CIV E 445 - APPLIED HYDROLOGY
SPRING 2014
LAB No. 8 SOLUTION

  • The plotting position table is shown below.

  • The Gumbel paper is constructed.

  • The plotting positions are plotted on the Gumbel paper.

  • The number of values is n = 20. The mean of the data is: 3407.25 cfs. The standard deviation is: 1492.46 cfs.

    From Table A-8, for n = 20, the mean and standard deviation of the Gumbel variate are 0.5236 and 1.0628, respectively. The computations are summarized in the following table.

    Return period
    (yr)     		Probability of exceedence
    (%)     		Gumbel variate Frequency factor Flood discharge
    (cfs) (Hand)     		Flood discharge
    (cfs) (Online)     		Difference
    (cfs)
    | Hand - Online |
    1.05 95 -1.113 -1.540 1109 1109 0
    1.11 90 -0.838 -1.281 1496 1495 1
    1.25 80 -0.476 -0.941 2003 2004 1
    2 50 0.367 -0.147 3188 3187 1
    5 20 1.500 0.919 4778 4778 0
    10 10 2.250 1.624 5830 5832 2
    25 4 3.199 2.517 7162 7164 2
    50 2 3.902 3.179 8150 8151 1
    100 1 4.600 3.836 9130 9132 2
    200 0.5 5.296 4.490 10106 10109 3

  • The Gumbel fit is plotted on the Gumbel paper.

  • The results are verified using ONLINE GUMBEL.

  • The comparison is shown on the table. The mean of the absolute value of the differences between hand-calculated and online results is 1.3 cfs.