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 for polluting the nearby stream, he decided to build a channel to transport the runoff from his feedlots to a treatment pond. He was advised to size 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 Survey site, and found that April rainfall varies from year to year. Please help the farmer and save him from another scandal.

Estimating Rainfall Quantity for Design

The design of water management systems is based more on extreme values than on average

values. If the mean value is used in the design of an irrigation system then on average, in one out of every 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 be

flooded. It is better to use design values with lower associated risk.

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.

80% Dependable RainfallThe value of period rainfall (monthly, seasonal, etc.) that will be exceeded 80% of the time. This

value ensures that on average, there will be enough water to meet the crop's need four out of

every five years.

80% Maximum RainfallThe value of period rainfall that on average, will

not 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.

Example : 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%

10 Step Procedure for Rainfall Frequency

Analysis

1.LocateDataSource

2.Extract as

SpecificData asRequired

3.Import into

Excel andconvert to

columns

4.Sort, andExtractTargetedData

5.Graph, and

check forjumps,trends orcycles

6. Sort the data in ascending order and determine the non-exceedance probability of each data value

7. Plot Probability of Non-exceedance vs Precipitation

(Empirical Distribution Function)

8. Determine the mean and standard deviation of the logs of the precipitation values

9. Determine the cumulative log normal values for the precipitation data

10. Plot the cumulative distribution function for the fitted logNormal Distribution

Return Period (T) =

1

P

1.012.5

= 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

Example: The chance that an 8-year return period storm will occur over the 5 year life of a project is

R = 1 - ( 1 - )n

1T

1 - ( 1 - )5 = (49%) 0.49

18

Multi-year Chance of Exceedance (R)

The probability of a given return periodstorm being equaled or exceeded within a given number of years.