Télédétection et ressources en eau/Remote sensing and water resources
307
T
r r T r r T r r T
r r r r r r
O
a g v
a v g
v g a
a g
a v
v g
=
+
+
+
+
(6)
B Determination
If a g is the fractional ground area, observed from the nadir, the measured infrared surface
temperature T s may be expressed as:
T s = T g a g +(1- a g ) T v
(7)
and we can write:
T s -T a = (T o -T a ) + a g (T g -T o ) + (T v -T o ) (1-a g )
(8)
Substituting (5) into (8) we have:
T s -T a = T o -T a + a g [ (rg/ra) (T o -T a ) - (rg/rv) (T v -T o ) ] + (1-a g ) (T v -T o )
(9)
For bare soil a g = 1 and r v → ∞.Thus:
T s - T a = (1+ rg/ra) (T o - T a )
(10)
If the canopy is fully closed a g = 0. This yields :
T s - T a =(T o - T a ) + (T v - T o )
(11)
that is, the measured surface temperature T s is equal to the foliage temperature T v , but T v is not
necessarily equal to T o .
Arranging equation (9)we have :
T s - T a = (T o - T a ) [1+ag (rg/ra)]+ [1 - a g -ag (rg/rv) (Tv - To)]
(12)
Using the concept of equivalent resistance, r a *, equation(4) can be written as:
ρ Cp (To - Ta) / ra= ρ Cp (Ts - Ta) / ra*
(13)
Substituting (12) into (13) we have:
(
)
(
)
T T
r
T T
r
r
T T
a a
r
r
r
o
a
a
o
a
g
a
v
o
g
g
g
v
a
− =
−
+





 +
−
− −






1
1
*
(14)