**6.2.5 Wind Speed Profiles**

Dispersion
models recommended for regulatory applications employ algorithms for
extrapolating the input wind speed to the stack-top height of the source
being modeled; the wind speed at stack-top is used for calculating transport
and dilution. This section provides guidance for implementing these
extrapolations using default parameters and recommends procedures for
developing site specific parameters for use in place of the defaults.

For
convenience, in non-complex terrain up to a height of about 200 m above
ground level, it is assumed that the wind profile is reasonably well
approximated as a power-law of the form:

The
power-law exponent for wind speed typically varies from about 0.1 on a sunny s
afternoon to about 0.6 during a cloudless night.
The larger the power-law exponent the larger the vertical gradient in the
wind speed. Although the power-law is a useful engineering approximation of
the average wind speed profile, actual profiles will deviate from this
relationship.

Site-specific
values of the power-law exponent may be determined for sites with two levels
of wind data by solving Equation (6.2.20) for p:

As
discussed by Irwin **[32**], wind profile power-law exponents are a
function of:

- stability,
- surface roughness
- the height range over which they are determined.

Hence, power-law exponents determined using two or more
levels of wind measurements should be stratified by stability and surface
roughness. Surface roughness may vary as a function of wind azimuth and
season of the year (see Section 6.4.2). If such variations occur, this would
require azimuth and season dependent determination of the wind profile
power-law exponents. The power-law exponents are most applicable within the
height range and season of the year used in their determination. Use of
these wind profile power-law exponents for estimating the wind at levels
above this height range or to other seasons should only be done with
caution. The default values used in regulatory models are given in Table
6-2.

The
following discussion presents a method for determining at what levels to
specify the wind speed on a multi-level tower to best represent the wind
speed profile in the vertical. The problem can be stated as, what is the
percentage error resulting from using a linear interpolation over a height
interval (between measurement levels), given a specified value for the
power-law exponent. Although the focus is on wind speed, the results are
equally applicable to profiles of other meteorological variables that can be
approximated by power laws.

Let
U_{l} represent the
wind speed found by linear interpolation and U the "correct" wind
speed. Then the fractional error is:

The
fractional error will vary from zero at both the upper, Z_{u} , and lower,
Z_{l } ,
bounds of the height interval, to a maximum at some intervening height, Z_{m} .
If the wind profile follows a power law, the maximum fractional error and
the height at which it occurs are:

As
an example, assume p equals 0.34 and the reference height, Z_{r} , is 10 m.
Then for the following height intervals, the maximum percentage error and
the height at which it occurs are: