Resistances scheme

According to Stanghellini (1987) the leaf resistance for sensible heat transfer rahiecan be expressed as where Nu is a mixed convection Nusselt number given by:

Nu=0.37(Gr+6.92Re2)OJS where Grthe Grashof number is:

and Reynolds number Re:

where :

I - characteristic dimension of the surface (m)

Aa - thermal conductivity of air (W m"1 K"1)

v - kinematic viscosity of air (m2 s"1)

g - acceleration due to gravity (m s"2)

/5 - coefficient of thermal expansion of air (K"1)

Tsurf - leaf surface temperature (K)

Tc.ref - air temperature at a reference height in the canopy (K)

After substitutions and using the numeric values of air properties, rah,e can be written as (see Stanghellini 1987 for details)

where Tv and Tac as defined above and Uo is wind speed at a level in the canopy, /v is the mean leaf size.

Using a parallel resistance scheme for leaf resistances, the total vegetation resistance is:

Experimental validation of this parameterization was given by Stanghellini (1987).

To parameterize the soil resistance in a similar way, a suitable linear dimension of the soil surface for the (vegetation + soil) mixture must be identified and estimated. We propose to take typical linear dimension of the soil surface as the square root of the fractional soil cover, i.e. the fraction of horizontal unit area occupied by soil:

where is the fractional vegetation cover, is then the fractional soil cover.

The parameterization for the soil resistance is then given by:

In neutral conditions, aerodynamic resistance for heat transfer between a level in the canopy and the reference height above the canopy is expressed as raho=ln[(zrefdj/zoj/fk2 ureJ)

where uref is the wind speed (m s"1) at the same height as Tref, k is the von Karman's constant taken as 0.4, d is the displacement (m) and z0 is the reference source height (m) in the canopy. Following the expressions given by Choudhury et al (1986) and Kalma and Jupp (1990) for incompletely covered surface, the stability corrected aerodynamic resistance is:

with p=0.75 in unstable conditions and p=2 in stable conditions, and

Aerodynamic surface temperature of the canopy, is not measurable directly as discussed above. In our dual-source model, is an ancillary variable. Combining Eq.(4), (5), (6) and (7), one can get:

Iterations are made between Eq.(14), Eq.(16), Eq.(18) and Eq.(20) to determine the values of the variables rac first, then rah, rahiV and rah,S! Hv, Hs and H are determined finally.

Renewable Energy 101

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