Precipitation unit 2

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 Spherical Conical 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.

16. Measurement of precipitation Rainfall and other forms of precipitation are measured in terms of depth , the values being expressed in millimeters and 10 th 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 .

17. Measurement of Precipitation 1. Amount of precipitation 2. Intensity of precipitation 3. Duration of precipitation 4. Arial extent of precipitation

18. 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

19. 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.

20. 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

21. 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 .

22. 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.

23. 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 .

24. 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.

25. 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

26. 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 type of gauge is used by IMD.

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

28. 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

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

30. 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.

31. 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

32. 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

33. 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.

34. 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

35. 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.

36. 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 : The site should be on level ground,i.e, sloping ground, hill tops or hill slopes are not suitable The site should be an open space. Horizontal distance between the rain gauge and the nearest object should be twice the height of the object Site should be away from continuous wind forces.

37. 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 . The site should be easily accessible. The gauge should be truly vertical . 10 % of total number of rain gauge stations of any basin should be self recording. The observer must visit the site regularly to ensure its proper readiness for measurement.

38. 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

39. 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 .

40. For sloping ground the gauge should be placed with the opening parallel to the ground The rainfall catch volume (mm 3 ) is then divided by the opening area that the rain can enter Placement of Rain Gauges

41. 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.

42. 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.

43. 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 ?

44. time Ordinate of mass curve (mm) Rainfall in 15 min interval (mm) Rainfall intensity i (mm/hr) 7:00 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

45. RAINFALL HYETOGRAPH

46. 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.

47. time Ordinate of mass curve ( mm ) rainfall for a period of 15 (min) 30 45 60 90 120 180 7:00 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 10:00 112 2 10 17 49 71.5 112

48. time Ordinate of mass curve ( mm ) rainfall for a period of 15 (min) 30 45 60 90 120 180 7:00 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 10:00 112 2 10 17 49 71.5 112

49. 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 =37.5 mm/hr

50. Max i (mm/hr) TIME (hours)

51. INTENSITY DURATION GRAPH

52. 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

53. 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

54. 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.

55. 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.

56. Raingauge density The W orld M eteorological O rganisation ( W.M.O ) recommends the following densities- In flat regions of tempreture,mediterranean and tropical zones IDEAL : 1 station for 600 to 900 km 2 ACCEPTABLE : 1 station for 900 to 3000 km 2 IN mountaneous region of temperature IDEAL : 1 station for 100 to 250 km 2 ACCEPTABLE : 1 station for 25 to 1000 km 2 In Arid & Polar zones -- 1 station for 1500 to 10,000 km 2

57. RAIN-GAUGE DENSITY In India, on an average, there is 1 rain-gauge station for every 500 km 2 , while in more developed countries, it is 1 station . for 100 km 2 . Area Rain gauge density Plains 1 in 520 Km 2 Elevated regions 1 in 260-390 Km 2 Hilly and very heavy rainfall areas 1 in 130 Km 2 with 10% of recording R.G

58. ADEQUACY OF RAIN GAUGE STATIONS The optimum number of stations that should exist to have %age error in estimation of mean rainfall N = ( C V / P ) 2 N = o ptimal number of stations P = a llowable degree of error in % C V = c oefficient of variation of rainfall values at existing m stations in %

59. N = ( C V / P ) 2 , c v =( s x / ͞x ) × 100 , s x 2 = ∑ ( x i ̶ ͞x 2 ) ( m ̶ 1) ͞ x = m ean rainfall of m number of stations S x = s tandard deviation of rainfalls C V = c oefficient of variation of rainfall values at existing m stations in % m = Existing number of stations x i = r ainfall at i th 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

60. 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 = ∑ x i / m = (105+79+70+66)/4 = 80 cm The standard deviation of rainfall is given by s x 2 = ∑( x i ̶ ͞x 2 )/( m ̶ 1) = { (105-80) 2 +(79-80) 2 + (70-80) 2 +(60-80) 2 } / ( 4-1 ) s x 2 = (922/3) = 307.33 s x = 17.53 cm c v =( s x / ͞x ) × 100 = (17.53/80) × 100 = 21.91 cm N = ( C V / 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

61. 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 = ∑ x i / 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 s x 2 = ∑( x i ̶ ͞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

62. s x 2 = 1227.584 s x = 35.04 cm c v =( s x / ͞x ) × 100 = ( 35.04 /118.6) × 100 = 29.54 cm N = ( C V / 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

63. 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 : d istance from the ocean. d irection of prevailing winds. t he mean annual temperature. a ltitude of place t opography

64. Interpretation Of Precipitation Data Interpretation of precipitation data includes:   Estimating missing precipitation data at a station Checking inconsistency in particular data at a station Averaging precipitation over an area

65. 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)

66. 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: P x = precipitation at the missing location P 1 to P m = precipitation at the m surrounding rain gauge stations M = number of rain gauges

67. 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: P x = precipitation at the missing location P 1 to P m = precipitation at m surrounding rain gauge stations N 1 to N m = normal annual rainfall at the m surrounding gauge stations N x = normal annual rain at gauge station x M = number of rain gauges

68. 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. N D =92.01, M =3 P A =91.11, P B =72.23, P C =79.89 N A =80.97, N B =67.59, N C =76.28 P D = P D = (92.01/3) × { (91.11/80.79) + (72.23/67.59) + (79.89/76.28) }= 99.41 cm.

69. 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 B y 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

70. Common causes of inconsistency of record Shifting of rain gauge station at a new location. The neighborhood of a station is undergoing a marked change. Change in the ecosystem due to calamities such as Forest fires, Land slides etc. Occurrence of observational error from a certain date.

71. 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.

72. 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 = P avg × A  

73. 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

74. 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 howeve r. Where: P x = precipitation at the missing location P i = precipitation at index station i M = number of rain gauges

75. 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

76. Thiessen polygons ……….

77. Thiessen polygons ………. A 1 A 2 A 3 A 4 A 5 A 6 A 7 A 8 P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8

78. Thiessen polygons ………. Generally for M station The ratio is called the weightage factor of station i

79. Theissen Polygon Method Divide the region (area A ) into sub-regions centered about each rain gauge; Determine the area of each sub-region ( A i) and compute sub-region weightings ( W i ) using: W i = A i /A Compute total aerial rainfall using Rainfall recorded at each station is given a weight age based on the area closest to the station.

80. 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

81. Planimeter for area measurement

82. 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 a 1 a 1 a 2 a 3 a 4 a 5

83. P 1 , P 2 , P 3 , …. , P n – the values of the isohytes a 1 , a 2 , a 3 , …., a 4 – are the inter isohytes area respectively A – the total catchment area - the mean precipitation over the catchment Isohyetal Method The isohyet method is superior to the other two methods especially when the stations are large in number. NOTE

84. 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);  

85. 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

86. Steps for isohyetal method Step 1 : Draw the area under study to scale M ark 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 . P av = A 1 (P 1 + P 2 )/2 + A 2 (P 2 + P 3 )/2 + . . . + A n-1 (P n-1 + P n )/2 (A 1 + A 2 + . . . + A n )

87. Comparison Between the Three Methods : Arithmetic mean method : This is the simplest and easiest method to compute average rainfall. In this method every station has equal weight regardless its location. If the recording stations and rainfall is uniformly distributed over the entire catchment, then this method is equally accurate. Thiessen method This method is also mechanical 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. It is commonly used for flat and low rugged areas. Isohyetal method: It is the best method for rugged areas and hilly regions. 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. Other points are as for Thiessen method.