheric windows. The cross-track
scan of VIRS covers a swath of 720 km, resolved by 261 pixels in a scan line with a
horizontal resolution of 2 km at nadir view. The radiometric noise in the infrared
channels is lower than 0.1 K, oVering a good opportunity for accurate surface
temperature retrievals.
2.2. Data entering the radiative transfer calculations
Radiative transfer calculations have to be carried out for a set of atmospheric/
oceanic situations representing the global variability over the tropical and subtropical
oceans. Such a dataset has been composed from marine radiosonde proŽ les covering
1. 161 tropical/subtropical radiosondes of the Thermodynamic Initial Guess
Retrieval (TIGR) dataset (Chedin et al. 1985),
2. 54 aerological datasets from the International Indian Ocean Expedition
1964/65 (Defant 1969),
3. 343 radiosonde ascents collected by the German research vessel Polarstern on
transit cruises to/from Antarctica during 1986–1989 (Schulz et al. 1993).
The 558 datasets contain vertical proŽ les of temperature and humidity from the
surface to the lower stratosphere. They are partly amended by surface temperature
and near-surface wind speed. Where this is not the case these variables are generated
from random distributions. For the sea surface temperature a mean of Ta 1.5 K
has been selected, where Ta is the surface air temperature from the lowest radiosonde
level, and a standard deviation of 3 K between air and surface temperature is assumed.
The wind speed is taken randomly from a Rayleigh distribution with a mean value
of 7.5 m s
.
Õ1
Gases other than water vapour are included corresponding their mixing
ratios. Some of them like ozone, nitric acid, and chloro uorocarbons have a non-
homogeneous vertical distribution. They are vertically distributed according to

Latent heat  ux at the sea surface
1979
standard proŽ les described by Anderson et al. (1986) and the World Climate Research
Program (WCRP 1986). Other gases are assumed to be well mixed (table 2).
Cloud and rain liquid water was not included in the measurements and
are randomly scattered into the proŽ les as well. A mean liquid-water density of
rl 0.1 g m
has been inserted with a standard deviation of 0.5 g mÕ3 . Resulting
Õ3
values less than 0 are set to 0 and the maximum columnar liquid-water amount of
a layer (deŽ ned by the vertical resolution of the radiosonde proŽ le) is set to half the
corresponding columnar water-vapour content of that layer. The surface rainfall rate
is selected randomly from an even distribution between 0 and 5 mm hÕ1 . Partly rain
or cloud covered areas (due to horizontal inhomogeneity within the sensor’s Ž eld of
view) are generated by combining clear cases with completely cloudy ones and with
completely rain-covered situations. The cloud or rain cover is generated from an
even random distribution between 0 and 1. The composition is handled as described
by Bauer and Schlussel (1993). This very simpliŽ ed cloud/rain model seems to be
¨
justiŽ ed here because no attempt is undertaken to retrieve cloud or rain parameters.
The inclusion of liquid water is merely thought as to include geophysical noise in
the radiative transfer calculations. Additionally, more complete cloud models that
are widely employed today for such simulations only represent distinct situations,
but not the global variability of cloud and rain water in the tropical atmosphere.
The relative wind direction must be included in the calculation of the surface
emissivity. As no information about the wind direction is available from the satellite
measurements under consideration and additional information about the actual wind
Ž eld will not be included in the retrieval schemes the relative wind direction is
entered as freely varying parameter. It is chosen from an even random distribution
between 0 and 360 .
The extinction of radiation by aerosol particles must be included in the radiative
transfer calculations for the infrared channels. This is accomplished by making use
of the OPtical Aerosol parameter Catalog (OPAC, Hess et al. 1998), deŽ ning diVerent
realistic aerosol types composed by aerosol particles of various origins. The vertical
distribution of the aerosols is implemented by inserting diVerent aerosol layers. Here
we have chosen a boundary layer aerosol, extending from the surface to 1.7 km. The
aerosol is composed by three components, ‘water soluble’, ‘sea salt in accumulation
mode’, and ‘sea salt in coarse mode’ (equally distributed). A second aerosol layer is
inserted in the stratosphere between 14 and 26 km, containing only one component,
Table 2. Mixing ratio of absorbing gases included in the radiative transfer calculations.
Gas
Volume mixing ratio
H2 O
CO2
O
variable proŽ le
355 ppm
tropical standard proŽ le
0.31 ppm
N32 O
CO
0.13 ppm
CH4
1.72 ppm
20.95%
78.08%
tropical standard proŽ le
tropical standard proŽ le
tropical standard proŽ le
O
N2
H2NO3
CCl F
CCl32 F2

1980
P. Schlussel and A. Albert
¨
a ‘dustlike background aerosol’. Mean aerosol particle densities are adopted from
Hess et al. (1998). The variability of the aerosol is represented by a Gaussian random
distribution around the logarithm of these means and standard deviations adopted
according to climatological distributions found over oceans (Koepke et al. 1997).
The optical depths of the resulting combined aerosol layers are 0.22, 0.11 and 0.19
in the 3.7, 10.8 and 12.0 mm channels, respectively. The corresponding range of
optical depths covered is 0.01–0.86, 0.01–0.82 and 0.01–1.25, respectively.
2.3. Validation data
For the validation of the theoretically elaborated retrieval schemes in situ meas-
urements are matched within speciŽ ed time and space windows with the TRMM
measurements. The in situ measurements are taken from moored buoys operated by
the US National Buoy Data Center in the Atlantic and PaciŽ c Oceans. For the
validation of the retrieval methods in this study measurements from 71 buoys have
been taken. Their geographical distribution is shown in Ž gure 1. The parameters of
interest that are measured by the buoys are surface (bulk) temperature, air temper-
ature, dewpoint temperature, wind vector and air pressure. For the time period
January to March 1998 available buoy data are collected and matched with TMI
and VIRS data when and where possible. As not all parameters are measured by all
buoys, due to requirement to observe diVerent match-up windows for the diVerent
parameters, and due to the diVerent cloud/rain constraints in the microwave and
infrared measurements the match-ups have been collected as shown in table 3.
Most of the buoys are situated close to coastlines and might therefore produce
Figure 1. Distribution of moored buoys used for the algorithm validation.
Table 3. Buoy–TRMM match-up database.
Parameter
Time window
Space window
No. of match-ups
Wind speed
SpeciŽ c air humidity
Sea surface temperature
30 min
30 min
12 h
0.3
0.3
5 km
36 609
12 947
3628

Latent heat  ux at the sea surface
1981
unreliable match-ups in cases where the satellite measurements contain partly land-
covered areas. To exclude such situations a high-resolution land–ocean database is
used to detect land surfaces in the vicinity of the buoys. The land–ocean mask
resolves 550 m and should be suited to detect even relatively small coastal irregularit-
ies. TMI measurements are excluded from the validation if any land surface is closer
in distance than 50 km from the centre of a footprint.
3. Radiative transfer calculations
Radiative transfer calculations are carried out for the set of atmospheric–oceanic
situations described in §2.2 for the infrared channels of VIRS and the TMI channels
between 10.65 and 37.0 GHz. In both spectral domains the radiative transfer equation
is integrated including absorption and emission of surface and atmosphere and
surface re ection. Additionally, the space emission is incorporated in the microwave
region. The spectral radiance at satellite altitude is represented by
*
n
L
e B (T0 )exp ( d /cos h)
B (T(d ))exp( d /cosh)dd
*
0
r exp( d /cosh) 0 B (T(d ))exp ( d /cos h)dd
*
*
n
B (TSp )exp( 2d /cos h)r
(6)
*
where n is the frequency, f is the polarization, B is Planck’s function, T is the
atmospheric temperature, e is the surface emissivity, r is the surface re ectivity,
d is the optical depth, d is the total optical thickness of the atmosphere, h is the
*
incidence angle, and TSp is the temperature of the galactic space.
The terms on the right side of (6) describe
1. the radiation emitted by the surface at temperature T0 at an emissivity e
transmitted through the atmosphere with optical depth d at an incidence
*
angle of h to the satellite,
2. the radiation emitted by the atmosphere at temperature T to the satellite,
3. the downward atmospheric emission re ected by the surface with surface
re ectivity r and transmitted to the top of the atmosphere, and
4. the galactic space emission transmitted through the atmosphere, re ected by
the surface and transmitted to the satellite.
Vertically and horizontally polarized components of the radiation are calculated for
the TMI. For the VIRS only the total radiance is simulated. The numerical model
based on (6) has been used for the development of a number of retrieval techniques
Ž tted to the SSM/I and AVHRR radiometers (e.g. Schlussel and Grassl 1990, Schlussel
¨
¨
and Emery 1990).
3.1. VIRS simulations
The band absorption in the 3.7, 10.8 and 12 mm channels of VIRS is described
by the k-distribution method (Hollweg 1993) to account for the selective absorption
by gases and its band overlapping eVects. The k-distributions are determined from
line-by-line calculations of the atmospheric transmission in each thermal VIRS
channel including as spectral weights the Planck function at diVerent temperatures

1982
P. Schlussel and A. Albert
¨
and the spectral Ž lter functions of the radiometer. The absorption line parameters
are taken from the 1996 edition of the HITRAN database (Rothman et al. 1998).
Quasi-continuous absorption by water vapour is included in the calculation of
the band absorption. The water vapour continuum in the 3.7 mm channel is described
following Bignell (1970). In the 10.8 and 12 mm channels we follow the description
by Clough et al. (1989) with a modiŽ cation according to more recent Ž eld data of
the tropical atmosphere by Kilsby et al. (1992). This continuum is described for
wavelengths above 10 mm. It is extrapolated here to cover the full range of the
10.8 mm channel which slightly extends to wavelengths below 10 mm. The extrapola-
tion is done using the functional form given by Kilsby et al. (1992 ).
The surface emissivity of the rough sea in the VIRS thermal channels is parame-
trized in terms of frequency, incidence angle and wind speed according to Masuda
et al. (1988) with an amendment including a wind-dependent fractional whitecap
coverage as described by Monahan and O’Muircheartaigh (1986). The infrared
emissivity has been set to ew 1 so that the total emissivity reads
e(h, n, u) (1 f (u))er (h, n, u) f (u)ew
(7)
where f is the fractional whitecap coverage and er is the emissivity of the rough, but
whitecap-free surface. In the VIRS channels the surface re ectivity is approximated
by r (1 e). The VIRS is operating in a cross-track scan mode. Consequently, we
have chosen to perform all calculations for zenith angles between 0 and 48 in steps
of 4 .
3.2. TMI simulations
The TMI measurements are considered to be monochromatic as the spectral
bandwidth of the radiometer is narrow compared to the spectral signatures of the
atmospheric absorption spectrum. The atmospheric absorption included in the
radiative transfer model is adopted from Liebe (1989), accounting for gaseous absorp-
tion by water vapour and molecular oxygen lines and continua. Additionally, the
liquid-water absorption coeYcients are given.
A new surface emissivity model for the microwave domain as described by
Lemaire (1998) This model is based on Ž rst principles physical model of the scattering
of electromagnetic waves by the ocean surface. It includes a variety of eVects that
have not been acknowledged before, describing the surface scattering in great detail.
In contrast to the infrared region the parametrization of r requires the inclusion
of the hemispherically integrated re ection of downwelling radiation, which is
accounted for by a model of Guissard et al. (1994). Here, a polynomial approximation
of the re ectivity, as calculated by Lemaire (1998), is used. The approximation
describes the surface re ectivity in terms of friction velocity, of the near-surface
atmosphere, surface rain rate, relative wind direction, frequency, polarization, and
incidence angle of the radiation.
4. Retrieval algorithms
The retrieval algorithms are derived from the simulated measurements and the
datasets inserted into the radiative transfer models assuming that these data represent
the correct atmospheric/oceanic situations. To the simulated measurements noise is
added representing the radiometric noise with zero mean and a normally distributed
random noise with standard deviation corresponding to NEDT.

Latent heat  ux at the sea surface
1983
4.1. Surface wind speed
Analysis of the simulated data shows that the brightness temperatures measured
at 10, 19 and 21 GHz contain suYcient information for a reliable wind-speed retrieval.
Additionally, the knowledge about the local incidence angle must be included to
account for variations in the surface re ectivity and emissivity with varying viewing
angles. Two diVerent tools are used to analyse the simulated data. A multiple linear
regression and an artiŽ cial neural network. It has been shown by Stogryn et al.
(1994) that an artiŽ cial neural network is an excellent tool for retrieving oceanic
wind speed from SSM/I measurements.
A test of both, the linear multiple regression and an artiŽ cial neural network,
designed a feed-forward fully connected network (Zell 1994) shows that the perform-
ance of the latter is superior to the linear approach. In particular, situations with
increasing atmospheric liquid-water contents are better handled by the non-linear
method without altering the retrieval coeYcients.
Several network architectures are tested, involving more or less computational
eVort; the Ž nal choice is made for a network that is not too complicated so that
even big data amounts can be processed within realistic time frames (Ž gure 2).
Another requirement is the requested retrieval accuracy for the wind speed which
has to be better than 1.3 m s (standard error). The resulting network consists of a
Õ1
feed-forward network containing one input layer, a hidden, and an output layer with
six input units, three hidden units, and one output unit. Each unit is fed with the
output of the previous unit o by the logistic activation
1
a
(8)
1
exp
w o
b
T10v
T10h
T19v
T19h
T
Q
22v
Input Layer
Hidden Layer
Output Layer
u
Figure 2. Neural network for wind speed retrieval from TMI.

1984
P. Schlussel and A. Albert
¨
where b are the biases given in table 4 and w are the weights given in table 5 and
0
1
a
if a
if a
0
1
o
(9)
otherwise
The coeYcients are found by the error-back-propagation method.
The input to the units of the input layer consists of scaled brightness temperatures
and scaled incidence angle according to
o
T /A , for i 1, ..., 5 corresponding to T1 9v, T1 9h , T2 1v, T1 0v, T1 0h (10)
and
o
h/A
The network output is the scaled wind speed
u/A
The scaling factors A , i 1, ..., 10 are given in table 4.
Cases with rain rates greater than 5 mm h or too high liquid-water columns
(11)
o
(12)
Õ1
(
120 mg cmÕ2 ) must be excluded from the wind-speed retrieval as the scattering at
liquid-water droplets tends to depolarize the radiation Ž eld which cannot be distingu-
ished from the depolarization of the surface re ection caused by increased surface
roughness at increasing wind. Furthermore, the atmospheric opacity increases at
high liquid-water loadings which diminishes the surface-leaving radiation to an
Table 4. Properties of the artiŽ cial neural network retrieving near surface wind speed.
Parameter
Unit
Type
input
Bias b
Scaling A
T1 9 v
T
1
2
3
4
5
6
7
8
9
0.20707
0.68079
0.29333
0.10683
0.36261
0.77286
7.21608
0.30457
5.61350
250 K
210 K
270 K
220 K
170 K
57
T1 9 h
T2 1 v
T1 0 v
h 1 0 h
hidden
output
1
u
10
35 m sÕ
Table 5. Weights of the artiŽ cial neural network retrieving the near-surface wind speed.
Target j Source i: Weight w
7
8
6:
3:
6:
3:
6:
3:
0.93429
3.05787
0.91113
0.96518
0.77119
4.87953
5:
2:
5:
2:
5.91802
1.91837
0.38558
1.81806
4: 1.26633
1: 8.66964
4: 2.58713
1: 2.79569
4: 4.07529
1: 13.74966
7: 6.06863
9
5: 14.7098
2: 10.7400
8:
10
9: 14.6978
3.37857

Latent heat  ux at the sea surface
1985
extent that renders the TMI measurements useless in such situations. Therefore, we
exclude those TMI measurements where (T3 7v T3 7h
)
20 K or T1 9h 190 K. This
technique has been proven useful in the wind-speed retrievals from SSM/I already.
We do not relax the thresholds in view of the availability of the 10 GHz channels.
Rather it is intended to keep high accuracy also in such cases for which the SSM/I
allowed only for retrievals with strongly degraded accuracy.
4.2. Air-speciŽ c humidity
Another analysis of the TMI simulations is performed with respect to the retrieval
of near-surface speciŽ c humidity. As justiŽ ed by earlier work (Schulz et al. 1993,
Schlussel 1996), the microwave measurements are suited to retrieve the water-vapour
¨
column of the 500 m deep atmospheric boundary layer. The boundary layer water-
vapour column is highly correlated with the near-surface speciŽ c humidity q. Thus,
q should be retrievable from TMI measurements. In the earlier studies measurements
at 19, 22 and 37 GHz were included. Here, the 22 GHz channel is replaced by one
at 21 GHz and additionally, a 10 GHz channel is available. Consequently, a new
multivariate analysis is carried out in order to Ž nd a useful combination of channels
to be included in a retrieval scheme. Again, linear and non-linear analyses are
performed. However, in this case the relatively weak non-linearity is superseded by
the variance of q not explained by the brightness temperatures so that we chose a
linear regression for the retrieval approach. SigniŽ cance tests show that the 21.8 GHz
channel is less suited than the 22.235 GHz channel of SSM/I but still useful to be
included. However, the availability of the 10 GHz channel and the restriction to
tropical and subtropical situations are favourable and the resulting linear algorithm
gives a retrieval accuracy of 1.2 g kg for q, which is only slightly worse than that
Õ1
of the corresponding SSM/I algorithm. The choice for the TMI algorithm reads
q
a0 a1 T
a2 T
a3 T
a4 T
a5 T
a6 T
a7 h
(13)
1 0v
1 0h
1 9v
1 9h
2 1v
3 7h
where the a , i 0, ..., 7 are coeYcients optimized by regression (table 6), requiring
a signiŽ cance of 99% to be included. Input to equation (13) are the brightness
temperatures in Kelvin and output is q in g kg
.
Õ1
As for the wind speed cases with high liquid-water columns have to be excluded.
The same thresholds are applied to the brightness temperatures as for the wind
speed to set the exclusion criterion.
4.3. Sea surface temperature
The sea surface temperature T0 is retrieved from VIRS by employing the well
known split- and triple-window algorithms for day- and night-time retrievals, respect-
ively (Schlussel 1996). Here, we have chosen to include quadratic dependencies on
¨
the channel diVerences in order to account for the strongly non-linear variation of
the water-vapour absorption in the tropical atmosphere:
T0 a0 a1 T1 1 a2 (T1 1
T
1 2 )(sec h 1) a3 (T1 1 T1 2
)
2
(14)
Table 6. CoeYcients for equation (13).
a0
a1
a2
a3
a4
a5
a6
a7
20.44
0.07330
0.1529
0.3547
0.3339
0.09973
0.2432 –0.3795

1986
and
P. Schlussel and A. Albert
¨
T0
a
a1 T
a2 (T3 .7 T1 1
)
a3 (T1 1 T1 2
)
a4 (T1 1
T
1 2 )(sec h 1) (15)
have been derived as the best approaches among others with diVerent channel
combinations. The initially determined coeYcients for 5180 simulated situations are
not listed here as the validation study shows that the simulations bear systematic
errors which are corrected in the course of the present study. The theoretically
derived retrieval accuracy is of the order 0.4 K. However, the real accuracy is rather
determined by the ability to detect clouds in the VIRS measurements and to eliminate
these cloud contaminated measurements from the temperature retrieval. An inclusion
of quadratic terms in (15) did not lead to a signiŽ cant improvement and have been
left out for the sake of simplicity.
5. Validation
The validation studies presented in the following are used to test the theoretically
derived retrieval algorithms, to analyse possible discrepancies between in situ
measurements and satellite retrievals, and to elaborate corrections if necessary.
5.1. TMI
The application of the wind algorithm to the TMI data of the match-up dataset
and subsequent comparison with the buoy measurements of wind speed shows
unexpectedly great systematic diVerences of about 3 m sÕ1. The reasons for this
deviation could be due to model deŽ ciencies, unrealistic representation of the natural
variability in the model simulations or measurement errors. In the course of analysing
the diVerent possibilities it has been found that the distributions of brightness
temperatures simulated and measured diVer systematically for all channels between
10 and 37 GHz. In all cases the measured brightness temperatures are higher than
the simulated ones as shown in Ž gure 3 for the 10 GHz channel at horizontal
polarization.
Discussion with the TRMM Mission Scientist Dr C. Kummerow at NASA/GSFC
on this issue revealed that the TMI suVers from systematic calibration errors. It is
thought that the TMI brightness temperatures are correctly calibrated at values near
300 K but show values at space view that are approximately too high by 10 K. To
account for this calibration error a correction was suggested that linearly depends
on the measured brightness temperature
DTSp
300 K
DTco r (300 K Tb )
(16)
where T is the brightness temperature measured, and DTSp is a temperature oVset
at spacebview which has to be determined for each individual channel. This is done
by varying the values DT of all used channels between 10 and 37 GHz until the
mean diVerences betweenSpin situ and satellite measured wind speed and speciŽ c
humidity vanish. The resulting values are speciŽ ed in table 7.
Analysis of three months of data shows that the corrections do not vary with
time. Following the calibration of the TMI the wind speed and humidity algorithms
are applied again to the satellite measurements co-located with the buoy observations
for further comparison. For the wind speed the standard deviation between satellite
and buoy-derived values is slightly less than 1.7 m sÕ1, the wind-speed distributions
are similar (Ž gure 4), but not identical. They clearly show that the buoys measure

Latent heat  ux at the sea surface
1987
(a)
(b)
Figure 3. (a) Measured and (b) simulated distribution of TMI brightness temperatures at
10 GHz, horizontal polarization before correction of the TMI calibration error.
D
Table 7. Calibration errors TS p at space view for the lower TMI channels.
Channel
10v
6
10h
6
19v
10
19h
10
21v
10
37h
10
D
TS p (K )
more wind speeds below 1 m s which might be due to the fact that the anemometers
Õ1
do not start turning at wind speeds below about 1 m s due to adhesive friction.
Õ1
High wind speeds are also less often measured by the buoys as the anemometer
height is typically 5 m above the sea level. High wind and swell waves could protect
the anemometers from the wind action while the buoys are in wave troughs. The
resulting eVect is a reduced mean wind speed in a fully developed sea at gale
force winds.
For the surface humidity validation we have only 12 947 match-ups as the
humidity is only measured by 47 buoys. The comparison (Ž gure 5) between satellite
and buoy-measured near-surface speciŽ c humidity shows a rather big scatter. The

1988
P. Schlussel and A. Albert
¨
(a)
(b)
Figure 4. Wind speed distributions at the buoy locations for the time period January to
March 1998 as derived from TMI (a) and buoy measurements (b).
standard deviation between both is 1.9 g kgÕ1. This is slightly worse compared to
the validation results obtained for the humidity retrieval with SSM/I in the tropical
and subtropical latitudes (40 S–40 N ) where a standard deviation of 1.8 g kg was
Õ1
found between satellite and in situ measurements (Schlussel et al. 1995).
¨
5.2. VIRS
Before any comparisons can be performed between buoy and satellite-derived
sea surface temperature the VIRS measurements have to undergo a thorough check
for cloud contamination. Earlier studies have shown that all available spectral
channels should be included for a proper cloud detection (e.g. Olesen and Grassl
1985, Saunders and Kriebel 1988).
The cloud detection scheme employed here begins with an application of a high-
resolution land mask to eliminate measurements which are too close to the coastlines.
A distance of 5 km has been chosen as minimum distance between VIRS measurement
and any coastline. Next, the spatial coherence is tested in a 3 3 pixel Ž eld
(Thiermann and Ruprecht 1992). The 11 mm brightness temperature of the pixel

Latent heat  ux at the sea surface
1989
q (g kg-1)
Figure 5. Comparison between satellite-derived near-surface air-speciŽ c humidity qS
(ordinate) and buoy-measured humidity qB (abscissa).
must not deviate by more than 1 K from the mean of the nine adjacent measurements.
Subsequently, the 3.7 and 11 mm brightness temperatures are checked. They have to
be greater than
T4 0
Teq
Tth
T
eq cos Q arccos
40
(17)
where T
17 C and T4 0 9 C, allowing for minimum brightness temperatures of
17 C at etqhe equator and 9 C at 40 latitude, respectively. The brightness-temperature
diVerence T1 1 T1 2 must lie in the range 0 T1 1 T1 2 3.5K. During night, the
diVerence T3 .7 T1 1 is tested, it must be within 0 T3 .7 T1 1 3 K. During daytime,
the solar channels are used. Their  ux densities must be in the range
0
L1 5 mW cm mm and 0 L2 1 mW cm mm and their ratio is required
Õ2
Õ1
Õ2
Õ1
to be within 0.05 L /L1 0.2 to identify the measurement as cloud-free.
Under twilight conditio2ns (solar zenith angle
90 but L1 and L still greater
than zero) the thresholds are modiŽ ed so that 0 L1 2 mW cm2 mm
and
Õ2
Õ1
0
L
0.5 mW cm mmÕ1, and 0.1 L2 /L1 5 must be fulŽ lled.
Õ2
T2hreshold values for these cloud tests have been obtained iteratively by visual
inspection of the VIRS images. They are rigorous in the sense that doubtful cases
are rather excluded than retained as cloud-free. The tests are henceforth used also
in the operational processing of the VIRS data.
The comparison of sea surface temperatures retrieved from VIRS with those
measured by the buoys have to be performed with great care because the satellite-
derived surface temperature represents an average temperature of the upper few

1990
P. Schlussel and A. Albert
¨
micrometres of the ocean while the buoys measure the temperature in the upper
part of the mixed layer at a depth of about one metre. The diVerence between both
temperature measurements is always determined by the temperature diVerence across
the oceanic cool skin and, temporarily, by the temperature diVerence across the
diurnal thermocline (Schlussel et al. 1990). Consequently, we must expect a systematic
¨
diVerence between buoy and satellite measured temperature of few tenths of a Kelvin.
This systematic diVerence is conŽ rmed by the comparison. During night-time the
mean diVerence between buoy and satellite measurements is 0.36 K, during daytime
it is 0.14 K, which both Ž t well to the known diurnal variability of the bulk versus
skin temperature diVerence.
At the same time, other systematic diVerences appear in the comparison. They
consist of a positive correlation of the diVerence DT between buoy and satellite
measurements with the buoy measurements. This means that the atmospheric correc-
tion applied to the satellite measured brightness temperature increases with increasing
surface temperature and therefore with increasing atmospheric water-vapour column.
The most likely source for this discrepancy lies in an inaccurate description of the
water-vapour continuum absorption. It has already been pointed out by Rudman
et al. (1994) that the magnitude of the continuum absorption still is underestimated
by the model of Kilsby et al. (1992) although it has undergone substantial changes
with respect to earlier descriptions. A further modiŽ cation of the continuum absorp-
tion seems to be necessary at wavenumbers 920 cm
k
1050 cm which aVects
Õ1
Õ1
the 10.8 mm channel only. A 25% increase of the continuum absorption coeYcient
above 1000 cmÕ1 , no change at 920 cm and a linear interpolation of this
k
Õ1
correction between 920 and 1000 cm
leads to the best results in minimizing the
Õ1
correlation between DT and buoy-measured surface temperature.
The continuum absorption coeYcients Ž nally adopted are shown in Ž gure 6
together with those of Kilsby et al. (1992) for two water-vapour densities of rw
1 g m
and r
10 g mÕ3. The resulting coeYcients for retrieval models (14) and
Õ3
(15) obtained wafter Ž nal modiŽ cation of the continuum absorption are listed in
table 8.
Buoy and satellite measured surface temperature are compared in Ž gure 7 separ-
ately for day and night conditions. As expected, we Ž nd a mean diVerence between
buoy and satellite measured temperature of 0.14 K and 0.36 K during day and night,
respectively. The standard deviation is 0.68 K in both cases. The systematic deviations
are in line with our picture of the oceanic cool skin which is most pronounced in
cloud-free areas during night-time. Cloud-free situation is also the required condition
for infrared remote sensing of sea surface temperature. During daytime the absorption
of solar radiation in the upper ocean partly compensates for the cool skin eVect
in calm situations, thus leading to a smaller systematic diVerence (Soloviev and
Schlussel 1996).
¨
6. Application
The retrieval schemes elaborated are applied to a time series of TMI and VIRS
data to obtain monthly mean Ž elds of surface temperature, wind speed, air humidity
and latent heat  ux. The VIRS and TMI data are combined by binning both to a
0.25 0.25 grid, where the TMI data are assigned to the nearest grid bin and the
VIRS data are averaged over the corresponding bins. We have chosen to present the
month of April 1998. In view of the non-linearity involved in equations (1) to (5) it
is not opportune to Ž rst calculate monthly mean values of T0 , u, q and then to use

Latent heat  ux at the sea surface
1991
(a)
0.006
0.005
0.004
0.003
0.002
0.001
0.000
"w =1gm-3
700
800
900
! (cm-1)
1000
1100
(b)
0.4
0.3
0.2
0.1
0.0
"w =10gm-3
700
800
900
! (cm-1)
1000
1100
Figure 6. Absorption coeYcient of the water-vapour continuum for absolute humidities of
3
3
1 gmÕ (a) and 10 g mÕ (b); the dotted lines represent the values calculated according
1
to Kilsby et al. (1992), the solid lines include the correction above 920cmÕ .
Table 8. CoeYcients for retrieval models (14) and (15).
Model
a0
a1
a2
a3
a4
Day (14)
Night (15)
5.16
4.60
1.02145
1.01557
0.9373
0.7469
0.02148
1.9701
0.6674
0.6235
these averages for the computation of E. Rather it is indicated to derive the latent
heat  ux from individual TMI and VIRS measurements. This is done in the following
where possible. However, the measurement of sea surface temperature requires cloud-
free atmospheric situations, so that in cloudy areas only wind speed and humidity
are measured. In such cases no latent heat- ux retrievals were possible if the surface

1992
P. Schlussel and A. Albert
¨
(a)
30
25
20
15
10
Day
10
15
20
25
30
TB (ÊC)
(b)
30
25
20
15
10
Night
10
15
20
25
30
TB (ÊC)
Figure 7. Comparison between satellite-derived sea surface temperature TS and buoy-
measured temperature TB , (a) day, (b) night.
temperature would not be a rather stable parameter. Owing to the large heat capacity
of sea water and the fact that the upper ocean is well mixed only small temporal
changes in the surface temperature are expected. The situation is diVerent in clear
areas where strong insolation during daytime and excessive nocturnal cooling of the
surface can cause diurnal changes. Fortunately, in such situations the infrared meas-
urements of T0 are more frequent. Hence, the error introduced in E by assuming
that the surface temperature stays constant over a certain time period, say 1 or 2
weeks, remains small. Even over a month we do not Ž nd greater variations in the

Latent heat  ux at the sea surface
1993
surface temperature where persistent cloud cover only allows few measurements in
a month as is the case in the inter tropical convergence zone. But, there are areas in
the tropical ocean where no surface temperature measurement was possible as all
during April 1998 (Ž gure 8). The area around Indonesia is known for persistent
cloud cover and a wide region was not covered by temperature measurements after
20 days. The eastern equatorial PaciŽ c, however, suVered from excessive cloud
coverage during this month because of the 1997/98 El Nino event.
˜
The monthly Ž elds of u and q completely cover the oceans (Ž gure 9) as only few
(a)
(b)
(c)
(d)
Figure 8. Mean Ž elds of sea surface temperature as measured by VIRS in April 1998. (a) First
Ž ve days, (b) Ž rst 10 days, (c) Ž rst 20 days and (d) entire month. White areas indicate
regions without measurements during the speciŽ ed time period.

1994
P. Schlussel and A. Albert
¨
(a)
(b)
(c)
Figure 9. Mean Ž elds of near-surface wind speed (a) and near-surface air humidity (b) as
measured by TMI in April 1998, and mean Ž eld of ocean to atmosphere latent heat
 ux calculated from VIRS-derived surface temperature and TMI retrieved wind and
humidity (c). White areas indicate regions with missing information.
measurements have to be rejected because of opaque clouds or rain in the sensor’s
Ž eld of view. Additionally, all areas close to coastlines are excluded to keep a
minimum distance of 50 km between the centre of a footprint and the nearest
coastlines.

Latent heat  ux at the sea surface
1995
The latent heat  ux calculated from T0 , u and q as retrieved from VIRS and
TMI for April 1998 covers a wide range of values. Nearly vanishing  uxes are found
in the northern China Sea and the North PaciŽ c Ocean, where warm and moist air
is advected over relatively cold water. Maximum values exceeding 200 W m
are
Õ2
seen in the subtropical region of the NE and SE PaciŽ c Ocean where the sea–air
humidity diVerences are big and the wind speed is greater than on average.
7. Conclusion
TRMM measurements are used to calculate the latent heat  ux at the sea surface.
Retrieval models for the measurement of sea surface temperature, surface wind speed
and near-surface air humidity are elaborated by means of radiative transfer calcula-
tions and validated with buoy measurements. The theoretical study has shown that
the single parameters needed for the calculation of the surface latent heat  ux can
be retrieved from the VIRS and TMI radiometers:
d
The sea surface temperature can be obtained with an accuracy near 0.4 K from
measurements at 3.7, 11 and 12 mm. A quadratic split-window approach has
been selected for daytime and a linear triple-channel algorithm for night-time.
d
The near-surface wind speed is retrieved with a predicted accuracy of 1.3 m s
Õ1
from a simple artiŽ cial neural network using measurements at 10, 19 and
21 GHz.
The near-surface air humidity can be measured with the TMI channels at 10,
d
19, 21 and 37 GHz, the predicted accuracy is 1.2 g kg
.
Õ1
The validation studies carried out with TRMM measurements co-located to buoy
observations in the time period January to March 1998 led to the following results:
d
The water-vapour continuum absorption was not properly described by the
available models. This fact caused a correlation between buoy versus satellite
measured temperature diVerences and the buoy-measured surface temperature.
This eVect could be removed by a modiŽ ed description of the continuum
absorption coeYcient. The modiŽ cation consists in a spectrally varying increase
of the coeYcients with a maximum correction of 25% near 10 mm.
d
After correction of the continuum absorption and re-iterated radiative transfer
simulations, leading to new retrieval coeYcients, a standard deviation of 0.7 K
is found between satellite and buoy measurements, excluding the eVect of the
temperature diVerence between skin measured by the satellite and buoy-
measured bulk temperature. This latter systematic diVerence amounts –0.36 K
during night and 0.14 K during daytime.
d
The distribution of simulated and measured TMI measurements show system-
atic diVerences because of TMI calibration errors. A frequency-dependent
correction is proposed that leads to useful satellite measurements which can
be entered into the developed retrieval schemes to obtain bias-free wind-speed
and humidity measurements. The standard deviations between satellite-derived
and in situ measurements of wind speed and air speciŽ c humidity are
1.7 m s and 1.9 g kgÕ1 , respectively.
Õ1
d
Threshold values for given cloud detection methods are proposed. The methods
adopted use all VIRS channels in a globally valid scheme to detect clouds
before using the VIRS measurements to calculate sea surface temperature.
The application of the developed methods to one month of global data (April 1998)

1996
P. Schlussel and A. Albert
¨
shows that the infrared measurements are suYciently dense to obtain almost complete
coverage of tropical and subtropical (within the scope of TRMM) oceans with sea
surface temperature measurements. Compared with earlier retrievals of the latent
heat, based on AVHRR and SSM/I measurements (Schlussel 1996), improvements
¨
could be found for the surface temperature and wind-speed retrievals in tropical
regions. The retrieval of the near-surface air humidity is slightly degraded when
compared with the SSM/I-based method.
Acknowledgements
This study was funded by the European Space Agency in the frame of the
EuroTRMM project. The TRMM data were kindly delivered by the TRMM
Science and Data Information System. Both supports are gratefully acknowledged.
We are indebted to Chris Kummerow for valuable hints in handling the TRMM
data and to David Lemaire for supplying the computer code calculating the rough
sea emissivity. Thanks are due to Darrel Knoll at the National Data Buoy Center
who made available the buoy data. All Ž gures have been drafted with free software
supplied by Wessel and Smith (1991).
References
Anderson, G. P., Clough, S. A., Kneizys, F. X., Chetwynd, J. H. and Shettle, E. P., 1986,
AFGL atmospheric constituents proŽ les (0–120km). Report AFGL-TR-86-0110, Air
Force Geophysics Laboratory, Hanscom, MA, U.S.A.
Bauer, P., and Schlussel, P., 1993, Rainfall, total water, ice water and water vapour over
¨
/
sea from polarized microwave simulations and SSM I data. Journal of Geophysical
Research, 98, 20737–20760.
Bignell, K. J., 1970, The water-vapour infrared continuum. Quarterly Journal of the Royal
Meteorological Society, 96, 390–403.
Chedin, A., Scott, N. A., Wahiche, C., and Moulinier, P., 1985, The improved initialization
inversion method: a high-resolution physical method for temperature retrievals from
satellites of the TIROS-N series. Journal of Climate and Applied Meteorology, 24,
128–143.
Clough, S. A., Kneizys, F. X., and Davies, E. W., 1989, Line shape and the water vapor
continuum. Journal of Atmospheric Research, 23, 229–241.
Defant, F., 1969, Aerologische Daten gewonnen durch Radiosonden-Aufstiege wahrend der
¨
/
Indischen Ozean Expedition, 1964 , 1965 des ForschungsschiVes ‘Meteor’.
‘Meteor’Forschungsergebnisse, Reihe B, 4, Meteorologie und Aeronomie.
Fairall, C., Bradley, E. F. Rodgers, D. P. Edson, J. B. and Young, G. S. 1996, The TOGA
COARE bulk  ux algorithm. Journal of Geophysical Research, 101, 3747–3764.
Guissard, A., Sobieski, P., and Laloux, A., 1994, Radiative transfer equation with surface
scattering for ocean and atmospheric parameters retrieval from radiometric measure-
ments. International Journal of Remote Sensing, 15, 1743–1760.
Hasse, L., 1993, Observations of air sea  uxes. In Energy and Water Cycles in the Climate
System, NATO ASI Series, edited by E. Raschke and D. Jakob (Berlin: Springer
Verlag), pp. 263–293.
Hess, M., Koepke, P., and Schult, I., 1998, Optical properties of aerosols and clouds: the
software package OPAC. Bulletin of the American Meteorological Society, 79, 831–844.
Hollweg, H.-D., 1993, A k-distribution method considering centers and wings of atmospheric
absorption lines. Journal of Geophysical Research, 98, 2747–2756.
Kilsby, C. G., Edwards, D. P., Saunders, R. W., and Foot, J. S. 1992, Water-vapour
continuum absorption in the tropics: aircraft measurements and model comparisons.
Quarterly Journal of the Royal Meteorological Society, 118, 715–748.
Koepke, P., Hess, M., Schult, I., and Shettle, E. P., 1997, Global aerosol data set. Report
243, Max-Planck-Institut fur Meteorologie, Hamburg.
¨
Kummerow, C., Barnes, W., Kozu, T., Shiue, J., and Simpson, J. 1998, The Tropical Rainfall

Latent heat  ux at the sea surface
1997
Measuring Mission (TRMM) sensor package. Journal of Atmospheric and Oceanic
Technology, 15, 809–817.
Lemaire, D., 1998, Non-fully developed sea state characteristics from real aperture radar
remote sensing. PhD dissertation, Universite´ Catholique de Louvain, Louvain, 220 pp.
Liebe, H. J., 1989, MPM—An atmospheric millimeter wave propagation model. International
Journal of Infrared and Millimeter Waves, 10, 631–649.
Liu, W. T., Zhang, A., and Bishop, K. B. 1994, Evaporation and solar irradiance as regulators
of sea surface temperature in annual and interannual changes. Journal of Geophysical
Research, 99, 12623–12637.
Masuda, K., Takashima, T., and Takayama, Y., 1988, Emissivity of pure and sea waters for
the model sea surface in the infrared window regions. Remote Sensing of Environment,
24, 313–329.
Monahan, E. C., and O’Muircheartaigh, I. G., 1986, Whitecaps and the passive remote
sensing of the ocean surface. International Journal of Remote Sensing, 7, 627–642.
Olesen, F. S., and Grassl, H., 1985, Cloud detection and classiŽ cation over oceans at night
with NOAA-7. International Journal of Remote Sensing, 6, 1435–1444.
Panofsky, H. A., and Dutton, J. A., 1984, Atmospheric Turbulence Models and Methods for
Engineering Application (New York: Wiley), 397 pp.
Ramesh Kumar, M. R., and Schlussel, P., 1998, Air–sea interaction over the Indian Ocean
¨
during the two contrasting monsoon years, 1987 and 1988, studied with satellite data.
Theoretical and Applied Climatology, 60, 19–231.
Rothman, L. S., Rinsland, C. P., Goldman, A., Massie, S. T., Edwards, D. P.,
Flaud, J.-M, Perrin, A. Camy-Peyret, C., Dana, V., Mandin, J.-Y., Schroeder, J.,
McCann, A., Gamache, R. R., Wattson, R. B., Yoshino, K., Chance, K. V.,
Jucks, K. W., Brown, L. R., Nemchinov, V., and Varasani, P., 1998, The HITRAN
molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation),
1996 edition. Journal of Quantitative Spectroscopy and Radiative Transfer, 60, 665–710.
Rudman, S. D., Saunders, R. W., Kilsby, C. G., and Minnett, P. J., 1994, Water vapour
continuum absorption in mid-latitudes: aircraft measurements and model comparisons.
Quarterly Journal of the Royal Meteorological Society, 120, 795–807.
Saunders, R. W., and Kriebel, K. T., 1988, An improved method for detecting clear sky and
cloudy sky radiances from AVHRR data. International Journal of Remote Sensing,
9, 123–150.
Schlussel, P., 1996, Satellite remote sensing of evaporation over sea. In Radiation and Water
¨
in the Climate System: Remote Measurements, edited by E. Raschke, NATO ASI Series,
I45 (Berlin: Springer Verlag), pp. 431–461.
Schlussel, P., and Emery, W. J., 1990, Atmospheric water vapour over oceans from SSM I
/
¨
measurements. International Journal of Remote Sensing, 11, 753–760.
Schlussel, P., and Grassl, H., 1990, SST in polynias: a case study. International Journal of
¨
Remote Sensing, 11, 933–945.
Schlussel, P., Emery, W. J., Grassl, H., and Mammen, T., 1990, On the bulk-skin temperature
¨
diVerence and its impact on satellite remote sensing of sea surface temperature. Journal
of Geophysical Research, 95, 13341–13356.
Schlussel, P., Schanz, L., and Englisch, G., 1995, Retrieval of latent heat  ux and longwave
¨
/
irradiance at the sea surface from SSM I and AVHRR measurements. Advances in
Space Research, 16, 106–116.
Schulz, J., Schlussel, P., and Grassl, H. 1993, Water vapour in the atmospheric boundary
¨
/
layer over oceans from SSM I measurements. International Journal of Remote Sensing,
14, 2773–2789.
Schulz, J., Meywerk, J., Ewald, S., and Schlussel, P., 1996, Evaluation of satellite-derived
¨
latent heat  uxes. Journal of Climate, 10, 2782–2795.
Soloviev, A. V., and Schlussel, P., 1996, Evolution of cool skin and direct air–sea gas transfer
¨
coeYcient during daytime. Boundary-Layer Meteorology, 77, 45–68.
Stogryn, A. P., Butler, C. T., and Bartolac, T. J., 1994, Ocean surface wind retrievals from
special sensor microwave imager data with neural networks. Journal of Geophysical
Research, 99, 981–984.
Taurat, D., 1996, Windfelder uber See unter Verwendung von Satellitendaten und
¨
Druckanalysen. Berichte aus dem Zentrum fur Meeres- und Klimaforschung der
¨
Universitat Hamburg, Hamburg, A22, 1–101.
¨

1998
Latent heat  ux at the sea surface
Thiermann, V., and Ruprecht, E., 1992, A method for the detection of clouds using AVHRR
infrared observations. International Journal of Remote Sensing, 10, 1829–1841.
Wessel, P., and Smith, W. H. F., 1991, Free software helps map and display data. Transactions
of the American Geophysical Union, 72, 441 and 445–446.
World Climate Research Programme, 1986, A primary cloudless standard atmosphere
/
for radiation computation, WCP-112, WMO TD-No 24. World Meteorological
Organization, Geneva, 36 pp.
Zell, A., 1994, Simulation Neuronaler Netze (Munich: R. Oldenbourg Verlag), 624 pp.