1. Lecture No. 15 Hazards Planning and Risk Management
Flood Frequency Analysis & Population Forecasting
Fall 2017
Picture source: Prof. Stephen A. Nelson (Tulane University) notes.
US – Pakistan Center for Advanced Studies in Water

2. Learning Outcome After this lecture, students will be able to
Calculate - floods with different recurrence intervals using historical data
Perform - population forecasting
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
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

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
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
Example 4.13 source: Elementary Engineering Hydrology By Deodhar M. J.

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

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

15. Discharge Vs. Recurrence Interval

16. 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.

17. 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

18. Estimate the 100 year Flood?
100 years flood = 0.01 exceeding probability

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

20. Urban Vulnerability Assessment Population Estimation
More Look at ‘RA Elective Element’ of ITC

21. Population Projection
Needed for planning purposes
Length of time in the future for projections
Short term (up to 10 years)
Long term (up to 50 years)
Both depend on past records

22. Population Forecasting
Model to estimate population
Direct Method
Indirect Methods

23. Direct Method

24. Methods for Estimation
Graphical methods
Extrapolation
Least squares regression
Mathematical methods
Assumes that population growth follows a mathematical relationship

26. Population Growth
Population growth is generally considered to be exponential
P=Po e rt
where:
P = future size of the population at time ‘t’
Po = current size of the population
t = number of years for the extrapolation
r = assumed constant rate for each of the ‘t’ years
Reference: class notes of Dr. deMonsabert (GMU)

27. How to Calculate r? r=(b-d)+(i-e)
The growth rate (r) is usually expressed as a fraction of the increase in population per year
Growth rate is also defined by the following equation:
r=(b-d)+(i-e)
where:
b = birth rate d = death rate
i = immigration rate e = emigration rate
i-e = net migration b – d = Natural increase of population
Net migration= the rate with which people moving into a region minus the rate with which people leaving that region

28. Example:
The 2010 population in a town is surveyed and determined to be 50,000 people. What would you predict the population to be in the years 2020 if birth rate is 40 persons / 1000 people (or 4 %), death rate 15 persons / 1000 and net migration is 10 persons / people?

29. Doubling Time
Double time represents the length of time for the population to double in size when growing with a constant growth rate (r)
Tdb =70/r
where:
Tdb = the doubling time
r = the constant growth rate in %

30. Indirect Method Population estimate derived from:
Household counts and occupancy rate
School registered children
Residential area with population density
Roof Area Method
Total Population = Total roof area of all buildings/average roof area per person
What about informal settlements?
Sample survey can be done to calculate population density or average roof area per person.

31. Source of Data
Existing registers: Census data, cadastral data, taxation data
Existing maps: Topo maps, cadastral map
Field surveys
Satellite images/aerial photographs
DEM and DSM (deriving building heights)

32. Statistics Characteristics
Number of inhabitants
Densities
Age composition
Gender distribution
Etc.

33. Dynamic Characteristics
Population is dynamic in space and time
Activity pattern
Distribution in space
Distribution in time

34. Daily Human Activities
Source: Dr. Richard Sliuzas, ITC
Similar charts for ‘Presence of school children’ and ‘presence of housewives’ during day for different days of a week.
Hourly presence of people = # of house holds* (persons) + # of shops* (persons) +# of other units *(persons)

35. Reading Material for Next Class
The Impacts of Natural Disasters: A Framework for Loss Estimation (Read Online or download at
How Accurate are Disaster Loss Data? The Case of U.S. Flood Damage pdf
HAZUS
Loss Module

36. Discussion/Comment/Question