# Optical and Thermal Remote Sensing for Monitoring Agricultural Drought
## 3 Thermal Remote Sensing  
### Thermal Properties of Crops and Soil  
Thermal infrared sensors mainly receive the thermal radiation emitted by the Earth itself, and its amplitude is related to the land surface temperature (LST) and land surface emissivity (LSE):  
\[L(\lambda,T)=\int_{\lambda_{1}}^{\lambda_{2}}\epsilon_{\rm s}(\lambda)\mu( \lambda,T)h(\lambda)\mathrm{d}\lambda \tag{9}\]  
where \(T\) is the LST, \(\lambda\) is the wavelength, \(L(\lambda,T)\) is the spectral radiance received by a thermal sensor, \(\epsilon_{\rm s}(\lambda)\) is the LSE, which is a function of \(\lambda\), \(\mu(\lambda,T)\) is the Planck function, and \(h(\lambda)\) represents the spectral response function. The integral of \(\mathrm{d}\lambda\) is done within the sensitive range \([\lambda_{1},\lambda_{2}]\) of the sensor. Thus, parameters, such as surface temperature and surface emissivity, can be retrieved after radiation calibration and atmospheric correction of the thermal radiation signal received by the spaceborne thermal infrared sensor. It should be noted that LST is a skin temperature, reflecting the temperature of the top 1-2 mm of the soil for bare surfaces [155; 156]. Under severe water stress, the evaporation of soil remarkably declines [157]. Meanwhile, the decrease of the stomatal conductance of crop leaves leads to the inhibition of \begin{table}
\begin{tabular}{l l l l} \hline
**Mission** & **Sensor** & **Time Range** & **References** \\ \hline \multirow{3}{*}{Greenhouse gases Observing SATellite (GOSAT)} & Thermal And Near-infrared Sensor for carbon & \multirow{3}{*}{2009–Now} & [142; 143] \\  & Observation Fourier Transform Spectrometer & & \\  & (TANSO-FTS) & & \\ \hline GOSAT-2 & TANSO-FTS/2 & 2018–Now & [144] \\ \hline \multirow{3}{*}{Meteorological Operational satellite (MetOp)} & Global Ozone Monitoring Experiment-2 & \multirow{3}{*}{2006–Now (MetOp-A); 2012–Now (MetOp-B); 2018–Now (MetOp-C)} & \\  & (GOME-2) & & \\ \hline \multirow{3}{*}{Environmental Satellite (EnviSat)} & SCanning Imaging Absorption spectroMeter for & \multirow{3}{*}{2002–2012} & [146; 147] \\  & Atmospheric CHartographY (SCIAMACHY) & & \\ \hline \multirow{3}{*}{Orbiting Carbon Observatory (OCO-2)} & Medium Resolution Imaging Spectrometer & \multirow{3}{*}{2014–Now} & \multirow{3}{*}{[148]} \\  & (MERIS) & & \\ \hline \multirow{3}{*}{Sentinel-5 Precursor (S-5P)} & PROPOspheric Monitoring Instrument & \multirow{3}{*}{2017–Now} & [149] \\  & (TROPOMI) & & \\ \hline \multirow{3}{*}{Carbon Dioxide Observation Satellite (TanSat)} & Atmospheric Carbon dioxide Grating & \multirow{3}{*}{2016–Now} & [150; 151; 152] \\  & Spectrometer (ACGS) & & \\ \hline \multirow{3}{*}{FLUorescence EXplorer (FLEX)} & FLuORescence Imaging Spectrometer (FLORIS) & 2024 (Planned) & [153; 154] \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of satellite missions capable of solar-induced chlorophyll fluorescence measurements. transpiration [158; 159]. The decline of evapotranspiration thus contributes to the rise in the observed LST. Moreover, the difference between the leaf/canopy temperature and the air temperature also increases [160]. LSE is also affected by soil moisture. Experiments [161; 162] show that the LSE of soil can increase up to 16-17% after wetting; the change varies for different soil types. [PERSON] et al. [163] further shows that it is possible to retrieve soil moisture from LSE with a standard estimation error of about \(\pm 0.08\) m\({}^{3}\cdot\) m\({}^{-3}\), but this method depends on known organic matter content and thus is not feasible for remote sensing use. Another important thermal property of the land surface is the thermal inertia, which is defined as follows:  
\[P=\sqrt{K\rho c_{\rm P}} \tag{10}\]  
where \(P\) is the thermal inertia, \(K\) is the thermal conductivity, \(\rho\) is the density, and \(c_{\rm P}\) is the specific heat at a constant pressure [164; 165].