lecture5a probability

8/10/2019 Lecture5A Probability

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(c) Dr. Shanker Kumar Sinnakaudan 2

Probability for Engineering

Hydrology

CEW 503




Flood ?Risk ?

Flood on 5 September 1999, Juru, Malaysia

Probability?

© Dr. Shanker Kumar Sinnakaudan




Rare Events in Hydrology

There are three main areas where it is

useful to estimate the occurrence ofrare events:

• Floods

• Low flows (droughts)

• Rainfall




Probability?

• A mathematical basis for prediction, which,

for a huge set of outcome, is the ratio of theoutcomes that will produce a given event to

the total number of possible outcomes,




Background

• Variability in rainfall and the resulting

stream flow must be dealt with in

planning and design• We cannot predict future with reliable

degree of certainty Solution is to apply

methods of probability and statistics




Why Use Probability in

Hydrologic Analysis?

• Hydrological systems are complex in nature

• Generalization of hydrologic features

• Statement of probability that an event will

equal or exceed (or be less than) a specific

value

• Not to eliminate but to reduce the frequency

of the event




Flood probability

• Refer to Flood peaks

• Must use relevant, adequate and accurate data

R = The data must indicate the problem

A = length of record

A = is the catchment is homogenous for last

10, 50 or 100 years ?(bunds , dams, Urbanization >> influence the flow

records in various stages)




Length of Record Required to estimate floods

of various probabilities with 95 % confidence

Acceptable error

Design

Probability 10 % 25%

0.1 90 18

0.02 110 39

0.01 115 45




Flood Frequency




Annual Floods

• •For flooding considerations, we want to

estimate the probability of an extreme event

occurring in some time period.




•Consider a levee adjacent to a

stream, where Q is the discharge that

just overtops the levee, and causesflooding




Annual Floods

• Define pqas the probability that discharge

equals or exceeds q at least once in a given

year

• The probability that flow isn’t exceeded is

the compliment, or 1 -pq




For annual floods make the following

assumptions:

• The exceedence probability in a given yeardoesn’t depend on what happened in

previous years

• The exceedence probability is constant fromyear to year

Annual Floods




• Note: 100 yr floods do not occur every 100 years!

• The average interval between annual floodsequaling or exceeding the 100 yr flood is 100

years

• Actual interval is highly variable:

• 5% of time actual interval ! 300 yrs

• 5% of time actual interval < 5 yrs

Average Recurrence Interval (ARI)




Return Period (Tr

)

• Given Tr = 100 yr. , what is the

probability that a given event will

occur in any one year?

Pr = 1/(Tr ) = 1/100 = 0.010.1 = 10 years ARI

0.02 = 50 years ARITr = 1/(Tr)




Risk Reliability & Safety Factor

• Risk of Failure of a design project

Exp: a weir has design life period of 50 yrs

designed for ARI = 100 yrs

Known: the weir will fail if a flood Q > than

ARI 100 yrs within weir life (50 yrs)P of occurrence an event (x xT) at least once

over a period of n successive years called RISK




Example:

Given:

Expected life of Permatang Rawa Bridge = 25 years

Design ARI = 100 years

a) Risk of Hydraulic Design ?

b) What is the percentage of Reliability ?c) If 10 % risk acceptable, what return period to be

adopted?




Solution

%2.22

222.0

100

111

100,25,

111:

25

R

yrsT yrsn Here

T RTherisk

na)

(The Inbuilt Risk)




Solution

b)

yrsT

T

T

R If

238

90.01

1

11110.0

10.0%10,

25

25

lecture5a probability

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