GCOM–C1/SGLI Land Surface Temperature Product
Algorithm Theoretical Basis Document
Masao Moriyama
Nagasaki University
Nagasaki, JAPAN.
May 28, 2020

Contents
1 Introduction

12 LST estimation algorithm
2.1 Physics of the LST estimation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 SGLI LST Split window algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Semi–analytical LST estimation algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Integration of the split window method and semi–analytical method . . . . . . . . . . . .
2.3.3 Numerical validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22244453 Operation
3.1 Input/Output Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 QA plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6664 Validation
4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 LST from longwave radiation measurement at the ﬂux site . . . . . . . . . . . . . . . . . . . . . .

888i

List of Figures
2.1
2.2
2.3
2.4

SGLI TIR channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 types of the split window coeﬃcient sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Regression error of the SGLI lST split window formula (Left: Comparison between model andestimated LST, Right: error histogram) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of the model and estimated LST (Left) and the LST estimation error summary (Right)

4.1
4.2
4.3
4.4

Schematic of the ﬂux site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Flux site used for SGLI LST validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Comparison between the SGLI LST and the longwave radiation based LST . . . . . . . . . . . . 10
SGLI LSTQA (Left), LST(Center) and RGB(Right) around Albuquerque, NM on June 18, 2018 10i33
45

List of Tables
2.1
2.2

Numerical simulation for the split window coeﬃcients deﬁnition . . . . . . . . . . . . . . . . . . .
The semi–analytical method simulation condition . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
53.1
3.2
3.3

The input dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The output dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SGLI LST QA plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

667

4.1

Fluxsites for the SGLI LST validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9ii

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, ATSR oboard the European satellite ESA published the land surface product. The operational land
surface temperature estimation has about 20 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 semi–analytical algorithm with the split–window formula will be described. Andalso 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

LST estimation 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 transferequation.
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 )Fiπ(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.
The previous operational LST products have been made by 2 kinds of algorithm, the split window and thesemi–analytical algorithm. The split window algorithm which is the multiple variable regression of the surface
temperature, emissivity and the observed brightness temperature is used by the wide swath sensor such as
MODIS, AATSR and VIIRS. The precondition of the split window algorithm is the surface emissivity have tobe known. The semi–analytical algorithm which solve the simultaneous formulae of the land leaving radianceat each channel (Eq. (2.2)) and the additional equation is used by ASTER which has 5 spectral channels inTIR region. In the ASTER LST estimation algorithm case the additional equation is the emperical relationshipbetween the statistical variables of the speectral emissivity. The precondition of the semi–analytical algorithm
is the radiometric parameters such as the total transmittance, the path radiance and the downward atmosphericirradiance have to be known.
By comparing the preconditions of the two previous LST estimation algorithm, The radiometric parametercomputation can be made by using the numerical foreacsting data, although the surface emissivity deﬁnition isdiﬃcult. So that the SGLI LST estimation algorithm uses the semi–analytical algorithm which add the split
window formula to the land leaving radiance formulae at two SGLI TIR channels.

2.2

SGLI LST Split window algorithm

As the additional formula of the semi–analytical LST estimation algorithm, the split window formula have tocontain the LST, emissivity and the observed brightness temperature at channels T1 and T2 (cf. Figure 2.1)
explicitly.
To meet the condition of the additional formulae, the following function type of the sploit window formula
is deﬁned.
Ts = A0 + (A1 r1 + A2 )T b1 + A3 r1 + (A4 r2 + A5 )T b2 + A6 r22(2.3)

Figure 2.1: SGLI TIR channels
where T b1 and T b2 are the brightness temperature at channels T1 and T2, As are the regression coeﬃcientsand r are the surface reﬂectivity (ri = 1 − εi , i = 1, 2).
To deﬁne the coeﬃcients, the following numerical simulation (cf. Table 2.1) are made.
Table 2.1: Numerical simulation for the split window coeﬃcients deﬁnition
Profile: ECMWF 2000 Monthly mean proﬁle (averaged over 10 [deg.] latitude interval)
Surface temperature: Air temperature at the surface + 0, 5, 10, 15, 20, 25, 30[K]Average emissivity ε̄: 0.95, 0.96, 0.97, 0.98, 0.99,1
Emissivity wavelength dependence a: -0.5, 0.25, 0, 0.25, 0.5
Observation zenith: 0, 15, 30, 45[deg.]

As the emissivity expression, the average emissivity ε̄ and the emissivity wavelength dependence a as Eq.
(2.4, 2.5) are used.
ε1 + ε22(2.4)

ε1 − ε2, (ε̄ < 1)
2(1 − ε̄)(2.5)

ε̄ =a=

To suppress the regression error of the split window formula, SGLI LST estimation algorithm uses the 3types of the split window coeﬃcient set as shown in Figure 2.2.

Figure 2.2: 3 types of the split window coeﬃcient sets
3

The regression error of the split window formulae are shown in Figure 2.3, Even in the worst case, theregression error is about 1.5[K] and it is suﬃcient for the semi–analytical LST estimation algorithm.

Figure 2.3: Regression error of the SGLI lST split window formula (Left: Comparison between model andestimated LST, Right: error histogram)

2.3

Semi–analytical LST estimation algorithm

2.3.1

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.

2.3.2

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. (2.6 – 2.8)) which contains
the radiative transfer equation which expresses the satellite detected brightness temperature instead of the landleaving radiance.
T b1 = B1−1 [τ1 (ε1 B1 (Ts ) + (1 − ε1 )F1) + Ia1 ]π(2.6)

T b2 = B2−1 [τ2 (ε2 B2 (Ts ) + (1 − ε2 )F2) + Ia2 ]π(2.7)

Ts = (A1 + A2 r1 )T b1 + A3 r1 + (A4 + A5 r2 )T b2 + A6 r2 + A0 (ri = 1 − εi )−1(2.8)where B is the Inverse Planck function. Among this simultaneous equation, the brightness temperature T b1and T b2 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.

42.3.3

Numerical validation

For the accuracy veriﬁcation, the LST estimation using the numerical simulated observed radiance is made.
The simulation condition is listed in Table 2.2. The terminate condition of the iteration scheme is the RMS
residual of the cost function, Eqs. (2.6 – 2.8) or the number of the iteration. If the RMS residual is less then
0.5[K] of the number of the iteration reaches to 10, the computation is terminated.
Table 2.2: The semi–analytical method simulation condition
Atmospheric proﬁleε̄aSurface temperature
Observation zenith
Observation error
Max. iteration number

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]): twice of the nominal value
10The comparison between the model and estimated LST and the error summary under the various RMS
residual and the trasmittance of channel T1 are shown in Figure 2.4.

Figure 2.4: Comparison of the model and estimated LST (Left) and the LST estimation error summary (Right)
From the results, the proposed LST estimation algorithm has the enought accuracy and the RMS residualof the const function and the trancemittance indicate the estimation accuracy.

5

Chapter 3Operation
3.1

Input/Output Dataset

The input dataset for LST estimation algorithm are summarized in Table 3.1.

abcde
fg

Table 3.1: The input dataset
DatasetPrecise geometrically corrected radiance (SGLI LTOAQ: 250[m] resolution)
Pixel wise Latitude and Longitude (To access the numerical forecasting data)
Pixel wise scan zenith angle (in LTOAQ: 250 [m])Cloud ﬂag (SGLI CLFGQ: 250[m] resolution)
Land mask (in LTOAQ: 250[m])Elevation
Nearest time numerical forecasting data (pressure, height, temperature, humidity)(Japan Meteorological Agency Grid Point Value: 6 hours interval, 0.5 [deg.] resolution)

The output dataset are summarized in Table 3.2. These are stored in product HDF ﬁle as an independentplane.

AB
CD3.2

Table 3.2: The output dataset
DatasetLand surface temperature
Land surface emissivity at 10.8 [µm]Land surface emissivity at 12.0 [µm]
QA

QA plane

The QA plane of SGLI/LST product is 2 bytes per pixel. The lower byte contains the information for the level 3data production and the upper byte contains the LST quality related information. The QA plane are descrived
in Table 3.3.
The upper byte of the QA plane is designed as the “Smaller the better concept”, this means the smaller
value of the upper byte shows the more accurate LST product.

6Table 3.3: SGLI LST QA plane
Bit
00
01
02
03
04
05
06
07

Contents
No input data
Land/Water (0: land, 1: water)
Spare
Spare
no VNIRSnowSensor zenith is larget than 33[deg.]
Sensor zenith is larget than 43[deg.]

Bit
08
09
101112131415

7

contents
T1 trancemittance is less then 0.6
The residual is within the range of 1 to 2 [K]The residual is larger than 2 [K]Probably cloudy
CloudyLST is out of range
Land/Water (0: land, 1: water)
No input dataChapter 4Validation
4.1

Overview

By comparing with the ocean buoy data which is used for the sea surface temperature product valition, there
are very few ground measured LST dataset. For SGLI LST product validation, the upward and downward
longwave irradiance data measured at the ﬂux site are mainly used, in addition the ground measured LST dataat the same time of the satellite passing are used.

4.2

LST from longwave radiation measurement at the flux site

For the constant monitoring of the energy and the material ﬂux near the surface, the various instruments are
installed in one place, such place is called the ﬂux site. The schematic of the ﬂux site is shown in Figure
4.2. Among the instruments, some sites install the 4 component radiometer which measure the upward anddownward short and longwave irradiance.

Figure 4.1: Schematic of the ﬂux site
The relationshio of the upward and downward longwave irradiance Lu, Ld the broadband emissivity e andLST are formulated as Eq. (4.1)
Lu = eσT s4 + (1 − e)Ld(4.1)

where σ is Stefan–Boltzmann constant. From the longwave radiation data, LST is computed at the satellitepassing time.
During 2018 to 2019, the ﬂux site in US and Canada listed in Table 4.1 are used for the SGLI LST productvalidation (cf. Figure 4.2). In this case the broadband emissivity is deﬁned as constant 0.98.

8

Table 4.1: Fluxsites for the SGLI LST validation
Name
US–Rls
US–NR1
CA–DBB
US–Ne2
US–Ro5
US–WCr
US–Syv
US–UMB
US–xBR
US–PHM
US–Tw3
US–Tw4
US–Vcp
US–Ses
US–ARM
US–MMS
US–NC3
US–KS3Tile
V04H09
V04H09
V04H09V04H10
V04H11
V04H11
V04H11
V04H12
V04H12
V04H12
V05H08
V05H08
V05H09
V05H09V05H10
V05H11
V05H11
V06H10

Cover
CSH
ENF
WET
CROCRO
DBF
MF
DBF
DBF
WETCROWET
ENF
OSHCRO
DBF
ENF
WET

Name
US–Me6
US–Rws
US–Ne1
US–Ne3
US–Ro6
US–Ro4
US–Los
US–UMd
US–xHA
US–Ho1
US–Tw1
US–Mpj
US–Seg
US–WjsUS–xKZ
US–NC2
US–NC4Tile
V04H09
V04H09V04H10
V04H10
V04H11
V04H11
V04H11
V04H12
V04H12
V04H13
V05H08
V05H09
V05H09
V05H09V05H10
V05H11
V05H11

Cover
ENF
OSH
CRO
CRO
CRO
GRA
WET
DBF
DBF
ENF
WET
ENF
GRA
SAV
GRA
ENF
WET

Figure 4.2: Flux site used for SGLI LST validation
From the ﬂux site data, 1303 truth data are available, and from the comparison between SGLI and truth
LST, it is clarify that the bias error is 0.47[K] and RMS error 2.36[K] (cf. Figure 4.3). It satisﬁes the successcriteria. As the processing example, SGLI LST, QA and RGB composite around Albuquerque, NM on June 18,
2018 are shown in Figure 4.4.

9

Figure 4.3: Comparison between the SGLI LST and the longwave radiation based LSTFigure 4.4: SGLI LSTQA (Left), LST(Center) and RGB(Right) around Albuquerque, NM on June 18, 201810