1. Analyses of Rainfall Hydrology and Water Resources RG744
Institute of Space Technology
October 05&11, 2013

2. 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
Mean annual rainfall: minimum of years of continuous records is desirable.
Deficit or surplus rainfall comparing with mean annual rainfall

3. Interception and Net Precipitation
Vegetation influence on pattern of deposition and amount of precipitation reaching the soil surface
Interception losses are less in arid and semiarid regions that have sparse vegetation
Net precipitation is gross precipitation (measured by gauge) minus interception loss
Net precipitation is the amount available either to replenish soil water deficits or to become surface, subsurface, or ground water flow.

4. Effective Rainfall
Rainfall component causing perceptible change in the stream flow
That is only a portion of the total rainfall recorded over the catchment
Rainfall that does not infiltrate the soil and moves into the stream as overland flow
Infiltration capacity: High in dry soil
No overland flow if precipitation is lower than infiltration capacity (but interflow may occur).
With persistence precipitation , the soil becomes wet and infiltration rate decreases causing runoff. 4

5. Flood/Storm Frequency
Flood frequency: number of times a particular flood/storm can be expected in a river/watershed in a given number of years
Example: 100 year flood – a flood that can be expected once in 100 years. (usually worked out by extrapolating the observed data)
Frequency is the percentage of years, during which a storm of a given magnitude may be equaled or exceeded
Recurrence interval/return period: Time interval after which a similar flood can be forecasted or expected.
Return Period: Time interval after which a storm of given magnitude is likely to recur.

6. Frequency Analysis Objective: to develop a frequency curve
Precipitation frequency curves can be developed to evaluate maximum events
Used for planning water resources structures
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
Probability or likelihood of having certain events occurring over a specified period is estimated
Source: Hydrology and the management of watersheds By Kenneth N. Brooks

7. Recurrence Interval of a Storm
Number of years within which a given storm may equal or exceed once - Also known as return period
Means this precipitation 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 .
Source: Hydrology Principles

8. Probability of Exceedance
The probability of occurrence of a flood (having a recurrence interval T-year) in any year,
Probability: Reciprocal of the return period
p = 1/ T
Example source: Elementary Engineering Hydrology By Deodhar M. J.
Frequency: Inverse of return period multiplied with 100 and expressed as %.

9. Frequency Frequency: Probability expressed in terms of percentage
Frequency of a rainfall of a given magnitude = the number of times the given event may be expected to be equaled or exceeded in 100 years
Example source: Elementary Engineering Hydrology By Deodhar M. J.
Frequency: Inverse of return period multiplied with 100 and expressed as %.

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

12. Hydrology and Management of Watershed by Kenneth.
Frequency curve of daily rainfall for a single station
The probability of having a 24 hr rainfall event of 100mm or more in any given year is about 0.02 (or a 50 year recurrence interval)

13. Prob (no occurrence in N years) = (1-p)N
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
Example: the probability of having a 24 hr rainfall event of 100mm or greater over a 20 year period is determined by (see solution in the end)

14. The percentage probabilities of floods (or rainfall) of different recurrence intervals (T) to occur in particular periods (N) are given in Table 8.4
Source: Hydrology Principles

15. Intensity Duration Analysis
Study of intensity and its duration is called Intensity Duration Analysis
Usually most intense storms last for shorter duration
As intensity reduces duration increases

16. Intensity Duration Curve
Graph of duration vs. intensity for an area
Normally follows the following equation
Where;
I = intensity in mm/hr
t = duration in minutes
C, a, b = constants for the specific area
Also known as intensity duration graph.
Source: Elementary Engineering Hydrology By Deodhar M. J.

17. Intensity Duration Curve
Intensity Duration Curve prepared for a specific study

18. Example: A storm occurred over a catchment area as under: Time (min) Precipitation (mm) Plot maximum duration intensity curve?

19. Intensity Frequency Duration Analysis
When sufficient data (say 50 years) for a catchment area is available
Analyze data for each storm
Analyze for:
Intensity
Frequency
Duration
Different graphs for different catchment areas depending on their hydrologic character

20. Intensity-Frequency-Duration Curve
Source: Hydrology by Das and Saikia
To know rainfall intensities of different duration and different return period

21. Isopluvial Maps
Combined map for large area for maximum rainfall depth for various combination of a return period and duration
These are Isohyets shown on regional rainfall map

22. Source: Engg Hydorlogy,3E
 By Subramanya

23. Depth-Area-Duration (DAD) Analysis
Average depth of storm and its duration for a specific area
Also called DAD study
Horton’s Equation
Pa =Poe-(KA)^n
Areal spread of rainfall within watershed. Amount of high rainfall that may be expected over the catchment.
Frequency analysis discussed before is based upon rainfall characteristics at a point or a specific location. The design of storage reservoir and other water resources related structures required that the watershed area to be taken into account. Because rainfall is usually not uniform, increasing the area of watershed the depth of rainfall with a certain probability will decrease.
Every storm has a center having maximum precipitation.
Po= maximum precipitation at the center of storm.
Pa=Average Precipitation over a specific area.
(Po-Pa) is positive value and its value increases with bigger catchment and decreases with smaller catchment.
K & n are regression constants varies with duration of storm.

24. DAD Curve Based on records of several storms on an area
Maximum areal precipitation for different durations corresponding to different areal extents
Source: Hydrology Principles

27. Depth-Area-Duration (DAD) Curve
Based on records of several storms on an area
Maximum areal precipitation for different durations corresponding to different areal extents

28. Index of wetness
Ratio of rainfall in a given year and average annual precipitation
When it is
Less than 1 - bad year/deficient year/ dry year
More than 1 – good year / surplus year / wet year
Equal to 1 – normal year
Source: Deodhar chapter 4

29. Probable Extreme Rainfall Events (Standard Design Storms)
Probable Maximum Precipitation
Standard Project Storm
Frequency based storm
Important for water resources engineering

30. Probable Maximum Precipitation (PMP)
Assumed physical upper limit of rain that will fall over a specified area in a given time (that’s physically possible)
Rainfall for a given area and duration that can be reached or exceeded under known meteorological conditions
Used to provide an estimate of the Probable Maximum Flood (PMF) hydrographs
For design of major structure with the threat of loss of life PMP is used (where no risk of failure accepted)
Source: usf
Amount of rainfall over a region that can not be exceeded over at that place. The greatest depth that can occur in a given duration at a given location
Higher in hot humid regions.
PMP is obtained by studying all the storms that have occurred over the region and maximizing them for the most critical atmospheric conditions (assuming maximum air moisture and maximum air inflow occurs simultaneously) .
PMF estimated after appropriate adjustment for infiltration losses.

31. Standard Project Storm (SPS)
Storm which is reasonably capable of occurring over the basin under consideration (actually occurred)
The heaviest rain storm occurred in the region during the period of rainfall records
Used for design project with economic considerations and low risk
SPS or SPF - Standard Project Flood

32. Frequency Based Storm
i: Frequency analysis of long term stream flow data at a site of interest Or
ii: Frequency analysis of rainfall data coupled with rainfall- runoff model to get design flood (if flow data is not available)
ii) When i data is not available

33. Solution to example
Source: Hydrology and the Management of Watersheds by Brooks