MODELING THE WATER BALANCE COMPONENTS OF THE SOYBEAN CANOPY BY SOIL-VEGETATIONATMOSPHERE TRANSFER MODEL - Soybean and Wheat Crops: Growth, Fertilization, and Yield - page 50

h

H a

() () 2

∫

u z dz =

∫

u z dz . (27)

h h

a

If we solve these integrals, keeping in mind that the functional form of u ( z ) is given by
Eq. (19), we get

⎧ ⎫

⎡ 1 h ⎤

⎛ ⎞

1 + 2 exp − β ⎝ 1 − ⎠

⎪
⎨

⎪
⎬

⎣ ⎦

4 4 H

h a = H 1 + ln . (28)

β 3

⎪
⎩

⎪
⎭

⎪ ⎪

The temperature inside the canopy air space, T a , is determined diagnostically using Eq.
(12). In that formula the three aerodynamic resistances, r a , r b , and r d , are calculated as
follows:

⎧ ⎫

⎪
⎨

⎪
⎬

⎡ ⎤

1 2 kH ⎡ 1 h ⎤ 1 z − d

⎛ ⎞

a r

r = exp β ⎝ 1 − ⎠ − 1 + ln (29)

⎢
⎣

⎥
⎦

⎣ ⎦

a

H − d

u 2 H k H − d

⎪
⎩

⎪
⎭

σβ ln

*

⎪ z ⎪

0

1 β C P k

s s

r = (30)

b

⎡ ⎤

u ⎡ ⎤

H − d 1 ⎛ h ⎞

*

4 H L ln 1 − exp − β 1 −

a

⎝ ⎠

⎢
⎣

⎥
⎦

⎣ ⎦

d

z 4 H

o

⎧

⎪
⎨

⎡ ⎤

1 2 kH ⎡ 1 h ⎤ ⎡ 1 h ⎤

⎛ ⎞ ⎛ ⎞

a

r = exp β ⎝ 1 − ⎠ − exp β ⎝ 1 − ⎠ − 1

⎢
⎣

⎥
⎦

⎣ ⎦

⎣ ⎦

d

H − d

u 2 H 2 H

⎪
⎩

σβ ln

*

⎪ z

0

⎫

⎡ ⎤

1 ⎛ h ⎞

−

exp β ⎝ 1 ⎠

⎪
⎬

⎣ ⎦

2 H h

2

+ ln (31)

H − d

z

⎪
⎭

k ln

g

z

⎪

o

The values for the leaf shelter factor, P s , and transfer coefficient, C s , used in the
simulation are listed in Mihailovic and Kallos (1997) [22]. The effect of atmospheric
nonneutrality in Eqs. (29)-(31) (i.e., their dependence on T a and T r ) is included in u * and
accordingly in other calculations. In Eqs. (29)-(31) is supposed a logarithmic wind profile
above a canopy.
In a sparse tall grass canopy (one in which the plant spacing is the order of the canopy
height or larger), K s is strongly affected by processes in the environmental space, including