engineering hydrology by PARIMAL JHA

1. UNIT- 2
PRECIPITATION

2. DEFINITION
 All types of moisture reaching the surface of earth from
atmosphere.
Precipitation is the basic input to the hydrology.
 Factors determining
precipitation or the
amount of atmospheric
moisture over a region
 Climate
 Geography
 Ocean surfaces is the
chief source of moisture
for precipitation

3. MECHANISM OF PRECIPITATION
 There are different kinds of
precipitation :
CONVECTIONAL: In this process, a fluid
is heated by a warm surface ,expands and
rises creating an upward flow. Convectional
precipitation results from the heating of the
earth's surface.
As the air warms the air becomes "lighter”
and rises rapidly into the atmosphere.

4.  (2) OROGRAPHIC : Orographic precipitation results when warm moist
air moving across the ocean is forced to rise by large mountains. As
the air rises, it cools at higher elevation results in cooler temperatures
and deeper clouds.

5. CYCLONIC OR FRONTAL PRECIPITATION
 Cyclonic or Frontal precipitation
results when the leading edge of a
warm, moist air mass(warm front)
meets a cool
 The warmer air mass is forced up
over the cool air. As it rises, the
warm air cools, the water vapour
in the air condenses, and clouds
and precipitation result.
 This type of system is called
Frontal Precipitation because the
moisture tends to occur along the
front of the air mass.

6. FORMS OF PRECIPITATION

7. RAIN
 Rain is the most common type of
precipitation in our atmosphere. Rain is
when liquid droplets fall to the surface of
the Earth.
 There are two different forms of rain, either
in the form of
 showers
 drizzles
 Showers are heavy, large drops of rain
and usually only last a period of time.
 Drizzles however usually last longer
and are made up of smaller droplets of
water.
 Rain can either be formed as ice crystals
melt or it can be smaller water droplets.
Light
I = 2.5mm/hr
Moderate
I = 2.6-7.5mm/hr
Heavy
I > 7.5 mm/hr

8. SNOW
 Snow is the second most common precipitation in
the North East.
 Snow forms when water vapor turns directly into
ice without ever passing through a liquid state.
This happens as water condenses around an ice
crystal.
Density of freshly fallen snow
varies between 125-500mm of
snow required to equal 25mm
of liquid water
Average density (specific
gravity) = 0.1

9. HAIL
 Hail is created when moisture and wind are together.
Inside the cumulonimbus clouds ice crystals form, and
begin to fall towards the surface of Earth. When this starts
to happen wind gusts start to pick up the ice crystals
pushing them up high into the clouds. As they start to fall
down again they continue to grow in size. A wind gust
might catch the hail stone again which will push it back up
into the cloud. This whole process gets repeated several
times before the hail stone becomes so big that it is too
heavy for the wind to carry so it must fall towards Earth.
Shapes of hail particles
1. Spherical
2. Conical
3. Irregular
Diameter range 5 to 125 mm
Specific gravity = 0.8
Average density (specific gravity) =
0.1

10. FOG
 There are four main types of fog,
 radiation fog
 advection fog
 upslope fog
 evaporation fog
 There is really no different between fog and the
clouds that are high in the sky. In simple terms
fog is a cloud that has formed near the surface
of the Earth.

11. DEW
 The small drops of water which can be found
on cool surfaces like grass in the morning.
 This is the result of atmospheric vapor
condensing on the surface in the colder night
air.
 Dew Point is the temperature in which
condensation starts to take place or when dew
is created.

12. MIST / DRIZZLE
 Mist is a bunch of small droplets of water which are
in the air. This occurs with cold air when it is above
a warm surface, for example water.
 Fog and mist are very similar, the only difference is
their visibility.
 If you cannot see 1 kilometer or less you know you're
dealing with fog.
 You can see visuals through mist and it is
more haze looking than a thicker substance.
Diameter range between 0.1
and 0.5 mm/hr

13. GLAZE
 Glaze is the ice coating, generally clear
and smooth, formed on exposed
surfaces by the freezing of super cooled
water deposited by rain or drizzle.
Specific gravity may be as high as 0.8-0.9

14. RIME
 Rime is the white opaque deposit of ice
granules more or less separated by
trapped air and formed by rapid freezing
of super cooled water drops impinging
on exposed objects.
Specific gravity may be as low as 0.2-0.3

15. SLEET
 Sleet consists of transparent, globular,
solid grains of ice formed by the freezing of
raindrops or freezing of largely melted ice
crystals falling through a layer of sub
freezing air near the earth’s surface.

17. MEASUREMENT OF PRECIPITATION
 Rainfall and other forms of precipitation are
measured in terms of depth, the values being
expressed in millimeters and 10th of millimeters.
 One millimeter of precipitation represents the
quantity of water needed to cover the land with a
1mm layer of water, taking into account that nothing
is lost through drainage, evaporation or absorption.
 Instrument used to collect and measure the
precipitation is called rain gauge.

18. MEASUREMENT OF PRECIPITATION
 1. Amount of precipitation
 2. Intensity of precipitation
 3. Duration of precipitation
 4. Arial extent of precipitation

19. MEASUREMENT METHODS
 Measurement of precipitation (Rain and Snow)
can be done by various devices. These
measuring devices and techniques are :
 Rain Gauges
 Snow Gauges
 Radars
 Satellites
 Scratching of snow packs
 Water equivalent in snow packs

20. RAIN GAUGES
 Rain gages are most commonly used for the
measurement of precipitation, both in terms of
rain fall and snow. The rain gauge is also
known as hyeto meter .
 Rain gauges have been used historically to
provide rainfall quantities and rates at a single
point in space
 The volume of water collected in a cylinder is
divided by the area of the cylinder opening and
converted into a depth or rain.

22. TYPES OF RAIN GAUGES
 There are two main types of rain gages
which are used to measure the
precipitation. These are:
 1. Non recording rain gages
 2. Recording rain gages

23. NON RECORDING RAIN GAUGES
 These are basic storage
devices that measure the
cumulative amount of rain. A
common type of these
gauges is called the 8-inch
Standard Rain Gauge (SRG)
which has been used by the
weather offices of US
National Weather Service
(NWS) for over 100 years.
The standard gauge is simply
a large cylinder with a funnel
and a plastic measuring tube
inside the cylinder.

24.  The non-recording rain gauge used in India is the Symons's
rain gauge .
 It consists of a funnel with a circular rim of 12.7 cm diameter
and a glass bottle as a receiver.
 The cylindrical metal casing is fixed vertically to the masonry
foundation with the level rim 30.5 cm above the ground
surface.
 The rain falling into the funnel is collected in the receiver and
is measured in a special measuring glass graduated in mm
of rainfall; when full it can measure 1.25 cm of rain.
 The rainfall is measured every day at 08.30 hours IST. The
collector is of size 100 to 200 cm.

25. During heavy rains, it must be measured three or four times
in the day, lest the receiver fill and overflow, but the last
measurement should be at 08.30 hours IST and the sum total
of all the measurements during the previous 24 hours entered
as the rainfall of the day in the register.
Usually, rainfall measurements are made at 08.30 hr IST and
sometimes at 17.30 hr IST also.
Thus the non-recording or the Symons rain gauge gives only
the total depth of rainfall for the previous 24 hours (i.e., daily
rainfall) and does not give the intensity and duration of rainfall
during different time intervals of the day.
It is often desirable to protect the gauge from being damaged
by cattle and for this purpose a barbed wire fence may be
erected around it.

26. RECORDING RAIN GAUGE
This is also called self-recording, automatic or
integrating rain gauge.
This type of rain gauge has an automatic mechanical
arrangement consisting of a clockwork, a drum with a graph
paper fixed around it and a pencil point, which draws the
mass curve of rainfall. From this mass curve, the depth of
rainfall in a given time, the rate or intensity of rainfall at any
instant during a storm, time of onset and cessation of
rainfall, can be determined.
The gauge is installed on a concrete or masonry
platform 45 cm square in the observatory enclosure by the
side of the ordinary rain gauge at a distance of 2-3 m from it.
The gauge is so installed that the rim of the funnel is
horizontal and at a height of exactly 75 cm above ground
surface. The self-recording rain gauge is generally used in
conjunction with an ordinary rain gauge exposed close by,
for use as standard, by means of which the readings of the
recording rain gauge can be checked and if necessary
adjusted.

27. TYPES OF RECORDING RAIN GAUGES
 There are three main types of recording rain
gauges
 1. Float type rain gauges
 2. Tipping bucket type rain gauges
 3. Weighing type rain gauges

28. FLOAT TYPE RAIN GAUGE
 In this type, as the rain is
collected in a float chamber, the
float moves up which makes a
pen to move on a chart wrapped
round a clock driven drum.
When the float chamber fills up,
the water siphons out
automatically through a siphon
tube kept in an interconnected
siphon chamber. The clockwork
revolves the drum once in 24
hours. The clock mechanism
needs rewinding once in a week
when the chart wrapped round
the drum is also replaced. This

30. The graphic rain gauge
1-receiver
2-floater
3-siphon
4-recording needle
5-drum with diagram
6-clock mechanism

31.  The rise of float with increasing catch of rainfall
is recorded. Some gauges must be emptied
manually while others are emptied
automatically using self starting siphons.
 In most gauges oil or mercury is the float and is
placed in the receiver, but in some cases the
receiver rests on a both of oil or mercury and
the float measures the rise of oil or mercury
displaced by the increasing weight of the
receiver as the rainfall catch freezes. Float may
get damaged by rainfall catch freezer

32. Disadvantages of float gauge :
 They are costlier than other non recording rain gauges
 Mechanical defects sometimes gives erroneous results

33. TIPPING BUCKET RAIN GAUGE
 This consists of a cylindrical receiver 30 cm diameter
with a funnel inside .
 Just below the funnel a pair of tipping buckets is
pivoted such that when one of the bucket receives a
rainfall of 0.25 mm it tips and empties into a tank
below, while the other bucket takes its position and
the process is repeated.
 The tipping of the bucket actuates on electric circuit
which causes a pen to move on a chart wrapped
round a drum which revolves by a clock mechanism.
This type cannot record snow.

34.  A tipping bucket rain gauge is used for
measurement of rainfall. It measures the rainfall
with a least count of 1 mm and gives out one
electrical pulse for every millimeter of rainfall

35.  Advantage of tipping bucket :
 it is the only recording gauge which can be used in
remote places by installing the recorder at a
convenient and easily accessible location
 Disadvantages of tipping bucket :
 If the bucket is designed to tip at a convenient
frequency for a particular intensity of rainfall , they
will tip either too soon or too late for other
intensities

37. WEIGHING TYPE RAIN GAUGE
 In this type of rain-gauge, when a certain
weight of rainfall is collected in a tank, which
rests on a spring-lever balance, it makes a
pen to move on a chart wrapped round a
clock driven drum. The rotation of the drum
sets the time scale while the vertical motion
of the pen records the cumulative
precipitation.

39.  Disadvantages of weighing type rain gauge :
 in heavy precipitation there is good chance
that bucket will overflow
 these instruments are costlier too
 Advantages of weighing type rain gauge :
it can measure all forms of precipitation
including snow and rain

40. ERRORS IN PRECIPITATION MEASUREMENT BY
RAIN GAUGES
 Instrumental errors
 Errors in scale reading
 Dent in receivers
 Dent in measuring cylinders
 About 0.25mm of water is initially required to wet the
surface of gauge
 Rain gauges splash from collector
 Frictional effects
 Non verticality of measuring cylinders (10° inclination gives
1.5% less precipitation)
 Loss of water by evaporation
 Leakage in measuring cylinder
 Wind speed reduces measured amount of rain in the rain
gauges.

41. LOCATION OF RAIN GAUGES
The amount of rainfall collected by a rain gauge depends on its
exposure conditions and there fore great care must be taken for
selecting suitable site for a rain gauge.
According to Indian standards the following precautions must be
taken while selecting a site for a rain gauge station :
1) The site should be on level ground,i.e, sloping ground, hill tops or
hill slopes are not suitable
2) The site should be an open space.
3) Horizontal distance between the rain gauge and the nearest object
should be twice the height of the object
4) Site should be away from continuous wind forces.

42. 5) Other meteorological object and the fencing of the site
should maintain the horizontal distance between the
rain gauge and the nearest object twice the height of
object.
6) The site should be easily accessible.
7) The gauge should be truly vertical.
8) 10% of total number of rain gauge stations of any basin
should be self recording.
9) The observer must visit the site regularly to ensure its
proper readiness for measurement.

43. PLACEMENT OF RAIN GAUGES
Gauges are affected by wind pattern, eddies, trees and
the gauge itself, therefore it is important to have the
gauge located and positioned properly.
• 1m above ground level is standard -
all gauges in a catchment should be the same height
• 2 to 4 times the distance away from an isolated object
(such as a tree or building) or in a forest a clearing
with the radius at least the tree height or place the
gauge at canopy level

44. PLACEMENT OF RAIN GAUGES
shielded to protect gauge in windy sites
or if obstructions are numerous they will reduce the wind-
speed, turbulence and eddies.

45. For sloping ground the gauge should be placed with the
opening parallel to the ground
The rainfall catch volume (mm3) is then divided by the opening
area that the rain can enter
PLACEMENT OF RAIN GAUGES

46. ANALYSIS AND INTERPRETATION OF RAINFALL
DATA
 The precipitation process is essentially random in nature. We can’t predict
with certainty what will be the rainfall for any given period in future.
 The rainfall magnitudes can be estimated only with some probability
attached to them. Therefore the analysis of rainfall data obtained over a
long period in the past would help the hydrologist to make reasonable
probabilistic estimates of rainfall to be used in various designs
 The rainfall obtained from single rain gauge station is known as the point
rainfall or station rainfall.
 If the data at the station covers a period of more than 30 years, the
normal annual rainfall, or the normal monthly rainfall for any month can be
computed
 The normal monthly rainfall of a station is computed as the arithmetic
average of the monthly rainfall or yearly rainfall in last 30 years.

47.  Hyetograph – it is a chart or graphic
representation of average
distribution of rain over the earth.
&
It is a plot of intensity of rain fall
against time interval
the hyetograph is derived from mass
curve and is usually represented as
bar chart
Rainfall intensity progressively
increases until it reaches a
maximum and then gradually
decreases.
Where this maximum occurs and
how fast the maximum is reached is
what differentiates one distribution
from another.

49. Q. A storm commenced at 7:00 hours. The
ordinates of the rainfall mass-curve of the storm
in mm as recommended by a recording rain
gauge at 15 min intervals are –
0,9.5,17,27,40.5,49,63,84,95,102,110,112,112
construct a hyetograph of this storm for a
uniform interval of 15 min ?

50. time Ordinate of
mass curve
(mm)
Rainfall in 15
min interval
(mm)
Rainfall intensity
i (mm/hr)
7:00 0 0 0
7:15 9.5 9.5 9.5/(1/4) =38
7:30 17 7.5 7.5/(1/4) = 30
7:45 27 10 10/(1/4) = 40
8:00 40.5
8:15 49
8:30 63
8:45 84
9:00 95
9:15 102
9:30 110
9:45 112
10:00 112

52. RAINFALL HYETOGRAPH

53. Q. For the storm commenced at 7:00 hours. The
ordinates of the rainfall mass-curve of the
storm in mm as recommended by a recording
rain gauge at different time intervals are –
0,9.5,17,27,40.5,49,63,84,95,102,110,112,
112
calculate the maximum rainfall intensities for
durations of 15,30,45,60,90,120 & 180 min
and plot the intensity duration graph.

54. time Ordinate of mass
curve (mm)
rainfall for a period of
15
(min
)
30 45 60 90 120 180
7:00 0 0
7:15 9.5 9.5
7:30 17 7.5 17
7:45 27 10 17.5 27
8:00 40.5 13.5 23.5 31 40.5
8:15 49 8.5 22 32 39.5
8:30 63 14 22.5 36 46 63
8:45 84 21 35 43.5 57 74.5
9:00 95 11 32 46 54.5 78 95
9:15 102 7 18 39 53 75 92.5
9:30 110 8 15 26 47 69.5 93
9:45 112 2 10 17 28 63 85

55. time Ordinate of mass
curve (mm)
rainfall for a period of
15
(min
)
30 45 60 90 120 180
7:00 0 0
7:15 9.5 9.5
7:30 17 7.5 17
7:45 27 10 17.5 27
8:00 40.5 13.5 23.5 31 40.5
8:15 49 8.5 22 32 39.5
8:30 63 14 22.5 36 46 63
8:45 84 21 35 43.5 57 74.5
9:00 95 11 32 46 54.5 78 95
9:15 102 7 18 39 53 75 92.5
9:30 110 8 15 26 47 69.5 93
9:45 112 2 10 17 28 63 85

57.  Maximum intensity for 15 min duration =
21/(1/4) mm/hr =84 mm/hr
 Maximum intensity for 30 min duration = mm/hr
 Maximum intensity for 45 min duration = mm/hr
 Maximum intensity for 60 min duration = mm/hr
 Maximum intensity for 90 min duration = mm/hr
 Maximum intensity for 120 min duration =
mm/hr
 Maximum intensity for 180 min duration =112/3

59. Max
i(mm/hr)
0
TIME (hours)

60. INTENSITY DURATION GRAPH

61.  The maximum intensity varies inversely with
the duration and generally an equation of
form is assumed between (I &T)
I=C/(t+a)b
 The values of C,a & b are obtained from
regression analysis

62. POINT RAINFALL
 Point rainfall is also known as station rainfall
refers to rainfall data of a station ,depending
upon the need data may be listed as
Daily,weekly,monthly,seasonal or annual
values

63. MOVING AVERAGE
 Moving average is a technique for smoothening
out the high frequency fluctuations of time
series and to enable the trend.
 The range of m years is selected starting from
first set of m years of data.
 The average of data of m years is calculated
and placed in middle year of range m.
 The process is repeated for next year.
 Normally 3 or more years are taken, usually an
odd value.
 More the years more smooth curve will be
obtained.

64. RAINGAUGE NETWORK
 Since the catching area of rain gauge is very
small compared to areal extent of storm.
 To cover large catchment area a number of
rain gauges would be required as large as
possible
 More the rain gauge more the accuracy.
 Economic considerations and other
considerations such as topography,
accessibility etc restrict number of rain
gauges to some extent.

65. RAINGAUGE DENSITY
 The World Meteorological Organisation (W.M.O)
recommends the following densities-
 In flat regions of tempreture,mediterranean and tropical
zones
IDEAL: 1 station for 600 to 900 km2
ACCEPTABLE: 1 station for 900 to 3000 km2
IN mountaneous region of temperature
IDEAL: 1 station for 100 to 250 km2
ACCEPTABLE: 1 station for 25 to 1000 km2
In Arid & Polar zones --1 station for 1500 to 10,000 km2

66. RAIN-GAUGE DENSITY
 In India, on an average, there is 1 rain-gauge
station for every 500 km2, while in more
developed countries, it is 1 station. for 100
km2.
Area Rain gauge density
Plains 1 in 520 Km2
Elevated regions 1 in 260-390 Km2
Hilly and very heavy rainfall
areas
1 in 130 Km2
with 10% of recording R.G

67. ADEQUACY OF RAIN GAUGE STATIONS
 The optimum number of stations that should
exist to have %age error in estimation of
mean rainfall
N= (CV/P)2
N =Optimal number of stations
P = Allowable degree of error in %
CV=Coefficient of variation of rainfall values at
existing m stations in %

68. N= (CV/P)2 , cv=(sx / ͞x ) × 100 , sx
2 = ∑(xi ̶ ͞x 2)
(m ̶ 1)
͞x = Mean rainfall of m number of stations
Sx = Standard deviation of rainfalls
CV = Coefficient of variation of rainfall values at existing m
stations in %
m = Existing number of stations
xi = Rainfall at ith station
If N<m no more gauges required
N>m (N ̶ m) additional gauges required
Note: Additional gauges are evenly distributed over entire catchment area

69. Q- The average annual rainfall in cm at 4 existing rain gauge stations at a basin are
105,79,70 & 66 cm.if the average depth of rainfall over the basin is to be estimated within
10% error , determine the additional number of gauges required.
Sol-
mean of the rainfalls at the existing gauges is given by
͞x = ∑xi /m
= (105+79+70+66)/4 = 80 cm
The standard deviation of rainfall is given by
sx
2 = ∑(xi ̶ ͞x 2)/(m ̶ 1)
={ (105-80)2+(79-80)2+ (70-80)2 +(60-80)2 } /(4-1)
sx
2 = (922/3) =307.33
sx = 17.53 cm
cv=(sx / ͞x ) × 100 = (17.53/80) × 100 = 21.91 cm
N= (CV/P)2 = (21.91/10) 2 = 4.80 , P=10 %
(N=4.80 > 4=m)
So number of additional gauges required =(N-m) = (4.80 - 4) = 0.80 ͌ 1 say

70. Q- A catchment area has six rain gauge stations. In a year, the annual rainfall
recorded by the gauges are as follows:
For a 10% error in the estimation of the mean rainfall, calculate the optimum
number of
stations in a catchment.
Sol-
mean of the rainfalls at the existing gauges is given by
͞x = ∑xi /m
= (82.6+102.6+180.3+110.3+98.8+136.7)/6 = 118.6 cm
The standard deviation of rainfall is given by
sx
2 = ∑(xi ̶ ͞x 2)/(m ̶ 1)
={ (82.6-118.6)2+(102.6-118.6)2+ (180.3-118.6)2 +(110.3-118.6)2 +
(98.8.3-118.6)2 +(136.7-118.6)2 } /(6-1)
Station A B C D E F
Rainfall(cm) 82.6 102.6 180.3 110.3 98.8 136.7

71. sx
2 = 1227.584
sx = 35.04 cm
cv=(sx / ͞x ) × 100 = (35.04 /118.6) × 100 = 29.54
cm
N= (CV/P)2 = (29.54/10) 2 = 8.726 , P=10 %
(N=8.726 > 6=m)
So number of additional gauges required =(N-m)
= (8.726 - 6) = 2.726 ͌ 3 say

72. AVERAGE ANNUAL RAINFALL
 The mean of yearly rainfall observed for a period of
35 consecutive years is called the
 average annual rainfall (a.a.r.) as used in India
 The A.A.R of a place depends upon:
1) Distance from the ocean.
2) Direction of prevailing winds.
3) The mean annual temperature.
4) Altitude of place
5) Topography

73. INTERPRETATION OF PRECIPITATION DATA
Interpretation of precipitation data includes:
1) Estimating missing precipitation data at a
station
2) Checking inconsistency in particular data at
a station
3) Averaging precipitation over an area

74. 1. ESTIMATING MISSING PRECIPITATION
DATA AT A STATION
Missing precipitation data is estimated by
two commonly used methods.
 Arithmetic Mean Method
 Normal Ratio Method (NRM)

75. ARITHMETIC MEAN METHOD
 If the normal annual precipitation at the adjacent
station under consideration is within 10% of the
normal annual rainfall of that station under
consideration then the missing rainfall data can
be easily estimated by arithmetic average of
rainfall at that adjacent station. This method is
least accurate however.
Where:
Px = precipitation at the missing location
P1 to Pm = precipitation at the m surrounding rain gauge stations
M = number of rain gauges

76. NORMAL RATIO METHOD (NRM)
 Normal ratio method (NRM) is used when the normal annual precipitation
at any of the index station differs from that of the interpolation station by
more than 10%. In this method, the precipitation amounts at the index
stations are weighted by the ratios of their normal annual precipitation
data in a relationship of the form:
Where:
Px = precipitation at the missing location
P1 to Pm = precipitation at m surrounding rain gauge stations
N1 to Nm = normal annual rainfall at the m surrounding gauge stations
Nx = normal annual rain at gauge station x
M = number of rain gauges

77.  The normal annual rainfall at stations A,B,C & D in the basin are
80.97,67.59,76.28 & 92.01 cm respectively. In the year 1975 the station D
was inoperative and the stations A,B,C recorded annual precipitations
of 91.11,72.23 & 79.89 respectively. Estimate the rainfall at station D In
that year.
Sol-
As the normal rainfall values vary more than 10% the normal ratio method
is
adopted. ND=92.01, M=3
PA=91.11,
PB=72.23,PC=79.89
NA=80.97,NB=67.59,NC=76.28
PD =
PD= (92.01/3) × { (91.11/80.79)+(72.23/67.59)+(79.89/76.28) }= 99.41 cm.

78. CHECKING INCONSISTENCY IN A
PARTICULAR DATA RECORD AT A STATION
Double Mass Curve Analysis.
 It is used to check the consistency of many
kinds of hydrologic data
 By comparing date for a single station with
that of a pattern composed of the data from
several other stations in the area
 The double-mass curve can be used to adjust
inconsistent precipitation data

79. COMMON CAUSES OF INCONSISTENCY OF RECORD
1) Shifting of rain gauge station at a new location.
2) The neighborhood of a station is undergoing a
marked change.
3) Change in the ecosystem due to calamities such as
Forest fires, Land slides etc.
4) Occurrence of observational error from a certain
date.

80. DOUBLE MASS CURVE ANALYSIS
The theory of the double-mass
curve is based on the fact that a
plot of the two cumulative
quantities during the same
period exhibits a straight line so
long as the proportionality
between the two remains
unchanged,
The slope of the line represents the
proportionality. This method can
smooth a time series and
suppress random elements in
the series, and thus show the
main trends of the time series.

81. AVERAGING PRECIPITATION OVER AREA
It is the amount of precipitation which can
be assumed uniform over an area. If the
average precipitation over an area is
known than total rain volume of water can
be computed for that area.
Rain volume = Pavg × A

82. METHODS FOR COMPUTING AVERAGE
PRECIPITATION OVER AN AREA
There are some widely used methods to
compute average precipitation over an area,
but the most common of these used are:
 Arithmetic mean method
 Theissen polygon method
 Isohyetal method

83. ARITHMETIC MEAN METHOD
 This is the simplest of three methods,this method is
also known as unweighted mean
method since the same
weightage is given to
rainfall record at all
the gauges irrespective
of their locations.
 Arithmetic mean method is used when area is flat &
normal annual precipitation is within 10% of the
gauge for which data are being reconstructed. This
method is least accurate however.
Where:

84. • The method of Thiessen polygons consists of
attributing to each station an influence zone in
which it is considered that the rainfall is equivalent
to that of the station.
• The influence zones are represented by convex
polygons.
• These polygons are obtained using the mediators
of the segments which link each station to the
closest neighboring stations
Method of Thiessen polygons

85. Thiessen polygons ……….

86. Thiessen polygons ……….
A1
A2
A3
A4
A5
A6
A7
A8
P1
P2
P3
P4
P5
P6
P7
P8

87.  m
mm
AAA
APAPAP
P



.....
.....
21
2211





M
i
i
i
total
i
M
i
i
A
A
P
A
AP
P
1
1
Thiessen polygons ……….
Generally for M station
The ratio is called the weightage factor of station i
A
Ai

88. THEISSEN POLYGON METHOD
 Divide the region (area A)
into sub-regions centered
about each rain gauge;
 Determine the area of each
sub-region (Ai) and compute
sub-region weightings (Wi)
using: Wi = Ai/A
 Compute total aerial rainfall
using Rainfall recorded at
each station is given a
weight age based on the
area closest to the station.

89. THEISSEN POLYGON METHOD
Consider a catchment area Catchment
area is drawn to scale and position of
these 6 stations is plotted on it. Stations
are joined so as to get a network of
triangles. Perpendicular bisectors are
drawn to each of the sides of these
triangles. These bisectors form a
polygon around each station. If the
boundary of catchment cuts the
bisectors, then boundary is taken as
outer limit of polygon. These bounding
polygons are called Thiessen Polygons.
The area of these polygons is
measured with a planimeter or by grid
overlay

93. PLANIMETER FOR AREA MEASUREMENT

95. • An isohyet is a line joining points of equal rainfall
magnitude.
Isohyetal Method
F
B
E
A
C
D
12
9.2
4.0
7.0
7.2
9.1
10.0
10.0
12
8
8
6
6
4
4
a1a1
a2
a3
a4
a5

96. • P1, P2, P3, …. , Pn – the values of the isohytes
• a1, a2, a3, …., a4 – are the inter isohytes area respectively
• A – the total catchment area
• - the mean precipitation over the catchment
Isohyetal Method
P
A
PP
a
PP
a
PP
a
P
nn
n 




 





 





 



2
...
22
1
1
32
2
21
1
The isohyet method is superior to the other two methods
especially when the stations are large in number.
NOTE

97. ISOHYETAL METHOD
 Plot gauge locations
on a map;
 Subjectively
interpolate between
rain amounts
between gauges at a
selected interval;
 Connect points of
equal rain depth to
produce lines of
equal rainfall
amounts (isohyets);

98. ISOHYETAL METHOD
Compute aerial rain using Isohyets –
 It is a line joining points of equal rainfall
magnitude.
 The catchment area is drawn to scale
and the rain gauge stations are marked
on it. The recorded rainfall values for
which aerial average is to determined are
marked at the respective stations.
 Neighboring stations outside the
catchment are also considered. Taking
point rainfall values as the guide,
isohyets of different rainfall values are
drawn (similar to drawing contours based
on spot levels.
 The area between adjacent isohyets is
measured using a planimeter. If isohyets
go out of the catchment, the catchment
boundary is used as the bounding line.
 It is assumed that the average value of
rainfall indicated by two isohyets acts
over the inter isohytal area

99. STEPS FOR ISOHYETAL METHOD
 Step 1:
 Draw the area under study to scale
 Mark rain gauges on it.
 Put the recorded values of rainfall at the station, for the period within
which the average is required to be determined
 Step 2:
Draw the isohyets of various values by considering the point rainfall data as
guidelines and interpolating between them. Also, incorporate the knowledge of
orographic effects.
 Step 3:
Determine the area between each pair of the isohyet lines, either by a
planimeter or by converting the areas into smaller regular geometric shapes.
 Step4:
Calculate the average rainfall using the following formula:
Pi = Value of Isohyet lines , Ai = Area between pair of isohyet lines.
Pav = A1 (P1 + P2)/2 + A2 (P2 + P3)/2 + . . . + An-1(Pn-1 + Pn)/2 (A1 + A2 + . . . + An)

100. COMPARISON BETWEEN THE THREE METHODS:
 Arithmetic mean method:
1) This is the simplest and easiest method to compute average rainfall.
2) In this method every station has equal weight regardless its location.
3) If the recording stations and rainfall is uniformly distributed over the entire
catchment, then this method is equally accurate.
 Thiessen method
1) This method is also mechanical
2) In this method the rainfall stations located at a short distance beyond the
boundary of drainage are also used to determine the mean rainfall of the basin,
but their influence diminishes as the distance from the boundary increases.
3) It is commonly used for flat and low rugged areas.
 Isohyetal method:
1) It is the best method for rugged areas and hilly regions.
2) It is the most accurate method if the contours are drawn correctly. However to
obtain the best results good judgment in drawing the isohyets and in assigning
the proper mean rainfall values to the area between them is required.
3) Other points are as for Thiessen method.