ANALYSIS OF THE SST SPLITWINDOW EQUATION USING THESYNERGY BETWEEN METEOSAT SECOND GENERATION ANDNOAA POLAR SATELLITES
José Antonio Valiente, Raquel Niclòs, María Jesús Barberá and María José Estrela
Fundación CEAM, C/ Charles R Darwin 14, 46980 Paterna, Valencia, Spain.
Abstract
In its first stage, the study uses AVHRR NOAA/NESDIS SST and SEVIRI O&SI SAF SST operationalalgorithms to compare SST values derived from concurrent AVHRR and MSG scenes centred on theIberian Peninsula and western Mediterranean sea. The comparison is performed on a set of paired AVHRR and SEVIRI images spaced no more than 10 minutes apart, and obtained from the highresolution transmissions from both MSG1 and NOAA–12, –15 and –17 series during the year 2005.The SST agreement is good for small AVHRR zenith angles but discrepancies are observed for angles larger than 40º. In the second stage of the study, a general splitwindow equation combiningtwo addends, one for the atmospheric correction and the other for an emissivity effect, is proposed toaccount for the observed differences in SST at large AVHRR angles. The functional form of theproposed equation is the same for both satellites, and its angular dependence is considered to beimplicit in the emissivity term. As the splitwindow channel filters are almost identical for both AVHRRand SEVIRI, concurrent spatial and temporal pairs of satellite data with almost identical zenith anglesare regressed to the atmospheric correction term of the proposed equation. This enables resolving theatmospheric splitwindow coefficients and subsequently estimating the emissivity term. We then carryout a simple variable substitution when one of the paired satellite zenith angles cancels and asuccessive value propagation when the paired zenith angles differ, to finally yield a plotting of thedependence of the emissivity term on the satellite zenith angle.
INTRODUCTION
Most of the operational algorithms for estimating Sea Surface Temperature (SST) are derived bymeans of multilinear regression to a family of proposed equations that combine brightnesstemperatures (BT) in different channels (Barton, 1995). Multichannel algorithms, MCSST, areobtained in this way by combining coefficients that can be either constants (McClain
et al
., 1985) or expressed in terms of sec(
θ
)1 where
θ
is the satellite zenith angle (François
et al
., 2002). Additionally,when the proposed equations include a firstguess SST in one of the coefficients, the algorithm isdenominated nonlinear or NLSST (Walton
et al
., 1998). The NLSST algorithms are routinely selectedby NOAA and EUMETSAT for an operational use.The data used for the multilinear regression are obtained either empirically or by means of simulations. The empirical procedure uses satellite derived SST data paired with concurrenttemperature measurements from buoys for a period of time, the socalled SST matchup datasets(Li
et al
., 2001). In the simulation procedure, a radiative transfer model is used for calculating syntheticradiances received by the satellite under specific conditions: a set of actual radiosoundingsdetermining the atmospheric profiles, the satellite zenith angles, sea surface temperature and seasurface emissivity (François
et al
., 2002).None of the operational family of equations uses a residual term to account for the emissivity of thesea surface. Conversely, operational splitwindow algorithms for Land Surface Temperature (LST)retrieval include emissivitydependent terms (Becker & Li, 1990; Coll & Caselles, 1997; Wan
et al
.,
2002). The emissivity of the sea surface is very different from a blackbody at moderate to largeobservation angles. It decreases as the angle increases, and it also varies as surface roughnesschanges (Masuda
et al
., 1988; Wu & Smith, 1997; Niclòs
et al
., 2005). Some operational algorithmsinclude seasurface emissivity implicitly when performing the regression, some consider emissivityclose to unity, and some are limited to a narrow range of observation angles where surface emissivityis practically constant. Therefore, the emissivity effect is to be examined explicitly and within its wholeangular range on the SST retrieval mainly at medium to large observation angles.
SATELLITE DATA AND OPERATIONAL SST COMPARISON
During the year 2005, a set of concurrent images spaced no more than 10 minutes apart in time wasselected from the high resolution transmissions from both MSG1 and NOAA–12, –15 and –17 series.One complete day for each month was captured from the transmissions, normally providing sixconcurrent satellite scenes for any 24hour period chosen. The selection of each of the specific dayswas based mainly on cloud clearing over the oceanic surfaces. This gave a good cover over theMediterranean Sea but few scenes over the Atlantic Ocean due to frequent cloudy conditions. Cloudypixel removal was performed on AVHRR and SEVIRI scenes using the cloud filters proposed byDerrien
et al
. (1993) and Derrien & Le Gléau (2005) for both nocturnal and diurnal conditions over thesea. Conversion to brightness temperatures followed Goodrum
et al
. (2000) and Tjemkes (2005).Both SEVIRI and AVHRR scenes are referenced to the same geographical framework, astereographic projection centred at the Iberian Peninsula, for pixel spatial conformity (
Badenas et al
.,1997; Wolf & Just, 1999; Dammann
et al
., 2005). AVHRR and SEVIRI satellitederived SST wereestimated using the nonlinear operational algorithms (NLSST) supplied from NOAA/NESDISCoastWatch equations (DiGiacomo, 2005) and MeteoFrance O&SI SAF equations (OSI SAF ProjectTeam, 2005), respectively. These operational temperatures are used for the sole purpose of evaluating the two algorithm performances at a range of zenith angles and temperatures. As an example of the SST comparison for a particular pair of AVHRR and SEVIRI scenes, figure 1shows operational SST differences on June 19
th
2005 at 17:45 GMT (MSG) and 17:55 GMT(NOAA15). Blank areas correspond to either removed clouds or absence of AVHRR data. WhileSEVIRI zenith angles move in the range of 40º to 60º, AVHRR angles show values from 0º to almost70º. Solid lines show identical zenith angles for the pair of scenes. Broken lines identify AVHRR zenithangles of 40º and 60º. One can observe that satellite SST differences are under 1 ºC when AVHRRangles are larger than 60º. For evaluating the goodness of a comparison of both SST operationalalgorithms, AVHRR zenith angles should be limited to a maximum of 40º as figure 1 shows, so that theassociated algorithm uncertainties, about 0.5 ºC, are comparable to the obtained SST differences.
Figure 1:
Operational SST differences for a particular pair of simultaneous AVHRR and SEVIRI scenes.
θ
NOAA
=
θ
MSG
ºC
∆
T
θ
NOAA
=
θ
MSG
θ
NOAA
= 40º
θ
NOAA
= 40º
θ
NOAA
= 60º
θ
NOAA
= 60º
For the comparison of NOAA/NESDIS and MeteoFrance OSI SAF operational NLSST algorithms, acluster of points (figure 2) was selected from the image set. Since a good comportment of thecomparison points was sought, the following conditions were observed in their selection: absence of cloudiness in each pair of satellite scenes, AVHRR satellite zenith angles below 30º, random spatialdistribution but regular spacing within the range of 1028 ºC for SST, and a limited maximum totalnumber. The SST comparison performed for the cluster of selected points is given in figure 3. Thediagonal line represents the 1:1 relation, with the standard deviation around this line being about0.4 ºC. As a first result, the SST correspondence between both algorithms when restrictions in the AVHRR zenith angle are considered is comparable to the estimation errors which are intrinsicallyassociated with each of the nonlinear algorithms.
Comparison between NLSST algorithms
101418222630101418222630
MSG NLSST (ºC)
A V H R R N L S S T ( º C )
Figure 2:
Selection of 30,000 points from the synergybetween AVHRR and SEVIRI, used for the comparison of operational NLSST algorithms
Figure 3:
Comparison of SSTs derived from the twooperational algorithms when the selection of points isused, i.e. AVHRR zenith angles are low.
If no restrictions in AVHRR zenith angles are considered, the comparison obtained for theNOAA/NESDIS and OSI SAF algorithms is given in figure 4. This comparison uses a more spreadoutcluster of points than the one represented in figure 2, accounting in this manner for large satellitezenith angles occurring in the AVHRR scenes. The difference between AVHRRderived and SEVIRIderived temperatures shows a decline as the AVHRR zenith angle increases in the form of
S
=sec(
θ
)1. The zenith angle must be stretched in this form to display the rapid decline. At low AVHRR zenith angles, below
θ
=40º or
S
=0.3, both algorithms coincide. For AVHRR angles as largeas
θ
=69º (
S
=1.8), the differences between AVHRRderived and SEVIRIderived operational SSTs canbe around –2 ºC.
NLSST
NOAA
NLSST
MSG
(ºC)
5432101200.40.81.21.62
S
NOAA
Figure 4:
Difference values between AVHRRderived and SEVIRIderived temperatures using the operational NLSSTalgorithms from NOAA/NESDIS and MeteoFrance OSI/SAF when no AVHRR zenith angle limit is considered. Valuesare plotted against AVHRR zenith angle in its
S
form,
S
=sec(
θ
)1.
(
θ
NOAA
<
30º)
The fact that the derived SST differences behave as a function of the AVHRR zenith angle could beexplained by the effect of the significant angular dependence of sea surface emissivity. It is alreadyknown that for large zenith angles, emissivity shows a strong decline, and it is also dependent on thesea surface roughness produced by wind (Wu & Smith, 1997). The angular range where theNOAA/NESDIS NLSST algorithm has been tested is much larger than the angular range for the OSISAF NLSST algorithm, i.e. the typical range around the Iberian Peninsula. Then, the angular dependence of the SST differences found is very evident in the case of the AVHRR zenith angle. Itcan be expected also that some emissivity effect is also influencing the SEVIRIderived temperaturesto the extent of its angular range. If this angular dependence of the surface emissivity is not correctlyconsidered in the SST algorithms, differences in derived temperatures, such as the observed in figure4, could be obtained for large satellite zenith angles. In the next section, we propose a splitwindowequation with a single functional form, which includes an emissivity term and can be used with bothSEVIRI and AVHRR scenes. Using only the empirical satellite brightness temperatures, we havedevised a method to obtain angle information on the abovementioned emissivity effect.
REGRESSION OF A SPLITWINDOW EQUATION WITH NO ANGLE LIMIT
Including a sea surface emissivity effect in the SST splitwindow equation is essential when emissivityvariability exists. The following generic splitwindow equation based on Coll & Caselles (1997)includes both an atmospheric correction expressed as a function of brightness temperatures and aresidual term dependent on emissivity:where:
a
i
are taken as constants for each of the satellite sensors
T
i
is the brightness temperature, BT, of channel
i
at 11
µ
m (ch4 for AVHRR and ch9 for SEVIRI)
T
ij
is the difference
T
ij
=
T
i
–
T
j
with
T
j
being the BT of channel
j
at 12
µ
m (ch5 for AVHRR andch10 for SEVIRI)
γ
(
ε
)
is a residual term dependent on the sea surface emissivity,
ε
, which in turn will dependbasically on the satellite zenith angle,
θ
, and to a lower degree on the atmospheric water vapour,
W
(Niclòs
et al
., 2007) Adapting this equation for each of the AVHRR and SEVIRI sensors on board the NOAA and MSGsatellites respectively, i.e. substituting the thermal channels at 11 and 12
µ
m with their specificchannel numbers, the equation becomes:The spectral filters of the thermal channels at 11 and 12
µ
m for MSG and NOAA satellites arepractically coincident (Goodrum
et al
., 2000), especially for NOAA–15 and –17. Thus, a surface spotseen simultaneously from the two satellites, MSG and NOAA, at equal zenith angles will yield identicalresidual emissivity terms, since channel emissivities will match for confluent bands. And as the sea surface pixel is at a unique temperature, it must follow that:So, for the group of pixel pairs that meet the condition of being observed from the same zenith anglemaintained by both satellites, it is possible to fit the following multilinear form to their brightnesstemperatures:
SST = a
0
+ a
1
T
i
+ a
2
T
i j
+ a
3
T
i j 2
+
γ
(
ε
)
SST
NOAA
= a
0
+ a
1
T
4
+ a
2
T
45
+ a
3
T
45 2
+
γ
(
ε
NOAA
)
SST
MSG
= b
0
+ b
1
T
9
+ b
2
T
910
+ b
3
T
910 2
+
γ
(
ε
MSG
)
γ
(
W,S
NOAA
)
=
γ
(
W,S
MSG
)when
S
NOAA
= S
MSG
SST = SST
NOAA
= SST
MSG
Making
c
0
=
a
0
–
b
0
,
α
i
=
a
i
/
c
0
and
β
i
=
b
i
/
c
0
, a proper expression for the multilinear regression would be:Figure 5 shows the comparison of the partial temperature terms given by the above multilinear expression when fitted to the brightness temperatures whose zenith angle pairs fulfil the condition
∆
S
<0.05. This is the same as saying that the pixel pairs used for the regression practically coincide inzenith angle. Data points spread out along a defined line indicate the goodness of the regression. Thenumerical analysis is done hereafter for only the synergy between MSG and NOAA–17 in diurnalconditions due to the larger and better quality of their data. The other NOAA satellites provideanalogous results, although their data points show a greater scattering.Once the above regression coefficients have been obtained, the known NOAA/NESDIS operationalNLSST algorithm is used for the computation of the remaining parameters
c
0
and
a
0
, necessary for acomplete solution of the problem. This operational algorithm must be used at the particular zenithangular range where the residual term due to the emissivity effect is negligible, i.e., for zenith angles
θ
<10º for example. At this angle range, a contribution from any emissivity effect would be incorporatedin the constants
a
0
and
b
0
, thus making the proposed emissivity effect become zero at very low zenithangles.The above equation can be fitted as a straight line to the satellite data. In this manner, figure 6 givesthe resultant fitting for NOAA–17 in diurnal conditions. The values found for
c
0
and
a
0
allow theestimation of parameter
b
0
and subsequently the determination of coefficients
a
i
and
b
i
.
3.944.14.24.33.944.14.24.3
β
1
T
9
+
β
2
T
910
+
β
3
T
910
2
1 (MSG term)
α
1
T
4
+
α
2
T
4 5
+
α
3
T
4 5
2
( N O A A  1 7 t e r m )
2842862882902922942962983003023.944.14.24.3
α
1
T
4
+
α
2
T
45
+
α
3
T
45
2
(NOAA17 term)
N O A A  1 7 N L S S T
Figure 5:
Goodness of the regression to the atmosphericcorrection term for the data pairs with practically the samezenith angles. Data correspond to NOAA17 versus MSGin diurnal conditions.
Figure 6:
Straight line fitting to derive remainingparameters
c
0
and
a
0
in the characterisation of theproposed splitwindow coefficients for the atmosphericcorrection term. Again data correspond to NOAA17 indiurnal conditions.
PLOTTING OF THE RESIDUAL EMISSIVITY TERM USING THE SYNERGY BETWEENMSG AND NOAA
For each pair of simultaneous AVHRR and SEVIRI scenes, any coincident pixel must present a singleand identical sea surface temperature. Moreover, each coincident pixel in both scenes is observedgenerally from two different zenith angles depending on the satellite used, MSG or NOAA. Therefore,the difference between the residual terms due to the emissivity effect for the coincident pixels
a
0
+ a
1
T
4
+ a
2
T
45
+ a
3
T
45 2
= b
0
+ b
1
T
9
+ b
2
T
910
+ b
3
T
910 2
α
1
T
4
+
α
2
T
45
+
α
3
T
45 2

β
1
T
9

β
2
T
910

β
3
T
910 2
=
1
NLSST
NOAA
=
a
0
+ a
1
T
4
+ a
2
T
45
+ a
3
T
45 2
= a
0
+ c
0
(
α
1
T
4
+
α
2
T
45
+
α
3
T
45 2
)for
θ
NOAA
<
10º
diurnal conditions
S
NOAA
≈
S
MSG
diurnal conditions
θ
NOAA
<
10ºregression line:
Y
=
a
0
+
c
0
X