3.4.3 CTSK2d
A. Algorithm Outline(1) Algorithm Code: CTSK2d(2) Product Code: SNGI, SNGI_p(3) PI Name: Dr. Knut Stamnes(4) Overview of Algorithm
The algorithm presented in this document consists of two parts: the retrieval of sea surface
temperatures for an open ocean area, and the retrieval of snow/ice surface temperatures for an
ocean area covered by snow/ice. This algorithm can also be applied to snow-covered land, if
the snow depth is larger than 5 cm. It works only under clear-sky conditions. Even though themethod and the technique used in this algorithm are similar to those used in estimating sea andland surface temperatures, this algorithm has been developed specifically for the polar regions
and for the use with GLI measurements. The IST part of this algorithm is the primary surface
temperature algorithm since the Arctic surface is covered with snow/ice most of the year. The
SST part of this algorithm will be applied to a mixture of snow/ice and water.
Although the thermal emissivity of snow/ice is quite insensitive to surface parameters
including density, grain size, thickness, liquid water content, and impurity content (Dozier andWarren, 1982; Warren, 1982), it has an angular and spectral dependency. In this study the
MODTRAN radiative transfer model is employed to simulate the radiances measured by thesatellite sensor (e.g., GLI) using the directional snow emissivities that are computed with the
DISORT radiative transfer model. Since MODTRAN has a 2 cm-1 spectral resolution, it isaccurate enough for the purpose of this study.
To simulate radiances in GLI and MAS (MODIS Airborne Simulator) thermal channels,
daily temperature and humidity profiles are used in the MODTRAN radiative transfer model.
Radiosonde ascents over the entire Arctic are taken from the NCEP/NCAR (National Center
for Atmospheric Research) Arctic Marine Rawinsonde archive. This data set contains 17,659
reports of ship (marine) rawinsondes (i.e., radiosondes: tracked from the ground by radar tomeasure variations in wind direction and wind speed with altitude) for the region north of 650.
Its record extends from 1976 to 1996. Sounding data from this NCAR Rawinsonde archive
cover different atmospheric conditions (such as those caused by regional and seasonalvariations).

GLI Algorithm Description

3.4.3-1

B. Theoretical Description(1) Physical and Mathematical Aspects of the Algorithm
The simple approach for atmospheric correction is to measure radiation from a given fieldof view at two or more window frequencies having different atmospheric absorption. The sea
surface temperature can then be estimated as a linear combination of measured brightness
temperatures at these frequencies:n

TS = a(θ ) + ∑ bi (θ )Ti

(2.1)

i =1

where TS is the measured surface temperature, θ is the satellite scan angle, a(θ) and bi(θ) arescan angle-dependent coefficients, Ti is the measured brightness temperature in each thermalchannel i, and n is the total number of channels used. The minimization of errors in the TS
measurements is dependent on the correct choice of the coefficients a(θ) and bi(θ).
There are two ways to determine the coefficients. One approach is to relate satellite
observations to surface temperature measurements with a simple regression model. However,for a robust solution a relatively large set of high-quality in-situ temperature and satellite data
is required. The other approach is the simulation method. A radiative transfer model is used
together with a large set of atmospheric profiles to simulate the satellite measurements under awide range of atmospheric conditions and surface temperatures. The simulated measurements
are then used with a set of assigned surface temperature values to derive the coefficients, again
by regression analysis.
Instead of computing a different set of coefficients for each scan angle increment, asshown in (2.1), here we use the equation
TS = a + b T11 + c (T11-T12) + d [(T11-T12) (secθ - 1)](2.2)

where TS is the estimated surface temperature (in K), T11 and T12 are the brightness
temperatures (in K) at 11 µm (GLI channel 35, MAS channel 45) and 12 µm (GLI channel 36,
MAS channel 46), respectively, and θ is the sensor scan angle. Coefficients a, b, c, and d arederived from multilinear regression. This approach using two “split-window'” infrared
channels at approximately 11 µm and 12 µm is commonly employed for SST retrieval (Minnett,
1990; Llewellyn-Jones et al., 1984; Barton, 1985), IST retrieval (Key and Haefliger, 1992;
Key et al., 1997), and snow-free LST retrieval (Key et al., 1997; Wan and Dozier, 1996).

GLI Algorithm Description

3.4.3-2

(2) Methodology and Logic Flow
For reaching high accuracy the MODTRAN radiative transfer model is employed for
simulating the radiances measured by GLI and MAS. In MODTRAN a narrow-band model isused for computing gaseous optical depth from the HITRAN database with wavenumber stepsof 1 cm-1. Then the MODTRAN has a spectral resolution of 2 cm-1 at FWHM (Full Width atHalf-Maximum) with averaged steps of 1 cm-1. Multiple scattering is also included in theradiative transfer model by combining MODTRAN (refer: MODTRAN version 3.5) andDISORT. For the GLI and MAS instruments, since the sensor scan angle lies between 0° and
50°, our simulations are done for viewing angles in the range of 0°-50° with increments of 5°.
The built-in standard subarctic winter and summer atmospheric profiles including trace gases
and the background aerosol model in MODTRAN are used in our simulations. Blanchet andList (1983) showed that the volume extinction coefficient of Arctic haze is generally of thesame order of magnitude as troposphere aerosols. Thus we use troposphere background aerosol
instead of Arctic haze. The calculations of retrieval coefficients in Eq. (2.2) using both GLI
and MAS channels are presented in this document for testing and validating the algorithm. The
sensor response functions both for GLI channels 35 and 36 and for MAS channels 45 and 46
are used to compute radiances at the top of the atmosphere, and the radiances are thenconverted to brightness temperature by use of the Planck function.
For IST retrieval, the surface is assumed to be snow/ice-covered. Directional surface
emissivities for snow are calculated based on an extended version of the DISORT radiativetransfer model appropriate for the coupled atmosphere-surface system. This algorithm allows
us to study the bidirectional reflectance and directional emissivity for a surface covered withdifferent types of snow and sea ice. Coefficients a, b, c, and d in Eq. (2.2) for IST retrieval arecalculated within the following three temperature ranges: (i) T11 < 240 K; (ii) 240 K < T11 <260 K; and (iii) 260 K < T11 < 271.4 K.
We now assume that the freezing point of sea water is 271.4 K based on the average
freezing point of empirical and reported values (Bialek, 1966; Massom and Comiso, 1994; Yu
and Rothrock, 1996; Riggs et al., 1997). For temperatures above the melting point, a mixtureof snow/ice and meltponds occurs. In such cases the code for open ocean SST retrieval will beapplied. An equation similar to Eq. (2.2) will be used, but the surface emissivities are assumed
to be an area-weighted sum of snow and water emissivities. For the surface temperature
retrieval of an area with a mixture of snow/ice and meltponds, only two situations are studied
here, i.e., (i) for T11 < 275 K, the weights are 0.8 for snow and 0.2 for water, respectively; and(ii) for T11 > 275 K, the weights are 0.2 for snow and 0.8 for water. Obviously, theapproximation of dividing all the cases with the presence of melt ponds into just two categories
will lead to an uncertainty in the estimated surface temperature.

GLI Algorithm Description

3.4.3-3

Surface physical properties
Observed atmospheric profiles
Directional emissivity of snow from

Radiative Transfer CodeDISORT

MODTRANSurface temperature
Satellite channel information

Rλ (Simulated radiance at wavelength λ)λ2

Ri = ∫ Rλφi (λ )d λλ1

Convert Ri to Ti
Ti (Brightness temperature at satellite cannel i)

Multiple Linear Regression Analysis

Coefficients in Eq.(2.2)

Error predictions

Fig.2.1 Flow chart for the numerical simulations of satellite measurements.

The procedure to determine the coefficients in Eq. (2.2) is summarized as follows (see Fig.
2.1). The surface physical properties, observed atmospheric profiles, sensor response function,and snow directional emissivities data calculated using the extended version of DISORT are
input into MODTRAN to simulate radiances at MAS or GLI channels for a wide range ofatmospheric conditions. In these simulations, the temperature of the first layer just above thesurface is taken as the surface temperature. The simulated radiances are integrated with thesensor response functions for the MAS or GLI channels:
λ2

Ri = ∫ R (λ )φi (λ )d λ
λ1

(2.3)

where Ri is the simulated radiance, and ϕi is the sensor response function for channel i. Then,the integrated, simulated radiances Ri are converted to brightness temperatures Ti. A leastsquares multilinear regression is used to determine the coefficients in Eq. (2.2). The
coefficients in Eq. (2.2) for the IST and SST algorithms are presented in Tables 2.1 and 2.2,
respectively. The correlation coefficients between estimated and actual surface temperature aswell as the RMSE (root-mean-square errors) are also given in Tables 2.1 and 2.2.
Table 2.1a The coefficients in Eq. (2.2) for IST algorithm using MAS data

GLI Algorithm Description

3.4.3-4

Temperature
range (K)< 240
240 - 260
260-271.4

a

b

c

d

-1.157655-1.587060-2.480842

1.005439
1.007282
1.010931

1.535782
1.500379
1.447117

2.239843
1.595407
1.087111

Correlation
coefficient
0.9997583
0.9999706
0.9997824

RMS
0.054294
0.045863
0.067924

Table 2.1b The coefficients in Eq. (2.2) for IST algorithm using GLI data
Temperature
range (K)< 240
240 - 260
260-271.4

a

b

c

d

-0.504486-0.688521-1.238140

1.00195
1.00274
1.00524

1.29798
0.912788
0.775538-0.701453
0.970363
0.566395

Correlation
coefficient
0.999874
0.999981
0.999885

RMS
0.039571
0.036509
0.043058

Table 2.2a The coefficients in Eq. (2.2) for SST algorithm using MAS data
Temperature
range (K)271.4 - 275
> 275

a

b

c

d

-5.607100-2.740712

1.022034
1.011390

1.725736
1.993035

1.250851
1.331676

Correlation
coefficient
0.9980459
0.9997357

RMS
0.063624
0.063551

Table 2.2b The coefficients in Eq. (2.2) for SST algorithm using GLI data
Temperature
range (K)271.4 - 275

a

b

c

d

-2.09631

1.008230.885022

0.477340

Correlation
coefficient
0.998565> 275-3.79538

1.01408

1.09925

0.424474

0.999717

RMS
0.04599
4
0.05615
8

In order to develop an algorithm using the split-window technique specifically for polar
regions, atmospheric profiles from the NCEP/NCAR Arctic Marine Rawinsonde Archive areused for simulating the sensor-measured radiances. More than 4000 radiosonde profiles areused for the surface temperature (both SST and IST) algorithm development. The data set fromthe NCEP/NCAR Arctic Marine Rawinsonde Archive covers a large range of atmosphericconditions including different seasons and different locations across the Arctic.

C. Practical Considerations(1) Programming Requirements
The following table shows information about the expected software generated from thisalgorithm:
Table 3.1 Program Requirements
Program Memory
Program Size
Required Channels
Necessary/Ancillary Data

400 KBytes
100 KBytes
35, 36

GLI Algorithm Description

3.4.3-5

Expected Disk Volume
Special Programs or Subroutines
Look-up tables

none(2) Calibration and Validation
Based on Tables 2.1 and 2.2, we apply the surface temperature retrieval algorithm
discussed above to estimate the surface temperature using GLI-observed data. This algorithm
can only be applied to cloud-free pixels over the snow. Before this surface temperature
retrieval algorithm is executed, the cloudy/clear and snow/sea-ice discriminators (cf. ATBD
for CTSK1a and CTSK1b submitted to NASDA by Knut Stamnes, PI of the contract
A2GSF004 for GLI program) will be applied for distinguishing cloudy-free snow pixels fromcloudy pixels and other surface pixels. Then, for identified cloud-free pixels, the surface
temperatures are estimated based on Eq. (2.2) and the coefficients given in Tables 2.1b and2.2b according to the brightness temperature in GLI channel 35.
In order to assess the accuracy of this surface temperature retrieval algorithm, we use the
MODTRAN radiative transfer model with the standard subarctic winter atmospheric profile tosimulate the brightness temperature at both MAS channels 45 and 46, and GLI channels 35
and 36 for the viewing angles of 0°, 10°, 20°, 30°, and 40°, respectively. Due to the lack ofsurface temperature data and the difficulty of defining appropriate boundary layer conditions
for all surface types and locations, the temperature of the first layer of the profile, 257.2 K, istaken as the surface temperature (Key et al., 1997). Of course, this assumption will lead tosome uncertainties, since the difference between surface temperature and air temperature of thefirst layer can be significant for some situations. Then, the surface temperature retrieval
algorithm is executed with brightness temperatures BT35 and BT36 (or BT35 and BT36 for MASdata) obtained from forward calculations using the MODTRAN radiative transfer model fordifferent viewing angles. The estimated surface temperature TS is obtained from Eq. (2.2), andlisted in Table 3.2. The differences (∆T) between the given surface temperature (TG) of theforward simulation and the estimated surface temperature (TS) of the inverse retrieval are also
shown in Table 3.2. From Table 3.2, the accuracy of the algorithm is better than 0.12 K.

Table 3.2a. The retrieved surface temperature for MAS channels (TG = 257.2 K).
View angle
BT45
BT46
Ts
∆T = TG - TS0°256.6921
256.5797
257.1429
0.0571

10°
256.6884
256.5770
257.1404
0.059620°
256.6777
256.5684
257.1321
0.067930°
256.6547
256.5522
257.1157
0.084340°
256.6187
256.5252
257.0834
0.1166

Table 3.2b. The retrieved surface temperature for GLI channels (TG = 257.2 K).
View angle

GLI Algorithm Description

0°

10°

3.4.3-6

20°

30°

40°

BT35
BT36
Ts
∆T = TG - TS

256.90256.65257.1436
0.0564256.90256.62257.1752
0.0248256.90256.62257.1884
0.0116256.88256.60257.1929
0.0071256.83256.55257.1838
0.0162

Fig.3.1 shows the retrieved surface temperature distribution based on the GLI observation
made on April 14 (Fig. 3.1a), and April 26 (Fig. 3.1b), 2003 over Barrow, Alaska. White color
area is for cloud pixels. These retrieved surface temperatures look very reasonable. We also
compared these data with the simultaueous field measured data at the Barrow site (71°18′00″N,
156°35′00″W) (See Table3.3). We use the average temperature at a 5×5 pixel box around thefield site to indicate the retrieval data. From the results, we will find IST retrieval shows agood match, but SST retrieval is underestimated.

Table 3.3 Comparison with match-up data at Barrow site
Pixel/line in

Field measured

Retrieved 5×5 box

image

surface temperature

average temperature

2003041453

1156/580- 7°C (266K)

266.215K

2003041457

482/279-4.5°C (268.5K)

267.321K

2003042653

1156/580

0.5°C (273.5K)

269.615K

2003042657

482/279

3.0°C (276K)

270.917K

GLI image

GLI Algorithm Description

3.4.3-7

Fig. 3.1 The retrieved surface temperature from the GLI data over Barrow of Alaska on (a)April 14, 2003 and (b) April 26, 2003.

(3) Quality Control and Diagnostic Information(4) Exception Handling(5) Constraints, Limitations, Assumptions
At present time, this algorithm is implemented for the analysis of clear-sky snow pixels
over the polar regions and mid-latitude regions (between 20° and 60° in latitude).

(6) Publications and Papers

GLI Algorithm Description

3.4.3-8

D. References
Barton, I.J., 1985: Transmission model and ground-truth investigation of satellite-derived sea
surface temperatures, J. Clim. Appl. Meteorol., 24, 508-516.
Bialek, E.L., 1966: Handbook of Oceanographic Tables. Special Publication, SP-68, U.S.
Naval Oceanographic Office, Washington D.C..
Blanchet, J. and R. List, 1983: Estimation of optical properties of arctic haze using a numericalmodel. Atmos. Ocean., 21, 444-465.
Dozier, J. and S.G. Warren, 1982: Effect of viewing angle on the infrared brightness
temperature of snow. Water Resour. Res., 18, 1424-1434.
Key, J., and M. Haefliger, 1992: Arctic ice surface temperature retrieval from AVHRR thermalchannels. J. Geophys. Res., 97, 5885-5893.
Key, J.R., J.B. Collins, C. Fowler, and R.S. Stone, 1997: High-latitude surface temperature
estimates from thermal satellite data. Remote Sens. Environ., 67, 302-309.
Llewellyn-Jones, D.T., P.J. Minnett, R.W. Saunders, and A.M. Zavody, 1984: Satellite
multichannel infrared measurements of sea surface temperature of the northeast Atlantic Ocean
using AVHRR/2. Q. J. R. Meteorol. Soc., 110, 613-631.
Massom, R. and J.C. Comiso, 1994: The classification of Arctic sea-ice types and thedetermination of surface temperature using advanced very high resolution radiometer data. J.
Geophys. Res., 99, 5201-5218.
McClain, E.P., W.G. Pichel, and C.C. Walton, 1985: Comparative performance of AVHRRbased multichannel sea surface temperature. J. Geophys. Res., 90, 11587-11601.
Minnett, P.J., 1990: The regional optimization of infrared measurements of sea surface
temperature from space. J. Geophys. Res., 95, 13497-13510.
Price, J.C., 1983: Estimating surface temperature from satellite thermal infrared data -- asimple formulation for the atmospheric effect. Remote Sens. of Environ., 13, 353-361.
Riggs, G.A., D.K. Hall, and S.A. Ackerman, 1997: Sea ice detection with the Moderate
Resolution Imaging Spectroradiometer Airborne Simulator (MAS). Remote Sens. of Environ.,in press.
Wan, Z. and J. Dozier, 1996: A generalized split-window algorithm for retrieving land-surface
temperature from space. IEEE Trans. Geosci. Remote Sens., 34, 892-905.
Warren, S.G., 1982: Optical properties of snow, Rev. Geophy. Space Phys., 20, 67-89.
Yu, Y. and D.A. Rothrock, 1996: Thin ice thickness from satellite thermal imagery. J.
Geophys. Res., 101, 25753-25766.

GLI Algorithm Description

3.4.3-9