779 
ie up of shrubs 
bution of each 
ffective surface 
i entire surface 
ited as an area 
Where T s is the temperature of the "illuminated "soil and r a 2 is the aerodynamic resistance 
of the compartement 2 . 
In this study we can legitimately consider that the surface heterogeneities do 
not exceed the turbulent mixing scales, therefore, the Atmospheric Boundary Layer (ABL) 
responds only to the composite surface structure. Thus, the atmospheric forcing parameters 
can be considered as constant over the entire surface (Raupach, 1991; Koster and Suares, 
1992). By assuming also that horizontal transfer are very small compared to vertical one, so 
that the inter compartments advection can be neglected, the total sensible heat flux can be 
is of effective 
formulated as an area weighted sum of those emanating from each compartment (Chehbouni 
etal., 1993): 
H = fHi + (l-f)H2 ( 6 ) 
:ssure (J/kg/K), 
r e ff (s/m) are, 
sible heat flux 
Where f and 1-f, are the fraction covered by the compartements 1 and 2 respectively. 
By matching Eqs 1, 2, 5 and 6 , effective surface temeprature and effective surface resistance 
to heat transfer can be derived as: 
Mai 
M = (7) 
fra 2 + (\-j)rc 
.rtment can be 
iting from this 
i be writen as: 
TV = fr“ 2T * + ( l ~ f )n ' Ts ( 8 ) 
fra 2 + (]-f)re 
1 stance to heat 
arameters are 
The above equations show that, the effective resistance can be represented by an area- 
weighted parallel sum of all the resistances of individual compartments, and the weighting 
factors for the temperature depend on the resistances of the individual compartments. 
It can be seen from Eqs 3 and 7, that the estimation of effective surface 
temperature requires three different temperatures (i.e., Tf, T s f, T s ). Since only T s and Tf 
were measured at the field, we have to develop a means to determine the temperature of the 
substrate under the canopy (T s f). Recent studies (Humes et al., 1993) showed that in arid and 
semi and regions, this temperature is most likely to oscillate between air and canopy- 
temperatures. Therefore it was assumed here that the temperature of soil under the shrubs is 
equal to the temperature of the shrubs: 
Tsf=T f (9) 
espectively, r a f 
ic resistance of 
2 1 Surface resistances 
>ily formulated 
The present model uses the Choudhury and Monteith (1988) formulations 
with minor modifications to compute the canopy and the substrate under the canopy 
resistances. The bulk boundary-layer resistance of the canopy was defined as : 
a»Jw/u(h) 
Kaf ~ ~ r ,. l[2cco{\ exp( oth/ 2 ))] ( 10 ) 
2 LAI 
where u(h) is the wind speed (m/s) at the canopy height obtained from the classical log- 
profile relationship. LAI is the actual Leaf Area Index of the shrubs, assumed to be uniform