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Title
Mesures physiques et signatures en télédétection

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.