Geoscience Reference
In-Depth Information
(k) At level (ii) the temperature will
be warmer
and the humidity will
change
little
.
(l) At level (iii) the temperature will
be warmer
and the humidity will
change
little
.
(m) At level (iv) the temperature will
be cooler
and the humidity will
be wetter
.
(n) At level (v) the temperature will
change little
and the humidity will
change
little
.
Answer 9
= 1.52 × 10
−5
m
2
s
−1
,
D
H
= 2.15 × 10
−5
m
2
s
−1
,
D
V
= 2.42 × 10
−5
m
2
s
−1
, and
D
C
= 1.47 × 10
−5
m
2
s
−1
.
If the in-canopy wind speed,
U
, is 0.5 m s
−1
for (spherical plate) leaves 0.05 m in
diameter the Reynolds number,
Re
, is 1649. Selecting the relevant empirical equa-
tion from Table 21.1, the Nusselt number,
Nu ≈
0.62 ×
Re
0.5
≈ 0.62 × 41 ≈ 25. From
Equation (21.9), the boundary-layer resistance for heat transfer for (spherical
plate) leaves 0.05 m in diameter is
R
H
(flat leaf ) ≈ 0.05/(2.15 × 10
−5
× 24) ≈ 92 s m
−1
.
(b) For (cylindrical) needles leaves, the Reynolds number is 82 and the Nusselt
number,
Nu
≈ 0.62 × 9.1 ≈ 5.6. From Equation (21.9) the boundary-layer
resistance for heat transfer for (cylindrical) conifer needles is
R
H
(needle) ≈
0.0025/(2.15 × 10
−5
× 5.6) ≈ 21 s m
−1
.
Assuming the transfer from individual vegetative elements is always by forced
convection and the relative transfer resistances for other exchanges is determined
only by their relative diffusion coefficients, see Equations (21.10) and (21.11), the
boundary-layer resistance for:
(a) At 20°C the molecular diffusion coefficients are
υ
(c) vapor transfer for coniferous needles is
R
V
(needle) ≈ 0.93 × 21 ≈ 19 s m
−1
.
(d) carbon dioxide transfer for coniferous needles is
R
C
(needle) ≈ 1.32 × 21 ≈
27 s m
−1
.
(e) The required plots of the ratio of zero plane displacement to vegetation
height versus leaf area index and of aerodynamic roughness to vegetation
height versus leaf area index are shown in Fig. 26.13.
As additional leaf area is included in a canopy (of fixed height) a progressively
greater proportion of the momentum is lost higher in the canopy - the limit of infinite
LAI
it is equivalent to raising the ground to the level by
h
. Initially this additional leaf
area raises the aerodynamic roughness above that of the bare soil by putting taller
roughness elements into the air stream. However, after the canopy begins to 'close'
(when
LAI
is around one) and becomes denser and denser, depressions in the top of
the canopy become less significant and the aerodynamic roughness progressively falls.
When
LAI
= 4 the values of (
d/h
) and (
z
o
/
h
) required for use in (f ) are 0.73 and
0.08, respectively.
(f ) The required plot of the aerodynamic resistance for a 10 cm high grass
stand, a 1 m high crop stand, and a 30 m high forest stand (all with
LAI
= 4)
is given in Fig. 26.14. Notice the large difference between these values of
