GCOM–C1/SGLI Land Surface Temperature Product
Algorithm Theoretical Basis Document
Masao Moriyama
Nagasaki University
Nagasaki, JAPAN.
Spt. 30, 2014

Contents
1 Introduction

12 Split window algorithm
2.1 Physics of the LST estimation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Overview of the split window algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Diﬀerence from SST estimation and modification . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Dynamic range compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Surface emissivity compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Accuracy and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Eﬀect of the assumptions of the blackbody observed brightness temperature estimation .
2.4.2 Emissivity misestimation eﬀect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2
2
2
2
3
5
8
8
8

3 Semi–analytical LST estimaton algorithm
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Integration of the split window method and semi–analytical method . . . . . . . . . . . .
3.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Numerical simulation for the accuracy verification . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Cross Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Quality assurance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 QA field bit assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
10
10
10
11
13
13
14

4 Operation
15
4.1 Input/Output dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 Data processing flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Validation
5.1 Basic concept of the validation of SGLI LST algorithm . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Estimated LST validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Estimated emissivity validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i

16
16
16
16

List of Figures
2.1
2.2
2.3
2.4
2.5
2.6

The surface air temperature (Left) and the surface temperature (Right) on 18:00, 1 July 2005. .
MODIS chs. 31, 32 normalized response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relationship of the 2 kinds of the temperature diﬀerence . . . . . . . . . . . . . . . . . . . . . . .
Various materials’ emissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Emissivity categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between blackbody and non–blackbody observed brightness temperature at MODIS
ch. 31 (Left) and 32 (Right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Relationship between blackbody observed brightness temperature conversion coeﬃcients and thesurface reflectivity at MODIS ch. 31 (Left) and 32 (Right) . . . . . . . . . . . . . . . . . . . . . .
2.8 Comparison between the model and estimated LST in the case of SGLI (Left) and MODIS (Right)
2.9 Comparison between the RMS error of the blackbody observed brightness temperature estimation
under the all and low surface temperature cases . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 LST diﬀerence relevant to 0.01 overestimated surface emissivity . . . . . . . . . . . . . . . . . . .
3.1

4
4
4
5
5
6
7
7
8
9

3.4
3.5
3.6
3.7

The numerical simulation results Left: RMS residue histogram, Middle: LST estimation error,
Right: Emissivity estimation error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dec. 31 2009 MOD11C1 product, Left: Daytime LST, Right: Daytime GOOD pixel (white) . . .
LST and emissivity estimation result from TERRA/MODIS data aquired on 0400Z Spt. 15 2000
(from Left to Right: True color composite, LST, emissivity at ch. 31, emissivity at ch. 32) . . . .
The scene center of MOD02 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LST estimation error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between two kinds of LST (Left: 1835Z, Right: 0400Z) . . . . . . . . . . . . . . . . .
LST diﬀerence histogram (Left: 1835Z, Right: 0400Z) . . . . . . . . . . . . . . . . . . . . . . . .

4.1

The data processing flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.1

Comparison between the ground measured and the satellite derived LST . . . . . . . . . . . . . . 17

3.2
3.3

i

11
12
12
13
13
13
13

List of Tables
2.1
2.2
2.3

The surface temperature range simulation condition . . . . . . . . . . . . . . . . . . . . . . . . .
The surface temperature range simulation condition . . . . . . . . . . . . . . . . . . . . . . . . .
Regression coeﬃcients and RMS error of the blackbody observed brightness temperature estimation

3.1
3.2

The semi–analytical method simulation condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
SGLI/LST QA field (Bit 0 means LSB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1
4.2

The input dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
The output dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

ii

4
5
6

Chapter 1

Introduction
This document describes the land surface temperature estimation algorithm for SGLI sensor. So far the land
surface temperature estimation from space is made by many kinds of sensors, as the operational product,
ASTER and MODIS onboard TERRA satellite made the land surface temperature product in late 90’s. Just
after this, ATS oboard the European satellite ESA published the land surface product. The operational land
surface temperature estimation has about 10 years history and the improvement of the estimation algorithm
are made.
For SGLI, the land surface temperature estimation algorithm will be made on the basis of these previous
algorithm and will be added the new improvement. The split window algorithm is used for MODIS and AATSR,
this is less computation time and suitable for the wide swath sensor but the surface emissivity has to be theknown variable. On the other hand, ASTER uses the semi–analytical method to estimate not only the surface
temperature but the emissivity, but it’s computation time consumable. For SGLI, the semi–analytical method
which uses the split window algorithm as the constraint of the land surface temperature/emissivity and theobserved brightness temperature.
From the next chapter, the split windows algorithm, the semi–analytical algorithm will be described. And
also the operational factor such as input and output and the data processing flow will be explained. At the endof this document, the validation plan will be noticed.

1Chapter 2

Split window algorithm
2.1

Physics of the LST estimation algorithm

The satellite detected radiance at i th. observation channel Ii is described as the following radiative transfer
equation.
Ii = τi (θ)Isi + Iai (θ)(2.1)
where τ , θ, Is and Ia are the total transmittance, the observation zenith, the land leaving radiance and thepath radiance respectively. And the land leaving radiance is expressed as Eq. (2.2).
Isi = εi Bi (Ts ) + (1 − εi )

Fi
π

(2.2)

where ε, B, Ts and F are the surface emissivity, Planck function, the surface temperature and the downward
atmospheric irradiance respectively. Even the atmospheric condition is known, the land leaving radiance contains
two kinds of unknowns, surface temperature and emissivity. Since the surface emissivity has the spectral
dependency, this problem is underdetermine in any numbers of the observation spectral channels.

2.2

Overview of the split window algorithm

Since the sea surface can be assumed the blackbody and the temperature range is up to 30 [K], The diﬀerence
between the sea surface temperature (SST) and the satellite detected brightness temperature is caused by theatmospheric eﬀect. Deschamps et al. found that the brightness temperature diﬀerence of 10.8 and 12.0 [µm]spectrum over the sea surface contains the atmospheric eﬀect and found the linear relationship between thediﬀerence of the true SST and the 10.8 [µm] spectrum brightness temperature [Deschamps and Phulpin, 1980].
After some improvements, the multiple regression formula between the brightness temperature of 10.8 and 12.0[µm] spectrum and the sea surface temperature which is called Multiple Channel Sea Surface Temperature
estimation scheme (MCSST) [McClain et al., 1985] is established for the satellite based SST estimation. The
MCSST formula is shown in Eq. (2.3),
Ts = C0 + C1 T1 + C2 (T1 − T2 )(2.3)

where Ts , T1 , T2 and Cs are sea surface temperature, brightness temperature at 10.8 and 12.0 [µm] spectrum andthe regression coeﬃcients respectively. The MCSST formula is widely used for about 40 years and continues tomake the high accuracy SST estimation. So that the SGLI land surface temperature (LST) estimation algorithm
starts from the MCSST formula and this is modified for the LST estimation.

2.3

Diﬀerence from SST estimation and modification

There are many types of the covering category of the land, although that of the sea is only one, water. Thisvariety of the land cover makes the temperature estimation diﬃcult. The diﬀerences between the LST and SST
estimation from the satellite are the followings.
2

1. The dynamic range of LST is wider than that of SST.
2. The land surface emissivity varies considerably, hence the sea surface emissivity is almost constant.
To compensate these 2 diﬀerence, the following modification are made.

2.3.1

Dynamic range compensation

For the sea surface case, the evaporation suppress the temperature increase so that the SST is almost same as
the surface air temperature, but the land surface case, especially the dry area in the daytime, the evaporation
cannot be expected so that the surface temperature is so much larger than the surface air temperature. As an
example of this, the surface air temperature and the surface temperature on 18:00(GMT), 1 July 2005 extracted
from the NCEP reanalysis data are shown in Figure 2.1. Around the great basin area, the diﬀerence between
the surface temperature and the surface air temperature is more than 10[K].

3

Figure 2.1: The surface air temperature (Left) and the surface temperature (Right) on 18:00, 1 July 2005.

To confirm the MCSST formula works in the case of the wide surface temperature range, the numericalsimulation is made that the satellite detected brightness temperature is computed under the condition shownin Table 2.1 using MODTRAN and define the regression coeﬃcients in MCSST formula. The RMS diﬀerence
between the model and estimated surface temperature is enough small (0.53[K]), so that the MCSST formulacan compensate the wide surface temperature range in the case of the blackbody surface. The relationshipbetween the 2 kinds of the temperature diﬀerence is shown in Figure 2.3.
Table 2.1: The surface temperature range simulation condition
Longitudinal mean with 10o latitude interval of 2000 ECMWF monthly mean atmosphere
1.0
Surface air temperature + 0, 5, 10, 15 [K]0, 15, 30, 45o
MODIS chs. 31, 32 (cf. Figure 2.2)

Atmospheric profile
Surface emissivity
Surface temperature
Observation zenith
Target sensor

40

2.5

ch. 31ch. 3235

Ts-0.944*T1 [K]Normalized response

2

1.5

1

25

20

15

0.5

0
10.4

30

10.6

10.8

11

11.2

11.4

11.6

11.8

12

12.2

12.4

10
-0.5

12.6

0

Figure 2.2: MODIS chs. 31, 32 normalized response.

0.5

1

1.5

2

2.5

3

3.5

4

T1-T2 [K]Wavelength [micrometer]

Figure 2.3: Relationship of the 2 kinds of the temperature diﬀerence

As a result, the linear relationship can be established as Eq(2.4) for the wide surface temperature range
blackbody observed case.
Ts = C00 + C10 T10 + C20 (T1 − T20 )
4

(2.4)

where T10 , 02 ans C 0 are the blackbody observed brightness temperature at 10.8 and 12.0 [µm] spectrum andthe regression coeﬃcients respectively.

2.3.2

Surface emissivity compensation

Same as the current similar sensor such as AATSR and MODIS, SGLI LST estimation algorithm treat thesurface emissivity as the known variables [Prata, 2002, Wan, 1999]. Since the MCSST formula works over theblackbody surface in the case of the wide surface temperature range, if the blackbody surface observed brightness
temperature is estimated from the actual non–blackbody surface observed brightness temperature, the MCSST
formula can estimates LST under the non–blackbody surface [Moriyama, 2009]. The above assumption is verified
through the following numerical simulation.
The various land cover materials’ emissivity is summarized as the spectral library [Salisbery and D’Aria, 1985].
From the spectral library, the spectral emissivity of MODIS chs. 31, 32 are computed and shown in Figure 2.4.
The emissivity category as shown in Figure 2.5 and compute the satellite detected brightness temperature under
the condition in Table 2.2. The comparison between the blackbody and non–blackbody observed brightness
temperature at MODIS chs. 31, 32 are made.
1

MODIS ch. 32 emissivity

0.98
1

MODIS ch.32 emissivity

0.98

0.96

0.94
0.92
0.9

0.94

0.88
0.84

0.92

0.86

0.88

0.9

0.92

0.94

0.96

0.98

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

MODIS ch. 31 emissivity

Water
Vegetation ans snow
ManmadeSedimental roock
Ignite rock
Metammorphoses rock
Soil

0.9

0.88
0.84

0.96

Water
Vegetation and snow
ManmadeSedimantal rockIgnite rock
Metamorphoses rockSoils
CAT 01
CAT 02
CAT 03
CAT 04
CAT 05
CAT 06
CAT 07

1

MODIS ch.31 emissivity

Figure 2.4: Various materials’ emissivity

CAT 08
CAT 09
CAT 10
CAT 11
CAT 12
CAT 13
CAT 14
CAT 15
CAT 16
CAT 17
CAT 18
CAT 19CAT 20Figure 2.5: Emissivity categories
Table 2.2: The surface temperature range simulation condition
Atmospheric profile
Surface emissivity
Surface temperature
Observation zenith
Target sensor

Longitudinal mean with 10o latitude interval of 2000 ECMWF monthly mean atmosphere
1.0, Average of each emissivity category
Surface air temperature + 0, 5, 10, 15 [K]0, 15, 30, 45o
MODIS chs. 31, 32 (cf. Figure 2.2)

The comparison results are shown in Figure 2.6. From the results, the linear relationship is found, so thatthe following conversion formula from the non-blackbody observed brightness temperature Ti to the blackbody
observed brightness temperature Ti0 .
Ti0 = ai Ti + bi

(2.5)

where subscript i, a and b are spectral channel and constants respectively. At each emissivity category, thecoeﬃcients are defined by the least square method. The coeﬃcients and RMS error are shown in Table 2.3.

5

310
MODIS 32 TBB from blackbody surface [K]

MODIS 31 TBB from blackbody surface [K]

310
300
290
280
270
260
CAT.01
CAT.06
CAT.09CAT.15
CAT.20

250
240
230

240

250

260

270

280

290

300

300
290
280
270
260

240
230

310

CAT.01
CAT.06
CAT.09CAT.15
CAT.20250

240

MODIS 31 TBB from non-blackbody surface [K]

250

260

270

280

290

300

310

MODIS 32 TBB from non-blackbody surface [K]Figure 2.6: Comparison between blackbody and non–blackbody observed brightness temperature at MODIS
ch. 31 (Left) and 32 (Right)

Table 2.3: Regression coeﬃcients and RMS error of the blackbody observed brightness temperature estimation
CAT.
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20

a
0.995
0.991
0.982
0.977
0.971
0.969
0.963
0.957
0.951
0.955
0.948
0.942
0.936
0.929
0.940
0.934
0.927
0.921
0.914
0.907

MODIS ch. 31
b RMS[K]
1.748
0.196
2.900
0.316
6.002
0.354
7.735
0.452
9.584
0.547
10.5580.542
12.5030.634
14.4540.727
16.4440.822
15.1520.735
17.2800.829
19.3510.920
21.4361.011
23.524
1.103
19.9020.929
22.1011.019
24.262
1.111
26.435
1.202
28.5881.294
30.833
1.385

a
0.988
0.993
0.968
0.975
0.982
0.948
0.956
0.964
0.972
0.929
0.937
0.946
0.954
0.963
0.910
0.918
0.927
0.936
0.945
0.953

MODIS ch. 32
b RMS[K]
3.869
0.317
2.261
0.196
10.238
0.476
7.977
0.375
5.756
0.275
16.5650.681
13.9740.580
11.435
0.482
8.870
0.381
22.6220.895
19.9410.797
17.2530.696
14.5500.595
11.8710.494
28.537
1.106
25.838
1.007
23.1160.907
20.3570.807
17.6430.705
14.915
0.604

Emissivity
MODIS ch. 31 MODIS ch. 32
0.992
0.987
0.988
0.993
0.974
0.966
0.966
0.974
0.959
0.981
0.954
0.946
0.946
0.954
0.938
0.962
0.929
0.971
0.934
0.926
0.926
0.934
0.917
0.943
0.908
0.952
0.900
0.961
0.914
0.905
0.905
0.914
0.896
0.923
0.888
0.933
0.879
0.942
0.869
0.951

By comparing the coeﬃcients and the emissivity, the linear relationship between the surface reflectivity(ri = 1−εi ) and the coeﬃcients can be found as Figure 2.7. From the results, the blackbody observed brightness
temperature estimation formula is express as the function of surface reflectivity and the non–blackbody observedbrightness temperature as Eq. (2.6).
Ti0 = (ai ri + bi )Ti + (ci ri + di )(2.6)

where a, b, c, d are the constants. From Eqs. (2.4, 2.6), the following SGLI split window LST estimation
algorithm is established.
Ts = A0 + (A1 r1 + A2 )T1 + A3 r1 + (A4 r2 + A5 )T2 + A6 r2(2.7)

where As are the regression coeﬃcients. This formula is used for the standard algorithm of the GCOM–
C1/SGLI LST product.
6

From the condition in Table 2.2, The regression coeﬃcients of Eq. (eq:sglilst) are defined by the least square
method and compute the RMS error of the estimated LST, From the same condition, the regression coeﬃcientsof the MODIS Generalized Split Window algorithm (GSW) [Wan, 1999] as Eq. (2.8) are also defined andcompute the RMS error.
))((
1 − ε̄
∆ε T1 + T2
1 − ε̄
∆ε T1 − T2
T s = A1 + A2
+ A3 2+ B1 + B2+ B3 2
+C
(2.8)
ε̄
ε̄
2
ε̄
ε̄
2
where A, B, C are the regression coeﬃcients and ε̄ and ∆ε are the average and diﬀerence of the surface
emissivity at the 10.8 and 12.0 [µm] spectrum respectively.
The RMS error in the case of the SGLI split window is 1.46[K] hence that in the case of MODIS GSW is1.50[K]. The comparison between the model and estimated LST in the case of SGLI split window and MODIS
GSW are shown in Figure 2.8. The SGLI split window algorithm has the comparable accuracy with the MODIS
GSW algorithm.
35

a
b

1

30

a
b

0.99
30

0.98
25

0.97
0.96

0.97

a

0.95
15

0.94
0.93

20

0.96

20
b

a

25

0.98

0.95

15

b

1
0.99

0.94
10

0.93

10

0.92

0.92

5

5
0.91

0.91

0.9
0

0.02

0.04

0.06

0.08

0.1

0.12

0
0.14

0.9

0
0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Reflectivity

0.1

Reflectivity

Figure 2.7: Relationship between blackbody observed brightness temperature conversion coeﬃcients and thesurface reflectivity at MODIS ch. 31 (Left) and 32 (Right)

320

RMSE: 1.46 [K]

310

310

300

300

Estimated LST [K] (GSW)

Estimated LST [K] (SGLI Split)

320

290
280
270
260
250
240
240

RMSE: 1.50 [K]

290
280
270
260
250

250

260

270

280

290

300

310

240
240

320

Model LST [K]

250

260

270

280

290

300

310

320

Model LST [K]Figure 2.8: Comparison between the model and estimated LST in the case of SGLI (Left) and MODIS (Right)

7

2.4

Accuracy and stability

2.4.1

Eﬀect of the assumptions of the blackbody observed brightness temperature
estimation

The RMS error of the MCSST formula in the case of the blackbody observation as Eq. (2.4) is about 0.53[K],on the other hand the RMS error of the blackbody observed brightness temperature estimation as Eq. (2.5) is
up to about 1.4[K] as shown in Table 2.3. So this assumption error is considered as one of the most significant
LST estimation error causes. This assumption error assumed to be caused by the wide range of the surface
temperature because of the non–linearity of the Planck function. To estimate the surface temperature range
eﬀect to the assumption error, the numerical simulation almost same as the previous blackbody observedbrightness temperature estimation except the surface temperature range. In this case the surface temperature
range is limited to the same as 5[K] above the surface air temperature, ans the other conditions are the sameas Table 2.2. The comparison between RMS error of the blackbody observed brightness temperature under the
all cases and low cased of the surface temperature is made and shown in Figure 2.9. The result shows that theblackbody observed brightness temperature estimation is accurate under the low surface temperature case.

RMS error [K] (Low surface temperature case)

1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2

MODIS31
MODIS32

0.1
0

0.2

0.4

0.6

0.8

1

1.2

1.4

RMS error [K] (All case)

Figure 2.9: Comparison between the RMS error of the blackbody observed brightness temperature estimation
under the all and low surface temperature cases

To reduce the LST estimation error, 2 sets of the regression coeﬃcients set will be defined for the high and low
surface temperature cases. The coeﬃcient set selection scheme will be the daytime/nighttime determination
because in the nighttime, the surface temperature of almost all land cover category will be balanced to thesurface air temperature.

2.4.2

Emissivity misestimation eﬀect

Since all measurement contain the observation error, the algorithm developer must consider the error propagation to the final product. Generally, the error propagation theory [Tayler, 1997] is used for the purpose as Eq.
(2.9).

yδy= f (x1 , x2 , . . . , xn )
n
∑
∂y
=
δxi
∂x
i
i=1
8

(2.9)

where y, x, f and δ are the output variable, input variables, the function from the input to the output andthe suﬃx means small change of the variable respectively.
The alternate cause of the LST estimation error using split window algorithm is the misestimation of
the surface emissivity. To estimate the emissivity misestimation eﬀect, Eq. (2.9) is used with the variable
conversion of xi = εi and y = Ts . The estimated surface temperature change relevant to 0.01 overestimatedsurface emissivity under the condition in Table 2.2 are computed in the case of SGLI split window algorithm
and MODIS GSW algorithm. The results are shown in Figure 2.10.
-0.3
-0.4

LST difference [K]

-0.5
-0.6
-0.7
-0.8
-0.9
-1
-1.1
-1.2
240

SGLI split
GSW
250

260

270

280

290

300

310

320

LST [K]

Figure 2.10: LST diﬀerence relevant to 0.01 overestimated surface emissivity

The results show that the estimated LST diﬀerence relevant to the misestimated surface emissivity in thecase of SGLI split window algorithm is almost smaller than that in the case of MODIS GSW algorithm. Thismeans that SGLI split window algorithm is more insensible with the misestimated surface emissivity than
MODIS GSW algorithm. This fact will be the big advantage of SGLI split window algorithm.

9Chapter 3

Semi–analytical LST estimaton
algorithm
3.1

Overview

As explained before, the land leaving radiance (cf. Eq. (2.2)) has two unknowns, the surface temperature andemissivity, and the surface emissivity has spectral dependency. Since this problem becomes underdetermine,
reduction of the unknown or addition of the extra formula is necessary to solve this problem. ASTER LST
estimation algorithm uses the additional formula which is defined from the statistics of the spectral emissivity of
the 5 TIR observation channels. But for the less observation channel sensor such as AVHRR, MODIS, there wereno additional formula because the two observation channels are not enough to establish the spectral emissivity
relationship.

3.1.1

Integration of the split window method and semi–analytical method

From the other viewpoint, the SGLI LST split window formula is regarded as the statistical relationship between
the observed value and the unknown variables and it has the enough accuracy so that this formula can be theadditional formula to the semi–analytical method. In this case, since the split window method contains thesatellite detected brightness temperature, the following simultaneous equation (Eq. (3.1 – 3.3)) which contains
the radiative transfer equation which expresses the satellite detected brightness temperature instead of the landleaving radiance.
T1 = B1−1 [τ1 (ε1 B1 (Ts ) + (1 − ε1 )F1) + Ia1 ]π(3.1)

T2 = B2−1 [τ2 (ε2 B2 (Ts ) + (1 − ε2 )F2) + Ia2 ]π(3.2)

Ts = (A1 + A2 r1 )T1 + A3 r1 + (A4 + A5 r2 )T2 + A6 r2 + A0 (ri = 1 − εi )

(3.3)

−1

where Bis the Inverse Planck function. Among this simultaneous equation, the brightness temperature
T1 and T2 are the observed value, the transmittance τ , the path radiance Ia and the downward atmosphericirradiance F is the computed value from the atmospheric condition and the surface temperature Ts and theemissivity ε are the solutions. To solve this simultaneous equation, the Newtonian iteration scheme is used.

3.2

Validation

3.2.1

Numerical simulation for the accuracy verification

For the accuracy verification, the LST estimation using the numerical simulated observed radiance is made. The
simulation condition is listed in Table 3.1, in the table, the average emissivity ε̄ and the spectral dependency

10parameter a are defined as follows.
ε̄ =ε1 + ε2
ε1 − ε2δε, δε =, a=, (−1 < a < 1)22
1 − ε̄

(3.4)

ε1 = ε̄ + (1 − ε̄)a, ε2 = ε̄ − (1 − ε̄)a(3.5)

Table 3.1: The semi–analytical method simulation condition
Atmospheric profileε̄aSurface temperature
Observation zenith
Observation error
Max. iteration

Longitudinal mean with 10o latitude interval of 2000 ECMWF monthly mean atmosphere
0.94, 0.95, 0.96, 0.97, 0.98, 0.99
-0.5, -0.25, 0, 0.25, 0.5
Surface air temperature + 0, 5, 10, 15 [K]0, 15, 30, 45o
0.2 [K] (@300 [K])10

As the results, RMS residual of the simultaneous equation histogram, LST estimation error and the emissivity
estimatation error are shown in Figure 3.1. The results show the estimation accuracy closely depends on the
RMS residual between the both hand side of the simultaneous equation Eq. (3.1–3.3), In the case of the RMS
residual is less than 1 [K], LST estimation error is less than 1.5 [K], almost same as the case of the split window
method even the surface emissivity is unknown.
11Frequency
Accumlated frequency

6

0.08

Bias
RMS

0.1

0.06

0.8

0.4

Emissivity estimation error

0.001

LST estimation error [K]0.6

Accumlated frequency

Frequency

4

0.01

3
2
1
0

0.0001

0.2

0
0

1

2

3

4

5

6

7

8

RMS residue [K]

0.05
0.04
0.03
0.02
0.01
0
-0.01

-1
1e-05

10.8[micrometer] Bias
12.0[micrometer] Bias
10.8[micrometer] RMS
12.0[micrometer] RMS

0.07

5

-0.02

-2

-0.03
0

1

2

3

4
RMS residue [K]

5

6

7

8

0

1

2

3

4

5

6

7

8

RMS residue [K]Figure 3.1: The numerical simulation results Left: RMS residue histogram, Middle: LST estimation error,
Right: Emissivity estimation error

3.2.2

Cross Validation

OutlineSince the surface temperature varies temporally and spatially, the LST ground truth dataset is diﬃcult togather. So in this paper, the cross validation between the proposed method and the other LST product. As
the comparison, MODIS daily global mapped Day/Night land surface temperature and emissivity product(MOD11C1) is used [Wan, 1999]. This product is made by the Day/Night algorithm which solve the simultaneous radiative transfer equation of the day and night observed radiance of 6 emission spectral channel dataat the same location. The surface emissivity is from the land cover classification data as an input and the
day and night surface temperature are the solution of this algorithm. If surface temperature and emissivity
satisfy the radiative transfer equation, these are marked as “GOOD” in the product quality assurance (QA)
field. Moreover, the Day/Night algorithm has the least assumptions in the present time. Figure 3.2 show thedaytime LST and Daytime GOOD pixel on Dec. 31 2009.
Validation Scheme
MODIS Day/Night LST product compensates the misalignment of the pixel with the spatial averaging into
5 × 5 pixel and MOD11C1 product reaveraged into the global 0.05 [deg.] grid. In this study, the input of11

Figure 3.2: Dec. 31 2009 MOD11C1 product, Left: Daytime LST, Right: Daytime GOOD pixel (white)

the semi–analytical LST estimation method is TERRA/MODIS 1 [km] resolution Satellite detected radiance(MOD02) acquired at 1835Z and 0400Z of every day in 2000, the estimated temperature and emissivity are
averaged into 0.05 [deg.] grid and are compared with MOD11C1 product. As the auxiliary data, the MODIS
location information (MOD03), the MODIS cloud mask (MOD35) and the nearest time NCEP 1 [deg.] mesh
forecasting data are used. As an example of the semi–analytical method output, the true color composite, theestimated LST and emissivity of TERRA/MODIS data which acquired on 0400Z Spt. 15 2000 are shown in
Figure 3.3.

Figure 3.3: LST and emissivity estimation result from TERRA/MODIS data aquired on 0400Z Spt. 15 2000
(from Left to Right: True color composite, LST, emissivity at ch. 31, emissivity at ch. 32)

LST comparison result
The scene center of each 1835Z and 0400Z MOD02 data are shown in Figure 3.4 and the bias and RMS diﬀerence
between the MOD11C1 LST and averaged LST from semi–analytical method are shown in Figure 3.5.
In the case of many averaged pixel, the bias and RMS diﬀerence is small, in other words, the less cloud sceneshows the good correspondence between two kinds of estimated LST. To clarify the cloud eﬀect, the comparison
between two kind of estimated LST with the diﬀerent averaged pixel number within the 0.05 [deg.] grid in
Figure 3.6 and 3.7. The large number of the averaged pixel mea ns this pixel is clear, so the proposed method
shows the good correspondence with the MODIS Day/Night LST product.

12

12

1835Z bias diff.
1835Z RMS diff.
0400Z bias diff.
0400Z RMS diff.

8010Bias and RMS LST difference [K]60

Latitude [deg.]

40
20
0
-20
-40

8
6
4
2
0
-2

-60
-4

1835Z
0400Z

-80
-150

-100

-50

0

50

100

-6
0

150

20000

40000

60000

80000

100000120000

Averaged pixel countLongitude [deg.]

Figure 3.4: The scene center of MOD02 data

Figure 3.5: LST estimation error

Figure 3.6: Comparison between two kinds of LST (Left: 1835Z, Right: 0400Z)

2
1.5
1e+06
1
0.5
0
-0.5

100000
0

5

10

15

20

1e+07

Bias
RMS
Averaged pixel count

2

1.5

1

1e+06

0.5

0

-0.5

25

1000000

Averaged pixel count

Averaged pixel count

2.5

2.5

Bias and RMS difference of LST [K]

1e+07

Bias
RMS
Averaged pixel count

Averaged pixel count

Bias and RMS difference of LST [K]

3

5

10

15

20

25

Averaged pixel countFigure 3.7: LST diﬀerence histogram (Left: 1835Z, Right: 0400Z)

3.3

Quality assurance

3.3.1

Concept

To notice the users about the quality of the product as well as the selection key of the spatial/temporal
integration, the quality assurance (QA) field is necessary. The structure of the QA field of the previous remotesensing data products have their own style. For example, MODIS and LANDSAT 8 show not only the quality

13

but the quality check routine is applied or not. For SGLI/LST case the limitation of the data size, only thequality will be shown. The basic concept of the SGLI/LST QA field is “smaller value is better”, the value ofzero of QA field is the best quality and the larget value of QA field means worse.

3.3.2

QA field bit assignment

SGLI/LST QA field has the single byte length and the bit assignment is shown in Table 3.2. If the bit 4 –7
is 1, the LST and emissivity set to 0. The residual of bit 1 and 2 is the RMS residual between the both handside of the simultaneous equation Eq. (3.1–3.3). From the numarical simulation result (cf. Figure 3.1), thelarge residual (bit 2 is 1) means the residual is larget than 2[K], the fairly large residual (bit 1 is 1) means theresidual is in the range of 1 to 2[K].
Table 3.2: SGLI/LST QA field (Bit 0 means LSB)
Bit Description
7
Non–data (=1)
6Non–land (=1)
5LST is out of range (=1)
4
Cloudy (=1)
3
Probably clear (=1)
Large residual (=1)
2
1
Fairly large residual (=1)
0Transmittance of 11[µm] is below 0.6 (=1)

14Chapter 4

Operation
4.1

Input/Output dataset

The input dataset for LST estimation algorithm are summarized in Table 4.1.

a
b
c
d
e
f

The output dataset are

Table 4.1: The input dataset
DatasetPrecise geometrically corrected radiance (250[m])Pixel wise Latitude and Longitude
Pixel wise scan zenith angle
Cloud flag
Land mask
Nearest time forecasting data (pressure, height, temperature, humidity)

summarized in Table 4.2. These are stored in product HDF file as an independent plane.

A
B
C
D

4.2

Table 4.2: The output dataset
DatasetLand surface temperature
Land surface temperature at 10.8 [µm]Land surface temperature at 12.0 [µm]QA filesData processing flow

The operation mode data processing flow are summarized in Figure 4.1. The precessing time for the single
MODIS scene (Figure 3.3) with JMA forecasting dataset is about 25[sec.]

Precise geometricallycorrected radianceLand mask

Latitude/Longitude
Scan zenith angle
Cloud flag

Numerical forecastingdata (nearest time)

LST estimation

Figure 4.1: The data processing flow

15

QA field
generation

Chapter 5

Validation
5.1

Basic concept of the validation of SGLI LST algorithm

Since the SGLI LST estimation algorithm contains the 2 kinds of algorithm, the split window algorithm for LST
estimation and surface emissivity algorithm, the 2 kinds of validation will be made. The first one is the estimated
LST validation and the second one is the estimated surface emissivity validation. Not only the following 2 kindsof validation, the cross comparison with the other satellite dataset such as NPP and SENTINEL will be made.
Also the higher level products which use the LST product will be the validation factor which shows how does
the LST product make the higher level products more accurate.

5.2

Estimated LST validation

SGLI LST estimation algorithm constructed under the 2 kinds of assumptions, MCSSTT formula can be applicable for the wide range of the blackbody surface temperature and the linear relationship can be establishedbetween the blackbody and non–blackbody observed brightness temperature. In the case that the surface emissivity is small, the second assumption (cf. Eq. (2.5)) is not so accurate by comparing with the accuracy of
MCSST formula (cf. Eq. (2.4)).
The MCSST formula validation for the wide blackbody surface temperature range cannot be made in thenatural condition because the blackbody or near blackbody surface temperature cannot be higher. For thispurpose, the numerical simulation with the truth of the sea surface temperature and the calibration result.
For the estimated surface temperature validation in the low emissivity case, the ground measurement methodof the surface temperature is established [Moriyama and Yano, 2000]. This method is for the bare soil area,
using the wide FOV thermometer [Murayama and Moriyama, 1999] with the concave mirror the actual surface
temperature can be measured without the emissivity measurement [Moriyama, 1999]. This data will be used
for the validation. This kind of ground measurement will be made with the constant period, and using the
ground measurement data and the numerically validated MCSST formula the total LST estimation algorithm
will be validated in the case of the lower surface emissivity surface. This will be the worst case of the SGLI LSTestimation. For the low emissivity case validation, the ground based LST observation synchronous with the
TERRA and AQUA are made from 2000 to 2012 at Railroad valley playa, NV. USA. the comparison between
the ground measured and estimted LST is shown in Figure 5.1. The total number of the data is 36 and the bias
and RMS diﬀerence is 0.6[K] and 2.1[K].

5.3

Estimated emissivity validation

As the estimated surface emissivity validation, the semi–analytical surface emissivity estimation mode will bemade and gather the surface emissivity data with the surface reflectance, the reflectance based surface emissivity
formula will be more accurate. Also as the surface emissivity dataset, ASTER surface emissivity product andthe FTIR sensor derived emissivity [Matsui and Moriyama, 2008] will be used for this purposes.

16

340

Ground measured LST [K]

335
330
325
320
315
310
Res. < 1[K], clear
Res. > 2[K], clear
Res. < 1[K], probably clear
Res. > 2[K], propbably clear

305
300
300

305

310

315

320

325

330

335

340

SGLI LST [K]Figure 5.1: Comparison between the ground measured and the satellite derived LST

17

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