# Optical and Thermal Remote Sensing for Monitoring Agricultural Drought
## 2 Optical Remote Sensing
### Spectral Indices as Drought Indicators
Due to the saturation of NDVI in the case of dense vegetation and its sensitivity to the soil background, a series of new vegetation indices have been proposed, such as the Soil Adjusted VI (SAVI) [68], the Atmospherically Resistant VI (ARVI) [69], the Enhanced VI (EVI) [70; 71], and the Inverted Difference VI (IDVI) [72], but none of these indices have taken the place of NDVI in agricultural drought monitoring. An alternative way to combine the information from multiple bands is the reflectance space, i.e., building a linear space with the spectral reflectance of each band. Figure 5 gives a sketch of the NIR-Red reflectance space. When enough vegetation and soil pixels are gathered in the plot, the outline of the points corresponding to the pixels will form a triangle. The points of bare soil pixels tend to form a line in this plot called the soil line. Based on the NIR-Red reflectance space, [PERSON] and [PERSON] [73] first established the Perpendicular Vegetation Index (PVI), which is the vertical distance from an observed point to the soil line. [PERSON] et al. [74] further found that the two-dimensional NIR-Red space is related to the characteristics of land cover and soil/vegetation water: the lower-left edge of the triangle represents the water-saturated status and the upper-right edge represents the extremely dry status, while the parallel lines of the soil line correspond to different vegetation covers. Based on this finding, [PERSON] et al. [75] proposed the Perpendicular Drought Index (PDI):  
\[\text{PDI}=\frac{1}{\sqrt{M^{2}+1}}(\rho_{\text{Red}}+M\rho_{\text{NIR}}) \tag{5}\]  
where \(M\) is the slope of the soil line. As is shown in Figure 5, PDI is the vertical distance from an observed point to the perpendicular line of the soil line which crosses the origin. PDI proves to be highly effective in soil moisture estimation over bare soil. To compensate for the effect of vegetation cover, [PERSON] et al. [76] further introduced the concept of vegetation coverage and proposed the Modified PDI (MPDI) to resolve this limitation:  
\[\text{MPDI}=\frac{1}{1-\text{FVC}}(\text{PDI}-\text{FVC}\cdot\text{PDI}_{\text {v}}) \tag{6}\]  
where FVC is the fractional vegetation cover, and \(\text{PDI}_{\text{v}}\) is the PDI value for fully covered vegetation, which is often taken as an empirical value. In this way, mixed pixels in the NIR-Red space are decomposed to obtain pure soil information. The MPDI can be applied to various land cover types and hydrothermal conditions and has a clear biophysical meaning. Moreover, it does not require complex calculations and can be easily interpreted. [PERSON] et al. [77] analyzed Landsat-derived MPDI and long-term Climatic Water Deficit (CWD) data for the year 2014 to evaluate the impacts of the 2014 California drought on forest and agriculture ecosystems in California, U.S. The results demonstrated that MPDI is an effective and direct method to monitor vegetation stress and forest declines at the landscape scale and provide land managers and stakeholders with forest management and planning guidance. To avoid the determination of \(\text{PDI}_{\text{v}}\), [PERSON] and [PERSON] [78] proposed the second Modified Perpendicular Drought Index (MPDI1):  
\[\text{MPDI1}=\sqrt{\text{PDI}^{2}+\text{PVI}^{2}} \tag{7}\]  
which equals segment DF in Figure 3:0 [PERSON] et al. [79] proposed the Ratio Dryness Monitoring Index (RDMI), which is defined as the ratio of the segment PE to the segment PQ in Figure 3:1 These two new indices can be directly obtained from the NIR-Red reflectance space, but more evaluations are required to compare their feasibilities with MPDI. Attempts have also been made to develop indices that utilize SWIR bands, which are more sensitive to water content [80,81]. [PERSON] [57] established the Normalized Difference Water Index (NDWI) based on a NIR band (860 nm) and a SWIR band (1240 nm). The NDWI can sensitively reflect canopy water levels because water absorption is enhanced by canopy decentralization.