Engineering Hydrology Questions and Answers – Gumbel’s Method – Set 2

This set of Engineering Hydrology Multiple Choice Questions & Answers (MCQs) focuses on “Gumbel’s Method – Set 2”.

1. In Gumbel’s method, the reduced mean and reduced standard deviation are functions of which of the following?
a) Return period
b) Sample size
c) Flood magnitude
d) Return period and sample size

Explanation: The reduced mean ($$\overline{y_n}$$) and reduced standard deviation (Sn) are important terms in Gumbel’s analysis and are part of the frequency factor. Both these terms depend only the sample size and they are standard table that give these values. For infinite sample size, ($$\overline{y_n}$$) = 0.577 and Sn = 1.2825.

2. Given below are the steps involved in Gumbel’s analysis to find the flood magnitude xT corresponding to a return period T, based on an annual flood series. Identify the correct sequence of steps.
A: Determine mean and standard deviation of the data
B: Determine the reduced variate
C: Determine the flood magnitude of return period T
D: Determine sample size, reduced mean and reduced standard deviation
E: Determine frequency factor
a) A→ B→ E→ D→ C
b) A→ D→ B→ E→ C
c) B→ E→ A→ D→ C
d) D→ E→ B→ A→ C

Explanation: Since the time period and sample size is known and the flood data is given, steps A, B and D can be carried out in any order. Calculation of the frequency factor requires reduced variate, reduced mean and reduced standard deviation. Hence, step E should be carried out only after step B and D. Step C is the final step.

3. As per Gumbel’s analysis for a very large sample size, what is the probability of occurrence of a mean annual flood?
a) 33.3%
b) 42.9%
c) 50%
d) 75.2%

Explanation: A flood discharge with a return period of 2.33 years is a mean annual flood as it is obtained as the average of annual series from Gumbel’s analysis. This is valid when the sample size is very large.
∴ Probability of occurrence =$$\frac{1}{T}=\frac{1}{2.33}$$=42.9%

4. What is the shape of Gumbel distribution when plotted on a Gumbel probability paper?
a) Straight line
b) Bell shaped
c) S-shaped
d) Parabolic

Explanation: Gumbel probability paper is a special graph to plot the Gumbel distribution in the form of discharge (ordinate) vs. return period (abscissa). Since a variate varies linearly with the reduced variate as per Gumbel’s equation, a linear plot is obtained on a Gumbel probability paper. This property is used in flood estimation by simple graphical extrapolation.

5. When using a semi-log graph for plotting discharge and return period in Gumbel’s analysis, only 3 sets of values are required.
a) True
b) False

Explanation: Unlike a Gumbel probability paper, a semi-log or a log-log graph will not give a straight line for a flood discharge vs. return period plot. Hence, a large number of values of return period and its corresponding flood value will be required to obtain the specific curve for the given annual series for the particular area.

6. What is the minimum set of values of return period and its corresponding flood discharge to be computed for Gumbel’s analysis by graphical method on a Gumbel probability paper?
a) 1
b) 2
c) 3
d) 4

Explanation: Since it is known that the relationship between flood discharge and return period is linear when plotted on a Gumbel probability paper, only two sets of values (points) are required to obtain a straight line, which can then be linearly extrapolated to obtain the required flood value.

7. Which of the following terms is used to construct the return period axis on a Gumbel probability paper?
a) Mean of variate
b) Standard deviation of variate
c) Reduced mean
d) Reduced variate

Explanation: The abscissa of a Gumbel probability graph is specially marked for return period scale by using values of reduced variate. The required values of return period are selected and their corresponding reduced variates are calculated. These are then plotted on a separate limited arithmetic scale of reduced variate values constructed below the return period axis. The return period scale is then marked using the values from the reduced variate axis.

8. Compute the frequency factor for Gumbel’s analysis for estimating a flood magnitude of return period 25 years. Assume a very large number of data in the annual flood series.
a) 1.56
b) 2.67
c) 2.04
d) 3.32

Explanation: For very large sample size, ($$\overline{y_n}$$)=0.577 and Sn = 1.2825.
Reduced variate, $$y_T=-ln⁡.ln⁡\frac{T}{T-1}=-ln⁡.ln⁡\frac{25}{24}$$=3.1985
∴Frequency factor, $$K=\frac{y_T-\overline{y_n}}{S_n} =\frac{3.1985-0.577}{1.2825}$$=2.04

Sanfoundry Global Education & Learning Series – Engineering Hydrology.