Environmental Engineering Reference
In-Depth Information
12.4.1 Data Binning
One distinction between different linear methods is how the data are binned, or grouped
in subsets. The so-called bulk method derives a single linear equation for all the data
at once. Directional methods, which are also quite popular, construct a different linear
equation for each of the several direction bins. Matrix methods go further and bin the
data by both direction and speed (and sometimes forego the full linear equation in
favor of a ratio) (14). Still other approaches bin the data by time of day (irrelevant
when daily averages are used) or time of year.
The bulk method is the simplest to use and probably the most robust, meaning
the least susceptible to large errors in inexperienced hands or under far-from-ideal
conditions. Other methods require more time and experience. One complication of
highly binned approaches is the need to deal with bins that have an insufficient number
of counts to provide a reliable fit or ratio. Adjacent bins can be merged or a flexible
bin size can be employed to overcome this difficulty.
Whether any particular approach produces a consistently more accurate estimate
of the long-term mean wind resource is unclear and depends at least in part on how
the objective is defined. When it comes to a single parameter, the mean wind speed,
one study employing eight different pairs of reference/target data sets found little
difference between three linear methods: a bulk linear regression method, a matrix
ratio method, and a variance ratio method (described later). 2 Another study found
a very slight reduction in error when employing various directional and time-of-day
binning approaches compared to a bulk linear regression approach (15).
When it comes to predicting the wind speed frequency distribution, however, the
bulk linear regression method does not perform as well. This issue is addressed below.
12.4.2 Fitting Methods
The simplest method of relating wind speed data from two towers is by taking the
ratio of their means (this is effectively a linear equation with b
0). The key problem
with this approach is that it assumes a perfect correlation: increasing the reference
wind speed by 10% produces a 10% increase in the target speed. If the correlation
is actually much less than one, the result can be a substantial error in the predicted
long-term mean wind speed, as too much weight is attached to the reference.
Binning approaches that employ ratios can get around this problem to some degree
by allowing additional freedom in defining the target - reference relationship. This
assumes that the bins span a wide range of wind speeds; directional binning alone
may not be enough. A matrix method that bins by speed meets this test.
Alternatively, a linear equation can be established through linear regression. All
spreadsheet programs and some commercial wind resource analysis software contain
routines to do this. The main thing to know about linear regressions is that they seek
to minimize the sum of squared errors, meaning they are quite sensitive to large
=
2 Table 4 in Rogers (2005). A fourth method, which creates a separate linear equation for each component
of the horizontal wind vector, performed poorly. Since this approach conflates wind direction and speed, it
is not treated as a linear method here.
Search WWH ::




Custom Search