1024 
are not necessarily more accurate and are certainly less practical than the zjh and dyh formulations. 
Consequently, he recommends that, in the absence of wind profile data, these relations may be used as a 
first approximation of zand d c . 
3: Soil heat flux (G) can be estimated as a fraction of dependent only upon V c (or SAVI). This assumption 
is supported by research results of Clothier et al. (1986), Kustas and Daughtry (1990) and Jackson et al 
(1987). 
Based on the above-mentioned theory and assumptions, it is possible to compute the vertices of the VIT 
Trapezoid using Eqs. (5)-(8) and measurements of VPD, and U and T. at height z for computation of r,. 
It is also necessary to estimate the following crop-specific values: 
1) Maximum possible plant height and minimum soil roughness [for estimation of z„ and d, in computation 
of rj; 
2) Maximum and minim um possible SAVI for full-cover and bare-soil conditions, respectively; 
3) Maximum possible LAI for computation of r Œ and r^ from r„ and respectively; and 
4) Maximum and minimum possible s to matai resistances (r„ and r^). 
In many cases, these inputs are known or can be reasonably estimated. Since we are dealing only with the 
extremes of the VIT Trapezoid, it is best to make reasonable but liberal estimates in order to describe the 
theoretical limits of the trapezoid such that no measurements will ever extend beyond the boundaries [by 
definition, resulting in values of (ET/ET^ > 1.0 or < 0.0]. 
Two other factors may affect the shape of the VIT Trapezoid in practice. The first is the possible change 
in red and near infrared reflectance of canopies experiencing severe water stress, which would alter limits of 
the upper right region of the trapezoid. The second factor is the thermal emissivity of the composite surface. 
As soils generally have lower emissivities than vegetation, the error in kinetic temperature based on radiometric 
temperature would increase as vegetative cover decreased. If the bare soil emissivity is known, the relation 
between vegetation index and emissivity as described by Van de Griend and Owe (1993) could be used to 
compensate for this error. 
3 - THE WATER DEFICIT INDEX 
3.1. Definition 
The relations presented in Eqs. (5)-(8) imply that variations in T,-T. are associated with variations in 
évapotranspiration (ET). Thus, it follows that for a partially-vegetated surface, 
WDI = 1-ET/ETp = [(T.-TJ p -(T.-TJ r ]/[(T.-TJ p -(T.-TJJ, (13) 
where WDI is the Water Deficit Index (a term coined here for this relation), ET is the évapotranspiration rate 
of the surface, ET p is the potential évapotranspiration rate, and the subscripts p, x and r refer to the minimum, 
maximum and measured values, respectively. The WDI is operationally equivalent to the CWSI for full-cover 
canopies, where measurement of T,=T 0 . Graphically, WDI is equal to the ratio of distances AC/AB in Figure 
1. Thus, WDI=0.0 for well-watered conditions and WDI = 1.0 for maximum stress conditions. 
3.2. Demonstration 
The WDI was verified with actual ground-based measurements of crop stress by Moran et al. (1994a). WDI 
will be demonstrated here as a tool for irrigation management using aircraft-based measurements of T, and 
SAVI of an alfalfa field at The University of Arizona Maricopa Agricultural Center (MAC), located 40 km 
south of Phoenix, Arizona. The aircraft was flown at 100 m above ground level over each field. The red, near 
infrared, and thermal radiometers had fifteen degree fields of view and pointed normal to the surface. Data 
for one harvest cycle and two sites (A and B), each consisting of 120 m transects, were processed for analysis. 
A comparison of the T,-T, and SAVI data for the two sites within the alfalfa over the harvest period 
illustrates the sensitivity of these measurements to irrigation practices and vegetation growth (Figures 2a and 
2b). Theoretically, for a constant SAVI value, the proximity of any point to the left or right limits of the 
trapezoid would indicate more or less évapotranspiration, respectively. On day of year (DOY) 213, the SAVI 
and T.-T. of sites A and B were very similar. By DOY 229, site B had been irrigated and site A had not. This 
resulted in a shift of site B data upward and to the left within the trapezoid, indicating a slight increase in 
vegetation and substantial decrease in T,-T, from DOY 213. Site A was irrigated with the same amount of 
water a couple of days later. However, it is apparent that the surface temperature of site A remained higher 
(and the SAVI remained lower) than that of site B for the next two weeks. This lag at site A could be an 
indication of lower plant biomass due to the late irrigation. Finally, by DOY 271, the two sites within the field