Precipitation and its losses part 1

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Dr. Sanghamitra Kundu

Dept. of Civil Engineering

Precipitation and its losses

Precipitation and its forms

� Any form of moisture reaching the earth’s surface from the atmosphere� Drizzle

� Water drops with dia. 0.1 – 0.5 mm

� Rain� Glaze� Sleet

� Pellets between 1 – 4 mm in diameter

� Snow� Hail

� Irregular bumps of ice > 5 mm

� Dew

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Measurement of Precipitation

� Measured on the basis of the vertical depth of water that would accumulate on a level surface if the precipitation is retained where it fell� 1 cm of rainfall over a catchment area of 1 km2 represents a volume of water equal to 104 m2

� Characteristics of Precipitation� Duration - Measured in units of minutes or hours

� Depth - Measured in units if mm or inches

� Rate Intensity - Measured in units of mm/hr or inch/hr

� Precipitation can be classified based on intensity as, � Trace → < 1 mm

� Light rain → up to 2.5 mm/h

� Moderate rain → 2.5 mm/h to 7.5 mm/h

� Heavy rain → >7.5 mm/h

� The instrument used to collect and measure the precipitation is called raingauge

Types of raingauges:

� Non-recording : Symon’s gauge

� Recording

� Tipping-bucket type

� Weighing-bucket type

� Natural-syphon type

Measurement of Precipitation

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Measurement of Precipitation� Measurement of rainfall is done by use of rain gauges

Symon’s Rain Gauge

(Non-recording type)

Tipping Bucket Rain Gauge

Weighing type Rain Gauge

(Recording type)

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Rainfall measurement devices

Standard Rain Gauge

Weighing Gauge

Tipping Bucket

Difficulties in the measurement of

precipitation

� Rain gauge itself may cause eddy currents and may affect thecatch of the rain gauge

� Evaporation of water collected in the rain gauge

� Some rainwater may be lost in wetting the sides of the funnel orthe measuring flask

� Splash into or out of the funnel may modify the true value ofrainfall

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Considerations for selecting site for a

Rain Gauge

� Site should be an open level ground

� Clear distance between the obstruction and the rain gauge should be at least twice the height of the obstruction� No nearer than 30 m

� Site should be representative of the area

� Roof installation and windward slopes should be avoided

� Rain gauge should be installed upright in a vertical mode

Placement and Installation of Rain Gauge

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Analysis and Interpretation of Rainfall Data

� Average precipitation� The average precipitation whether it is annual, seasonal or daily, is taken as average of the last 30 years

� Revised after every 10 yrs by deleting the previous 10 yr data and adding the recent 10 yr data

� Also termed as Normal rainfall

� Wetness Index� Ratio of rainfall in a given year to annual average precipitation

� Value < 1 , bad year or deficient year or dry year

� Value = 1, normal year

� Value > 1, good year or surplus year or wet year

� A bar chart of time versus precipitation is known as hyetograph.

� The hourly precipitation data during a storm are as follows: Plot 1. Hyetograph 2. Mass Curve

Time (h) 0 1 2 3 4 5 6 7 8 9 10

Precipitation (mm) 0 30 25 50 5 0 10 15 25 20 0

Precipitation (mm) 0 30 55 105 110 110 120 135 160 180 180

Analysis and Interpretation of Rainfall Data

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� For any design problem� Intensity, duration, frequency and areal distribution

� Point rainfall� Also known as station rainfall

� Depending on the need, the data can be listed as daily, weekly, monthly, seasonal or annual values for various periods

� Represented graphically as plots of magnitude vs chronological time in the form of bar diagram

� Not convenient in discerning a trend in the rainfall

� Moving Average� Smoothens out the extreme variations and indicate the trend or cyclic pattern, if any, more clearly.

Analysis and Interpretation of Rainfall

Data

Example

� Annual rainfall values recorded at station M for the period of 1950 to 1979 is given. Represent this data as a bar diagram with time in chronological order. � Find the average and standard deviation of the annual rainfall.

� Identify those years in which the annual rainfall is � Less than 20% of the mean,

� More than the mean

� Plot the three-year moving mean of the annual rainfall time series.

Year 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964Annual Rainfall

(mm), Pi 676 578 95 462 472 699 479 431 493 503 415 531 504 828 679

Year 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979Annual Rainfall

(mm), Pi 1244 999 573 596 375 635 497 386 438 568 356 685 825 426 612

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Analysis and Interpretation of Rainfall

Data

� Frequency Analysis or Recurrence Interval of a Storm or Return Period� If data for a station or an area is available for n years, then precipitation data may be arranged in descending order

� The serial number of a specific value of precipitation in descending order is known as ranking of the storm (m)

� Exceedence probability is the probability, an observation with rank m is equalled or exceeded m out of n times (P = m/n)

� Recurrence Interval of a Storm or Return Period is the number of years within which a given storm may equal or even exceed (Tr)

1/r

T n m P= = California FormulaCalifornia Formula

� Disadvantage of California Formula:� For m=n, it gives an exceedence probability of 1 which should not be the case with a finite sample.

� Hazen’s Formula

� Gives exceedence probability < 1 for m=n

� Gives a return period double the size of the sample for m=1

� The most commonly used Formula

Analysis and Interpretation of Rainfall

Data

2

2 1r

nT

m=

−

1

r

nT

m

+=

2 1

2

mP

n

−=

1

mP

n=

+

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Solve� The record of annual rainfall at station A covering a period of 22 years is given below. (a) Estimate the annual rainfall with the return periods of 10 years and 50 years. (b) What would be the probability of an annual rainfall of magnitude equal to or exceeding 100 cm occurring at station A? (c) What is the 75% dependable annual rainfall at station A?Year Annual rainfall (cm) Year Annual rainfall (cm)

1960 130 1971 90

1961 84 1972 102

1962 76 1973 108

1963 89 1974 60

1964 112 1975 75

1965 96 1976 120

1966 80 1977 160

1967 125 1978 85

1968 143 1979 106

1969 89 1980 83

1970 78 1981 95

Intensity duration analysis

� A knowledge of maximum intensity of rainfall of specified returnperiod and of duration equal to the critical time of concentration is ofconsiderable practical importance in evaluating peak flows related tohydraulic structures

� Study of intensity and its duration is known as Intensity DurationAnalysis� It has been observed that the most intense storms last for very shortdurations

� As intensity reduces, the duration of the storm increases and vice versa

� Intensity-Duration Curve� Graph normally follows the following equation:

• where, I = intensity in mm/h• t = duration in minutes• C, a, b = constant for the specific area

( )b

at

CI

+=

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Procedure for developing Intensity

duration curves

� Preparation of annual maximum data series

� From the available rainfall data, rainfall series for different durations (e.g.,1-hour, 2-hour, 6-hour, 12-hour and 24-hour) are developed.

� For each selected duration, the annual maximum rainfall depths are calculated

� Graph is plotted with duration in the abscissa and maximum intensity as ordinate

� A storm occurred over a catchment area as under:

Plot the maximum intensity duration curve.

� Solution:

Time (min) 0 10 20 30 40 50 60 70 80 90

Precipitation (mm) 0 19 22 7 20 23 33 28 8 6

Time (min) Incremental depth of rainfall (mm) in various durationsDurations (mins)

10 20 30 40 50 60 70 80 900 010 1920 22 4130 7 29 4840 20 27 49 6850 23 43 50 72 9160 33 56 76 83 105 12470 28 61 84 104 111 133 15280 8 36 69 92 112 119 141 16090 6 14 42 75 98 118 125 147 166Maximum Intensity (mm/h) (33/10)*60 = 198 183 168 156 134 133 130 120 110

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Intensity duration curve

198183

168156

134 133 130120

110

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80 90 100

Log. ()

Solve

� A mass curve of rainfall in a storm of total duration 270 mins is given below.� Draw the hyetograph of the storm at 30-minutes time step.

� Plot the maximum intensity duration curve for this storm

Time since start in minutes 0 30 60 90 120 150 180 210 240 270

Cumulative rainfall (mm) 0 6 18 21 36 43 49 52 53 54

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� Hyetograph

Time since start in minutes 0 30 60 90 120 150 180 210 240 270

Cumulative rainfall (mm) 0 6 18 21 36 43 49 52 53 54

Incremental depth of rainfall(mm)

0 6 12 3 15 7 6 3 1 1

Intensity (mm/h) 12 24 6 30 14 12 6 2 2

12

24

6

30

1412

6

2 2

0

5

10

15

20

25

30

35

30 60 90 120 150 180 210 240 270

Rainfall intensity (mm/h)

Time (mins)

Hyetograph

� Maximum-intensity duration relation

Time (min) Incremental depth of rainfall (mm) in various durations

Durations (mins)

30 60 90 120 150 180 210 240 270

0 0

30 6

60 12 18

90 3 15 21

120 15 18 30 36

150 7 22 25 37 43

180 6 13 28 31 43 49

210 3 9 16 31 34 46 52

240 1 4 10 17 32 35 47 53

270 1 2 5 11 18 33 36 48 54

Maximum Intensity (mm/h) (15/30)*60 = 30 22 20 18.5 17.2 16.3 14.8 13.25

12

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30

2220

18.517.2 16.3

14.813.25

12

0

5

10

15

20

25

30

35

0 50 100 150 200 250 300

intensity (mm/h)

duration (mins)

Intensity-Frequency-Duration Analysis

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Average depth of precipitation

� Precipitation over a catchment area is never uniform

� Average depth of precipitation at different rain gauge stations in acatchment vary

� Representative of a catchment:� Average depth of precipitation over the entire catchment/equivalentuniform depth of rainfall

� Calculated by the following methods:� Arithmetic mean method

� Thiessen polygon method

� Isohyetal method

� Theissen Polygon method

� Isohyetal method

Isohyets are contours of equal rainfall.

� Arithmetic mean method