Return to Task 3. Determine Ordinal Association Between Variables in R.

In this step, you will fit a marginal distribution to each of the datasets (3-day annual peak precipitation, near coincident flow, 1-day annual peak flow, and near coincident precipitation). 

This task is optional. HEC-Neptune will fit marginal distributions to the samples within the Copula Analysis. However, version alpha does not provide any plots (CDF, PDF, Q-Q, or P-P plot) to visualize the distribution fits nor does it compute goodness of fit metrics. Therefore, we recommend using HEC-SSP Distribution Fitting Analysis to fit distributions to the samples, particularly the near coincident event samples, prior to starting a Copula Analysis.

A univariate distribution fitting analysis will be implemented in a future version of HEC-Neptune.

Import Coincident Event Datasets

  • Open the precipitation_dominant.csv  file for the near coincident flow events.
  • In HEC-SSP, select Data | New | Using Import Wizard.
  • In the Short ID field, enter FlowCoincident and select Next.
  • Select Manual as the Source and click Next.
  • Enter the following for the Pathname Parts:
    • A: TYGART VALLEY RIVER
    • B: PHILIPPI WV
    • C: Flow
    • E: IR-Century
    • F: USGS
  • Make sure the the Data Units are cfs and the Type is INST-VAL.
  • Click Next.
  • Enter the following based on the date of the first flow in the precipitation_dominant CSV:
    • Start Date: 05Jun1941
    • Start Time: 24:00
  • Copy and paste the values from the flow_date and flow columns into the Import Wizard. Use the Paste button within the Importer rather than Ctrl + P on your keyboard.
    • Note that SSP will add a time of 24:00 to the dates.
  • The Import Wizard should appear as in the image below. Click the Plot button to confirm.
  • Click Next.
  • Check that everything looks correct and click Import.
  • You should see a dataset named FlowCoincident appear in the project tree under the Data node.
  • Repeat the above steps to import the coincident precipitation dataset.
  • Open the flow_dominant.csv  file for the near coincident flow events.
  • Enter PrecipitationCoincident as the Short ID.
  • Select Manual as the Source and click Next.
  • Enter the following for the Pathname Parts:
    • A: TYGART VALLEY RIVER
    • B: PHILIPPI WV
    • C: Precipitation
    • E: IR-Century
    • F: USC00466982
  • Make sure the the Data Units are in and the Type is INST-VAL.
  • Click Next.
  • Enter the following based on the date of the first precipitation value in the flow_dominant CSV:
    • Start Date: 28Aug1941
    • Start Time: 24:00
  • Copy and paste the values from the precipitation_date and precipitation columns into the Import Wizard. Use the Paste button within the Importer rather than Ctrl + P on your keyboard.
  • Click Next.
  • Check that everything looks correct and click Import.

Marginal Distribution for 3-day Annual Peak Precipitation

Peaks vs. Paired Peaks

The precipitation_dominant.csv and flow_dominant.csv files contains paired precipitation and flow events spanning WY 1941-2010. The precipitation station contains measurements from March 1896 to December 2010. The streamflow gage has daily measurements from WY 1941-2025. Therefore, the overlapping period is WY 1941-2010. 

In this step, we will fit marginal distributions to all peaks (i.e. precipitation peaks from March 1896 - December 2010 and streamflow peaks from WY 1941-2025), rather than just to the peaks that have coincident data. 

Convergence of a sample to an extreme value distribution depends on the number of events per block and on the number of blocks forming the estimate. In this example, the number of blocks means the sample size of WY peaks. Therefore, we will fit distributions to all peaks, rather than just the peaks between WY1941-2010. This should serve as a hint for selecting an appropriate distribution for each extremal (peak) dataset.

The HEC-Neptune Copula Analysis will compute dependence between the variables using only the paired events.

  • In HEC-SSP, create a new Distribution Fitting Analysis by selecting Analysis | New | Distribution Fitting Analysis or right clicking on the Distribution Fitting node and selecting New.
  • Enter Precipitation_3day_AMS as the Name and enter a description.
  • In the Data Set dropdown menu, select the TYGART VALLEY RIVER-PHILIPPI WV-PRECIPITATION-USC00466982 3 DAY AMS dataset.
  • The editor should appear like the image below.
  • Navigate to the Analysis tab.
  • In the Distribution Filter panel, select Display All Distributions.
  • In the Distribution Fitting Methods panel, uncheck Product Moments (PM) and check L-Moments (LM).

    We are using maximum likelihood estimation (MLE) as the distribution fitting method because the alpha release of HEC-Neptune fits marginal distributions using MLE within the Copula Analysis. Future versions of Neptune will allow users to select from a variety of distribution fitting methods.

  • Investigate the fits of various distributions and select one by selecting the Accept Distribution radio button in the rightmost column of the table.

Question 3. Which distribution did you select and why? 

The Generalized Extreme Value (GEV) distribution was selected since it is used to model the maximum value from uniformly sized non-overlapping blocks (e.g. the 3-day maximum in each year).

Marginal Distribution for 1-day Annual Peak Flow

  • In HEC-SSP, create a new Distribution Fitting Analysis.
  • Enter Flow_1day_AMS as the Name and enter a description.
  • In the Data Set dropdown menu, select the TYGART VALLEY RIVER-PHILIPPI, WV-FLOW-USGS-AMS dataset.
  • The editor should appear like the image below.
  • Navigate to the Analysis tab.
  • In the Distribution Filter panel, select Display All Distributions.
  • In the Distribution Fitting Methods panel, uncheck Product Moments (PM) and check L-Moments (LM).
  • Investigate the fits of various distributions and select one by selecting the Accept Distribution radio button in the rightmost column of the table.

Question 4. Which distribution did you select and why?

The Generalized Extreme Value (GEV) distribution was selected since it is used to model the maximum value from uniformly sized non-overlapping blocks (e.g. the 3-day maximum in each year).

Marginal Distribution for Near Coincident Precipitation Events

  • In HEC-SSP, create a new Distribution Fitting Analysis by selecting Analysis | New | Distribution Fitting Analysis or right clicking on the Distribution Fitting node and selecting New.
  • Enter Precipitation_Coincident as the Name and enter a description.
  • In the Data Set dropdown menu, select the PrecipitationCoincident dataset.
  • The editor should appear like the image below.
  • Navigate to the Analysis tab.
  • In the Distribution Filter panel, select Display All Distributions.
  • In the Distribution Fitting Methods panel, uncheck Product Moments (PM) and check L-Moments (LM).
  • Investigate the fits of various distributions and select one by selecting the Accept Distribution radio button in the rightmost column of the table.

Question 5. Which distribution did you select and why?

The Logistic distribution was selected since it is a heavy-tailed distribution. The QQ and PP Plots show a reasonably good fit.

Marginal Distribution for Near Coincident Flow Events

  • In HEC-SSP, create a new Distribution Fitting Analysis by selecting Analysis | New | Distribution Fitting Analysis or right clicking on the Distribution Fitting node and selecting New.
  • Enter Flow_Coincident as the Name and enter a description.
  • In the Data Set dropdown menu, select the Flow_Coincident dataset.
  • The editor should appear like the image below.
  • Navigate to the Analysis tab.
  • In the Distribution Filter panel, select Display All Distributions.
  • In the Distribution Fitting Methods panel, uncheck Product Moments (PM) and check L-Moments (LM).
  • Investigate the fits of various distributions and select one by selecting the Accept Distribution radio button in the rightmost column of the table.

Question 6. Which distribution did you select and why?

The Gamma distribution was selected since it is often used to model values that are positive and skewed. It is also used to model values that are larger than their typical value, as is the case here with the near coincident events.


Continue to Task 5. Create an HEC-Neptune Project and Import Data.