Coincident Events - West Branch Susquehanna River

The WBSusquehanna_Correlation example demonstrates the usage of the Correlation Analysis in order to determine how closely related annual maximum peak discharges at several stream gages are to one another.

Input Data

In this example, time series representing annual maximum inflow to four multi-purpose reservoir projects within the West Branch Susquehanna River watershed are analyzed.  The first time series is from the West Branch Susquehanna River at Bower, PA stream gage, which is located just upstream of Curwensville Dam.  The second time series is from the First Fork Sinnemahoning Creek at Wharton, PA stream gage, which is located just upstream of George B. Stevenson Dam.  The third time series is from the Kettle Creek at Cross Fork, PA stream gage, which is located just upstream of Alvin R. Bush Dam.  The fourth time series is from the Bald Eagle Creek bl Spring Creek at Milesburg, PA stream gage, which is located just upstream of Foster Joseph Sayers Dam.  The location of these stream gages is shown in Figure 1.  The time series are plotted within Figure 2 and tabulated within Table 1.

Table 1. Input Time Series for WBSusquehanna_Correlation Example

General Tab

A Correlation Analysis has been developed for this example. To open the analysis, either double-click on the analysis labeled WBSusquehanna_Correlation from the study explorer or from the Analysis menu select open, then select WBSusquehanna_Correlation from the list of available analyses. When WBSusquehanna_Correlation is opened, the General tab within the Correlation Analysis editor will appear as shown in Figure 3. For this analysis, the Time Series | Coincident Events computational method was selected and four locations were defined. The default Plotting Position formula (Weibull) and Output Frequency Ordinates were left unchanged. No modifications were made to the time window.

Location Information Tab

The Location Information tab contains four sub-tabs, one for each of the previously defined locations.

Bower

On the Bower sub-tab, the Log and Exceedance Probability (p, Zp) transformations were selected, as shown in Figure 4.  1000 cfs was entered as the replacement value if/when zeroes or negatives were encountered.  A typical event length of 7 days was also defined.  The default Output Labeling was left unchanged.  Finally, a frequency curve that was fit to the Bower time series was defined using a Log Pearson Type III (LPIII) distribution and the flow-frequency curve was computed.

Wharton

On the Wharton sub-tab, the Log and Exceedance Probability (p, Zp) transformations were selected, as shown in Figure 5.  1000 cfs was entered as the replacement value if/when zeroes or negatives were encountered.  A typical event length of 7 days was also defined.  The default Output Labeling was left unchanged.  Finally, a frequency curve that was fit to the Wharton time series was defined using a Log Pearson Type III (LPIII) distribution and the flow-frequency curve was computed.

Cross Fork

On the Cross Fork sub-tab, the Log and Exceedance Probability (p, Zp) transformations were selected, as shown in Figure 6.  1000 cfs was entered as the replacement value if/when zeroes or negatives were encountered.  A typical event length of 7 days was also defined.  The default Output Labeling was left unchanged.  Finally, a frequency curve that was fit to the Cross Fork time series was defined using a Log Pearson Type III (LPIII) distribution and the flow-frequency curve was computed.

Milesburg

On the Milesburg sub-tab, the Log and Exceedance Probability (p, Zp) transformations were selected, as shown in Figure 7.  1000 cfs was entered as the replacement value if/when zeroes or negatives were encountered.  A typical event length of 7 days was also defined.  The default Output Labeling was left unchanged.  Finally, a frequency curve that was fit to the Milesburg time series was defined using a Log Pearson Type III (LPIII) distribution and the flow-frequency curve was computed.

Each of the previously mentioned time series and frequency curves can be plotted by pressing the Plot All Input Frequency Data button, as shown in Figure 8.

Computing the Analysis

Once all of the General and Location Information details have been selected and/or defined, the user can press the Compute button to perform the analysis. A Compute Warnings message will be shown noting that some values for each pair of time series were removed from consideration within the correlation calculations.  For instance, when comparing the Bower and Wharton time series, 98 values were removed from consideration.  This was partly due to the fact that the Bower time series begins in 1889 while the Wharton time series begins in 1984.  However, several values within the Bower time series could not be found within the Typical Event Length of 7 days, which was defined on the Location Information sub-tab, when compared against the Wharton time series.  This is visualized within Figure 9, these values for the 1994 water year were removed from the analysis since the measurements were not recorded within 7 days of one another.

Only events like those shown within Figure 10, which both fell within the Typical Event Length of 7 days were used within the correlation computations.

Once the computations have been completed, a message window will open stating Compute Complete.

Results Tab

Upon a successful compute, the Results tab will become selectable.  The Results tab contains three sub-tabs, one for each of the previously defined transformations.  Within each transformation sub-tab, results will be presented consisting of:

• A Correlation Matrix of computed correlation coefficients,
• A plot of the selected pair(s),
• A Statistics table of the entire time series (all values are considered within these statistics), and 
• An Events table consisting of the overlapping date range and number of values that were considered within the correlation computations for the selected pair(s).

One or more pairs within the correlation matrix can be selected.  By default, the upper-left most cell will be selected upon navigating to these sub-tabs for the first time, as shown in Figure 11.  However, if more than one cell is selected, additional information will be shown within the plot as well as the Events table, as shown in Figure 12.

Log

The results using the Linear or Log transformation will be shown on this sub-tab, as shown within Figure 11.

Exceedance Probability

The results using the Exceedance Probability transformation will be shown on this sub-tab, as shown within Figure 13.

Standard Normal Deviate

The results using the Standard Normal Deviate transformation will be shown on this sub-tab, as shown within Figure 14.

In addition to the tables and plots on each sub-tab, two buttons are available to create summary plots for all data and transformations: Plot all Pairs and Plot all Transformations.  When the Plot all Pairs is clicked, a figure is created that shows the correlation matrix at the top with multiple plots below, one for every pair of time series, as shown in Figure 15.  The results for this plot will be shown for the currently-selected tab.

When the Plot all Transformations button is pressed, a figure will be created that has the correlation matrix and one plot containing the data pairs for all the currently selected cells in the correlation matrix for every selected transform.  For example, when the Bower-Wharton and Milesburg-Wharton pairs are selected for this study, the Plot all Transformations button will generate a plot that resembles Figure 16.  

The Plot all Transformations button will only be active when the Exceedance Probability transform has been selected for at least 2 time series on the Location Information tab and a compute has been successfully completed.  

The correlation coefficients computed for this example are very strong.  Per EM 1110-2-1415, datasets are often considered well correlated when the absolute value of the correlation coefficient is greater than 0.4.  Also, Bulletin 17C recommends the usage of data with high cross correlation when performing record extension, an example of which can be found here.

Report File

In addition to the tabular and graphical results, there is a report file that echoes the input data, selected computational options, and results. To review the report file, press the View Report button at the bottom of the analysis window. When this button is selected a text viewer will open the report file and display it on the screen, as shown in Figure 17. 

Different types and amounts of information will show up in the report file depending on the data and the options that have been selected for the analysis.