1022
a more thorough understanding of this relationship was deemed necessary.
A new theoretical concept was developed to delimit the two-dimensional space in which the vegetation index
of a unit area (such as an image pixel) is plotted against the surface temperature T, (a composite of both soil
and plant canopy temperatures) min us air temperature (TJ of the same unit area (Moran et al., 1994a). The
space occupied by all possible combinations of vegetation index/surf ace-min us-air temperature pairs, for a
particular crop and a given set of meteorological conditions, is shaped somewhat like an airplane’s tail with the
leading edge to the right (Figure 1), and is termed the Vegetation Index/Temperature (VIT) Trapezoid.
The spectral vegetation index used in this analysis was the Soil-Adjusted Vegetation Index (SAVI), where
SAVI = (Pira“PfoiV(PNiR"*"P«
and and p^ are the near-IR and red reflectances, respectively, and L is assumed to be 0.5 for a wide
variety of leaf area index (LAI) values. The SAVI is relatively insensitive to differences in soil brightness
(Huete, 1988).
Ts-Ta (C) 2
Figure 1. The hypothetical trapezoidal shape that would result from the relation between surface-min us-air
temperature (T.-TJ and the soil-adjusted vegetation index (SAVI), which generally ranges from a value of 0.1
for bare soil to 0.8 for a complete canopy. For a SAVI-(T.-TJ pair located at point C, it is possible to equate
the ratio of actual to potential ET with the ratio of distances CB and AB.
2 - THEORY
2.1. Definition of Trapezoid Vertices
Physical energy balance equations were used to define the vertices of VIT space in a plot of surface-minus-air
temperature (T.-TJ versus SAVI that described the four extreme cases that can be found over one crop under
a particular set of meteorological conditions: (1) a well-watered complete canopy, (2) a severely water-stressed
complete canopy, (3) a water-saturated bare soil surface, and (4) a completely dry bare soil surface. In the
following discussion it is useful to keep in min d the differences between the terms T„ T 0 , and T,. T„ is the
foliage or crop canopy temperature, T„ is the temperature of an exposed soil surface, and T, is die surface
composite temperature; a weighted average of soil and foliage temperatures. When the surface is completely
covered with vegetation, T, = T„, and when the surface is bare soil, T, = T c . All temperatures in this
discussion are assumed to be kinetic values, with radiometric temperature measurements corrected for surface
emissivity.
For full-cover, well-watered vegetation,
(T.-TJ, = [r.(R,-G)/CJ[y(l + VrJ/{A+y(l + VrJ}]-[VPD/{A+y(l + r^rj}], ®
where and the subscript n of (T.-TJ, refers to the vertex number in Figure 1. For full-cover vegetation with
