Page 154 - Fluid Power Engineering

W ind Resource Assessment 129

Correlate
The purpose of correlation is to understand if the measurement data
and the long-term reference data are similar over the measurement
(concurrent) period. If the two data series are similar, then the wind
regimes are similar and, therefore, a valid hindcast can be generated.
The meaning of correlation and its use is described next.
Consider two data series: M i is the measured data series and L i is
the long-term reference data series. If

M i = aL i + b then correlation is + 1
M i =−aL i + b then correlation is − 1
M i , L i are unrelated random series, then correlation is 0

where i is an index that goes from 1 to N, and N is the number of
points in the data series that correspond to concurrent time periods.
Correlation is 0 when two data series are independent.
In general, correlation index is defined as:

ρ = cov(M, L)/(σ M .σ L ) = E[(M − μ M) . (L − μ L )]/(σ M .σ L )
N

= (M i − μ M)(L i − μ L )/(N.σ M .σ L ) (7-1)
i=1
where ρ is the correlation between M and L time series, cov() is the
covariance function, E[] is the expected value function, σ M ,σ L are
standard deviation, and μ M ,μ L are mean of M and L.
Often the time series M i , L j do not have the same measurement
interval. For example, a typical interval for measurement data is
10 min whereas interval for airport reference data is 1 h and interval
for reanalysis NCAR data is 6 h. If a 10-min interval and 1-h interval
data are correlated, then there are two options for synchronizing the
time series:
Compute hourly average of the 10-min interval data and align
with L j , or pick data points in M i that have the shortest time difference
with data points in L j .
The choice of method depends on how the long-term data is col-
lected and recorded. If L j contains average wind speed data, then
the first method is appropriate. However, in most cases, information
about method of long-term data collection and recording is not avail-
able. In such cases, both methods may be tried and the method that
yields the higher correlation should be chosen.
Correlation values of 0.9 or above are considered excellent cor-
relation. To provide context to value of correlation, consider correla-
tion between Valentine met-tower data from anemometers at 40 and
25 m, and 45- and 10-m heights. Correlation values are in Table 7-4.