Exercise 1 - Simonton Problem
Exercise 1

Flooding Along The Brazos River Near Simonton, Texas

    An incomplete analysis of the maximum annual discharge near Simonton, Texas is given in the table below. There are 77 years of data in the complete set but only the top 5 events are presented. Your task is to fill in the missing data using what you have learned up to this point.

    The N Maximum Annual Discharge data were ranked with the largest discharge having rank M = 1 and the smallest rank M =77 (in this case).

    The Recurrence Interval (RI) is the average interval, in years, between occurrences of two discharges of equal (or greater) magnitude. This relationship, known as the Weibull equation, can be written:

      RI = (N+1)/M

    where N and M are defined as above.

    The Annual Exceedence Probability (P) is the probability (expressed as a percentage) that a flood of that magnitude or greater will occur in a given year and is given by:

      P = (1/RI)100

    For the problem as stated, the numerator of the Weibull equation (RI = (N+1)/M ) has a value of:

    [Click on the blank and the cursor should appear. Type in the answer and hit return. If you entered a wrong value the correct value will appear in red]

    [Remember that there are 77 years of data in the complete set - therefore N = 77]

    The largest value of M in this abreviated data set (the ranking of a particular event) is :

    C A L C U L A T O R

    Click on the blank on the left and center a value. Hit the tab key and enter the other value. Click on the operation that you want to preform.

    YearMaximum Annual
    Discharge (cfm)
    RankRecurrence InternalExceedence Probability
    1929123,000 cfm1781.28%
    1957 119,000 cfm
    1941117,000 cfm3
    196598,900 cfm4
    199294,000 cfm
    Multiple choice  

    What is the Recurrence Interval for the largest event out of 77 events?


    What is the probability of occurance of an event with a discharge of 94,000 cfm?

      much greater than 6%
      about 6%
      much less than 6%

    An event has a Recurrence Interval of 19.5. This means that there is an average interval of 19.5 years between events of this (or greater) magnitude.


    It has been determined that a flood on the Brazos near Simonton, Texas with a discharge of more than 90,000 cfm will do major damage. You have a chance to invest in a hunting camp that fronts on the Brazos River at Simonton. Is this a good investment?


    Print a copy of your answers for future reference. Some browsers will not print the colored text or the filled in circles. You can print the page and add your answers in pencil. Not very fancy but it will work.

    Or, you could do a "screen dump" and take a picture of your screen. For the Macintosh you would hold down the Shift, Command and 3 keys. This produces a PICT file that you can save for future reference.

    A plot of Recurrence Interval (RI) versus Maximum Annual Discharge is given below.

    From the diagram given above, estimate the discharge of the 100 year flood near Simonton, TX.

      about 120,000 cfm
      about 100,000 cfm
      about 200,000 cfm

    According to this diagram, what is the recurrance probability for a flood with a discharge of more than 90,000 cfs?

      about once every 20 years
      about once every 10 years
      about once every 5 years