**4. Combining below- and above-ground processes**

(1987), Gates (1980), Monteith and Unsworth (1990) and Nikolov *et al*. (1995).

A tree is an organism with leaves and has a capacity to store water in its boles. The transport of water through the water storage in the tree causes hysteresis between rates of soil water uptake and transpiration (Jones, 1982). Landsberg (1986) pointed out that it becomes necessary to include the fluxes in and out of storage in models that predicts the time course of leaf and other tissue water potentials. Trees use stored water to keep stomata open and maintain transpiration in the face of limiting soil moisture or excessive atmospheric demand. Therefore, water movement can be modelled in terms of water potentials and resistances via exchangeable water storages.

Having identified the major soil and environmental variables affecting the movement of water from soil to the atmosphere through trees and the subsequent changes in flow associated with resistances in the previous sections, it is possible to combine all this understanding of below- and above-tree water movement into a predictive model. Soil and root resistances, and soil water potential come from the below-ground models whereas the above-ground models contribute stomatal (*Rtp*) and boundary layer (*Ra W <sup>p</sup>*) resistances, vapor densities at the surface and the air temperature. Initial rates of water uptake (*FU*p) and transpiration (*F*TP) are used to estimate the exchangeable water storage (*Vp*) and leaf water potential (ψLp). Since ψLp is a function of *Rtp*, an iterative procedure is required to estimate the final value of *F*TP.

It is possible to eliminate the intermediate water potentials mathematically by neglecting any storage of water at the surface or in the tree (Thornley and Johnson, 1990). Campbell (1991) has employed a multi-layered root zone to include variable rooting density conditions into the water uptake estimations.

Monteith (1980) stated that latent energy for evaporation must be supplied from an external source (according to the law of conservation of energy), and the saturated water vapor in contact with the wet surface must be swept away and replaced by dry air which becomes saturated in turn. To sustain vaporization, however; there must not only be a continual supply of energy, but also an inward flow of liquid water from the soil or the plant (McIlroy, 1984). Accepting this, it is reasonable to assume that there is exchangeable water stored in the plant (Weatherley, 1970 and Jarvis, 1975). Until recently, tree water storage has been largely ignored in soil-tree-atmosphere models. The exchangeable water in the plant allows transpiration to exceed, equal or be less than water uptake by the roots at any given time. This concept of exchangeable water in the plant was used by Kowalik and Ekersten (1984) to formulate a continuous simulation model for transpiration and was solved numerically.

#### **4.1 Modelling water uptake and transpiration**

The flow of water through the soil-tree-atmospheric continuum can be divided into three components: (a) water uptake by roots; (b) exchangeable water in storages; and (c) water

Soil-Tree-Atmosphere Water Relations 181

flow in roots in the soil layer *i* (kg-1 m4 s-1), *Rli* is axial resistance for the water flow in roots in the soil layer *i* (kg-1 m4 s-1), *Rst* is stem resistance (assumed negligible), *z*p is gravitational

The transpiration rate is driven by the difference in vapour pressure between that inside the stomatal cavities and that of the air outside. When the air in stomatal cavities is assumed to be saturated, the transpiration rate in sub-canopy *P* (kg h-1) can therefore be calculated as

( ) *<sup>P</sup>*

*T W*

*W*

 

*PLL <sup>P</sup>*

*V*

potential within the sub-canopy can be predicted.

processes in at least the lower part of the canopy.

the soil-tree-atmospheric water relations.

**5. Further research** 

() () <sup>3600</sup>

max min max

 

*L L*

*V*

min *<sup>P</sup>*

where ΨLmin is minimum leaf water potential (J kg-1), ΨLmax is maximum leaf water potential (J kg-1) and *V*max p is maximum easily-exchangeable water. A linear relationship between Ψ<sup>L</sup> and exchangeable water storage in the canopy was also suggested by Tyree (1988) from experimental data taken from Brough *et al.* (1986). The idea of a minimum leaf water potential originated from Cowan (1965), who called it the 'supply function'. Jarvis (1975) suggested that the threshold leaf water potential equates to minimum stomatal resistance until the onset of leaf water stress. The leaf water potential is not uniform throughout the tree (Landsberg and McMurtrie, 1984). ΨLp can be calculated from equation 16, provided that *Vp* is calculated in an iteration. As stated earlier, it is considered that water in the tree is assumed to be in storages in each sub-canopy *P*, and thus, the variation of leaf water

The soil-tree-atmosphere water relations consists of important physiological and physical processes which control the soil water dynamics, water uptake by roots, energy and water transfer from the canopy. The following issues have identified for further advancement in

1. The resulting increase in humidity from soil evaporation can be added to the canopy

2. The trade-off between small and large sub-canopies is that large sub-canopies can affect the accuracy while small sub-canopies can increase the model computational time

(17)

(18)

*<sup>p</sup>* is leaf boundary layer resistance for water vapor

*PS P a P*

*c e Ts e Ta*

*Rt Ra*

where ρ is the specific density of moist air (kg m-3)*,* γ is the psychrometric constant (kPa K-1), λ is the latent heat of vaporization of water (MJ kg-1), *c*<sup>P</sup> is specific heat per unit mass of air (MJ kg-1 K-1), *e*a(*Ta*)*<sup>P</sup>* is vapour density (kPa) at *Ta*P in the sub-canopy *P*, *e*s(*Ts*)*P* is vapour density

transport in the sub-canopy *P* (s m-1) and *Rtp* is stomatal resistance in the sub-canopy *P* (s m-1). A linear relationship between exchangeable water storage and leaf water potential is employed after Federer, (1979); Kowalik and Eckersten, (1984); Eckersten, (1991) and

*P P*

potential (J kg-1) and *LAP* is leaf area of the sub-canopy *P* (m2).

*F*

(Eckersten, 1991):

(kPa) at *TsP* in the sub-canopy *P*, *Ra*

Cienciala *et al.* (1994), as follows:

loss by leaves. All necessary components related to (a) are given in Section 2 whereas for (c), they are given in Section 3.

The essential concept is that the water storage in the canopy for a given period is governed by water lost by transpiration and water supplied by roots. The volumetric change of the water storage in the sub-canopy *P* during one time step is the difference between water uptake and transpiration:

$$
\delta V\_p = \int\_{t-\delta t}^{t} \left( F\_{\mathcal{U}\_P} - F\_{\mathcal{T}\_P} \right) dt \tag{13}
$$

where *F*Up is root water uptake to computational sub-canopy *P* (kg h-1), δ*VP* is change of the amount of exchangeable water stored for a given time (kg) and *F*TP is transpiration from the sub-canopy *P* (kg h-1). The purpose of introducing the exchangeable water stored in the tree is to show the effects of stored water in a coupled soil-tree-atmospheric model on the transpiration flux and leaf water potential. *VP* is the state variable. The water uptake by trees, *F*U,and transpiration from the leaves, *F*T, are the main driving variables.

It is possible to eliminate intermediate water potentials mathematically by neglecting any storage of water at the surface or in the tree. Thus, the water flow from the soil to the plant (Thornley and Johnson, 1990) was written as:

$$F = \frac{\wp\_s - \wp\_L}{R\_s + R\_r} \tag{14}$$

where *Rs* is flow resistance from bulk soil to root surface (kg-1 m4 s-1), *Rr* is flow resistance from root surface to xylem (kg-1 m4 s-1), ψs is soil water potential (J kg-1) and ψL is leaf water potential (J kg-1).

Equation 14 is not particularly useful because it assumes a constant rooting density with respect to depth in the soil. To extend the equation to include variable rooting density conditions, (the root volume is assumed to be made up of zones with constant root densities), Campbell (1991) has employed a multi-layered root zone as follows:

$$F\_{l\bar{l}} = \int\_{i=1}^{n} \left(\frac{\nu\_{s\_i} - \nu\_L}{R\_{s\_i} - R\_{r\_i}}\right) \tag{15}$$

The amount of water uptake by roots for the sub-canopy P (kg h-1) can be computed by expanding equation 8 as follows (after Thornley and Johnson, 1990; Campbell, 1991; Eckersten, 1991):

$$F\_{L\_p} = \int\_{i=1}^{l} \left(\frac{\nu\_{s\_i} - \nu\_{L\_p} - Z\_P}{R\_{s\_i} + R\_{r\_i} + R\_{l\_i} + R\_{st}}\right) LA\_P \text{3600} \tag{16}$$

where ψsi is soil water potential in the soil layer *i* (J kg-1), ψLp is leaf water potential in the sub-canopy *P* (J kg-1), *l* is number of soil layers, *Rsi* is soil resistance for the water flow from soil to the root surface in the soil layer *i* (kg-1 m4 s-1), *Rri* is root radial resistance for the water

loss by leaves. All necessary components related to (a) are given in Section 2 whereas for (c),

The essential concept is that the water storage in the canopy for a given period is governed by water lost by transpiration and water supplied by roots. The volumetric change of the water storage in the sub-canopy *P* during one time step is the difference between water

> *t p UT t t V F F dt*

trees, *F*U,and transpiration from the leaves, *F*T, are the main driving variables.

*F*

densities), Campbell (1991) has employed a multi-layered root zone as follows:

*U*

*F*

1

*l*

*P*

*P P*

where *F*Up is root water uptake to computational sub-canopy *P* (kg h-1), δ*VP* is change of the amount of exchangeable water stored for a given time (kg) and *F*TP is transpiration from the sub-canopy *P* (kg h-1). The purpose of introducing the exchangeable water stored in the tree is to show the effects of stored water in a coupled soil-tree-atmospheric model on the transpiration flux and leaf water potential. *VP* is the state variable. The water uptake by

It is possible to eliminate intermediate water potentials mathematically by neglecting any storage of water at the surface or in the tree. Thus, the water flow from the soil to the plant

> *s L s r*

*R R* 

where *Rs* is flow resistance from bulk soil to root surface (kg-1 m4 s-1), *Rr* is flow resistance from root surface to xylem (kg-1 m4 s-1), ψs is soil water potential (J kg-1) and ψL is leaf water

Equation 14 is not particularly useful because it assumes a constant rooting density with respect to depth in the soil. To extend the equation to include variable rooting density conditions, (the root volume is assumed to be made up of zones with constant root

1

*iii*

*F LA RRRR*

 

 

*i i i*

*R R* 

3600 *i P*

*Z*

*s r i*

The amount of water uptake by roots for the sub-canopy P (kg h-1) can be computed by expanding equation 8 as follows (after Thornley and Johnson, 1990; Campbell, 1991;

> *sL P U P s r l st i*

where ψsi is soil water potential in the soil layer *i* (J kg-1), ψLp is leaf water potential in the sub-canopy *P* (J kg-1), *l* is number of soil layers, *Rsi* is soil resistance for the water flow from soil to the root surface in the soil layer *i* (kg-1 m4 s-1), *Rri* is root radial resistance for the water

*<sup>n</sup> s L*

 

(13)

(14)

(15)

(16)

they are given in Section 3.

uptake and transpiration:

potential (J kg-1).

Eckersten, 1991):

(Thornley and Johnson, 1990) was written as:

flow in roots in the soil layer *i* (kg-1 m4 s-1), *Rli* is axial resistance for the water flow in roots in the soil layer *i* (kg-1 m4 s-1), *Rst* is stem resistance (assumed negligible), *z*p is gravitational potential (J kg-1) and *LAP* is leaf area of the sub-canopy *P* (m2).

The transpiration rate is driven by the difference in vapour pressure between that inside the stomatal cavities and that of the air outside. When the air in stomatal cavities is assumed to be saturated, the transpiration rate in sub-canopy *P* (kg h-1) can therefore be calculated as (Eckersten, 1991):

$$F\_{T\_P} = \frac{\rho c\_P \left(e\_S (Ts)\_P\right) - e\_a (Ta)\_P}{\lambda \mathcal{I} \{R t\_P + R a\_P^{W'}\}} 3600 \tag{17}$$

where ρ is the specific density of moist air (kg m-3)*,* γ is the psychrometric constant (kPa K-1), λ is the latent heat of vaporization of water (MJ kg-1), *c*<sup>P</sup> is specific heat per unit mass of air (MJ kg-1 K-1), *e*a(*Ta*)*<sup>P</sup>* is vapour density (kPa) at *Ta*P in the sub-canopy *P*, *e*s(*Ts*)*P* is vapour density (kPa) at *TsP* in the sub-canopy *P*, *Ra W <sup>p</sup>* is leaf boundary layer resistance for water vapor transport in the sub-canopy *P* (s m-1) and *Rtp* is stomatal resistance in the sub-canopy *P* (s m-1).

A linear relationship between exchangeable water storage and leaf water potential is employed after Federer, (1979); Kowalik and Eckersten, (1984); Eckersten, (1991) and Cienciala *et al.* (1994), as follows:

$$V\_P = \left(\wp\_{L\_p} - \wp\_{L,\min}\right) \left(\frac{V\_{\max\_P}}{\wp\_{L\_{\max}} - \wp\_{L\_{\min}}}\right) \tag{18}$$

where ΨLmin is minimum leaf water potential (J kg-1), ΨLmax is maximum leaf water potential (J kg-1) and *V*max p is maximum easily-exchangeable water. A linear relationship between Ψ<sup>L</sup> and exchangeable water storage in the canopy was also suggested by Tyree (1988) from experimental data taken from Brough *et al.* (1986). The idea of a minimum leaf water potential originated from Cowan (1965), who called it the 'supply function'. Jarvis (1975) suggested that the threshold leaf water potential equates to minimum stomatal resistance until the onset of leaf water stress. The leaf water potential is not uniform throughout the tree (Landsberg and McMurtrie, 1984). ΨLp can be calculated from equation 16, provided that *Vp* is calculated in an iteration. As stated earlier, it is considered that water in the tree is assumed to be in storages in each sub-canopy *P*, and thus, the variation of leaf water potential within the sub-canopy can be predicted.

#### **5. Further research**

The soil-tree-atmosphere water relations consists of important physiological and physical processes which control the soil water dynamics, water uptake by roots, energy and water transfer from the canopy. The following issues have identified for further advancement in the soil-tree-atmospheric water relations.


Soil-Tree-Atmosphere Water Relations 183

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#### **6. References**


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**9** 

*Algeria* 

**Solar Radiation Modeling and** 

Fouzia Houma1 and Nour El Islam Bachari2

*Laboratory Marine and Coastal Ecosystems,* 

*1National School for Marine Sciences and Coastal Management (ENSSMAL), Campus Dely Ibrahim Bois des Cars, Algiers* 

*2Faculty of Biological Sciences, University of Science and Technology Houari Boumediene, USTHB, BP 32 El Alia, Bab Ezzouar Algiers Laboratory analysis and application of radiation (LAAR) USTO, Oran* 

All bodies emit and reflect the flow of energy in the form of electromagnetic radiation. The relative variation of the energy reflected or emitted as a function of wavelength, is the spectral signature of the object considered in a given state. The spectrum can be used to identify and determine its status. For a satellite, making measurements in a number of spectral bands, the spectral signature of an object will correspond to different levels of

The principle of remote sensing is the detection of electromagnetic radiation that carries information from the soil-atmosphere either by reflection or by transmission from a radiometer on board the satellite. The signal received by the radiometer is the result of physical, biological and geometrical objects on the ground. For a better use of satellite measurements, we must answer the following questions: At what point on the earth's

Answering these questions requires the definition: What exactly are the physical quantities measured by the measurement system? What disturbs the measurement system does what it is supposed to measure? Which model can you describe the disturbances? How does one

To understand this complex phenomenon, we have developed an analytic model (SDDS) of radiatif transfer simulation in water coupled to an atmospheric model in order to simulate measure by satellite. This direct model permits to follow the solar radiance in his trajectory Sun-Atmosphere - Sea - Depth of sea- sensor. The goal of this simulation is to show for every satellite of observation (SPOT, Landsat MSS, Landsat TM) possibilities that can offer

An interaction model of the solar spectrum with the Earth-atmosphere system is developed to calculate the various components of solar radiation at ground and upper atmosphere.

**1. Introduction** 

radioactivity recorded in each of them.

characterize the quality of measurement?

in domain of oceanography. (Bachari,1997)

(Bachari, 1999; Houma and al.,2010)

surface so far is it? What is the value of measuring that?

**Simulation of Multispectral Satellite Data** 

Zermeno, G.A., Hipps, L.E. (1997). Downwind evolution of surface fluxes over a vegetated surface during local advection of heat and saturation deficit. J. Hydrol. (Amsterdam) 192: 189-210.
