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Extreme Wind Speeds: Software

Computational Issues When analyzing a univariate set of data consisting of extreme winds, the following tasks typically need to be performed. Later on this page, we discuss software that can be used to perform some of these tasks.
Graph the Data Some useful initial graphs of the data are:
  • A run sequence plot of the data is useful for showing time dependent patterns in the data. For extreme value analysis, it can be helpful to draw reference lines at certain threshold values.

  • Graphs showing the distributional shape can be useful. The most common types of distributional graphs are histograms and kernel density plots.
Determine an Appropriate Distribution For extreme values, the following are the most commonly used distributions:
Estimate the Parameters of the Distribution There are a number of methods for estimating the parameters of a distribution. These include: Maximum likelihood procedures are well developed for Gumbel, Frechet, and Weibull distributions. Maximum likelihood for the generalized Pareto distribution is problematic in that the maximum likelihood solution does not exist for certain domains of the shape parameter.

The PPCC/probability plot method works well for the five extreme value distributions considered here. For the Frechet distribution, using the Kolmogorov-Smirnov plot may improve upon the PPCC plot.

One issue in developing distributional models for extreme winds data is that we typically want a distributional model for the extreme points (i.e., the points above a given threshold) of the data rather than the full data set.

Assess Goodness of Fit Once a candidate model has been fit, the next to step is to assess the goodness of fit of that model. Some methods for doing this are:
  • The Kolgmogorov-Smirnov goodness of fit test can be applied to ungrouped data.

  • The Anderson-Darling goodness of fit test is a refinement of the Kolmogorov-Smirnov test. Although the Anderson-Darling test is more powerful than the Kolmogorov-Smirnov test, the critical values must be determined for each different distribution. These critical values have been worked out for the Gumbel, Weibull, and generalized Pareto distributions.

  • The chi-square goodness of fit test can be used for grouped data.

  • The probability plot provides a graphical assessment of goodness of fit.

    We recommend complementing any quantitative test with a probability plot.

  • You can generate a histogram with the fitted distribution overlaid.
Using the Fitted Model Once an adequate distributional model has been found, this model will typically be used to estimate some quantities of of interest. For example,
  • Estimate specific quantiles of the distribution

    Quantiles are estimated from the percent point function (also known as the inverse cumulative distribution function).

  • Estimate return intervals and wind speeds corresponding to a given return interval

    The return interval (or mean recurrence interval) of a given wind speed, in years, is defined as the inverse of the probability that the wind speed will be exceeded in any one year. It is defined as

      1/(1 - F(x))

    with F(x) denoting the cumulative distribution function.

    More often, we would like to compute the wind speed that corresponds to a given mean return interval. The solution to this is given by solving the above equation for x

      X(R) = G(1 - (1/R))

    with G and R denoting the percent point function and the desired mean recurrence interval, respectively.

    The above formula is for the case of a set consisting of single yearly maxima. If lambda is mean number of threshold crossings of the extreme speed record per year, the formula is

      X(R) = G(1 - (1/(lambda*R)))

    See Simiu and Scanlan for a more complete discussion of mean recurrence intervals.

Software for Extreme Wind Speeds We discuss how some of these computational issues can be addressed in a few different software environments. We also provide several Fortran-based codes that can be used to analyze some of the data sets provided on this web site.
  1. Fortran-based Program for Analyzing Hurricane Wind Speeds

  2. Fortran-based Program for Analyzing Daily Maximums

  3. Dataplot

  4. e-FITS web site (currently restricted to NIST staff)

  5. Excel-based procedures

  6. ASOS data

    Software is provided for extracting wind speed data from ASOS data sets. The software has the capability of extracting separately non-thunderstorm and thunderstorm wind speeds.

Note that the above list is not exhaustive. Many commercial statistical/mathematical programs can be used to analyze extreme value data. The software described above is intended to provide an example of how these analyses can be performed and is not meant to imply that these software programs are recommended for this task.
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Date created: 03/05/2004
Last updated: 03/10/2011
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