Analyses of Rainfall

Hydrology and Water Resources RG744Institute of Space TechnologyOctober 05&11, 2013

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

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.

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

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.

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

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

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

Frequency

Frequency: Probability expressed in terms of percentage

Frequency = p * 100

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:

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)

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) thenProb (no occurrence in N years) = (1-p)N

Therefore; Prob (at least 1 occurrence in N years) = 1-(1-p)N

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

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

Intensity Duration Curve

Example: A storm occurred over a catchment area as under:

Time (min) Precipitation (mm)

0 0

10 19

20 22

30 7

40 20

50 23

60 33

70 28

80 8

90 6

Plot maximum duration intensity curve?

Intensity Frequency Duration Analysis

When sufficient data (say 50 years) for a catchment area is available

Analyze data for each storm

Analyze for:IntensityFrequencyDuration

Different graphs for different catchment areas depending on their hydrologic character

Intensity-Frequency-Duration Curve

To know rainfall intensities of different duration and different return period

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

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

DAD Curve Based on records of several storms on an area

Maximum areal precipitation for different durations corresponding to different areal extents

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

Probable Extreme Rainfall Events (Standard Design Storms) Probable Maximum Precipitation

Standard Project Storm

Frequency based storm

Important for water resources engineering

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)

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

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)

Solution to example