1. Hazards Planning and Risk Management Flood Frequency Analysis
Lecture No. 13
Flood Frequency Analysis
Fall 2016
Picture source: Prof. Stephen A. Nelson (Tulane University) notes.
US – Pakistan Center for Advanced Studies in Water

2. Learning Objective
How to calculate floods with different recurrence intervals using historical data
Picture from Internet.

3. Reading Material
Elements of Physical Hydrology By George M. Hornberger, Patricia L. Wiberg, Jeffrey P. Raffensperger, Paolo D'Odorico
A limited preview available on Google Books.

4. Flood Response of river to precipitation
An unusually high stage of a river
Peak in a hydrograph
Fills up the stream up to its banks and often spills over to the adjoining flood plain
Fills up the stream…….: when river is in its natural state that’s no hydraulic structures.
Peak in a hydrograph regardless of whether river actually leaves its banks and causes damages. Flood hydrographs are characterized by a steeply rising section followed by a less steeply falling segment as the flood passes.
Flood occur throughout the year but the magnitude of peak discharge varies seasonally in response to changing weather conditions.
Poplar creek is perennial and Frio is ephemeral (dry for long periods with occasional large floods) stream.

5. Mean Rainfall
Mean Annual Rainfall: determined by averaging the total rainfall of several consecutive years at a place
Mean monthly Rainfall: by averaging the monthly total rainfall for several consecutive years

6. Natural Floodplain Features
Floodplain: Normally dry land area adjoining rivers, streams, lakes, bays or ocean that is undated during flood events
Floodplains carry flow in excess of the channel capacity.
Provides both conveyance mechanism and a temporary storage area for excess water

8. Flood Estimates
Estimate of extreme flood flow is required for the design of flood control hydraulic structures and Disaster Risk Assessment
Magnitude of flood may be estimated in accordance with the mitigation measures
2104

9. Flood Estimation: Frequency Analysis
Objective is to develop a frequency curve
Probability or likelihood of having certain events occurring over a specified period is estimated
Frequency curves can be developed to evaluate maximum events
Used for planning water resources structures and for flood mitigation
Relationship between the magnitude of events and either the associated probability or the recurrence interval
Weather systems vary year to year and hence magnitude of future events can not be predicted accurately
Have to rely on statistical analyses of rainfall amounts over certain period
Frequency distribution of past events
Source: Hydrology and the management of watersheds By Kenneth N. Brooks
Reservoirs, waterways, irrigation networks should be planned and designed for future events.

10. Recurrence Interval of a Storm
Number of years within which a given flood may equal or exceed
Also known as return period
Tr = (n+1)/m
Where;
Tr = Return Period
n= Number of years of record
m= Rank of the event (storm) (descending order)
Means this discharge value or more than that occurs m times in n years
Ranking: The serial number of a specific value of precipitation in the descending order
Return Period: Time interval after which a storm of given magnitude is likely to recur.

11. Frequency = p * 100 = m/(n+1)* 100
Probability: Reciprocal of the return period
p = m/(n+1)= 1/ Tr
Frequency: Probability expressed in terms of percentage
Frequency = p * 100 = m/(n+1)* 100
Example 4.13 source: Elementary Engineering Hydrology By Deodhar M. J.
Frequency: Inverse of return period multiplied with 100 and expressed as %. Frequency of a rainfall of a given magnitude means the number of times the given event may be expected to be equaled or exceeded in 100 years

12. Example: Solution: Excel file
Highest or peak discharges (floods) in each year used for calculation.
If there are 20 years of record for a station we may expect that the largest recorded flood is an approximation to the “20-years flood”….. A flood that occurs, on average” once in 20 years.
Depends on both type of structure and damage or loss of life expected if the design flow exceeded. Typically 20 years flood for road culverts and 10,000 for major dams.
Series of the largest flood in each year is termed as “annual series”.

13. Discharge Vs. Recurrence Interval

14. The probability of a certain-size flood occurring during any period can be calculated using the following equation:
Pt = 1-(1-p)N
Even though the 100 year flood has a 0.01 or 1% chance of occurring in any year, this does not mean that the 100 year flood has a 100% chance of occurring every 100 years.

15. Prob (no occurrence in N years) = (1-p)N
Explanation
Once the frequency curve is developed, the probability of exceeding certain rainfall amount over a specified period can be determined
The probability that an event with probability p will be equaled or exceeded x times in N years is determined by:
If x=0 (no occurrence in N years) then
Prob (no occurrence in N years) = (1-p)N
Therefore;
Prob (at least 1 occurrence in N years) = 1-(1-p)N

16. Estimate the 100 year Flood?
100 years flood = 0.01 exceeding probability
Source:?

17. Floodplain Zoning Zoning features of a regulated floodplain
The flood hazard area is generally defined at the 100-year floodplain.

18. Flood Frequency Analysis
Source: Elements of physical hydrology By George M. Hornberger
As records become longer, estimates of extreme events become better.

19. Ref: Flood Estimates
Source: Elements of physical hydrology By George M. Hornberger

20. Discussion/Comment/Question