Computing a Correlation Analysis

To compute a Correlation Analysis, Press the Compute button located at the bottom of the editor once options have been set on the General tab and the required input has been entered on the Location Information tab(s). If the compute is successful, the user will receive a message that says Compute Complete. At this point, the user can begin to review the results. Multiple Correlation Analyses can be computed using the Compute Manager. To open the Compute Manager, click the Analysis | Compute Manager menu option. Then, select the analyses to be computed and press the Compute button.

Computational Methods

Linear correlation coefficients are computed using the following formula:

$\begin{array}{l}\displaystyle \text { Correlation } (x, y)=\frac{\sum(x-\bar{x})(y-\bar{y})}{\sqrt{\sum(x-\bar{x})^2 \sum(y-\bar{y})^2}}\end{array}$

When using the default transformation choice of None, no transformation is required to compute linear correlation coefficients. When using the Log transformation, the logarithm (base 10) for each data point will be computed prior to computing the linear correlation coefficients. When using the Exceedance Probability transformation, the exceedance probability for each data value will be extracted from the input frequency curve. The standard normal deviate associated with that exceedance probability will also be computed.

If the user has elected to perform a log operation (i.e. Log transform, using the Log Pearson Type III or Log Normal (base 10) distribution, etc), zeroes/negatives are contained within the linked data set, and the user does not enter a non-zero/positive value within the replacement field on the Location Information tab, the zeroes/negative values for that time series will be removed from consideration. However, the user can enter a non-zero/positive value within the Replace Zeroes and/or Negative Values entry field. The zeroes/negative values will then be replaced with the user-defined value and used when computing the linear correlation coefficient.

Correlation coefficients will be computed for each pair of locations for the chosen primary transformation (i.e. None or Log), regardless of whether or not they share the same transformation. For instance, if the None transform is specified for data set #1 and the Log transform is specified for data set #2 the correlation of linear values for data set #1 and logarithmic values for data set #2 will be computed. If the user chooses the Exceedance Probability transformation for a given time series, the exceedance probability and standard normal deviate transformations will be used to compute the correlation coefficient only with other locations that also have this transformation specified. Therefore, each time series will be used in either 1 or 4 correlation matrices.