## Crop Parameters in the Penman Monteith Equation

The fluxes of sensible and latent heat between the evaporative surface and the atmosphere depend upon the gradients of temperature and vapor from the surface to the atmosphere. However, these processes are also governed by the momentum transfer, which affects the turbulent transfer coefficients.

Assuming thermal neutrality, the wind velocity profile u(z) (ms—') above a plane surface (Fig. 5.2a) can be described by a logarithmic function of the elevation zm (m) above that surface.

When the evaporative surface is a vegetated one, the height and architecture of the vegetation bring the zero reference level to a plane above the ground (Fig. 2b), the zero plane displacement height, d (m). Then, the generalized form for the wind profile becomes u(z) = Uk ln ((5.3) k \ Zom J

where zom is the roughness length (m) relative to the momentum transfer and depends on the nature of the surface, u+ is the friction velocity due to the eddy momentum transfer, and k is the von Karman constant.

Both parameters, d and zom, depend on the crop height, h (m), and architecture. The determination of zom and d from field micrometeorological measurements is presented by several authors [9, 10]. Information exists relating d and zom to h. Most of the proposed relationships are crop specific and represent unique functions of crop height [10]. However, more general functions also consider the leaf area index (LAI) [11, 12] or a plant area index [13].

From the preceding assumptions, the transfer of heat and vapor from the evaporative surface into the air in the turbulent layer above a canopy is determined by the aerodynamic resistance ra between the surface and the reference level (at height zm) above the canopy; that is, ln (zm-d) ln (^)

k2Uz where ra is the aerodynamic resistance (s m-1), zm is the height of the measurements of wind velocity (m), zh is the height of air temperature and humidity measurements (m), d is the zero plane displacement height (m), zom is the roughness length relative to momentum transfer (m), zoh is the roughness length relative to heat and vapor transfer (m), uz is the wind velocity at height zm (m s-1), and k is the von Karman constant (= 0.41).

Equation (5.4) assumes that the evaporative surface represented by the "big leaf" is inside the canopy. However, exchanges in the top layer of the canopy, between heights d + zom and h, are important as a source of vapor fluxes. Adopting the height d +zom as the level of the evaporative surface would lead to overestimation of ra and underestimation of rs [7]. Thus, in the alternative, ra can be computed from the top of the canopy [14]:

k2Uz

The application of Eqs. (5.4) and (5.5) for short time periods (hourly or less) using aerodynamic approaches requires the inclusion of corrections for stability [10, 12, 15-18]. These corrections are not considered when weather factors are measured at only one (reference) level, that is, under the assumption of neutral conditions stated earlier, and are less important under well-watered conditions.

The height zoh is estimated as a fraction of zom, commonly zoh = 0.1 zom, for short and fully covering crops (see [2, 19-21]). However, the factor 0.2 is prefered by some authors for tall and partial cover crops (see [17, 22]) whereas the ratio 1:7 is assumed by others (see [23-26]). Computation of the roughness length zoh for heat and vapor is not a problem in itself because there is relatively little effect on the ET calculations from selecting a zohi¡zom ratio between 0.1 and 0.2.

The surface resistance for full-cover canopies is often expressed [4] as rs = ri/LAIeff, (5.6)

where rs is the surface resistance (sm-1), rl is the bulk stomatal resistance of a well-illuminated leaf (sm-1), and LAIeff is the effective leaf area index ( ). A common formulation is that assumed by Szeicz and Long [27] and reviewed by Allen etal. [21],

which takes into consideration that only the upper half of a dense canopy is actively contributing to the surface heat and vapor transfer. Other formulations have been proposed, namely by Ben-Mehrez et al. [28],

This equation provides for a somewhat higher effective LAI for the initial crop stages (small LAI) and somewhat smaller values when the crop develops and LAI increases.

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