IEEE Geoscience and Remote Sensing Magazine - September 2021 - 114

time [21]. Satellite-derived LST is based on Planck's law
[22], which states that total radiative energy emitted by the
ground surface or subsurface increases with an increase
in temperature.
Using the radiative transfer equation and assuming a
cloudless atmosphere in local thermodynamic equilibrium,
the channel infrared radiance Iobs received by a sensor at the
top of the atmosphere can be written as [6]
IB TR R
RR
= mm satsl..+- m
(, )( ,)
1
+
++ sl
at-is
the surface emissivity, (),BTs
m
obs(, )( )( (, )[ ]( (, )( ,)))
(1)
mx mm m
mm
ii ff ii
ii
where m is the wavelength, i is the satellite viewing angle,
fm
describing radiance emitted at surface temperature ( ),Ts
is the downward solar diffusion radiance, Rat .
xim
is the upward path solar radiance.
,
is the Planck function
Rsl .
is the downwelling
thermal irradiance, () is the atmospheric transmittance,
Rat - is the upward atmospheric thermal radiance,
and Rsl -
Equation (1) shows that retrieval of LST from satellite
TIR data depends on surface parameters such as emissivity,
surface conditions such as heterogeneous and nonisothermal
factors, and atmospheric effects such as water vapor and
clouds [23]. These are responsible for the lack of clarity in the
physical meaning of satellite-derived LST, whereas the atmospheric
effects make TIR-based retrieval algorithms favorable
only for images observed under clear-sky conditions [24].
The definition of satellite-derived LST for heterogeneous
and nonisothermal surfaces is still controversial [23]. Although
several classical retrieval methods, such as split-window,
mono-window, and single-channel algorithms, have
MODIS LST
AMSR-E LST
1 January 2011
Landsat LST
been widely used to generate LST data with acceptable accuracy
[6], invalid values of cloud pixels have been observed
in LST images.
Conversely, PMW data penetrate clouds, making all-sky
subsurface temperature retrieval possible in cloudless and
cloudy conditions based on various approaches, such as
empirical and physics-based methods and neural networks.
However, such techniques have ambiguous physical mechanisms
and assumptions regarding the land surface emissivity
and atmospheric effects, which reduces the feasibility of
measuring and the accuracy of subsurface temperatures [6].
Moreover, subsurface temperatures retrieved from PMW data
show an average value of the soil temperature from the land
surface to a particular depth beneath the surface and differ
from TIR LST obtained at several microns of depth. A conversion
model developed to consider the thermal conductivity
equation of soil would offer strong potential for the PMW LST
data to match the LST value of TIR images.
As an important variable, LST can also be derived from
the surface energy balance (SEB) equation by identifying the
surface-related energy components [10]. Over the land surface,
the SEB formula is applied as follows:
GS FH LEnn
where G is the ground heat flux, Sn
= --- ,
(2)
is the net solar (or shortwave)
radiation derived from incoming shortwave radiation
minus outgoing shortwave radiation, Fn
reflects upwelling
longwave radiation minus downwelling longwave radiation,
and H and LE denote the sensible and latent heat
flux, respectively.
LST Products
2 January 2011
Spatial
Discontinuities
Low Spatial Resolution
(a)
Low Temporal Resolution
Spatially Continuous and High
Spatiotemporal Resolution
(b)
FIGURE 1. (a) A comparison of spatially discontinuous LST data and that of low spatial and temporal resolution. (b) An example of spatially
continuous LST at high spatiotemporal resolution.
114
IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE SEPTEMBER 2021
Time Dimension
IEEE Geoscience and Remote Sensing Magazine - September 2021

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