wind speed can be larger than the average by threefold; (ii) the resonance between
the natural period of oscillation of plants and the dominant period of turbulent
eddies over the canopy and eventual diseases in plants grown in the field. The
collapse of rice plants in the field due to drag forces was shown to occur when
plants achieved 0.84 m height and windspeed exceeded 20 ms
−1 .
Results of wind tunnel simulations with tree canopies showed that the mean drag
on sheltered tree specimens was only about 6–8% of that of isolated specimens
subjected to airflow. This result was interpreted as consequent to the exponential
decay of wind speed from the top to the bottom in specimen canopies, with change
the air velocity field, by comparison with a uniform air velocity which remains
almost unchanged with exposure to individual specimens.
Foken (2008) suggests typical values for roughness height for sublayer, Z Ã , over
the canopy top of about two or three times the tree height. Fazu and Schwerdtfeger
(1989), report that the interface, z à , between the roughness and inertial sublayers, is
about 50–100 times the height of the momentum roughness length, z 0M , where
z à ¼ Z à À d. Garratt (1980) gives experimental values for the ratio z ÃH =z 0 , of the
order of 100 for the temperature profile and 35 and 150 for the velocity profile for
dense and less dense tree canopies, respectively. For z 0M values of the order of 5–
10% of the height of the canopy, h, this author suggested that for dense canopies the
z ÃM =z 0 ratio can be about 10. Monteith and Unsworth (1991) suggest a z à of about
10 z 0 , considering z 0 of the order of 0.1 h. Mihailovic et al. (1999) report that in tree
canopies, the length of the roughness sublayer ranges from d þ 10z 0M to h þ 20z 0M .
They reported that with z 0M of the order of 0.1 h, the height of the rough sublayer
will vary one- or twofold with the canopy height.
Cellier and Brunet (1992) suggest the following expressions, corrected for
dimensionless gradients (Eqs. 2.37 and 2.38, in Chap. 2):
dðuÞ
dðzÞ
kðz À dÞ
u Ã
¼ /
Ã
M n;
z À d
ZÃ À d
% u M n
ð Þu
Ã
M
z À d
ZÃ À d
ð4:4Þ
d T
ð Þ
d z
ð Þ
k z À d
ð
Þ
T Ã
¼ /
à H n;
z À d
Z Ã À d
% / H n
ð Þ/
Ã
M
z À d
Z Ã À d
ð4:5Þ
in which /
Ã
M is given by Garrat (1994):
/
Ã
M
z À d
z à À d
¼ exp 0:7 1 À
z À d
Z Ã
ð4:6Þ
where / M and / H are functions given by Eqs. (2.52) and (2.53) in Chap. 2.
Potential temperature profiles (Fig. 4.1) within the canopy indicate that thermal
stability within the atmosphere varies significantly in the vertical direction (Kaimal
and Finnigan 1994). During the day, in the lower inner zone, the Richardson
gradient number, Ri g (Eq. 2.45) is positive, indicating stability and the Richardson
flux number Ri f (Eq. 2.46) is negative, indicating instability. This situation is due to
110
4 Exchange of Energy and Mass Over Forest Canopies
the natural period of oscillation of plants and the dominant period of turbulent
eddies over the canopy and eventual diseases in plants grown in the field. The
collapse of rice plants in the field due to drag forces was shown to occur when
plants achieved 0.84 m height and windspeed exceeded 20 ms
−1 .
Results of wind tunnel simulations with tree canopies showed that the mean drag
on sheltered tree specimens was only about 6–8% of that of isolated specimens
subjected to airflow. This result was interpreted as consequent to the exponential
decay of wind speed from the top to the bottom in specimen canopies, with change
the air velocity field, by comparison with a uniform air velocity which remains
almost unchanged with exposure to individual specimens.
Foken (2008) suggests typical values for roughness height for sublayer, Z Ã , over
the canopy top of about two or three times the tree height. Fazu and Schwerdtfeger
(1989), report that the interface, z à , between the roughness and inertial sublayers, is
about 50–100 times the height of the momentum roughness length, z 0M , where
z à ¼ Z à À d. Garratt (1980) gives experimental values for the ratio z ÃH =z 0 , of the
order of 100 for the temperature profile and 35 and 150 for the velocity profile for
dense and less dense tree canopies, respectively. For z 0M values of the order of 5–
10% of the height of the canopy, h, this author suggested that for dense canopies the
z ÃM =z 0 ratio can be about 10. Monteith and Unsworth (1991) suggest a z à of about
10 z 0 , considering z 0 of the order of 0.1 h. Mihailovic et al. (1999) report that in tree
canopies, the length of the roughness sublayer ranges from d þ 10z 0M to h þ 20z 0M .
They reported that with z 0M of the order of 0.1 h, the height of the rough sublayer
will vary one- or twofold with the canopy height.
Cellier and Brunet (1992) suggest the following expressions, corrected for
dimensionless gradients (Eqs. 2.37 and 2.38, in Chap. 2):
dðuÞ
dðzÞ
kðz À dÞ
u Ã
¼ /
Ã
M n;
z À d
ZÃ À d
% u M n
ð Þu
Ã
M
z À d
ZÃ À d
ð4:4Þ
d T
ð Þ
d z
ð Þ
k z À d
ð
Þ
T Ã
¼ /
à H n;
z À d
Z Ã À d
% / H n
ð Þ/
Ã
M
z À d
Z Ã À d
ð4:5Þ
in which /
Ã
M is given by Garrat (1994):
/
Ã
M
z À d
z à À d
¼ exp 0:7 1 À
z À d
Z Ã
ð4:6Þ
where / M and / H are functions given by Eqs. (2.52) and (2.53) in Chap. 2.
Potential temperature profiles (Fig. 4.1) within the canopy indicate that thermal
stability within the atmosphere varies significantly in the vertical direction (Kaimal
and Finnigan 1994). During the day, in the lower inner zone, the Richardson
gradient number, Ri g (Eq. 2.45) is positive, indicating stability and the Richardson
flux number Ri f (Eq. 2.46) is negative, indicating instability. This situation is due to
110
4 Exchange of Energy and Mass Over Forest Canopies