reporting 3a

7/31/2019 Reporting 3a

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PROBABILITY IN

HYDROLOGY:

A BASIS FOR PLANNING



GOAL :

Not to eliminate all floods but to

reduce the frequency of flooding and,hence, the resulting damages.



Does a flood have anything to dowith earthquakes and tsunamis ?

Yes, because those things causefloods.

Some other causes are soil erosion

and too much precipitation (snow andrain).



Is flood water fresh water or salt water?

If you guessed fresh water you aremostly right.Floods usually come from a body of freshwater caused by precipitationIf you guessed salt water you were

right in one caseFloods caused by tsunamis are salt



FLOOD PROBABILITY

SELECTION OF DATA

PLOTTING POSITIONS

THEORETICAL

DISTRIBUTION OF FLOODS



SELECTION OF DATA

RELEVANCEImplies that the data must deal with the problem.

ADEQUACY

refers primarily to length of record.

ACCURACY

refers primarily to the problem of homogeneity.



)( E Return Period

Random variable:

Threshold level:

Extreme event occurs if:

Recurrence interval:Return Period:

Average recurrence interval between events

equaling or exceeding a threshold

If p is the probability of occurrence of an extremeevent, then

or

Return Period

X

T x

T x X

T

x X of ocurrencesbetweenTime

)( E

pT E 1

)(

T

x X P T

1)(



PLOTTING POSITIONS

The plotting position formulae are applied to

compute the probability of occurrence of observed

Weibull’s Formula:

F(Q) = i/(N+1)Gringorten Formula:F(Q) = (i-0.44)/(N+0.12)

Where F(Q) = Non-exceedance probabilityi = Rank (1,2,3,…., N) N = Total number of data points



Probability plot of flood flows



Goal: to determine design

discharges

• Flood economic studies require flooddischarge estimates for a range of returnperiods

– 2, 5, 10, 25, 50, 100, 200, 500 years• Flood mapping studies use a smaller

number of return periods – 10, 50, 100, 500 years

• 100 year flood is that discharge which isequaled or exceeded, on average, onceper 100 years.



x

f X ( x)

sK T

x

T x

T x X P T

1)(

Frequency Factors

Chow proposed using:

Where:

sK x x T T

deviationstandardSample

meanSampleperiodReturn

factorFrequency

magnitudeeventEstimated

s

xT

K

x

T

T

x

f X ( x)

sK T

x

T x

T x X PT

1)(



More on return period

If p is probability of success, then (1-

p) is the probability of failure

Find probability that (X ≥ xT) at least

once in N years.

N

N

T

T T

T

T

T

p years N inonceleast at x X P

years N all x X P years N inonceleast at x X P p x X P

x X P p

111)1(1)(

)(1)()1()(

)(



0

100

200

300

400

500

600

1905 1908 1918 1927 1938 1948 19 58 1 968 197 8 198 8 1998

Year

A n n u a l M a x F l o w ( 1

0 3 c

f s ) Return period example

Dataset – annual maximumdischarge for 106 years on

Colorado River near AustinxT = 200,000 cfs

No. of occurrences = 3

2 recurrence intervals

in 106 years

T = 106/2 = 53 years

If xT = 100, 000 cfs7 recurrence intervals

T = 106/7 = 15.2 yrs

P( X ≥ 100,000 cfs at least once in the

next 5 years) = 1- (1-1/15.2)5 = 0.29



Frequency curve plotted on

Gumbel probability paper

reporting 3a

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