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1. Hydrology By:- Mulugeta Abebe Plus Application of GIS in Hydrology PART-1

2. Outline Introduction Return period Time of concentration Metrology station selection (Estimating areal precipitation from point value ) Design storm rainfall Statistics for hydrological analysis Data test Probability distribution Estimation of peak discharge

3. What is hydrology ?

4. Introduction Hydrology is broadly defined as the geosciences that describes and predicts the occurrence, circulation, and distribution of water of the earth and its atmosphere.

5. Why we study hydrology?

6. The study of hydrology helps us to know:- Maximum probable flood and its frequency; necessary for design of drains and culverts, dams and reservoirs, channels and other flood control structures. Water yield from a basin - its occurrence, quantity and frequency; necessary for the design of dams, municipal water supply, water power, river navigation, The ground water development for which a knowledge of the hydrogeology of the area. Maximum intensity of storm and its frequency for the design of a drainage project in the area.

7. Water is a finite Resources both in terms of spatial and temporal availability. The use of water at any one time is therefore subtractible , meaning that the use by somebody may preclude the use by somebody else Increasing subtraction of water at upstream will decrease supply downstream eventually fomenting conflicts In engineering term: We can quantify the availability of water Measurement, Water balance analysis, etc 7

8. 8 Basic Hyd. Cycle – Standard concept Ocean Evaporation Evaporation (ET) runoff Precipitation Aquifer Infiltration Evaporation Precipitation Evaporation/ET Surface Water Groundwater

9. The Hydrologic Cycle P Runoff Runoff Evap ET Evap Streams Lake Reservoir GW Atmospheric Moisture

10. Runoff is that balance of rain water, which flows or runs over the natural ground surface after losses by evaporation, interception and infiltration. The yield of a catchment is the net quantity of water available for storage, after all losses, for the purposes of water resources utilization and planning, like irrigation, water supply, etc. Maximum flood discharge is the discharge in times of flooding of the catchment area, i.e., when the intensity of rainfall is greatest and the condition of the catchment regarding humidity is also favorable for an appreciable runoff. The maximum flood that any structure can safely pass is called the “ design flood” and is selected after consideration of economic and hydrologic factors.

11. The most important task to be conducted before the design of any hydraulic and irrigation structure :- Collecting relevant data, Test of the appropriateness of data‘s and Analysis of data by applying appropriate methods. Errors in the estimates of peak flood will result in a structure that is either under sized or over sized.

12. Data type and Sources Depending upon the problem at hand, a hydrologist would need data relating to the various relevant aspects of the hydrologic cycle. These data may include:- Weather records: - temperature, humidity, and wind velocity, Precipitation data, Stream-flow records, Infiltration and transpiration data, Evaporation characteristics of the area, Ground water characteristics, Physical and geological characteristics of the area under consideration.

13. Sources of Data: Meteorological data ----From EMSA. Stream flow data---From MoWR or any other concerned bureaus or departments. Data on Evaporation, transpiration, infiltration--MoA, or water resources or any other concerned departments. The physical data of the area---EMA or specific studies conducted at the respective areas.

14. The following factors which affect the runoff are evaluated for hydrologic analysis:- Drainage basin characteristics including: size, shape, slope, land use, geology, soil type, surface infiltration, and storage Size of watershed: Generally, runoff rates and volumes increase with increasing drainage area. Watershed shape: a long, narrow watershed is likely to experience lower runoff rates than a short, wide watershed of the same size and other characteristics. Slope: The rate of runoff increases with increasing slope. Furthermore, rates of runoff decrease with increasing depression storage and detention storage volumes.

15. Stream channel characteristics including geometry and configuration, natural and artificial controls, channel modification, aggradation - degradation, and debris Flood plain characteristics and Meteorological characteristics such as rainfall amounts and type, time rate of rainfall (hyetograph)

16. Return period Frequency is the number of times a flood of a given magnitude can be expected to occur on average over a long period of time. Frequency analysis is the estimation of peak discharges for various recurrence intervals. Another way to express frequency is with probability. Probability analysis seeks to define the flood flow with a probability of being equaled or exceeded in any year.

17. Design flood frequency is expressed by return period, i.e., the probability (expressed in years) where a flood of a target size/magnitude is likely to occur. The probability of occurrence of a flood (having a recurrence interval T- yr ) in any year, i.e., the probability of exceedance, is or the percent chance of its occurrence in any one year, i.e., frequency ( F ) is & the probability that it will not occur in a given year, i.e., the probability of non- exceedance , P‘ = 1 - P

18. While designing a weir, provision must be made for the flood that is likely to occur during the lifetime of the structure. However, one can neither choose a very high nor a very low flood magnitude for the design. A very high flood never occurs during the lifetime of the structure. If such magnitude it will result in a costly structure. On the other hand, if a very low flood magnitude is chosen for the design and exceeded, it will result in the failure of the structure, Therefore designer must chose a design frequency appropriate for the structure.

19. The recommend peak river discharge for diversion weir design are 25 to 50 & 50 to 100 years return period for small & medium scale structures respectively (MoWR,2001).

20. Time of concentration The time of concentration ( Tc ) is the time at which the entire watershed begins to contribute to runoff. This is calculated as the time taken for runoff to flow from the most hydraulically remote point in the watershed to the outlet. Tc influences the peak discharge. For the same size watershed, the shorter the Tc , the larger the peak discharge . This means that peak discharge has an inverse relationship with Tc .

21. The time of concentration can be computed by Kirpich‘s equation which is widely used to estimate Tc : Where: Tc = Time of concentration ( hr ) L = Length of the main water course (m) S = slope of the main water course (m/m)

22. Exercise Determine the time of concentration for a given watershed having the following data: Longest stream length = 798.2 m Elevation @ U/S (m) = 3067.50 m Elevation @ D/S (m) = 2946.90 m

23. Thiessen Polygon Method Construct polygons by connecting stations with lines Bisect the polygon sides Estimate the area of each stations polygon Sum the areas Determine the stations weights by dividing the station area by the total area Determine areal precipitation by summing weighted precipitation for each station

24. Thiessen Polygon Method

25. Thiessen Polygon Method

26. Thiessen Polygon Method

27. Thiessen Polygon Method Unique for each gage network Allows for areal weighing of precipitation data Does not allow for orographic effects (those due to elevation changes) Most widely used method

28. Isohyetal Method Draw lines of equal precipitation Estimate precipitation in each grid area within basin Sum the values in each grid area Divide the sum by the number of grid areas to obtain a watershed areal estimate of precipitation

29. Isohyetal Method

30. Isohyetal Method

31. Isohyetal Method Watershed precipitation = 2.20 in.

32. Isohyetal Method Watershed precipitation = 2.20 in.

33. Isohyetal Method Magnitude and extent of resultant rainfall areas are calculated One of most accurate methods Difficult to draw accurately Can overlay topographical maps to take into account orographic effects and storm morphology

34. Distance Weighting (From: WW 2010 Project University of Illinois, Point Precipitation Measurements, Areal Estimates and Relationships to Hydrologic Modeling, via ABRFC Home Page - http://info.abrfc.noaa.gov/)

35. simple arithmetic average Choose three rain gauge stations as close to and as evenly spaced around the station with missing record (station X). Collect the rainfall data for the three stations (1,2,3) on the day(s) for which the data at station X are missing. The average annual rainfall values at all the four stations (1,2,3,X) should also be known.  If the average annual rainfalls of stations 1,2 &3 differ with in 10% of the average annual rainfall of station X, then simple arithmetic average of the three index stations will give the estimate for the missing record. i.e,

36. If N 1 , N2, N 3 and N x represent AARFof stations 1,2,3, & X respectively and when the average annual precipitation at any of these three differ from that of the station by more than 10%, the normal ratio method is used.

37. Example : Precipitation station X was inoperative for part of a month during which a storm occured. The respective storm totals at three surrounding stations A,B,and C were 107, 89, & 122mm. The normal annual precipitation amounts of stations X, A, B and C are respectively 978, 1220, 935 & 1200mm. Estimate the storm precipitaion for station X.

38. Solution   N x = 978mm & 10% N x = 97.8mm. Thus maximum permissible annual precipitation of any of the three stations for taking ordinary mean = 978 +97.8 = 1075.8mm < 1120 & 1200mm. Hence, the annual precipitations at three stations differ by more than 10% of N x . Hence, weighted mean should be used. That is  

39. Element of statistics for hydrological data The following are the sample statistics that are commonly used in fitting distributions for hydrological analysis. (1) Sample mean Sample mean is generally used to represent measures of central tendency. Where n is the number of sample size (2) Sample standard deviation Sample standard deviation is the measure of the spread of the distribution around the central value/mean. The square of the sample standard deviation is the variance, s2.

40. The standard deviation divided by the mean is called the coefficient of variation. It is a dimensionless desperation parameter.

41. 4) Sample Skew coefficient Skew measure the symmetry of a distribution. The lack of symmetry of a distribution is called skewness or asymmetry. The sample skew is given by: The degree of the skewness of the distribution is usually measured by the “coefficient of skewness ” (Cs) and is given by:

42. (5) Kurtosis Kurtosis provides information about the peakdness of the central portion of the distribution & is given by:

43. Checking rainfall Data Reliability Standard error of mean, = Relative standard = where n-1 =standard deviation Xm = mean n= sample size Hence the data series could be regarded as reliable and adequate if the relative standard is less than 10%.

44. Example Number of data = 39 Standard deviation, 12.38 Mean, X m = 51.81mm

45. Testing for outliers The procedure followed for detection and treatment of high and low outliers are summarized below:- If the station skew is greater than +0.4, test for high outliers are considered first; If the station skew is less than -0.4, tests for low outliers are considered first; Where the station skew is between ±0.4, test for both high and low outlier should be applied before eliminating any outliers from the data set.

46. As quoted by Rao , Grubs and Beck (1972) used the following equations to calculate outliers. In this test the quantities X H and X L are calculated by using: Where x=mean and s = STDV of the natural logarithms of the sample, KN = frequency factor and N = number of samples At 10% significant level, the following approximation for KN, proposed by Pilon et al (1985) for N number of sample size. Sample values >XH ---- high outliers Sample values < XL ---- low outliers

47. Tabulated value of Kn for different sample size

48. Example Year Flow Log (e) (Flow) Year Flow Log (e) (Flow) ( cfs ) ( cfs ) ( cfs ) ( cfs ) 1962 3990 8.29 1980 6140 8.72 1963 3390 8.13 1981 1180 7.07 1964 4160 8.33 1982 3060 8.03 1965 1500 7.31 1983 2260 7.72 1966 632 6.45 1984 2050 7.63 1967 2540 7.84 1985 4590 8.43 1968 3150 8.06 1986 2450 7.8 1969 2790 7.93 1987 798 6.68 1970 2180 7.69 1988 2750 7.92 1971 1710 7.44 1989 5130 8.54 1972 2910 7.98 1990 2240 7.71 1973 2240 7.71 1991 6890 8.84 1974 2720 7.91 Mean 2891 7.84283 1975 2270 7.73 STDV 1439.16 0.53825074 1976 3700 8.22 N   30 1977 1260 7.14 KN   2.56397912 1978 2760 7.92 XL   640.83 1979 3290 8.10 XH   10126.28 Skew=-0.66, there fore lower outlier should be checked first. Check Sample value < XL and Sample Value >XH 632 is <XL is considered as low outlier, there is no higher outlier .

49. Probability distribution Since most hydrologic events are represented by continuous random variables, their density functions denote the probability distribution of the magnitudes. Some of the frequently used density functions in hydrologic analysis are given below: Normal distribution Lognormal distribution Extreme value distribution Extreme value type I distribution ( Gumbel distribution, 1941) Extreme value type II distribution ( Frechert , 1927) Extreme value type III distribution ( weilbull , 1939) Pearson‘s Type-III distribution Logarithmic Pearson Type-III distribution EVI distribution and Log Pearson Type III distribution which are commonly used for used extreme hydrological series are described here in this manual.

50. Selecting appropriate distribution D-Index Coefficient of determination (R2)

51. Hydrology cont’d…

52. Exercise The maximum daily rainfall of x-meteorological station is shown in the following table. Maximum daily highest rainfall for 19 year period of x- meteorological station Calculate the mean, standard deviation, coefficient of variation, skew coefficient for the sample data Test the data for the outlier Compute the design storm for 50 year return period using the EVI distribution using tabular value of Yn and sn Compute the design storm for 50 year return period using EVI distribution ( Gumbel distribution) using Chow (1953) frequency factor

53. Design or peak flood estimation The flood used for spillway design against failure is termed as the “Project design flood”. It can usually be determined by estimating the runoff that results from an occurrence of design storm based on meteorological factors. This hydro-meteorological based flood estimating is necessary and the only way because stream flow records often are not available at the required.

54. To estimate the magnitude of a flood peak, the following alternative methods are available:- Rational formula USSCS (United states soil conservation service) method Empirical formula Synthetic unit hydrograph technique Regional Flood frequency analysis. In this particular training we will see the first two methods only.

55. The use of each particular method depends on:- The desired objective The available data The importance of the project Size of the catchment area.

56. 1. Rational Formula It is suitable where the time of concentration may be less than 1 hour. It is applicable in urban drainage design and in the design of small culverts and bridges. Even for larger watershed if it is possible to obtain accurate rainfall intensity (Michael, 1999).

57. The equation of the rational method is given by:- Where, Q: design peak discharge (m 3 /sec). C= runoff coefficient that can be taken from table. I = rainfall intensity in mm/h for the design return period and for a duration equal to the “time of concentration” of the watershed. A= the watershed area (km 2 ).

58. The C values are applicable for storms of 5-yr to 10-yr frequencies. Less frequent, higher intensity storms will require modification of the coefficient because infiltration and other losses have a proportionally smaller effect on runoff. The adjustment of the Rational method for use with major storms can be made by multiplying the right side of the rational formula by a frequency factor C f . The rational formula now becomes:

59. Frequency Factors for Rational Formula

60. Runoff Coefficient The runoff coefficient, C is a dimensionless ratio intended to indicate the amount of Runoff generated by a watershed given an average intensity of precipitation for a storm. It is implied by the rational method, that intensity of runoff is proportional to intensity of rainfall. Calibration of the runoff coefficient has depended on comparing the total depth of runoff with the total depth of precipitation , Where R = Total depth of runoff (mm), and P = Total depth of precipitation (mm).

61. The recommended runoff coefficient (C) for pervious surfaces by selected hydrologic soil groupings and slope ranges. Where the watershed comprises more than one characteristic, the C values for each area segment is estimated individually and then a weighted C value is calculated using the following equation:

62. Where: C = weighted (composite) runoff coefficient C1, C2, C3,… Cn = runoff coefficients applicable to areas A1, A2, A3 … An n = number of different type of area within watershed At = total area = A1+A2+A3+…An

63. Intensity of rainfall It is the rate at which rainfall occurs and expressed in cm/hr or mm /hr or mm/day. Getting intensity of rainfall for a certain area is a great challenge. The non-recording type of rain-gage records only depth of rainfall . Recording type rain-gage records both depth and duration of rainfall in the form of mass curve on rain-gage chart. For non recording type of rain-gage, intensity is obtained by dividing the total rainfall depth with its duration.

64. Example: From the total catchment area of 4ha, 2ha is covered by clay soil of flat terrain, 1ha is rolling terrain cover by sandy soil and 1ha is covered by silt loam soil of mountainous terrain. What will be the weighted runoff coefficient that can be used to estimate the design discharge of the catchment? Weighted C = (2ha×0.18)+(1ha×0.12)+ (1ha×0.21) 2+1+1 ha = 0.173

65. When there is no choice of getting intensity of rainfall the following techniques are employed 1. Regional IDF curves or 2. Richard's equation can be used for simple estimation of intensity: Where P= 24 hr design precipitation (computed), T= rainfall duration usually = 6hrs tc =time of concentration for the watershed outlet.

66. Intensity Duration Frequency (IDF) curve An IDF is a three parameter curve, in which intensity of a certain return period is related to duration (time of concentration) of rainfall. A more generalized Intensity- Duration – Frequency is given by Sherman equation :- where K, x, a and n are constants for a given catchment. T= recurrence interval (T) and t= time of concentration

67. DATA TO DEVELOP IDF CURVE IN ETHIOPIA

68. Exercise Determine the rainfall intensity and peak runoff produced by a watershed near to Debre Tabor by Rational method. Size of the catchment = 5 km2 Time of concentration = 0.445 hr Runoff coefficient = 0.15 Use ERA 2013 IDF curve

69. 2.USSCS method It is originated from conservation that a hydrograph could be represented in a simple geometric form as a triangle.

70. 2.2 Watershed parameter Data’s Total catchments area (A) in km 2 from DEM Automatic watershed delineation using Arc GIS or 1:50,000 scale Topo-map. Length of Main river course with in the watershed from the weir site to the far divide of the catchment. It is also obtained from Automatic delineation or 1:50,000 scale Topo-map. Elevation difference of the main river course from the weir site to the far divide of the catchment from DEM.

71. Automatic watershed delineation Arc GIS interface Arc SWAT software is used. Take elevation values at point 1, 2, 3 and 4 from the DEM or simply at 1and 4. tc =t1+t2+t3 where tc is total time of concentration the main water course from watershed divide to the proposed diversion (L)

72. Time of concentration Kirpich formula to calculate total time of concentration:- L = L1+L2+L3 H=(H1+H2+H3)/3 As MoA in 1994 If Tc < =3hr then rainfall duration can be taken as D= 0.5 hr If 3 < Tc <10 hr then rainfall duration can be taken as D=1hr If Tc > 10hr then rainfall duration can be taken as D=2hr

73. Once we know the duration D interval, then Time to peak, tp =0.5*D+0.6* Tc Time base, tb =2.67* tp and Lag time, tl =0.6* tc From this peak unit rate of discharge QP=0.21*A/ tp in m3/s/mm

74. runoff curve number ( CN ) The runoff curve number is an empirical parameter used in hydrology for predicting direct runoff or infiltration from rainfall excess. The runoff curve number was developed from an empirical analysis of runoff from small catchments and hill slope plots monitored by the USDA (Chow, 2004). It is widely used and is an efficient method for determining the approximate amount of direct runoff from a rainfall event in a particular area. The runoff curve number is based on the area's hydrologic soil group , land use , treatment and hydrologic condition. used to estimate runoff from small- to Medium-sized watersheds.

75. Cover description Curve numbers for Hydrologic soil group Cover Type Treatment 2 Hydrologic condtion 3 A B C D Fallow Bare soil Crop residue cover (CR) - Poor Good 77 76 74 86 85 83 91 90 88 94 93 90 Row Crops Straight row (SR) Poor Good 72 67 81 78 88 85 91 89 Group A: Sand, loamy sand or sandy loam . Soils having a low runoff potential due to high infiltration rates. Group B: Silt loam, or loam . Soils having a moderately low runoff potential due to moderate infiltration rates. Group C: Sandy clay loam . Soils having a moderately high runoff potential due to slow infiltration rates. Group D: Clay loam , silty clay loam , sandy clay , silty clay or clay . Soils having a high runoff potential due to very slow infiltration rates.

76. Land Use Description on Input Screen Description and Curve Numbers from TR-55 Cover Description Curve Number for Hydrologic Soil Group Cover Type and Hydrologic Condition A B C D Agricultural Row Crops - Straight Rows + Crop Residue Cover- Good Condition  (1) 64 75 82 85 Commercial Urban Districts: Commercial and Business 89 92 94 95 Forest Woods (2)  - Good Condition 30 55 70 77 Grass/Pasture Pasture, Grassland, or Range (3)  - Good Condition 39 61 74 80

77. The runoff equation is Where Q is runoff (mm) , P is rainfall (mm) , S is the potential maximum soil moisture retention (mm) , I a is the initial abstraction (mm) it is generally assumed that I a = 0.2 S. The runoff curve number, CN , is then related CN has a range from 0 to 100, and the equation is in metric unit.

78. lower numbers indicate low runoff potential while larger numbers are for increasing runoff potential. The lower the curve number, the more permeable the soil is. CN for wet antecedent moistures condition III (AMC-III) is simply obtained from table. if it is in AMC- II form, will be converted using the following relationship: Derivation of the above equations will result the following final known equation (Chow, 2004) Where R is accumulated direct runoff (mm), S is rainfall to infiltration potential ratio (Decimal), and P is accumulated rainfall or potential maximum runoff (mm),

79. Graphical Peak discharge Methods (TR55) The following equation is used for the estimation of peak discharge by Graphical peak discharge method: Where: Qp = peak discharge, m3/s qu = unit peak discharge, m3/s/km2/mm A = drainage area, km2 Q = Depth of runoff, mm

80. The unit peak discharge is obtained from the following equation, which requires the time of concentration ( Tc ) in hours and the initial abstraction rainfall ( Ia /p) ratio as input: Where: C0, C1 & C2 = regression coefficient given in Table for various Ia /P ratio & distribution type II = unit conversion factor equal to 0.000431 in SI unit Tc = time of concentration (hours)

81. Coefficients for SCS Peak Discharge Method Coefficients for SCS Peak Discharge Method This method has a number of limitations which can have an impact on the accuracy of estimated peak flows:  Basin should have fairly homogeneous CN values  CN should be 40 or greater  Tc should be between 0.1 and 10 hr  Ia /P should be between 0.1 and 0.5

82. Synthetic Hydrograph We have 6 hydrographs from H 1 to H 6 each with having beginning, peak, end time and the discharge magnitude in m3/s. Each hydrograph will be made using the summation of the two limbs as shown below:

83. Example Step_1 The maximum daily rain fall of Gashena meteorological station for 14 years of record is shown in the following table. Calculate the design storm that can be used for the determination of design discharge for the design of diversion weir for 50 years return period. = 56.51 σ = 28.53 Y 50 = -LN(LN(50/(50-1))) = 3.9 X 50 =56.51 + (0.779*3.9 - 0.4498)*28.53 = 130.4 mm Year 1987 1988 1996 1997 1999 2000 2001 2002 2003 2004 2005 2006 2009 2010 Rainfall (mm) 140 45 45.9 60 52.3 44.3 46.3 77.4 37.6 32.5 71.4 74 33.4 31

84. Step_2 Delineate the watershed automatically/manually Data Required Outlet coordinate /at proposed diversion site/ e.g. E= 408296 ,N 1320030 DEM Software used Arc SWAT Arc GIS interface Outputs Watershed parameter like Area Average slope of the main river course Length of the main stream can be calculated easily

85. Watershed parameters Area= 64.8 Km2 Average slope = 00112 Length of the main stream = 24000 m

86. Data/Map include in documentation Delineated Watershed DEM Soil (Type and Texture) Land cover Slope maps

87. no Designation/Formula Symbol Unit Value 1 Area of catchment (This can be determined from 1:50,000 scale topographical maps or automatic delineation) A Km2 64.8 2 Length of main watercourse from watershed divide to proposed diversion to proposed diversion or storage site (topographical map or from automatic delineation) L m 24000 3 Elevation of watershed divide opposite to the main water course (topographical map) = inlet elevation H 1 m 3228 4 Elevation of streambed at proposed diversion site (topographical map) = outlet elevation H 2 m 2960 5 Slope of main watercourse, S = (H 1 –H 2 )/L S m/m 0.0112 6 Time of concentration, Tc= 1/3000 (L^1.155/H^0.385) T C hr 4.4 7 Rainfall Excess duration, D=0.5 if Tc <3hrs , D≈1hr if 3< Tc >10 hrs , D≈2hr if Tc >10hrs D hr 1.0 8 Time to peak, T p = 0.5D + 0.6TC T p hr 3.16 9 Time base of hydrograph, T b = 2.67T p T b hr 8.4 10 Lag time, T L = 0.6 T C T e hr 2.66 11 Peak rate of discharge created by 1mm runoff excess on whole of the catchment, qp=(0.21A)/Tp q p m 3 /s /mm 4

88. Sub Step_1 Design Rainfall arrangement Input data Length of duration D is known; 1 hr Design storm is computed and known ;130.4 mm Look at two important Tabulated data values a) Rainfall profile % in 24 hrs the graph given b) Arial to point rainfall ratio for the given catchments area given from table for the area and each duration of hours.

89. Figure 1: Percent Rainfall profile chart for 24 hr storm

90. Area km 2 Duration (hrs) 0.50 1.00 2.00 3.00 4.00 5.00 6.00 9.00 12.00 15.00 18.00 21.00 24.00 25 66 78 82 85 87 88 88 91 92 93 93 94 94 50 61 71 78 82 84 85 87 89 90 91 92 92 93 75 57 67 75 79 82 84 83 87 89 90 91 91 92 100 54 65 73 78 80 82 83 86 88 89 90 91 91 125 52 63 72 76 79 81 82 85 87 88 89 90 91 150 50 61 70 75 78 80 61 84 86 88 89 89 90 175 48 59 69 74 77 79 81 84 86 87 88 89 90 200 46 58 68 73 76 78 80 83 85 87 88 88 89 225 45 57 57 72 75 77 72 82 85 86 87 88 89 250 44 55 66 71 74 77 78 82 84 86 87 88 88 275 42 54 65 70 74 76 78 81 84 85 86 87 88 300 41 53 54 70 73 75 77 81 83 85 86 87 88 325 40 53 63 58 72 73 77 80 83 84 86 87 87 350 38 52 63 68 72 74 76 80 82 84 85 86 87 375 39 51 62 68 71 74 78 80 82 84 85 86 87 400 38 50 61 67 71 73 75 79 82 83 85 86 87

91. 425 37 50 61 67 70 73 75 79 81 83 84 85 86 450 36 49 60 66 70 72 74 79 81 83 84 85 86 475 36 48 60 66 69 72 74 78 81 83 84 85 86 500 35 48 59 66 69 72 74 78 80 82 84 85 86 525 34 47 59 65 68 71 73 78 80 82 83 85 85 550 34 47 58 64 68 71 73 77 80 82 83 84 85 575 33 46 58 64 68 71 73 77 80 82 83 84 85 600 33 45 57 63 67 70 72 77 79 81 83 84 85 625 32 45 57 63 67 70 72 76 79 81 83 84 85 680 32 45 56 63 67 69 72 76 79 81 82 84 84 675 31 41 56 62 66 69 71 76 79 81 82 83 84 700 31 44 56 62 66 69 71 76 78 80 82 83 84 725 31 45 55 62 66 69 71 75 78 80 82 83 84 750 30 43 55 61 65 68 71 75 78 80 82 83 84 49 Figure 2 Point to Arial rainfall ration table for area km 2 and indicated duration.

92. Column no. Description of each column 12 Fill in 0-D hr, D-2D hr, … 5D-6Dhr. 13 Determine the magnitude of the daily rainfall with the given recurrent interval by applying statistical method. 14 Read from figure. 1 the rainfall profile (%) occurring in D, 2D, 3D … 6D hours, and enter in 14. 15 Multiply 13 and 14 to find the rainfall profile (mm) and enter in 15 16 From Figure 2 , read areal to point rainfall ratio for different duration and particular catchment area. The method is based on research conducted in India and influenced by return period, magnitude of storm shape and orientation of area etc. Alternatively for small catchment, you can use area reduction factor, ARF so that column17 can be obtained by multiplying ARF with column 16, ARF=1-0.044A^0.275 17 Multiply 15 and 16 and file in 17

93. 18 Calculate incremental rainfall by deducting the current areal rainfall from the preceding areal rainfall as listed in (18). 19 Assign order to the rainfall depths in descending order 1 to 6 20 From 19, mention the rearranged order as 6, 4, 3, 1, 2, 5 (arbitrarily) but considering ascending and descending feature of the hydrograph ordinates, where peak value is around the middle of the hydrograph. 21 Fill in the corresponding incremental rainfall value to the rearranged order of 20 from 18. 22 Fill in the cumulative rainfall values of 21 by adding with the rainfall values in the preceding duration 23 Fill in the time of beginning of hydrograph as 0, D, 2D … 5D hr. 24 Fill in the time to peak as T p , D+ Tp , 2D+T p … 5D + T p or add T p in every value of 23 and mention in 24. 25 Add T b in every value of 23 and fill in 25

94. 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Time (hr) Daily point rain fall (mm) Rainfall profile (%) Rain fall profile (mm) 13*14 Arial to point R.F ratio (%) Area rain fall (mm) 15*16 Incremental Rain fall (mm) Descending order Re arranged order Rearranged incremental rainfall (mm) Cumulative rainfall (mm) Time of beginning (hr) Time of Peak (hr) Time to end (hr) 0-1 130.4 34 44.3 58.63 26.0 26.0 1 6 4.8 4.8 3.16 8.4 1-2 45 58.7 68.63 40.3 14.3 2 4 7.6 12.4 1 4.16 9.4 3 53 69.1 72.43 50.1 9.8 3 3 9.8 22.2 2 5.16 10.4 3-4 58 75.6 76.22 57.6 7.6 4 1 26 48.2 3 6.16 11.4 4-5 63 82.1 78.22 64.3 6.61 5 2 14.3 62.5 4 7.16 12.4 5-6 66 86.1 80.22 69.0 4.8 6 5 6.61 69.11 5 8.16 13.4

95. Column no. Descriptions 26 Identify all types of land use cover such as cropped area, fallow land, pastures, meadow, forest etc. from the catchment map. 27 Find ratio of each type of land use cover to the total catchment area and enter in 27. 28 Ascertain treatment practice of each type of land use cover, hydrologic condition corresponding to it from the catchment map and enter in 28. 29 Ascertain hydrologic soil groups for each type of land use cover as below: Group A: Low runoff potential Group B: Moderate runoff potential Group C: Soil having high runoff potential Group D: Soil having very high runoff potential 30 Multiply 27 and 29 and enter in 30. 31 Add 30. This curve number is corresponding to antecedent moisture condition II (AMC-II). Find “CN” for AMC III from Table 1-5. Description of each column

96. 32 Find maximum potential difference S between Rainfall (P) and Direct Runoff (Q) from S=254(100/CN-1) Where CN = Value corresponding to AMC III as obtained in 31. 33 Substitute the value of S in the following formula, giving the relation between Direct Runoff Q and rainfall P, Q=(P-0.2S)^2/((P+0.8S) ) 34 Substitute values of P 1 as mentioned in 22, in the above formula and find the corresponding values of Q (34) .Enter the value of Q in 36. 35 Enter the same time as in 12 i.e. 0 – D, D – 20, 2D – 3D, … 5D – 6D 36 There are the values of Q as found out in 34 corresponding to the value of P. 37 Find incremental runoff by reducing the values of 36 by preceding values.

97. 38 Multiply 37 with peak rate of runoff corresponding to mm runoff excess as found at 11. 39 Plot triangular hydrograph, Figure1-1, with time of beginning, peak time and, time to end as mentioned in 23, 24, 25 and peak runoff as mentioned in 38. 40 Plot a composite hydrograph, Figure1-1, by adding all the triangular hydrographs. The resultant hydrograph will be composite hydrograph of desired return period. The coordinate of the peak of this hydrograph will give the peak runoff with desired return period. 41 bring the beginning, time to peak and end times and put in time order

98. Sub Step 2: Estimation of direct runoff Input data Land cover ,treatment, hydrologic condition and hydrologic soil group 26 27 28 29 30 31 Land use cover Area Ratio Hydrologic Condition Curve No. “CN” Weighted “CN” Sum Weighted “CN” grass land 0.61 Fair 84 51 AMC CN cultivated land 0.37 Good 81 30 II 83 shrub and bush land 0.02 Poor 83 2             III 92.5 No Description/Formula Symbol Unit Example 32 Find maximum potential difference S between Rainfall (P) and Direct Runoff (Q) from S=254(100/CN-1) Where CN = Value corresponding to AMC III as obtained in 31. S mm 20.6

99. Preparation of Synthetic Hydrograph 33 34 35 36 37 38 39 40 23 24 25 P (mm) Q (mm) Duration (hr) Cumulative Runoff(mm) Incremental Runoff (mm) Peak Runoff for Increment (m3/s) Time of Beginning (hr) Time to Peak (hr) Time to End (hr) Hydrograph Synthesis  4.8 0.0 0-1 0.094 0.0 3.2 8.4 H1 12.4 2.4 1-2 2.4 2.4 10.1 1.0 4.2 9.4 H2 22.2 8.5 2-3 8.5 6.1 26.2 2.0 5.2 10.4 H3 48.2 30.0 3-4 30.0 21.6 92.9 3.0 6.2 11.4 H4 62.5 43.2 4-5 43.2 13.1 56.4 4.0 7.2 12.4 H5 69.11 49.4 5-6 49.4 6.2 26.7 5.0 8.2 13.4 H6

100. Arrange the synthetic Hydrograph Now in the above example, we have 6 triangular hydrographs from H1 to H 6 each with beginning, peak, end time and the discharge magnitude in m3/s. Arrange tb , tp , te in ascending order

101. Time ( tb,tp,te ) (41) H1 H2 H3 H4 H5 H6 H total 0.0 0.00           0.0 1.0 0.03 0.00         0.0 2.0 0.06 3.20 0.00       3.3 3.0 0.09 6.40 8.27 0.00     14.8 3.2 0.09 6.92 9.61 4.78     21.4 4.0 0.08 9.60 16.54 29.37 0.00   55.6 4.2 0.08 10.12 17.88 34.15 2.90   65.1 5.0 0.06 8.52 24.80 58.74 17.84 0.00 110.0 5.2 0.06 8.21 26.15 63.53 20.74 1.37 120.1 6.2 0.04 6.29 21.20 92.90 38.58 9.80 168.8 7.2 0.02 4.37 16.25 75.31 56.42 18.23 170.6 8.2 0.01 2.46 11.30 57.72 45.74 26.65 143.9 8.4 0.00 1.92 9.90 52.76 42.72 25.23 132.5 9.4   0.00 4.95 35.18 32.04 20.19 92.4 10.4     0.00 17.59 21.36 15.14 54.1 11.4       0.00 10.68 10.09 20.8 12.4         0.00 5.05 5.0 13.4           0.00 0.0

102. Thank you

103. Design storm rainfall Extreme values of rainfall are of prime interests as inputs to simulation models used to estimate design floods. Point rainfall is the rainfall at a single station occurring at single point in space as opposed to areal rainfall which is over a region. The annual maximum rainfall for a given duration is used as input for estimating point rainfall.