where a ' is an accumulated proportionality constant. SAVI is the Soil Adjusted Vegetation Index defined as,
SAVI - [ ( p - p R££>) I ( p njr + p ppn + L) ] ( 1+L ) (6)
where p and p are the near-infrared and red reflectance factors, respectively, and L is assumed to be
0.5 for a wide variety of LAI values (Heute 1988). Since we assume that the "potential" daily transpiration Tr
is proportional to the ARs / A , it is expressed as,
Tr p = a SAVI Rs (7)
where a is a coefficient including a ' and the latent heat of vaporization A .
Next, we can estimate the "actual" daily transpiration rate (Tr a ) by combining this concept with the
Jackson-Idso Crop Water Stress Index (CWSI; Idso et al. 1981, Jackson et al. 1981). The CWSI is proposed as
an indicator of crop water status, and CWSI values can be calculated based on canopy and air temperatures (t c
and t f ) and vapor pressure deficit (VPD). The CWSI for plants is defined theoretically as CWSI = 1 - Tr a / Tr p ,
which is discussed in detail in the next section. Therefore, Tr a can finally be estimated by,
Tr t = a SAVI Rs (1-CWSI) (8)
based on the combination of remotely sensed spectral and infrared thermal measurements with sound physical
foundation.
2*2 Evaluation of CWSI
A number of scientists have examined the CWSI and/or related methods for various crops over a wide range of
environmental conditions and confirmed the effectiveness of such methods (e.g., Diaz et al. 1983, Hattendorf et
al. 1988). The usefulness and limitations of the CWSI are summarized by Jackson (1982), O' Toole et al.
(1984), Hatfield (1990), and Choudhury (1989) .
According to Jackson et al. (1981), CWSI was expressed theoretically as
CWSI =1-E/E p = [( 7 (l + r c / V7 )- 7 *]/[A +7 (l + r a / r c )] (9)
where r c / r a = [( y r a Rn c / (Cv) - (t c -t a X y + A ) - VPD] / [ y {( t c -t a ) - r a Rn c / (Cv)}], E and E p are the actual and
potential évapotranspiration, y is the psychrometric constant, y * is y (1 - r^ / r a ), r and r a are the
canopy resistance at the potential transpiration and the aerodynamic resistance, respectively, A is die slope of
the saturated vapor pressure versus temperature curve, VPD is the vapor pressure deficit (kPa), and Cv is the
volumetric heat capacity of air. Although CWSI is expressed as 1 - E / Ep in Eq.9, as Jackson (1982) warned,
"it is important that the soil background not appear in the field of view of the infrared thermometer. Plant
temperature only is desirable for the calculation of CWSI", as the CWSI is calculated with an assumption that
the surface is full-vegetation canopy. In other words, CWSI can be expressed as 1 - T / T p in his context
because the difference between E and T is minor for full-vegetation canopy. This is the main reason why
application of the CWSI has been hampered by the difficulty of measuring foliage temperature in partially-vegetated
fields.
All input parameters necessary for CWSI can be computed using theoretical and/or empirical equations.
As for the aerodynamic resistance which is one of the most important parameters in the above equation, a
variety of published equations are available, ranging from simple (a function of wmdspeed (u) only; e.g., Thom
and Oliver 1977) to quite rigorous (accounting for atmospheric stability and based on values of u, the surface
and air temperature difference, surface "aerodynamic" roughness, and other parameters; e.g., Kustas et al.
1989). Further improvements of the index have been suggested for extending its applicability or for simplification
(Clawson et al. 1989, Moran et al. 1993).
3. EXPERIMENTAL DATA FOR AN INITIAL TEST
Two data sets were used for an initial test of the method; 1) an experiment in an alfalfa field at the U. S. Water
Conservation Laboratory, Phoenix in 1985, and 2) an experiment in a semi-arid rangeland (Walnut Gulch
Experimental Watershed) near Tombstone, Arizona, in 1992. Methods and results from these measurements
have been presented by Moran et al. (1989, 1993) and Kustas et al. (1991), respectively. Because actual
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