Example 8. [inf – inf] Perception Threshold – Pembina River at Neche, ND

Example 8 demonstrates how an [inf – inf] perception threshold can be used to compute a peak flow frequency curve using EMA and Bulletin 17C procedures.  The use of an [inf – inf] perception threshold for missing years implies that no knowledge is available for those missing years.  This produces a result that is equivalent to the elimination of the missing years from the analysis. The data for this example comes from the USGS gage 05100000 Pembina River at Neche, North Dakota.  The annual maximum series for this example contains 109 peaks beginning in 1904 and ending in 2016.  Two periods of missing data exist within this record, 1909 and 1916-1918.  The annual maximum series is plotted in Figure 1 and tabulated in Table 1.

Table 1.  Pembina River at Neche, ND Annual Peak Flow Record.

A Bulletin 17 Analysis using EMA and Bulletin 17C procedures has been developed for this example. To open the analysis, either double-click on the analysis labeled "B17C Example 8" from the Study Explorer or from the Analysis menu select open, then select "B17C Example 8" from the list of available analyses. When "B17C Example 8" is selected, the Bulletin 17 analysis editor will appear as shown in Figure 2. As shown, the Skew option was set to use the Station Skew.

No changes to the Options tab are necessary. The EMA Data tab for this example is shown in Figure 3. This example uses an annual maximum series consisting of systematic data with two missing periods. The missing periods include 1909 and 1916 – 1918. Since 17C EMA requires a non zero – inf perception threshold for all periods of missing data, a total of three perception thresholds are required. An inf – inf perception threshold is used to convey zero additional knowledge about the missing periods because the complementary flow range for such a perception threshold is zero – inf. Using the aforementioned perception thresholds and flow ranges is equivalent to removing the missing periods of record from the computations. Once all three perception thresholds have been entered as shown in Figure 3, click the Apply Thresholds button to assign the complementary flow ranges for the periods of missing data.


Once all of the General and EMA Data tab settings are set or selected, the user can press the Compute button to perform the analysis. Once the computations have been completed, a message window will open stating Compute Complete. Close this window and then select the Tabular Results tab. The analysis window should resemble Figure 4.

In addition to the tabular results, a graphical plot of the computed frequency curves can be obtained by pressing the Plot Curve button at the bottom of the analysis window. The Log Pearson Type III distribution fit using EMA to the input annual maximum flow data set, the 5% and 95% confidence limits, and the computed plotting positions are shown in Figure 5.

As shown in Figure 6, four years were demarcated using an inf – inf perception threshold (and zero – inf flow range). These annual peak flows were then removed from the EMA computations, as shown in Figure 7.