This set of Engineering Hydrology Multiple Choice Questions & Answers (MCQs) focuses on “Frequency of Point Rainfall”.

1. The probability of occurrence of an extreme rainfall is estimated by which analysis?

a) Depth analysis of rainfall data

b) Frequency analysis of point rainfall data

c) Duration analysis of point rainfall data

d) Forecasting of point rainfall data

View Answer

Explanation: When an extreme rainfall occurs in a year, it should be further analyzed. This analysis is done to find out the probable time when this extreme rainfall is going to occur again. This evaluation of probability of occurrence of the extreme rainfall is done with the help of frequency analysis of point rainfall data.

2. The data series in which the maximum annual rainfall data is listed is known as ___________

a) Year series

b) Depth series

c) Storm series

d) Annual series

View Answer

Explanation: The data series in which the annual values of an event is noted is called annual series. If the maximum rainfall in a year is listed, then it also constitutes annual series.

3. Which parameter represents the average interval between occurrence of an event having magnitude greater than or equal to a specified magnitude?

a) Running period

b) Post interval

c) Return period

d) Maximum period

View Answer

Explanation: When an event occurs, it is analyzed to find out the probability of its occurrence. The probability of occurrence of that event having magnitude equal to or greater than a specified magnitude can be determined. The average time interval between the occurrence of such event is known as return period. It is also called recurring interval.

4. The return period of an event is inversely proportional to the probability of occurrence of that event.

a) True

b) False

View Answer

Explanation: When a storm occurs, it should be analyzed to find out the probability of its occurrence. The probability of occurrence of an event having magnitude greater than or equal to a specified magnitude is related to the average time interval between the occurrence of the event. The average time interval that is the return period is inversely proportional to the probability of occurrence of the event.

5. Which of the following formula correctly represents the relation between probability of occurrence of an event and its return period?

a) T = 1 / (2 * P)

b) T = 1 / P

c) P = 1 / T^{n}

d) P = n / T

View Answer

Explanation: The relation between the probability of occurrence and return period is given by the following formula:

T = 1 / P

Where,

P = Probability of occurrence of an event having magnitude greater than or equal to a specified magnitude

T = Average time interval between the occurrence of an event which is known as return period

6. What will be the probability of a storm occurring in any one year if the return period of the storm is 20 years?

a) 0.0008

b) 0.05

c) 0.08

d) 0.02

View Answer

Explanation: Given,

Return Period (T) = 20 years

Probability of a storm occurring in any one year (P) = 1 / T = 1 / 20 = 0.05

7. What will be the probability of non – occurrence of 100mm rainfall in a year if its return period is 15 years?

a) 0.088

b) 0.067

c) 0.933

d) 0.885

View Answer

Explanation: Given,

Return Period (T) = 15 years

Probability (P) = 1 / T = 1 / 15 = 0.067

Probability of not occurring of an event (q) = 1 – 0.067 = 0.933

8. State the formula used to find out the probability of occurrence of an event for r times in n successive years.

(Note – Symbols have their usual meaning)

a) P_{r,n} = nC_{r} * P^{r} * q^{n-r}

b) P_{r,n} = nC_{r} * P^{r} * q^{n}

c) P_{r,n} = nC_{r} * P * q^{n-r}

d) P_{r,n} = nC_{r} * P^{r}

View Answer

Explanation: The formula of probability of occurrence of an event r times in n successive years is given by a binomial distribution. The formula is as follows:

P

_{r,n}= nC

_{r}* P

^{r}* q

^{n-r}

P

_{r,n}= Probability of random hydrologic event

P = Exceedance probability

n = No. of successive years

r = No. of occurrences of the event

q = Probability of the event not occurring in a year

9. Using binomial distribution, what is the probability of an event not occurring at all in ‘n’ successive years?

a) nC_{r} * P^{r} * q^{n}

b) q^{n}

c) nC_{r} * P^{r}

d) P^{r}

View Answer

Explanation: Using binomial distribution, the probability of occurrence of an event is given by

P

_{r,n}= nC

_{r}* P

^{r}* q

^{n-r}

Solving the above equation, we get,

The probability of an event not occurring at all in ‘n’ successive years is given by

P

_{0,n}= q

^{n}

Where,

P

_{r,n}= Probability of random hydrologic event

P = Exceedance probability

n = No. of successive years

r = No. of occurrences of the event

q = Probability of the event not occurring in a year

10. Using binomial distribution, what is the probability of an event occurring at least once in ‘n’ successive years?

a) nC_{r} * Pr

b) 1 – q^{n}

c) P^{r}

d) q^{n-r}

View Answer

Explanation: Using binomial distribution, the probability of an event occurring at least once in ‘n’ successive years is given by

P

_{1}= 1 – q

^{n}

P

_{1}= Probability of an event occurring at least once in ‘n’ successive years

q = Probability of the event not occurring in a year

r = No. of repetitions of the event

11. What will be the probability of flood occurring 3 times in next 10 years if the return period is 30 years?

a) 0.0008

b) 1.51 * 10^{-3}

c) 2.41 * 10^{-3}

d) 3.41 * 10^{-3}

View Answer

Explanation: Given,

Return Period (T) = 30 years

Probability (P) = 1 / T = 1 / 30 = 0.033

Probability of not occurring of an event (q) = 1 – 0.033 = 0.967

Probability of flood occurring 3 times in next 10 years = P

_{3,10}

= nC

_{r}* P

^{r}* q

^{n-r}

= {n! / (r! * (n – r)!)} * P

^{r}* q

^{n-r}

= {10! / (3! * 7!)} * 0.033

^{3}* 0.967

^{10-3}

= {10! / (3! * 7!)} * 0.033

^{3}* 0.967

^{7}

= 3.41 * 10

^{-3}

12. According to Weibull’s formula, what the formula of probability of occurrence of an event?

a) P = (N + 1) / m

b) P = N + 1

c) P = m / N

d) P = m / (N + 1)

View Answer

Explanation: Using Weibull’s formula, the probability of occurrence of an event is given by:

P = m / (N + 1)

Where,

m = Order no. of the annual extreme series arranged in descending order

N = Numbers of years of record

P = Probability of an event having magnitude greater than or equal to a specific magnitude

13. Based on Weibull’s formula, what is the mathematical expression for return period?

a) T = (N + 1) / m

b) T = N + 1

c) T = m / N

d) T = m / (N + 1)

View Answer

Explanation: Using Weibull’s formula,

Probability of an event = m / (N + 1)

We know,

Return period (T) = 1 / P

Therefore, Return period (T) = 1 / (m / (N + 1))

= (N + 1) / m

14. What is the purpose of frequency analysis of an annual series?

a) Obtaining relation between magnitude of event and its exceedance probability

b) Obtaining magnitude of event only

c) Obtaining exceedance probability only

d) Obtaining depth of rainfall only

View Answer

Explanation: An extreme storm is of great importance. It is analyzed using frequency analysis to find out the probability of its occurrence in the upcoming years. The probability of the storm to reappear is set for a magnitude equal to or greater than the present extreme storm. Thus, the frequency analysis of the annual series gives the relation between the magnitude of the event and its exceedance probability.

15. Which of the following is an analytical method considering frequency factors which is used to estimate the reappearance of magnitude of rainfall having specific duration?

a) Gumbel’s extreme value distribution

b) Exponential extreme value distribution

c) Rutherford’s value distribution

d) Lagrange’s distribution

View Answer

Explanation: After calculating probability of occurrence of an extreme rainfall, a graph is plotted to estimate the return period of that rainfall having specific duration. To make the results more accurate, certain analytical methods are used. Gumbel’s extreme value distribution is one of the analytical methods.

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