ich the vegetation index 
i composite of both soil 
an et al., 1994a). The 
smperature pairs, for a 
1 airplane’s tail with the 
(VTT) Trapezoid, 
in Index (SAVI), where 
(4) 
id to be 0.5 for a wide 
ences in soil brightness 
no water available to the plants, 
(T.-TJ 2 =[r.(R 11 -G)/CJt7(l+r a ,/rJ/{A+7(l +r„/rJ}]-[VPD/{A+7(l-f rjrj}], (6) 
where r a is the canopy resistance associated with nearly complete stomatal closure. For saturated bare soil, 
where r c =0 (the case of a free water surface), 
(T.-TJj=[r„(R„-G)/C„] [7/(Д + y)]-[VPD/(Д+7)], (7) 
and for dry bare soil, where r c = 00 (analogous to complete stomatal closure), 
(T,-TJ<=[r.iR^-G)/CJ. (8) 
Monteith (1973) suggested the values of r^ and г ш could be obtained from measurements of stomatal 
resistance (rj and LAI, where 
r^, = r 4 /LAI and t a = r n /LAI, (9) 
where LAI >0. Values of minimum and maximum stomatal resistance (r^ and r„, respectively) are published 
for many agricultural crops under a variety of atmospheric conditions. If values are not available, reasonable 
estimates of ^=25-100 s m' 1 and r B = 1000-1500 s m' 1 will not result in appreciable error. That is, when r c 
is very large or very small (relative to rj, its influence on the magnitude of (T.-TJ in Eqs. (5) and (6) is small. 
2.2. Discussion 
5 
The assumptions associated with the VIT Trapezoid warrant some discussion. First, the VTT Trapezoid is 
based on the premise that measurements of V 0 (fraction of vegetative cover) are linearly related to SAVI. There 
is some evidence that the relation of spectral vegetation indices with V„ is relatively linear over a large range 
of V c values (Huete and Jackson, 1988; Huete, 1988; Moran et al., 1994b), though this relation is not unique 
but rather both crop- and site-specific. Consequently, two sites with the same vegetation cover but different 
vegetation distribution could yield different values of vegetation index. Though issues such as these must be 
addressed in each application of the VIT Trapezoid, the evidence that the relation is nearly linear over a wide 
range of values will suffice here for development and demonstration of the concept. 
Second, one must assume that T,-T. is a linear function of vegetation cover (VJ, canopy-air temperature (T 0 - 
TJ and soil-air temperature (T C -TJ, where 
т.-T. = V 0 (T 0 -TJ + (l-VJOVTJ. (10) 
itween surface-minus-air 
nges from a value of 0.1 
2, it is possible to equate 
This assumption allows straight lines to be drawn between points 2 and 4 and between points 1 and 3 in Figure 
1. This assumption is supported by research results of Kustas et al. (1990), Kimes (1983) and Heilman et al. 
(1981). 
A third assumption that links the VIT Trapezoid to crop water conditions is that, for a given R„, VPD and 
r„ variations in T 0 -T, and T 0 -T. are linearly associated with variations in evaporation (E) and transpiration (Г). 
That is, 
plot of surface-minus-air 
und over one crop under 
a severely water-stressed 
Dare soil surface. In the 
T e , and T,. T„ is the 
ce, and T, is the surface 
the surface is completely 
All temperatures in this 
arts corrected for surface 
T 0 -T. = а+Ь(Г), and (11) 
T 0 -T. = a’+b’(E), (12) 
where a, a’, b and b’ are semi-empirical coefficients. This assumption has been verified for full cover and bare 
soil conditions (Vidal and Perrier, 1989) and remains valid if there are no convective energy exchanges (i.e., 
no coupling) between soil and vegetation. There is some evidence that these exchanges are coupled 
(Shuttleworth and Wallace, 1985), and the sensitivity of the VTT Trapezoid concept to this phenomenon is 
currently being addressed. 
In an operational mode, several more assumptions would make application easier: 
I.' A single value ofR, (measured on-site) can be used in calculations for both bare soil and vegetated targets. 
In many cases, the total difference in for bare soil and full-cover vegetation is less than 1056 of the actual 
value of R, for full-cover vegetation (R.D. Jackson, personal communication). There is other evidence, 
however, that the differences between R„ for bare soil and vegetated fields can be up to 20® (Daughtry et 
al., 1990). Future work should address the computation of bare soil and vegetation R, values using the 
techniques proposed by Jackson et al. (1985), where net radiation is calculated using reflected solar and 
emitted longwave radiation as measured from the remote sensing platform, combined with ground-based 
(5) 
full-cover vegetation with 
meteorological data. 
2.' Values of roughness length (zj and displacement height (dj for computation of aerodynamic resistance (rj 
con be derived from roughness element height or plant height [h (m)J, where z. = 0.13h and d„ — 0.67h 
for both bare soil and mature plants. Brutsaert (1982) suggests that complicated formulations for z„ and d.