## Biodiversity Reserve

5.1 Application of the Radiative Transfer Equations Inside the Oasis

A vegetation canopy is a porous medium for the radiation. In more specific term it is considered as semi-transparent to solar radiation. At macro-scale, the plants intercept a part of the incoming radiation and diffuse (ascendant flux and descendant flux) the others. This is done by the participation of all the vegetation components (leaf, fruit, branch, trunk). At micro-scale (molecule level) the plant canopy absorb a share of the incident radiation and diffract (reflection and transmission) the rest. The farming canopy is accounted as participating environment for solar radiation. The oasis that is expanded over a vast region can be treated as homogeneous, participating and fluid medium where the solar radiation arrives at any point in all directions from the atmosphere. For such a medium the most used equation to describe the radiative transfer is (Lopez and Semel 1999; Kryzhevoi et al 2001):

^)+Kv(s,t)®Q,v(s,t)+ov(s,t)\$Q,v(s,t)=0Vv(s,t)^av(s,t) j>(a^Q)Oa,,v(s,t)Q

®Qv is the spectral specific intensity of radiation v is the frequency of the radiation Q is the direction of propagation s is the position t is the time

Kv is the spectral volumetric absorption ov is the spectral diffusion terms 0Jv(s , t) the spectral emission terms

P(Q) is the scattered radiation angular distribution function (phase function)

If we consider the solar radiation as source, the second term on the left represents the amount of solar radiation absorbed by the vegetation at any position s and any time t. It is analogues to the part of radiation intercepted. The third term on the left represents the radiation scattered out the oasis, it is equivalent to the solar radiation reflected by a vegetation layer or to that ascendant at any level of the oasis. The first term on the right express the spectral radiation emitted by the components of the oasis canopy (leaves, branch, trunk). The second term on the right show the scattering phenomenon inside the studied environment. For the oasis, an important part of the incident solar radiation will undergo a multiple re-diffusion to be arrested later by the vegetation elements. This radiation is putted on by the phase function. It can be considered as the radiation path or the optical depth.

If we assume some hypothesis related to the vegetation properties (homogeneous or pseudo-homogeneous), integrating the above equation from the entrance of the canopy to a point inside located by leaf area index, and after summing on all direction in space, we can express the solar radiation intensity by the following general expression (Lopez and Semel 1999; Kryzhevoi et al 2001):

Ov=J <&o,v(&,ç>,t)exp - j^s,t)ds q dQdv

O0v(Q,t) is the radiation intensity at the top of the farming

Q(0,9) is the solid angle over which we have integrated for all possible directions (0, 9) of the incoming radiation from the atmosphere.

s=sr

This radiation must be absorbed or intercepted by a material point or a vegetation layer inside the oasis. Consequently, it represents the amount of spectral incident radiation really used by plants in photosynthetic activity (agricultural productivity and biomass production) or for transpiration (water consumption). Many empirical formulas exist in the literature to make the conversion. The knowledge of the radiative climate inside the oasis by modelling solar radiative transfer within is important for more than one practical implications. First, to evaluate intercropping performances, identification of environmental resources and different planting configurations may be tested when we think to renew the oasis. Second, models can be used when tools for studying mono-crops are inadequate or in order to infer radiation variables difficult to obtain from field measurements.

5.2 Reasoning to Model the Oasis Architecture for an Optimal Use of Resources

5.2.1 Formulating Solar Radiative Transfer Inside the Oasis

The diffuse radiation received from the celestial vault at depth f can be expressed by ®rd =Ord,o exp[-^(a,hr) ]

The global solar radiation received at the level f inside the oasis is:

^(a ,hs) extinction coefficient for the direct solar radiation hs is the sun elevation f the leaf area index accounted from the top of the oasis O rs 0 is the direct solar radiation received above the canopy

Ord,o is the diffuse solar radiation received above the oasis ^ (a, hr) is the mean extinction coefficient for the diffuse flux density a is the mean inclination of leaves on the trees hr the mean elevation of the radiation sector

After penetrates inside the vegetation, the incident beam will suffered a multiple rediffusion under the effect of leaves, trunks and branches. The beam will be scattered in upward and downward directions. The study of the multiple scattering process at the scale of all the canopy needed to elaborate the radiative balance for a thin canopy layer inside the vegetation and the use of some hypothesis. We can found the following 2nd order linear differential equations:

d20-df2

<df2

R2 _ (1 _ T2)]o- = Rß( -1)0rs,0 exp(-ßf) + Rß'(ß - 1)0rd,o exp(-ßf)

R2-(1-T)2 ]+ =-4(l-T)r+R2+ßT ] ra,oexp(-ßf ) ßR-T)+R2+ßT ] ,*oexp(-ß f )

0+ is the ascendant rescattred flux density ( upward direction).

O- is the descendant rescattred flux density (downward direction) T is the transmittance factor of the leaves or the plant in a stand R is the reflectance factor of the leaves or the plant in a stand

| is the extinction coefficient for rescattered radiation

The general analytical solutions of the 2nd order linear differential equations are: 0+ (f ) — Xi exp(nf ) + X2 exp(-nf ) + Y1O rs,o exp(-|f ) + ¥2\$^ exp(-|'f )