Finding the Zero Plane Displacement and the Roughness Length
the values for the underlying surface. Figure 5.5 does not show this.
However, the simulation was not intended to show the effects of very low
plant density and the extrapolation to PA1 = 0 is therefore not reliable.
If we take PA1 = 3 as representative of a range of agricultural crops
then Fig. 5.5 gives
and
Using the simple relation between z, and d from Maki (1975), if z, =
O.lh then d = 0.75h; this is in reasonable agreement with Fig. 5.5 at
high PAI, where the relation of Maki (1975) would be expected to hold.
When only canopy height is known, Eqs. (5.2) and (5.3) can be used to
estimate d and z,. If an estimate of the plant area density is available,
then Fig. 5.5 can be used. If wind profile data are available, it is best to
find z, from the wind profile data.
Example 5.1. Four anemometers are to be placed at different heights
above a plant canopy to measure wind speeds for a wind profile. At what
heights should the anemometers be placed to give the most information
about the wind profile? Assume the canopy is 40 cm tall.
Solution. Since wind speed varies with the logarithm of height above
the zero plane, the most information is obtained (largest differences between readings) if the anemometers are logarithmically spaced. If the
top anemometer is placed 2 m above d + z,, then the others could be
at 1, 0.5, and 0.25 m above d + z,. The zero plane displacement is at
0.65 x 0.4 = 0.26m, so the heights above the ground would be 0.51,
0.76, 1.26, and 2.26 m.
Example 5.2. The average wind speed measured 3 m above a golf course
was found to be 2.7 mls. What is the wind speed at the surface of the turf?
Assume the grass is 3 cm tall.
Solution. From Eqs. (5.2) and (5.3), d = 0.02 m and z, = 0.003 m.
Using these, with z = 3 m gives
Solving for u* gives u* = 0.16 mls. The friction velocity is constant
for all heights, so this value can now be used to determine the average
wind speed at any height. The wind speed at h (the top of the canopy) is
therefore given by
the values for the underlying surface. Figure 5.5 does not show this.
However, the simulation was not intended to show the effects of very low
plant density and the extrapolation to PA1 = 0 is therefore not reliable.
If we take PA1 = 3 as representative of a range of agricultural crops
then Fig. 5.5 gives
and
Using the simple relation between z, and d from Maki (1975), if z, =
O.lh then d = 0.75h; this is in reasonable agreement with Fig. 5.5 at
high PAI, where the relation of Maki (1975) would be expected to hold.
When only canopy height is known, Eqs. (5.2) and (5.3) can be used to
estimate d and z,. If an estimate of the plant area density is available,
then Fig. 5.5 can be used. If wind profile data are available, it is best to
find z, from the wind profile data.
Example 5.1. Four anemometers are to be placed at different heights
above a plant canopy to measure wind speeds for a wind profile. At what
heights should the anemometers be placed to give the most information
about the wind profile? Assume the canopy is 40 cm tall.
Solution. Since wind speed varies with the logarithm of height above
the zero plane, the most information is obtained (largest differences between readings) if the anemometers are logarithmically spaced. If the
top anemometer is placed 2 m above d + z,, then the others could be
at 1, 0.5, and 0.25 m above d + z,. The zero plane displacement is at
0.65 x 0.4 = 0.26m, so the heights above the ground would be 0.51,
0.76, 1.26, and 2.26 m.
Example 5.2. The average wind speed measured 3 m above a golf course
was found to be 2.7 mls. What is the wind speed at the surface of the turf?
Assume the grass is 3 cm tall.
Solution. From Eqs. (5.2) and (5.3), d = 0.02 m and z, = 0.003 m.
Using these, with z = 3 m gives
Solving for u* gives u* = 0.16 mls. The friction velocity is constant
for all heights, so this value can now be used to determine the average
wind speed at any height. The wind speed at h (the top of the canopy) is
therefore given by