Polar Surface Temperature Retrieval From Space:
Coefficients

This page provides updates to the snow/ice and snow-free land surface temperature retrieval procedure detailed in Key et al. (1997). The coefficients are based on modelled radiances in the 11 and 12 um bands using Arctic and Antarctic temperature and humidity profiles and angular emissivity models for snow. The equations do not include a bias term to account for differences between modelled and actual radiances. This has not been necessary for NOAA-14, which as validated extensively with surface data from the SHEBA experiment. It may or may not be necessary for other platforms. See Key et al. (1997) for additional details.

Ice Surface Temperature

For ice/snow surface temperature (IST) retrieval from the AVHRR and MODIS we use the equation
(1)
where Ts is the estimated surface temperature (K), T11 and T12 are the brightness temperatures (K) at 11 um (AVHRR channel 4, MODIS band 31) and 12 um (AVHRR channel 5, MODIS band 32) and q is the sensor scan angle. Coefficients a, b, c , and d are derived for the following temperature ranges: T11  < 240K, 240K <  T11  < 260K, T11  > 260K.

For the ATSR we use the relationship

(2)
where T11 and T12 are the brightness temperatures of the 11 and 12 um channels in Kelvin and the subscript nadir and forward refer to the two viewing angles.

 



 
 
AVHRR and MODIS Arctic Snow/Ice Coefficients (Equation 1).
Satellite
Temperature

Range
a
b
c
d
NOAA 7
<240 K
-3.82468
1.01452
2.22875
-1.29408
240-260 K
-4.60504
1.01761
1.79531
-0.08029
>260 K
-4.41581
1.01648
1.66647
0.68402
NOAA 9
<240 K
-5.48207
1.02179
1.99583
-1.18365
240-260 K
-6.54114
1.02586
1.64728
0.27868
>260 K
-5.25491
1.02043
1.63575
1.14777
NOAA 11
<240 K
-4.65532
1.01810
2.19679
-1.26894
240-260 K
-5.39334
1.02096
1.76399
0.04116
>260 K
-4.76934
1.01813
1.66489
0.84750
NOAA 12
<240 K
-2.79827
1.01039
2.10004
-1.02716
240-260 K
-3.47596
1.01312
1.68157
-0.01882
>260 K
-4.12109
1.01502
1.66900
0.54726
NOAA 14
<240 K
-3.846001
1.014939
1.904878
-0.879747
240-260 K
-4.397758
1.017179
1.411066
0.213224
>260 K
-4.498451
1.017059
1.402800
0.690478
NOAA 15
<240 K
-4.034918
1.015444
2.222340
-1.228140
240-260 K
-4.728985
1.018188
1.757905
-0.001810
>260 K
-4.633262
1.017383
1.659278
0.733954
NOAA 16 <240 K -1.453829 1.004601 1.946308 -0.907209
240-260 K -2.304536 1.008018 1.637119 -0.131031
>260 K -3.676576 1.012527 1.690164 0.347890
MODIS
<240 K
-1.571123
1.005477
1.853279
-0.790518
240-260 K
-2.372697
1.008604
1.694824
-0.205252
>260 K
-4.295305
1.015018
1.949525
0.197133


 
 
AVHRR and MODIS Antarctic Snow/Ice Coefficients (Equation 1).
Satellite
Temperature

Range
a
b
c
d
NOAA 7
<240 K
-1.21619
1.00433
1.36556
-0.65060
240-260 K
-6.40072
1.02561
0.98103
0.56256
>260 K
-7.00035
1.02736
1.07976
0.88936
NOAA 9
<240 K
-1.76282
1.00745
0.47768
-0.08011
240-260 K
-8.08351
1.032878
0.60057
1.15843
>260 K
-7.98541
1.03176
0.92139
1.43351
NOAA 11
<240 K
-1.46611
1.00567
1.09288
-0.47756
240-260 K
-7.10043
1.02863
0.85709
0.76661
>260 K
-7.39846
1.02914
1.03573
1.07391
NOAA 12
<240 K
-0.80019
1.00228
1.72955
-0.75776
240-260 K
-4.82371
1.01908
1.13866
0.38312
>260 K
-6.11450
1.02361
1.17492
0.67614
NOAA 14
<240 K
-1.180768
1.003951
1.616824
-0.729174
240-260 K
-5.647473
1.022697
0.919952
0.552105
>260 K
-6.602028
1.025938
0.963384
0.793529
NOAA 15
<240 K
-1.258905
1.004476
1.430976
-0.661893
240-260 K
-6.381229
1.025568
0.973153
0.607435
>260 K
-7.036723
1.027533
1.085787
0.920915
NOAA 16 <240 K -0.292169 1.000107 1.506015 -0.566436
240-260 K -3.650344 1.013983 1.181797 0.194899
>260 K -5.768286 1.021676 1.215382 0.477659
MODIS
<240 K
-0.159480
0.999926
1.390388
-0.413575
240-260 K
-3.329456
1.012946
1.214573
0.131017
>260 K
-5.207360
1.019429
1.510250
0.260355


 
 
ATSR-1 Arctic and Antarctic Snow/Ice Coefficients (Equation 2).
Polar Region
Temperature

Range
a
b
c
d
e
Arctic
<240 K
-0.34213
0.66340
-0.15849
1.38082
-0.88586
240-260K
-0.79801
1.50374
-0.45245
0.33780
-0.38684
>260 K
-0.56158
2.23152
-0.91817
-0.40756
0.09610
Antarctic
<240 K
0.00314
1.060343
-0.42877
1.04872
-0.68183
240-260 K
-0.95689
1.86848
-0.75113
0.00039
-0.11458
>260 K
-0.60407
1.89027
-0.58023
-0.14938
-0.15887


 
 
ATSR-2 Arctic and Antarctic Snow/Ice Coefficients (Equation 2).
Polar Region
Temperature

Range
a
b
c
d
e
Arctic
<240 K
-0.242288
0.764270
-0.252640
1.301810
-0.814004
240-260K
-0.562328
1.560470
-0.476826
0.222039
-0.304391
>260 K
-0.420010
2.326056
-0.998923
-0.514060
0.188233
Antarctic
<240 K
-0.011518
1.023552
-0.462198
1.103719
-0.666580
240-260 K
-0.694934
1.863442
-0.640912
-0.116670
-0.103843
>260 K
-0.484481
1.852347
-0.642554
-0.086014
-0.122636

Snow-free Land Surface Temperature

The regression model for snow-free land using the AVHRR and ATSR is:
(3)
where e is the emissivity at the wavelength denoted by the subscript. Note: ATSR-2 coefficients have not been developed for snow-free land.


 
 
AVHRR and ATSR Polar Land Coefficients (Equation 3).
Satellite
Temperature

Range
a
b
c
d
e
NOAA 7
<240 K
26.0309
4.0147
-2.9919
-165.0710
133.5685
240-260 K
32.1194
3.5683
-2.5444
-164.3970
126.3626
>260 K
44.4224
3.6507
-2.6387
-181.1707
133.4351
NOAA 9
<240 K
23.0055
4.4368
-3.4103
-181.5454
152.2116
240-260 K
29.3755
3.6499
-2.6167
-167.8258
130.4036
>260 K
41.5469
3.7915
-2.7710
-188.3021
141.5502
NOAA 11
<240 K
24.5757
4.2369
-3.2127
-173.8222
143.4666
240-260 K
30.9222
3.5992
-2.5714
-165.6568
127.9483
>260 K
43.0879
3.7034
-2.6874
-183.7980
136.5114
NOAA 12
<240 K
29.1836
3.4836
-2.4606
-144.4215
109.7186
240-260 K
34.8680
3.5896
-2.5732
-166.2492
127.2383
>260 K
46.9049
3.6529
-2.6470
-181.5388
132.7192
NOAA 14
<240 K
27.8690
3.2520
-2.2260
-133.0235
98.9686
240-260 K
33.5189
3.2796
-2.2587
-150.3413
111.6787
>260 K
45.9367
3.3803
-2.3725
-166.7875
118.6037
NOAA 15
<240 K
26.0307
3.9893
-2.9655
-164.3357
132.5978
240-260 K
32.0778
3.5843
-2.5600
-165.3660
127.3099
>260 K
44.1398
3.6687
-2.6554
-182.2059
134.4543
NOAA 16 <240 K 31.7447 3.2120 -2.1935 -133.4750 97.1853
240-260 K 37.6640 3.5496 -2.5422 -164.6871 124.9140
>260 K 49.0214 3.5950 -2.5950 -178.4917 128.7903
ATSR-1
<240 K
30.0063
3.6227
-2.6021
-151.2939
116.3105
240-260 K
35.7733
4.1795
-3.1719
-195.1314
157.2663
>260 K
46.6237
3.6624
-2.6527
-182.4819
132.8915

References

Key, J., J. Collins, C. Fowler, and R. Stone, 1997. High-latitude surface temperature estimates from thermal satellite data. Remote Sensing Environ., 61, 302-309.

Revision History

v1.1, 2 August 2001
  - Added NOAA 16
v1.0, 1 June 2000
  - First web page with coefficients