MODELING THE WATER BALANCE COMPONENTS OF THE SOYBEAN CANOPY BY SOIL-VEGETATIONATMOSPHERE TRANSFER MODEL - Soybean and Wheat Crops: Growth, Fertilization, and Yield - page 48

du

τ = ρ . (23)

h s h

dz

Combining Eqs. (17), (19), (21), and (23), after some simple algebra we get an equation
for the parameter σ of the form

2 H = βσ . (24)

dg

Finally, substituting β from Eq. (20) in Eq. (24) and solving for the scaling length, σ , we
reach

2
dg

2 C H

σ , (25)

C L ( H − h )

d d

which expresses σ through the morphological and aerodynamic parameters describing the
stand canopy in the “sandwich” approach. Figure 3 depicts calculated values of σ as a
function of the leaf drag coefficient, canopy density, canopy height, and canopy bottom
height for three tall grass canopy heights. In these calculations we used Eqs. ( 22) and (25). It
can be seen that lower values of tall grass canopy height and density

( )

[ ]

− cause
rapid growth of the scaling length. Such a plant canopy architecture includes more air space,
so physically the turbulent transport of momentum, heat and water vapor more closely
res e mbles the energy and momentum exchange above bare soil. In contrast, for values of
(

C L H h

d d

)

− that are typical of tall grass canopy (0.5 to 0.7) according to Sellers et al. (1986),
σ has a lower value. It means that the turbulent transfer coefficient, K s , within a dense tall
grass canopy, where eddies are small and dissipate quickly, tends to have lower values.
To our knowledge, the literature contains no information on how to reliably estimate
canopy bottom height. The only information available is the h values of 1 m to 2.5 m reported
for tall grass canopies by Dubov et al. (1978), Goudriaan (1977), Sellers (1986), Xue et al.
(1991), Mihailovic and Kallos (1997), and Mihailovic et al. (2000) [32,33,21,34,22,35].
Using these data, we found a functional dependence of h on the canopy height, H , using a
fifth-degree polynomial fitting procedure (Figure 4). This dependence can be helpful in land
surface schemes using the “sandwich” approach to describe the vegetation layer. We checked
the representativeness of this curve indirectly by calculating the zero plane displacement, d ,
and roughness length, z 0 , for tall grass canopies of known morphological characteristics,
using maize data from Wilson et al. (1982) and van Pul (1992) [36,37]. The derived z 0 /H and
d/H values of 0.08 and 0.71 for the Wilson et al. case and 0.051 and 0.76 for the van Pul case
are within the range of values reported by Uchijima (1976) [38]: 0.05-0.15 for z o /H and 0.53-
0.8 for d/H .

C L H h

d d