0PAR, is the sum of individual leaf photosynthesis Cv is a conversion constant
Ypsl is average leaf photosynthesis rates for sunlit leaves
Ypsh is average leaf photosynthesis rates for shaded leaves
Aabs is absorptance of plants
LAIsl is leaf area index for sunlit leaves
We can remark easily that the proposed formulations of mass and heat transfer inside the oasis are opened over the proposed formulation of solar radiative transfer. A model for heat and mass transfer inside a traditional oasis of Tozeur utilising both the basic equations presented above and the output of the model of solar radiative transfer ( Sellami and Sifaoui, 1999) had been established (Sellami and Sifaoui, 2008). Scaling up for all the oasis of North Africa and applying the out put for genetic biodiversity conservation needs thorough knowledge of the physiological properties of all the species and the different microenvironments inside the oasis of the region (set of resistances, optical properties of the species components, microclimatic parameters).
5.3 Method for Scaling Up Models Elaborated for One Oasis to all the Oasis of North Africa
The goal we seek is producing mechanistic models of conductance, assimilation, and transpiration that are transferable among species, sites, and various altered climates. As said above the traditional oasis in the region of North Africa is formed of three canopy stories where we found the majority of species either for the market gardening, fruit trees and date palm. The microenvironment, microclimate and kind of soil differ from level to level and place to place in the same oasis and they differ from oasis to oasis. Establishing relationships and models that can be applied to all the oasis of the region is an important goal for agricultural water management inside (Andrew et al. 2006; Mike Austin, 2007). This generalisation need the use of the scaling up and extrapolation tools (Hinckley et al, 1997). There validation demands repeated experimentations in time ( hours, day, seasons) and space ( many oasis in the region and many position in the same oasis). The survey of microenvironment distribution must be done from leaves level to branch, plant, stand and to regional levels (Gutschick., 1991). This survey must extend to species in many oasis in the region and must covered at list 2 years in order to follow the season variation effect and to verify with the second years the results recorded in the first. I should signal that at larger scales many additional phenomena appear, such as soil evaporation, canopy boundary-layer resistances, aerodynamic resistances, stomata and leaf boundary-layer resistances. We should consider them in all the stapes when extrapolating the results from scale to scale. To resolve which physiological (and micrometeorological) features explain the most variance in observations, it is better to develop models of observed fluxes in a hierarchy, from simple to more complex. A requisite for understanding larger-scale fluxes in terms of vegetation amount and physiology is quantifying the amount of vegetation, as leaf area index, and also the species components. We can do direct measurement of the geometrical properties (leaves inclinations and surfaces, diameter and length of the trunks and branches, densities of the components of the species and of the plants on the stands, projected surfaces of plants, fruit geometry) on a representative numbers of plants for all the region. Also we can proceed by doing aerial photography of select sites. The analysis of images permits to quantify leaf area index, using pixel-wise classification into leaf, non-leaf, and mixed pixels. The fraction of leaf in view will be related to LAI with models of canopy structure and light penetration. After, distributions and autocorrelation functions that link the surface or the volume occupied by every plant component and by every kind of plant in the stand to the surface or the volume dominated by the oasis of a zone and to that of all the region (François et al, 2007). Those function would be used later to extrapolate all the flux measured or modelled ( sap flow, intercepted solar radiation flux, photosynthetic radiation, water potential, transpiration, sensible and latent heat flux) at leaf scale to branch scale, from branch to trees level, from trees to stand and from a stand to the oasis of all the region.
Scaling up requires not only technologies to measure fluxes on different time and space scales. But to establish many empirical relationships from repeated filed measurement in space and time scales for the same oasis and for the majority of oasis in North Africa. Those equations should relate between flux measured (gas exchange, air temperature and humidity, shortwave and thermal infrared flux densities, windspeed, CO2 concentration) and the physiologic parameters of local species inside those oasis. They must consider, the detailed characterization of leaf microenvironments (leaves on a plant are displayed at different angles and at different optical depths, temperatures, etc.), and of single plants within a stand, and of small regions within a large region which are distributed rather than uniform (Baldocchi and Harley 1995, Waring et al 1995). We must know these distributions. If elaborated for a representative number of oasis in the region, those empirical relationships can be used to extrapolate the results of the models and microclimatic measurement found in the oasis of Tozeur to other oasis in North Africa.
5.3.2 Scaling Up Method used to Search the Oasis Transpiration in Tozeur
To scale up the sapwood section from a tree level to all the stand we have studied all the trees of the plot and we have measured their geometrical properties (high, diameter at different position of the trunk, number of palms and leaves, ...) and we have made a classes of trees as function of those dimension. The distribution of the sapwood cross-sectional area, tree health, stem shape and contact with neighbouring crowns of the trees sampled were considered as criteria for determining the selection of a sample in the oasis. After sampling, 20 date palms and 20 fruit trees, that represented the circumference's range of the plot (every tree from the 20 chosen represents a class), were selected. The cross sectional area of sapwood of each tree was calculated from its total circumference. The cross sectional sapwood area of the stand per unit of the ground was given by the arithmetic mean of the sapwood surface values of the sample of 20 trees, expressed per unit of ground area (Granier, Loustau, 1994; Sellami and Sifaoui, 2003). The total sap flow transpired by a tree on a day is equal to the sum of the sap flow transpired every hour. The transpiration for the entire stands and for every storey of the oasis is assimilate for its total sap flow (sap flow transpired by all the trees of the stand). The mean sap-flow density per unit area of sapwood in the oasis was estimated from the arithmetic mean of the sample averaged by the cross-sectional area of sapwood (Jarvis and McNaughton 1986). The transpiration for fruit trees and date palm were estimated from:
Eft Fruit trees transpiration (mm h-1)
Edp Palm date transpiration (mm h-1)
J f Mean sap flow density per unit area of sapwood for fruit trees expressed as kg dm-2
J p Mean sap flow density per unit area of sapwood for date palm expressed as kg dm-2
Sf and Sdp are, respectively, the cross-sectional sapwood area of fruit trees and date palm expressed as dm2 m-2
After calculus we found that the total transpiration of the stand is about 3.11 mm /day (1.91 for date palms and 1.2 for fruit trees). Monitoring this parameters at the scale of the hours is very needed to fix the irrigation gift. But the sap flow apparatus are very sensitive to climatic condition they can't be installed for all times. So elaborating models to estimate the heat and mass transfer and after the evapotranspiration inside the oasis is very profitable for water management. The results of a model in this direction established by my self is the object of a paper published (Sellami and Sifaoui, 2008).
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