Finding the Zero Plane Displacement and the Roughness Length
69
the wind occurs at the surface, and d' = 0. For a crop, the drag occurs
throughout the crop, but a single surface placed at some height below the
top of the crop can be imagined which would have an effect equivalent to
the wind. If z in Eq. (5.1) is measured from that point, then there would be
no need for a zero plane displacement in the equation. Normally, however,
we want to measure z from the soil surface. When doing this, d' needs to be
subtracted to place the effective location of drag near the top of the crop.
An intuitive feeling for the meaning of z, and u* is harder to obtain.
The units of u* are velocity or speed. Its value is directly proportional to
the wind speed at height z, as can be seen from Eq. (5. l), but also depends
on the friction of the wind with the surface. Thus the name "friction
velocity." While z, has units of length, one should not try to interpret it
as a measurable physical length. It is a measure of the form drag and skin
friction in the layer of air that interacts with the surface. It is most reliably
determined empirically by measuring wind speed at several heights above
a surface and plotting ln(z - d) versus u (z) . A straight line should result
which can be extrapolated to u = 0. If we set u(z) = 0 in Eq. (5.1),
it can be seen that ln(z - d) = In(z,). The intercept, where u = 0,
is ln(z,). The value of z, is the exponential of this intercept. Table 5.1
gives several values of z, determined in this way. It should be pointed out
that these are values from particular experiments and are not necessarily
representative of all surfaces like the one described. The wind can make
the surface rougher or smoother and the direction of the wind with respect
to rows or other regular features of the surface can have a big effect on the
roughness length. The wind obviously has a big effect on the roughness
of water surfaces, but the effect on plant canopies can also be substantial.
Maki (1 975) did an extensive set of z, and d measurements on a full-cover
Teosinte canopy while its height (h) changed from 0.68 m to 1.45 m (LA1
increased from 2 to 6) and observed a strong linear relationship between
zm and u* as well as d and u* over a range of u* from 0.05 to 0.5 m/s;
furthermore, z, was related to d. Fitting data from the five measurement
TABLE 5.1. Empirically determined values of roughness length for
various surfaces (from Hansen, 1993).
Q p e of Surface
z , (cm)
Type of Surface
Zm (cm)
Ice
Dry lake bed
Calm open sea
Desert, smooth
Grass, closely mowed
Farmland, snow covered
Bare soil, tilled
Thick grass, 50 cm high
Forest, level topography
Coniferous forest
Alfalfa
Potatoes, 60 cm high
Cotton, 1.3 m tall
Citrus orchard
Villages, towns
Residential, low density
Urban bldgs, business dist.
69
the wind occurs at the surface, and d' = 0. For a crop, the drag occurs
throughout the crop, but a single surface placed at some height below the
top of the crop can be imagined which would have an effect equivalent to
the wind. If z in Eq. (5.1) is measured from that point, then there would be
no need for a zero plane displacement in the equation. Normally, however,
we want to measure z from the soil surface. When doing this, d' needs to be
subtracted to place the effective location of drag near the top of the crop.
An intuitive feeling for the meaning of z, and u* is harder to obtain.
The units of u* are velocity or speed. Its value is directly proportional to
the wind speed at height z, as can be seen from Eq. (5. l), but also depends
on the friction of the wind with the surface. Thus the name "friction
velocity." While z, has units of length, one should not try to interpret it
as a measurable physical length. It is a measure of the form drag and skin
friction in the layer of air that interacts with the surface. It is most reliably
determined empirically by measuring wind speed at several heights above
a surface and plotting ln(z - d) versus u (z) . A straight line should result
which can be extrapolated to u = 0. If we set u(z) = 0 in Eq. (5.1),
it can be seen that ln(z - d) = In(z,). The intercept, where u = 0,
is ln(z,). The value of z, is the exponential of this intercept. Table 5.1
gives several values of z, determined in this way. It should be pointed out
that these are values from particular experiments and are not necessarily
representative of all surfaces like the one described. The wind can make
the surface rougher or smoother and the direction of the wind with respect
to rows or other regular features of the surface can have a big effect on the
roughness length. The wind obviously has a big effect on the roughness
of water surfaces, but the effect on plant canopies can also be substantial.
Maki (1 975) did an extensive set of z, and d measurements on a full-cover
Teosinte canopy while its height (h) changed from 0.68 m to 1.45 m (LA1
increased from 2 to 6) and observed a strong linear relationship between
zm and u* as well as d and u* over a range of u* from 0.05 to 0.5 m/s;
furthermore, z, was related to d. Fitting data from the five measurement
TABLE 5.1. Empirically determined values of roughness length for
various surfaces (from Hansen, 1993).
Q p e of Surface
z , (cm)
Type of Surface
Zm (cm)
Ice
Dry lake bed
Calm open sea
Desert, smooth
Grass, closely mowed
Farmland, snow covered
Bare soil, tilled
Thick grass, 50 cm high
Forest, level topography
Coniferous forest
Alfalfa
Potatoes, 60 cm high
Cotton, 1.3 m tall
Citrus orchard
Villages, towns
Residential, low density
Urban bldgs, business dist.