Task 1: Heterogeneous Sample

Start HEC-SSP and open the “extreme_winds” project.  You will find the three data sets in the project (Figure 1).

Figure 1.  Watershed explorer view of the "extreme_winds" project with the three initial datasets.

Create a new Distribution Fitting Analysis (see Figure 2) and title it “PDS All” (use a description of “partial duration series, all data”) and select the “CID_All_Independent-CID-WIND-SPEED” dataset (see Figure 3).

Figure 2. Creating a new Distribution Fitting Analysis from the menu bar.

Figure 3. DFA heading for the first analysis.

The current dataset contains each independent observation of extreme wind, regardless of meteorological cause, for the period of record.  Check to make sure there are no systematic discrepancies in the time-series data by selecting the “XY” plot type in the lower right corner of the window (Figure 4).

Figure 4. All data XY plot.

You should see that the minimum recording threshold changed in about 1995.  To ensure we are only keeping observations that were measured in the same way for the entire period, use the “Filter Data” tool (Figure 5) to drop out observations below 42 mi hr^-1 by setting a minimum threshold value (Figure 6).

Figure 5. Location of data filtering tool.

Figure 6. Setting a minimum threshold in the data filter tool.

You will notice that the XY plot and the data table now have values in red, which indicate that they were filtered out.  Select “Apply” in the lower right corner of the window to apply the changes, and then switch to the “Analysis” tab near the top left of the panel (Figure 7).  The data in the analysis will be the values that were retained after filtering.  You can verify this by selecting the “Data Summary Statistics” button in the lower left of the panel (Figure 8), which will display various summary statistics for the original and filtered data.  Check to see that the minimum value for the “Processed Data” is not below the selected value of 42 mi hr^-1.

Figure 7. Locating the Analysis tab.

Figure 8. Locating the Data Summary Statistics button.

Allow the display of all probability distributions by selecting “Display All Distributions” under “Distribution Filter” (Figure 9).  Normally, this option aids the user by displaying only distributions that are relevant for the kind of data being used (inferred from the DSS information).  There are no defaults for wind speed data, so the parameter-based list is a default of commonly used distributions.

Figure 9. Distribution filter.

Question 1: Based on your knowledge of extreme value theory, which probability distribution would you expect to be a good model for this kind of data (all independent observations of extreme wind speeds)?

You can check your answer for each question on the child page to these instructions before proceeding on in the workshop.

Instruct HEC-SSP to estimate probability distribution parameters using the method of L-moments by checking “L-moments” then unchecking "Product Moments" (Figure 10).

Figure 10. Changing the parameter estimation method.

HEC-SSP will immediately compute the estimated probability distribution parameters using the method of L­-moments after selecting it.  Sort the table by the Kolmogorov-Smirnov (KS) test statistic by clicking on the Kolmogorov-Smirnov (Test Statistic) heading in the table. The best fitting distributions (smallest test statistic) will be at the top of the list.  KS is a good default to use and we will keep it.

Question 2: Which probability distribution has the best goodness-of-fit statistic?  Is this distribution different from what you were expecting?

Switch the display from “CDF” to “CDF-Plotting Position” to show a plot that looks more like a flow-frequency curve (Figure 11).

Figure 11. Changing the plot type.

In the distribution table, select the “Generalized Pareto (LM)” distribution by selecting the box underneath “Median Curve” (Figure 12).

Figure 12. Selecting the Generalized Pareto distribution.

Question 3: How do you feel about the goodness of fit based on the “CDF-Plotting Position” plot?  Do the data and model show good agreement?

Try some other distributions by turning them on and off in the first column of the distribution table.  After looking at the difference between them, return to only having the generalized Pareto distribution selected, and select “Accept Selected Distribution” on the rightmost column of the Generalized Pareto (LM) distribution in the table (Figure 13).

Figure 13. Accepting the selected distribution.

Change to the “Results” tab (Figure 14) and record the resulting location, scale and shape parameters, as well as the sample size from the filtered data in Table 1.

Figure 14. Locating the Results tab.

Table 1. Results for all storm types, partial duration series.

Next, we will estimate parameters for the corresponding annual maximum series model.  Select “OK” in the lower right corner of the panel, then save the project.

Create a new Distribution Fitting Analysis (see Figure 2) and title it “AMS All.”  Select the “All Independent” dataset as you did in the first analysis.  Instead of filtering out winds below 42 mi hr^-1, we will use a filter based on annual maxima.  Select the Data Filter tool (Figure 5) and on the Peaks tab, select “Filter to Annual Maxima” (Figure 15), and enter a date of 01Oct (roughly the time of year when storms transition from thunderstorms to extra-tropical cyclones in this area, and have a slight lull in storm events.)  Press OK to apply the filter and exit.

Figure 15. Annual maximum filter.

Press “Apply” in the lower right corner and switch to the “Analysis” tab (Figure 7).  Select “Display All Distributions” under the Distribution Filter (Figure 9).  Set the parameter estimation method to L-moments by selecting L-moments and then unselecting Product Moments (Figure 10).  Sort the resulting distributions by their KS Test Statistic by clicking on the column header.

Question 4: Based on your knowledge of extreme value theory, which probability distribution would you expect to be a good model for this kind of data (block maxima of wind speeds)?

Question 5: Which probability distribution has the best goodness-of-fit statistic?  Is this distribution different from what you were expecting?

The KS statistic for the top four distributions on the list (Gumbel, generalized logistic, generalized extreme value and log-logistic) are very similar to each other.  Compare the difference in behavior of these four distributions by turning their curve display on and comparing their CDF-Plotting Position plots (Figure 11).

Question 6: Which probability ranges of the four models show the most similarity?  Where are they the most different?

Question 7: What is special about the relationship between the Gumbel and generalized extreme value distribution?  Which would be considered a more “flexible” distribution, and why?

Select only the generalized extreme value distribution and accept that distribution (Figure 13).  Switch to the “Results” tab (Figure 14).  Record the estimated distribution parameters and filtered data sample size in Table 2.

Table 2. Results for all storm types, annual maximum series.

Press "OK" in the lower right to save the analysis.  Then, save your project.

Next step: Task 2: Homogeneous Samples