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Modern Geomatics Technologies and Applications

each LSE estimation method gets a validity according to the root mean square error (RMSE) obtained from the LSE product of
a given sensor from Equation (1).
∑ m (   ) 1
j=1
j
ij
 ( ) = ; ( = 1, … , ; = 1, … , ) = (1)
∑ m j ℎ j [ ( −  )]
j=1
ij
i
(VAvg) CM Sensor
where, εi is the emissivity of the ith pixel for the VAvg method, εij is the coordinate matching of εij and εi which
in this study is obtained by (3) and RMSE is achieved by the comparison of the emissivity of each method with the LSE product
of a given sensor. Indeed, Vj is the validity of the jth method for the whole image pixels. Evidently, each method may have
appropriate potentials, according to its condition and assumption to yield the emissivity of special classes properly. Hence, the
CBVA
emissivity of the ith pixel in class k by the CBVA method, εik , is obtained from Equation (2).

∑ m (   ) 1
kj
j=1
ij
 ( ) = ; (k = 1, … , nC) ℎ = (2)
∑ m kj [ ( − −  )]
j=1
ij
i
CM-k is coordinate matching of εij of
where, WKj is the validity of the jth method for class k, nC is the class number and εij
Sensor CM CM-k
class k and εi which in this study is obtained by (6). It is worthy to note that εij in (3) and εij in (4) should have the
CM-k should be the
same geographic coordinate matching as sensor data. In other words, the spatial and spectral resolution of εij
sensor
same as εi . The corresponding validity in the VAvg (1) and CBVA (2) methods express the impact of the each LSE method
in the knowledge based schemes (i.e. the LSE method with the highest validity has the greatest affect, and vice versa). It is
worthy to note that the VAvg and CBVA methods calculate equal validity for pixels of the whole image and each class,
respectively. It is worth noting that the corresponding validity in VAvg and CBVA methods are dynamic and adaptively are
computed for each individual LSE method in a given scene. In other words, the assigned validity to the individual LSE methods
can change with land cover variation and various individual methods of LSE.
In this study, the LSE product of MODIS (MOD11_L2) was used as the knowledge to calculate the validity. MOD11_L2 is
an LST/E product that has been achieved via the CBEM at 1 km spatial resolution [31].In order to utilizes product of MODIS,
three issues of viewing angle effect, time and coordinate matching against LDCM data should be addressed. In calculating the
weight of methods, the MODIS viewing angle effect on the LSE was skipped. Since, the LSE is almost time invariant, the LSE
of the MODIS product possibly close to the overpass time of LDCM was selected. In the coordinate matching task, the LSE of
LDCM data and LSE product of MODIS must be aggregated to the same spatial and spectral resolution. For spatial resolution,
an area-weighted algorithm is employed according [32] to TIRS of LDCM data. Moreover, the spectral relationship between the
emissivity of the corresponding TIR channels of the LDCM and MODIS data was calculated from Equation (3).
 = 0.9662  ( 10) + 0.0337
{ } (3)
 = 0.9964  ( 11) + 0.0036

TIRS TIRS CM CM
where, ε10 and ε11 of the LDCM data are corresponding to ε 31 and ε32 of the MODIS data, respectively. To solve
(3), the spectral emissivities, including water, vegetation, soil, minerals, man-made and so on (extracted from the University of
California, Santa Barbara (UCSB) MODIS emissivity library) were convolved with the spectral response functions (SRF) of the
corresponding thermal bands of LDCM and MODIS.
3. Materials
3.1. Research area
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The study area is an arid and semi-arid region with an area of 226255 km , which is has various climate types with a diverse
land cover including mixed pixels covered by different vegetation, soil, and rocky types. It lies between latitudes 26° 25'–32°
44'N and longitudes 50° 32'–55° 54'E. The land use/land cover data including seventeen classes and two scenes of LDCM data,
Level 1T, captured on 14 and 21 June 2013 are shown in Fig. 1 (Because the LSE product of Advanced Spaceborne Thermal
Emission and Reflection Radiometer (ASTER) was purchased as validation data in 2013, LDCM data were obtained on the same
date).

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