# Optical and Thermal Remote Sensing for Monitoring Agricultural Drought
## 4 Combination of Optical and Thermal Remote Sensing
### The Concept of Temperature-Vegetation Space  
Simple integrations like VSWI or VHI are easy to apply while lacking a solid physical foundation, and thus cannot be theoretically interpreted. Emerging for the first time in the 1990s, the Temperature-Vegetation space (also called LST-FVC or LST-VI space in other literature; here, LST is short for Land Surface Temperature, and FVC is short for Fractional Vegetation Cover) is considered to be a vital tool for estimations of surface energy fluxes and soil moisture [209]. As the name suggests, the space leverages both LST from thermal observation and vegetation conditions, usually from optical remote sensing. The basic idea is that LST, and, by association, the surface turbulent energy fluxes, are sensitively dependent on soil moisture and water fluxes [PERSON] [200], and this dependence can be modulated by vegetation through the process of transpiration [PERSON] et al. [210]. Practically, the space appears when drawing LST-FVC or LST-VI pairs obtained from a remotely sensed image as a scatter plot. Since the outline of the scatter plot is usually a triangle or a trapezoid, the Temperature-Vegetation space is also called the triangle or trapezoid space. Simulations using several soil/vegetation/atmosphere transfer (SVAT) models also strongly support the existence of such a triangular or trapezoidal outline [200; 211]. Figure 7 conceptually illustrates the evolution of the understanding of the Temperature-Vegetation space. The most significant properties of the Temperature-Vegetation space are the wet edge and the dry edge, which are the lower and the upper boundary of the triangle or trapezoid, respectively. In some literature, e.g., [PERSON] [200], the wet edge is also called the cold edge, while the dry edge is also called the warm edge. The difference between the triangle and the trapezoid lies in the temperature variation under full vegetation coverage. In the triangle (Figure 7a), vegetation transpiration is considered to occur at near potential regardless of the surface soil moisture, so there is no temperature variation when a pixel is fully covered by vegetation (\(T_{\text{v}}\) is a constant). This assumption precludes any analysis of the water stress on vegetation [200]. In the trapezoid (Figure 7b), however, vegetation is no longer considered to be unaffected by soil moisture variation. Thus, there is temperature variation from \(T_{\text{v}}^{\text{min}}\) to \(T_{\text{v}}^{\text{max}}\) even under full vegetation coverage. Recently, a two-stage explanation of the Temperature-Vegetation trapezoid has attracted much attention. Conventionally, the sloping straight lines connecting quantile points on the left and the right border of the trapezoid (dashed lines in Figure 7b) are considered to be soil moisture availability isopleths, based on the assumption that soil evaporation and vegetation transpiration change synchronously. Nevertheless, due to the difference in their direct source (surface soil moisture for soil evaporation and root-zone soil moisture for vegetation transpiration), this assumption can hardly hold [211]. In the two-stage trapezoid(Figure 7c), however, it is assumed that soil evaporation varies first, while vegetation transpiration does not start to change until the surface soil moisture availability drops to 0 (\"Dry Edge I\" in Figure 7c). Thus, points which fall below the Dry Edge I have near-potential vegetation transpiration, while points above Dry Edge I have minimum soil evaporation. In this way, both surface and root-zone soil moisture availability can be obtained. According to [PERSON] [211]'s simulations (Figure 4 in the same paper), although there are still some mismatches, the two-stage explanation better reflects the variation of surface and root-zone soil moisture. No matter which hypothesis is chosen (triangle, trapezoid, or two-stage trapezoid), once the outline is determined, the soil moisture availability of a given \((\text{FVC},T)\) pair can be easily calculated. Therefore, the primary issue is to determine the outline.