Rainfall Frequency Analysis

8/13/2019 Rainfall Frequency Analysis

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I am sure you have heard about the

farmer in Sidell, Illinois. After that

fiasco with the cheese being left

standing alone taking the blame forpolluting the nearby stream, he

decided to build a channel to transport

the runoff from his feedlots to a

treatment pond. He was advised tosize the channel based on the

expected rainfall in April. However, he

is a bit confused. How much rain falls

in Sidell in April? He found historic

rainfall data for Sidell online at an

Illinois State Water Surveysite, and

found that April rainfall varies from

year to year. Please help the farmer

and save him from another scandal.
http://www.sws.uiuc.edu/data/climatedbhttp://www.sws.uiuc.edu/data/climatedb


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Estimating Rainfall Quantity for Design

The design of water management systems is

based more on extreme valuesthan on average

values. If the mean value is used in the design of

an irrigation system then on average, in one out ofevery two years there will not be enough water to

meet the demands of the crop and yield will be

reduced. If the mean is used in drainage design,

then one out of every two years the crops will beflooded. It is better to use design values with

lower associated risk.


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Estimating 80% Dependable

Rainfall and 80% Maximum Rainfall

from mean and standard

If only the mean and standard deviation of monthly

rainfall are known then

80% Dependable Rainfall = Mean - 0.84 x Standard

Deviation

80% Maximum Rainfall = Mean + 0.84 x Standard

Deviation.


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80% Dependable Rainfall

The value of period rainfall (monthly, seasonal,

etc.) that will be exceeded 80% of the time. Thisvalue ensures that on average, there will be

enough waterto meet the crop's need four out of

every five years.

80% Maximum Rainfall

The value of period rainfall that on average, willnot be exceeded 80% of the time. This value

ensures that on average, a drainage system or a

sedimentation pond will have adequate capacity

four out of every five years.


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Examp le : For Sidell the mean rainfall for April

is 3.75" and the standard deviation is 1.78

80% Dependable Rainfall = 3.75 - 0.84 x 1.78 =

2.25

80% Maximum Rainfall = 3.75 + 0.84 x 1.78 =

5.25"

-0.84 0.84

20% 20%


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10 Step Procedure for

Rainfall Frequency Analysis


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1.

LocateData

Source


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2.

Extract as

SpecificData as

Required


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3.

Import into

Excel andconvert to

columns


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4.Sort, and

ExtractTargeted

Data


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5.

Graph, and

check forjumps,

trends or

cycles


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6.

Sort the data in

ascending orderand determine the

non-exceedanceprobability of each

data value


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7. Plot Probability of Non-exceedance vs Precipitation

(Empirical Distribution Function)


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8. Determine themean and standard

deviation of the

logs of theprecipitation

values


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9. Determine the cumulative log normal

values for the precipitation data


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10. Plot the cumulative

distribution function forthe fitted logNormal

Distribution


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Return Period (T) =1

P

1.0

12.5

= 8 yrs

P = probability of exceedance

Return Period (Recurrence Interval)

The frequency with which, on average, a given

precipitation event is equaled or exceeded.

Example: If there is a 12.5 percent chance

that a storm of a certain magnitude will

occur, the return period for that storm is


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Example: The chance that an 8-year return

period storm will occur over the 5 year lifeof a project is

R = 1 - ( 1 - )n1T

1 - ( 1 - )5 = (49%) 0.4918

Multi-year Chance of Exceedance (R)

The probability of a given return period

storm being equaled or exceeded within a given

number of years.

Rainfall Frequency Analysis

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