Now that you have fit distributions to the Mixed-Snow, Rain-Only, and TC/TSR annual maximum series, you will create a Mixed Population analysis to create a combined flow-frequency curve that represents the reflects the true probability of more than one type of flood type using the probability of union concept.

Compute a Combined Frequency Curve

  • Select Analysis | New | Mixed Population Analysis.
  • Name the new analysis “Sayers_MPA” and add an adequate description.
  • On the General tab:
    • Increment the spinner within the Number of Curves panel to 3.
    • Within the Extrapolate Input Data panel, click the Allow Extrapolation of Input Data button.
    • Check the boxes for Data Label and Data Units. Add “Flow” and “cfs” within the label and units entry fields, respectively.
    • Within the Output Frequency Ordinates panel, enter 4 new ordinates representing the 0.01, 0.02, 0.05, and 0.1% annual exceedance probabilities (AEP)
  • The General tab should resemble the following figure:

Sayers_MPA General Tab

  • Move to the Frequency Curves tab:
    • Change the name of Frequency Curve 1, Frequency Curve 2, and Frequency Curve 3 to MixedSnow, RainOnly, and TC_TSR, respectively.
    • Select the Analytical Distribution radio buttons for both MixedSnow and RainOnly frequency curves and ensure the Log Pearson Type III distribution is selected within the drop down menu.
      • For the MixedSnow frequency curve, enter the computed mean, standard deviation, and skew from the MixedSnow_B17C analysis.
      • For the RainOnly frequency curve, enter the computed mean, standard deviation, and skew from the RainOnly_B17C analysis.
      • Click the Compute buttons above the flow-frequency table to populate the input frequency curves.

There are multiple Compute buttons within the Mixed Population Analysis editor.  The Compute button at the very bottom of the editor will attempt to compute the entire analysis.  The Compute button within the Frequency Curve X panel will fill out the frequency curve table using the defined analytical distribution and parameters.

Clicking the Compute Button to Populate the Input Frequency Curve Panel 

    • Select the Manual Entry radio button for the TC_TSR frequency curve.  Copy and paste the empirical distribution from the Sayers_MPA General Frequency analysis into the frequency curve table.
  • The Frequency Curves tab should resemble the following figure.

Sayers_MPA Frequency Curves Tab

  • Click the Plot Input Frequency Curves button.  The resulting plot should resemble the following figure:

Sayers_MPA Input Frequency Curves Plot

  • Click the Compute button at the bottom of the editor.
  • Move to the Results tab.  The Results tab should resemble the following figure.

Sayers_MPA Results Tab

  • Click the Plot Mixed Population Frequency Curves button.  You should see a plot of the imported curves as well as the combined curve within the same plot.  Click on the legend items to better identify which line style corresponds to which curve.

Question 1:  Describe the behavior of the combined frequency curve?  Is there an inflection point in the combined frequency curve?  If so, at what AEP is the inflection most pronounced?  Which flood mechanism causes this inflection?  Which flood mechanism(s) most strongly influence the behavior of the combined flood frequency curve throughout the full range of AEP?

The combined frequency curve exhibits a relatively smooth transition in estimated flood frequency from 0.99 to 0.5 AEP.  Within this range, the mixed-snow and rain-only input frequency curves strongly influence the overall shape and estimated quantiles.  However, past the 0.2 AEP, the combined curve sharply transitions upwards.  This is due to the presence of the TC_TSR input frequency curve, which was defined for AEP rarer than 0.5.  Beginning at the 0.5 AEP, the TC/TSR flood mechanism dominates the behavior of the combined curve.

Compute Confidence Limits Around the Combined Frequency Curve

  • Return to the General tab.
  • Within the Confidence Limits panel, click the Compute Using Order Statistics radio button.
  • Enter a valid number of years within the Equivalent Years of Record entry field.
  • Click the Compute button at the bottom of the editor.
  • Move to the Results tab.  The Results tab should resemble the following figure.

Sayers_MPA Results Tab with Uncertainty

Question 2:  What Equivalent Record Length (ERL) did you use to quantify uncertainty around the combined curve?  How did you estimate this value?

An ERL of 69 years was entered on the General tab and used to compute confidence limits around the combined curve.  This value was inferred from the Mixed-Snow, Rain-Only, and TC/TSR AMS.  Each of these AMS represented 69 years' worth of information.  This is also reflected within the computed ERL within the MixedSnow_B17C and RainOnly_B17C analyses.

Continue to Task 5. Compare the All-Season and Mixed Population Analysis Results.