# Optical and Thermal Remote Sensing for Monitoring Agricultural Drought
## 3 Thermal Remote Sensing
### Temperature-Based Drought Indices  
To retrieve parameters such as thermal inertia or ATI, diurnal surface temperature changes have to be determined. However, many widely used thermal sensors do not provide nighttime data products, e.g., Landsat-8 [180], limiting the application of thermal inertia to sensors that offer day-night observations, e.g., MODIS [181]. To monitor drought severity from a single thermal observation, additional information is needed. [PERSON] [102] used the maximum and minimum changes in surface temperature to monitor agricultural drought and constructed the TCI by using a long time-series of daytime LST:  
\[\text{TCI}=100\frac{T_{\text{max}}-T}{T_{\text{max}}-T_{\text{min}}} \tag{12}\]  
where \(T\) is the smoothed weekly temperature, and \(T_{\text{max}}\) and \(T_{\text{min}}\) are the multi-year maximum and minimum. Originally, the brightness temperature is used as \(T\) for simplicity [102; 182], while LST is used instead in the most recent literature to exclude the influence of the atmosphere [183; 184; 185]. Similar to VCI, TCI weakens the impact of the uncertainty of the relationship between drought and LST on drought assessment by integrating historical data as a reference [186]. The advantage of TCI is that its calculation is simple and requires lower temporal resolution than thermal inertia or ATI. Nevertheless, the calculation of TCI requires accumulating a long time series of surface temperature data that must include extremely dry and wet conditions to ensure representativeness. In addition, seasonal variation in surface temperature influences TCI. In different seasons, the same drought conditions can lead to different TCI values, which adds to the uncertainty of TCI [187]. [PERSON] et al. [188] and [PERSON] et al. [189] constructed the Normalized Difference Temperature Index (NDTI) by applying daytime surface temperatures obtained from the Advanced Very High Resolution Radiometer (AVHRR) to eliminate the influence of seasonal changes. The NDTI is defined as:  
\[\text{NDTI}=\frac{T_{\infty}-T_{\text{s}}}{T_{\infty}-T_{0}} \tag{13}\]  
where \(T_{\infty}\) is the LST when the composite surface resistance \(r_{\text{s}}\) is infinity and the evapotranspiration (ET) is zero, \(T_{\text{s}}\) is actual LST, \(T_{0}\) is the LST when \(r_{\text{s}}\) is zero and the ET is equal to the potential ET. The actual LST can be obtained through thermal remote sensing, and the LST under boundary conditions can be obtained by inverting a resistance energy balance model (REBM) [190]. In contrast to TCI, NDTI does not need a long time series: only a single observation phase is required for calculation. NDTI does not suffer from seasonal changes and is a close approximation to soil moisture availability. Given the latter characteristic, NDTI can be used as an easily calculable surrogate for moisture availability in drought monitoring [187]. The simulation of LST under boundary conditions, however, relies on high-resolution meteorological parameters. Thus, the application of the NDTI is limited because meteorological data associated with satellite observation times are often difficult to obtain. When the temporal resolution of surface temperature data is no longer an issue, as in the case of geostationary satellites, [PERSON] et al. [191] proposed a new index called the Temperature Rise Index (TRI), defined as:  
\[\text{TRI}=\frac{(\text{d}T/\text{d}t)_{\text{max}}-(\text{d}T/\text{d}t)_{i} }{(\text{d}T/\text{d}t)_{\text{max}}-(\text{d}T/\text{d}t)_{\text{min}}} \tag{14}\]in which \(\mathrm{d}T/\mathrm{d}t\) is the slope of the LST-time fitting line for the observations within the time span of 1.5-3.5 h after the sunrise. Furthermore, \((\mathrm{d}T/\mathrm{d}t)_{i}\) is the average value for a compositing period, and \((\mathrm{d}T/\mathrm{d}t)_{\mathrm{max}}\) and \((\mathrm{d}T/\mathrm{d}t)_{\mathrm{min}}\) are the maximum and minimum for the same period among multiple years.