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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL

ISSN NO: 0369-8394

Isopluvial Maps of Daily Maximum Precipitation for Different Frequency for Upper Cauvery Karnataka Mohammed Badiuddin Parvez1, Chalapathi k2,Amritha Thankachan3, M .Inayathulla4 1,2,3

Research Scholar, Department of Civil Engineering, UVCE, Bangalore University, Bangalore, Karnataka, India. 4 Professor, Department of Civil Engineering, UVCE, Bangalore University, Bangalore, Karnataka, India. Email: parvezuvce@gmail.com

ABSTRACT Probable maximum precipitation (PMP) is widely used by hydrologists for appraisal of probable maximum flood (PMF) used for soil and water conservation structures, and design of dam spillways. The estimation of design storm for example depends on availability of rainfall quantities and their durations. Daily maximum multiannual series are one of the main inputs for design streamflow calculation. The study generated annual series of Daily maximum rainfall for fourty four stations by using statical approach such as Normal distribution, Log-Normal Distribution, Pearson type III distribution and Gumbel’s Distribution .Results reveals that among the different statical approaches Log-Normal distribution fits the best compared to others. Isohyetal Maps of study area at different frequency are produced by using GIS tools, the maximum intensity varies from 2.5 mm/hr to 628 mm/hr. Key words: Climate change, Daily Maximum Rainfall, Gumbel’s distribution, Isopluvial Maps, Log-Normal Distribution, Maximum intensity, PMP, Rainfall Duration.

1 INTRODUCTION Water scarcity appears to be a future problem for Karnataka. This problem is an existential threat which can potentially hurt economic growth as well as agricultural growth. Water is expensive and inexpensive depending on its availability according to law of demand and supply. Rainfall as an environmental phenomenon is of immense importance to mankind. Hence the significance of studies to understand the rainfall process cannot be overemphasized. Floods, droughts, rainstorms, and high winds are extreme environmental events which have severe consequences on human society. Planning for these weather-related emergencies, design of engineering structures, reservoir management, pollution control, and insurance risk calculations, all rely on knowledge of the frequency of these extreme events The total rainfall and its intensity for a certain period of time are variable from year to another. The variation for depth of rainfall and its intensity depend on the climate type and the length of the studied period. It can be noted in arid and semi-arid areas, there is a significant change in the value of rain from time to another. Due to the significant variation in rainfall and its intensity in a consider time, the design and construction of storm water drainage systems and flood control systems are not depend only on the average of long-term rainfall records but on particular depths of precipitation that can be predicted for a certain probability or return period. These depths of rainfall can only be determined through a comprehensive analysis of a long time series of historical rainfall data. The historical rainfall data series are distinguished by medium and standard deviation, this information cannot be randomly used to predict the rainfall depths that can be estimated with a specific probability or return period for design and management of storm water drainage. Application of this technique to a data set can lead to misguiding results where the actual properties of the distribution are neglected. To avoid mistake, it is necessary to verify the integrity of the assumed distribution before estimating the design depths of the rainfall. There is a need for information of the extreme amounts of rainfall for various durations in the design of hydraulic structures and control storm runoff, such as dams and barriers, and conveyance structures etc.

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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL

ISSN NO: 0369-8394

2 MATERIALS AND METHODS A Study Area The study area geographically lies between 750 29’ 19” E and 760 37’ 40” E longitude and 110 55’ 54” N and 130 23’ 12.8” N latitude, as shown in Figure 1, the study area has an area of 10874.65 Sq km. The maximum length and width of the study area is approximately equal to 143.73 km and 96.75 km respectively. The maximum and minimum elevation of the basin is 1867 m and 714 m above MSL, respectively. Fourthy Four raingauge stations namely kushalnagar, malalur, mallipatna, nuggehalli, periyapatna, ponnampet, sakaleshpur, salagame, shantigrama, arehalli, arkalgud, attigundi, basavapatna, bettadapura, bilur, channenahally, chikkamagalur, doddabemmatti, galibidu, gonibeedu, gorur, hagare,halllibailu, hallimysore, harangi, hassan, hosakere, hunsur, kechamanna hosakote, naladi, shantebachahalli, belur, belagodu, javali, talakavery, shravanabelagola, siddapura, srimangala, sukravarsanthe, krishnarajpet, virajpet and yelawala were considered as shown in Figure 2.

Figure 1 Location Map of Study Area

Figure 2 Location of raingauge stations

B Methodology

Figure 3 Methodology for Isopluvial maps

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ISSN NO: 0369-8394

2.B.1 Estimation of Short Duration Rainfall Equation I was used for the estimation of various duration like 5minutes, 10minutes, 15minutes, 30minutes,1-hr, 2-hr, 6-hr, 12-hr rainfall values from annual maximum values. t

1 3

Pt = P24 (24)

(Equation I)

where, Pt is the required rainfall depth in mm at t-hr duration, P24 is the daily rainfall in mm and t is the duration of rainfall for which the rainfall depth is required in hr. Twenty Two years (1995-2016) rainfall data was used for the estimation of Short duration rainfall by using above equation for various stations as tabulated in Table 1 to Table 4. Table 1 shows the tabulation of short duration rainfall of station Krishnarajpet. Table 2 shows the tabulation of short duration rainfall of station Melkote. Table 3 shows the tabulation of short duration rainfall of station Hagare. Table 4 shows the tabulation of short duration rainfall of station Belagodu. Similarly the short duration rainfall was tabulated for the remaining Fourty stations. Then statical approach was made with log normal, Normal, Pearson Type III and Gumbel’s Distributions and they are checked for the best fit using Chi-square test for all the stations. C Probability distribution In this study the maximum rainfall intensity for various return periods were estimated using different theoretical distribution functions. Normal, Two-Parameter Lognormal, Pearson Type III, Extreme Value Type I (Gumbel) etc were used for probability distribution of the daily rainfall data. 2.C.1 Normal distribution Normal probability distribution, also called Gaussian distribution refers to a family of distributions that are bell shaped. The PDF for a normal random variable x is 1 đ?‘Ľâˆ’Âľ 2

1

đ?‘“(đ?‘Ľ) = đ?œŽâˆš2đ?œ‹ exp [− 2 (

đ?œŽ

) ] (đ?œŽ > 0)

(Equation II)

Where exp is the exponential function with base e = 2.718. Âľ is the mean and Ďƒ the standard deviation. 1/ (Ďƒâˆš (2Ď€)) is a constant factor that makes the area under the curve of f(x) from -∞ to ∞ equal to 1. 2.C.2 Log-normal distribution Variables in a system sometimes follow an exponential relationship as x = exp (w). If the exponent is a random variable, say W, X = exp (W) is a random variable and the distribution of X is of interest. An important special case occurs when W has a normal distribution. In that case, the distribution of X is called a lognormal distribution. The name follows transformation In (X) = W. That is, the natural logarithm of X is normally distributed. (Kreyszig, 2006) Probabilities for x are obtained from the transformation to W, but we need to recognize that the range of X is (0, ∞). Suppose that W is normally distributed with mean θ and variance ω 2; then the cumulative distribution function for x is đ?‘Ľ

đ??š(đ?‘Ľ) = âˆŤ 0

1 đ?‘Ľđ?‘?√2đ?œ‹

exp {−

(ln đ?‘Ľâˆ’đ?‘Ž)2 2đ?‘?2

} ⅆ�;

đ?&#x2018;&#x201A;<đ?&#x2018;Ľ<â&#x2C6;&#x17E;

(Equation III)

2.C.3 Gumbel distribution Gumbel distribution is a statistical method often used for predicting extreme hydrological event such as floods. The equation for fitting the Gumbel distribution to observed series of flood flow at different return periods T is â&#x2C6;&#x2019;

đ?&#x2018;Ľđ?&#x2018;&#x2021; = đ?&#x2018;Ľ + đ?&#x2018;&#x2DC;đ?&#x153;&#x17D;đ?&#x2018;Ľ (Equation IV) â&#x2C6;&#x2019; Where xT denotes the magnitude of the T-year flood event, K is the frequency factor,đ?&#x2018;Ľ= mean and đ?&#x153;&#x17D;đ?&#x2018;Ľ = standard deviation of the variate X. The frequency factor K for Gumbel distribution is expressed as

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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL

ISSN NO: 0369-8394

â&#x2C6;&#x161;6(0.5772+InIđ?&#x2018;&#x203A; (đ?&#x2018;&#x2021;â&#x2C6;&#x2022;(đ?&#x2018;&#x2021;â&#x2C6;&#x2019;1))

đ??ž = â&#x2C6;&#x2019;[

]

đ?&#x153;&#x2039;

(Equation V)

2.C.4 Pearson type III distribution The Pearson type III distributions are commonly used to fit a sample of extreme hydrological data. A closed-form expression for the CDF of the Pearson III distribution is not available. Tables or approximations must be used. Many tables provide frequency factors Kp(Îł) which are the pthquantile of a standard Pearson III variate with skew Îł, mean zero and variance 1. For any mean and standard deviation, pth Pearson III quantile can be written as đ?&#x2018;Ľđ?&#x2018;? = đ?&#x153;&#x2021; + đ?&#x153;&#x17D;đ?&#x2018;&#x2DC;đ?&#x2018;? (đ?&#x203A;ž) (Equation VI) D Chi-Square Test To identify a specific theoretical distribution for the available data it is important to do a test. The aim of the test is to find how good a fit is between the observed and the predicted data. Chi-square is one of the most widely used tests to find the best fit theoretical distribution of any specific dataset which is represented by Equation 2.17. đ?&#x2018;&#x203A;

Ď&#x2021;2 = â&#x2C6;&#x2018;đ?&#x2018;&#x2013;=1(đ?&#x2018;&#x201A;đ?&#x2018;&#x2013; â&#x2C6;&#x2019; đ??¸đ?&#x2018;&#x2013; )2 â&#x2C6;&#x2022; đ??¸đ?&#x2018;&#x2013;

(Equation VII)

where, Oi and Ei represent the observed and expected frequencies respectively. 3 Results and Discussions All the time series of the stations gives best fit using log normal distribution hence rainfall Intensities of all the station obtained by log-normal distributions is considered. Considering lower return periods might not be appropriate considering the fact that, generally the life of a structure is more than 25 years. The short durations of 5, 10, 15, 30, 60. 120, 720 and 1440 minutes isopluvial maps were generated as the intensity decreases with the increase in duration for return period of 25years, 50years,75years and 100years as shown in Tables 5 to Table 8 and IDW analysis was done and the maps were obtained as shown in figure 4 . A Estimation of Short Duration Rainfall Table 1 Short duration rainfall for Krishnarajpet Year

Rainfall (mm) Duration in minutes

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

74.000 105.000 50.600 70.800 60.000 76.800 85.600 55.400 65.200 85.600 82.500 64.500 60.000 62.000 97.200 58.600 80.200 66.000 42.000 93.400 65.500 45.000

t

1 3

Pt = P24 ( ) 24

in mm where, time t is in hours

5

10

15

30

60

120

720

1440

11.206 15.900 7.662 10.721 9.086 11.630 12.962 8.389 9.873 12.962 12.493 9.767 9.086 9.388 14.719 8.874 12.144 9.994 6.360 14.143 9.918 6.814

14.118 20.033 9.654 13.508 11.447 14.652 16.331 10.570 12.439 16.331 15.740 12.306 11.447 11.829 18.544 11.180 15.301 12.592 8.013 17.819 12.496 8.585

16.161 22.931 11.051 15.462 13.104 16.773 18.695 12.099 14.239 18.695 18.018 14.086 13.104 13.540 21.228 12.798 17.515 14.414 9.173 20.398 14.305 9.828

20.362 28.892 13.923 19.481 16.510 21.132 23.554 15.244 17.940 23.554 22.701 17.748 16.510 17.060 26.746 16.124 22.068 18.161 11.557 25.700 18.023 12.382

25.654 36.401 17.542 24.545 20.801 26.625 29.676 19.206 22.604 29.676 28.601 22.361 20.801 21.494 33.697 20.315 27.804 22.881 14.561 32.380 22.708 15.601

32.322 45.863 22.102 30.925 26.207 33.545 37.389 24.198 28.479 37.389 36.035 28.173 26.207 27.081 42.456 25.596 35.031 28.828 18.345 40.796 28.610 19.656

58.734 83.339 40.161 56.194 47.622 60.956 67.941 43.971 51.749 67.941 65.480 51.194 47.622 49.209 77.148 46.511 63.655 52.384 33.335 74.132 51.987 35.717

74.000 105.000 50.600 70.800 60.000 76.800 85.600 55.400 65.200 85.600 82.500 64.500 60.000 62.000 97.200 58.600 80.200 66.000 42.000 93.400 65.500 45.000

Table 2 Short duration rainfall for Melkote

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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL Year

Rainfall (mm) Duration in minutes 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

160.000 110.200 60.400 60.800 100.400 65.000 78.600 60.000 90.200 58.300 140.000 84.000 97.800 74.600 79.800 90.000 83.000 93.400 60.000 94.200 57.600 46.400

t

1 3

Pt = P24 ( ) 24

5

in mm where, time t is in hours 10

24.228 16.687 9.146 9.207 15.203 9.843 11.902 9.086 13.659 8.828 21.200 12.720 14.810 11.296 12.084 13.628 12.568 14.143 9.086 14.264 8.722 7.026

ISSN NO: 0369-8394

15 30.526 21.025 11.523 11.600 19.155 12.401 14.996 11.447 17.209 11.123 26.710 16.026 18.659 14.233 15.225 17.171 15.835 17.819 11.447 17.972 10.989 8.852

30 34.943 24.067 13.191 13.278 21.927 14.196 17.166 13.104 19.699 12.732 30.575 18.345 21.359 16.292 17.428 19.656 18.127 20.398 13.104 20.573 12.580 10.134

60 44.026 30.323 16.620 16.730 27.626 17.885 21.628 16.510 24.819 16.042 38.522 23.113 26.911 20.527 21.958 24.764 22.838 25.700 16.510 25.920 15.849 12.767

120 55.469 38.204 20.940 21.078 34.807 22.534 27.249 20.801 31.271 20.211 48.535 29.121 33.905 25.862 27.665 31.201 28.774 32.380 20.801 32.657 19.969 16.086

720

1440

69.886 48.134 26.382 26.557 43.854 28.391 34.332 26.207 39.398 25.465 61.151 36.690 42.718 32.585 34.856 39.311 36.254 40.796 26.207 41.146 25.159 20.267

126.992 87.466 47.940 48.257 79.688 51.591 62.385 47.622 71.592 46.273 111.118 66.671 77.624 59.210 63.337 71.433 65.877 74.132 47.622 74.767 45.717 36.828

160.000 110.200 60.400 60.800 100.400 65.000 78.600 60.000 90.200 58.300 140.000 84.000 97.800 74.600 79.800 90.000 83.000 93.400 60.000 94.200 57.600 46.400

Table 3 Short duration rainfall for Hagare Year

Rainfall (mm) Duration in minutes 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

34.000 60.000 61.000 95.000 89.000 67.800 56.100 67.000 78.000 44.000 42.200 54.800 51.100 110.400 72.400 103.000 56.200 60.800 44.200 62.000 59.400 40.000

t

1 3

Pt = P24 ( ) 24

in mm where, time t is in hours

5

10

15

30

60

120

720

1440

5.149 9.086 9.237 14.386 13.477 10.267 8.495 10.146 11.811 6.663 6.390 8.298 7.738 16.717 10.963 15.597 8.510 9.207 6.693 9.388 8.995 6.057

6.487 11.447 11.638 18.125 16.980 12.935 10.703 12.783 14.881 8.395 8.051 10.455 9.749 21.063 13.813 19.651 10.722 11.600 8.433 11.829 11.333 7.631

7.425 13.104 13.322 20.748 19.437 14.807 12.252 14.632 17.035 9.609 9.216 11.968 11.160 24.111 15.812 22.495 12.274 13.278 9.653 13.540 12.973 8.736

9.355 16.510 16.785 26.140 24.489 18.656 15.437 18.436 21.463 12.107 11.612 15.079 14.061 30.378 19.922 28.342 15.464 16.730 12.162 17.060 16.345 11.006

11.787 20.801 21.148 32.935 30.855 23.505 19.449 23.228 27.041 15.254 14.630 18.998 17.715 38.274 25.100 35.708 19.483 21.078 15.323 21.494 20.593 13.867

14.851 26.207 26.644 41.495 38.874 29.614 24.504 29.265 34.070 19.219 18.433 23.936 22.320 48.222 31.624 44.989 24.548 26.557 19.306 27.081 25.945 17.472

26.986 47.622 48.416 75.402 70.639 53.813 44.527 53.178 61.909 34.923 33.494 43.495 40.558 87.625 57.464 81.751 44.606 48.257 35.082 49.209 47.146 31.748

34.000 60.000 61.000 95.000 89.000 67.800 56.100 67.000 78.000 44.000 42.200 54.800 51.100 110.400 72.400 103.000 56.200 60.800 44.200 62.000 59.400 40.000

Table 4 Short duration rainfall for Belagodu Year

Rainfall (mm) Duration in minutes 1995 1996

51.200 77.000

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t

1 3

Pt = P24 ( ) 24

in mm where, time t is in hours

5

10

15

30

60

120

720

1440

7.753 11.660

9.768 14.691

11.182 16.816

14.088 21.187

17.750 26.694

22.364 33.633

40.637 61.115

51.200 77.000

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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

80.000 75.000 70.000 100.000 80.400 40.000 50.000 80.000 180.000 60.000 132.400 90.000 90.000 110.000 50.500 53.200 108.300 62.200 77.400 83.400

12.114 11.357 10.600 15.143 12.175 6.057 7.571 12.114 27.257 9.086 20.049 13.628 13.628 16.657 7.647 8.056 16.399 9.419 11.720 12.629

15.263 14.309 13.355 19.079 15.339 7.631 9.539 15.263 34.341 11.447 25.260 17.171 17.171 20.986 9.635 10.150 20.662 11.867 14.767 15.912

17.472 16.380 15.288 21.840 17.559 8.736 10.920 17.472 39.311 13.104 28.916 19.656 19.656 24.023 11.029 11.619 23.652 13.584 16.904 18.214

ISSN NO: 0369-8394 22.013 20.637 19.261 27.516 22.123 11.006 13.758 22.013 49.529 16.510 36.431 24.764 24.764 30.268 13.896 14.639 29.800 17.115 21.297 22.948

27.734 26.001 24.268 34.668 27.873 13.867 17.334 27.734 62.403 20.801 45.901 31.201 31.201 38.135 17.507 18.443 37.546 21.564 26.833 28.913

34.943 32.759 30.575 43.679 35.118 17.472 21.840 34.943 78.622 26.207 57.831 39.311 39.311 48.047 22.058 23.237 47.304 27.168 33.808 36.428

63.496 59.528 55.559 79.370 63.814 31.748 39.685 63.496 142.866 47.622 105.086 71.433 71.433 87.307 40.082 42.225 85.958 49.368 61.432 66.195

80.000 75.000 70.000 100.000 80.400 40.000 50.000 80.000 180.000 60.000 132.400 90.000 90.000 110.000 50.500 53.200 108.300 62.200 77.400 83.400

Table 5 Rainfall Intensity in mm/hr for 25 years return period

Sl No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

Raingauge Station Arehalli Arkalgud Attigundi Basavapatna Balagodu Belur Bettadapura Bilur Channenahally Chikkamangalore Doddabemmatti Galibeedu Gonibeedu Gorur Hagare Halekote Hallibailu Hallimysore Harangi Hassan Hosakere Hunsur Javali Kenchammana hoskote Krishnarajpet Kushalnagar Malalur Mallipatna Melkote Naladi Nuggehalli Periyapatna Poonampet Sakleshpura Salagame Shantebachahalli Shantigrama Shravanabelagola

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Time (t )in minutes 30 60

5

10

15

120

720

1440

226.392 148.505 244.284 139.880 189.033 167.993 136.843 382.195 154.250 143.691 109.376 364.342 262.871 146.478 144.517 147.669 329.504 137.854 153.765 162.395 486.738 150.837 325.228

142.618 93.553 153.889 88.119 119.084 105.829 86.206 240.768 97.172 90.520 68.903 229.521 165.598 92.276 91.040 93.026 207.575 86.843 96.866 102.303 306.626 95.022 204.881

108.838 71.394 117.439 67.247 90.878 80.763 65.787 183.740 74.156 69.079 52.582 175.157 126.375 70.420 69.477 70.992 158.409 66.273 73.923 78.072 234.000 72.515 156.353

68.564 44.975 73.982 42.363 57.249 50.877 41.443 115.749 46.715 43.517 33.125 110.342 79.611 44.362 43.767 44.722 99.791 41.750 46.568 49.182 147.411 45.682 98.496

43.192 28.333 46.606 26.687 36.065 32.051 26.108 72.917 29.429 27.414 20.867 69.511 50.152 27.946 27.572 28.173 62.865 26.301 29.336 30.983 92.863 28.778 62.049

27.209 17.848 29.360 16.812 22.719 20.191 16.447 45.935 18.539 17.270 13.146 43.789 31.594 17.605 17.369 17.748 39.602 16.568 18.481 19.518 58.500 18.129 39.088

8.240 5.405 8.892 5.092 6.881 6.115 4.981 13.912 5.615 5.230 3.981 13.262 9.568 5.332 5.260 5.375 11.994 5.018 5.597 5.911 17.717 5.490 11.838

5.191 3.405 5.601 3.207 4.335 3.852 3.138 8.764 3.537 3.295 2.508 8.354 6.028 3.359 3.314 3.386 7.556 3.161 3.526 3.724 11.161 3.459 7.457

207.910 150.862 133.985 108.237 146.863 188.813 626.061 177.353 139.599 341.927 266.588 151.176 194.550 134.625 183.882

130.975 95.038 84.405 68.185 92.518 118.945 394.394 111.725 87.942 215.401 167.940 95.235 122.559 84.809 115.838

99.953 72.527 64.413 52.035 70.604 90.772 300.979 85.262 67.112 164.382 128.162 72.678 93.530 64.721 88.401

62.966 45.689 40.578 32.780 44.478 57.183 189.605 53.712 42.278 103.554 80.737 45.784 58.920 40.772 55.689

39.666 28.782 25.562 20.650 28.019 36.023 119.444 33.836 26.634 65.235 50.861 28.842 37.117 25.685 35.082

24.988 18.132 16.103 13.009 17.651 22.693 75.245 21.316 16.778 41.095 32.041 18.169 23.382 16.180 22.100

7.568 5.491 4.877 3.940 5.346 6.873 22.788 6.455 5.081 12.446 9.704 5.503 7.081 4.900 6.693

4.767 3.459 3.072 2.482 3.368 4.329 14.356 4.067 3.201 7.840 6.113 3.466 4.461 3.087 4.216

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PRAXIS SCIENCE AND TECHNOLOGY JOURNAL 39 40 41 42 43 44

Siddapura Srimangala Sukravarashante Talakavery Virajpet Yelawala

212.360 351.820 306.295 578.434 320.613 154.014

133.779 221.633 192.954 364.391 201.974 97.023

102.092 169.137 147.251 278.082 154.135 74.042

ISSN NO: 0369-8394 64.314 106.550 92.763 175.181 97.099 46.644

40.515 67.122 58.437 110.357 61.168 29.384

25.523 42.284 36.813 69.521 38.534 18.511

7.730 12.806 11.149 21.055 11.670 5.606

4.869 8.067 7.023 13.264 7.352 3.532

Table 6 Rainfall Intensity in mm/hr for 50 years return period

Sl No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

Raingauge Station Arehalli Arkalgud Attigundi Basavapatna Balagodu Belur Bettadapura Bilur Channenahally Chikkamangalore Doddabemmatti Galibeedu Gonibeedu Gorur Hagare Halekote Hallibailu Hallimysore Harangi Hassan Hosakere Hunsur Javali Kenchammana hoskote Krishnarajpet Kushalnagar Malalur Mallipatna Melkote Naladi Nuggehalli Periyapatna Poonampet Sakleshpura Salagame Shantebachahalli Shantigrama Shravanabelagola Siddapura Srimangala Sukravarashante Talakavery Virajpet Yelawala

Time (t )in minutes 30 60

5

10

15

120

720

1440

226.768 148.738 244.700 140.087 189.384 168.286 137.042 382.952 154.516 143.854 109.504 364.766 263.332 146.674 144.737 147.954 329.889 138.000 154.023 162.623 487.317 151.083 325.612

142.855 93.699 154.152 88.249 119.304 106.014 86.331 241.245 97.339 90.622 68.983 229.789 165.889 92.399 91.179 93.205 207.818 86.935 97.029 102.447 306.991 95.177 205.123

109.019 71.506 117.640 67.347 91.046 80.903 65.883 184.104 74.284 69.158 52.644 175.361 126.597 70.514 69.582 71.129 158.594 66.344 74.047 78.181 234.278 72.633 156.538

68.677 45.046 74.108 42.426 57.356 50.966 41.504 115.979 46.796 43.567 33.164 110.471 79.751 44.421 43.834 44.808 99.908 41.794 46.646 49.251 147.586 45.756 98.613

43.264 28.377 46.685 26.727 36.132 32.107 26.146 73.062 29.480 27.445 20.892 69.592 50.240 27.983 27.614 28.227 62.938 26.329 29.385 31.026 92.973 28.825 62.122

27.255 17.876 29.410 16.837 22.762 20.226 16.471 46.026 18.571 17.289 13.161 43.840 31.649 17.628 17.396 17.782 39.649 16.586 18.512 19.545 58.569 18.158 39.135

8.254 5.414 8.907 5.099 6.893 6.125 4.988 13.939 5.624 5.236 3.986 13.277 9.585 5.339 5.268 5.385 12.008 5.023 5.606 5.919 17.738 5.499 11.852

5.200 3.411 5.611 3.212 4.343 3.859 3.142 8.781 3.543 3.299 2.511 8.364 6.038 3.363 3.319 3.393 7.564 3.164 3.532 3.729 11.174 3.464 7.466

208.201 151.038 134.148 108.363 147.010 189.114 627.082 177.701 139.775 342.726 267.005 151.435 195.050 134.842 184.251 212.685 352.406 306.649 579.272 321.171 154.224

131.158 95.148 84.508 68.264 92.611 119.135 395.038 111.945 88.053 215.904 168.203 95.398 122.874 84.946 116.071 133.983 222.002 193.177 364.919 202.325 97.155

100.093 72.612 64.492 52.095 70.675 90.917 301.470 85.430 67.197 164.766 128.363 72.802 93.770 64.826 88.579 102.248 169.419 147.422 278.485 154.403 74.143

63.054 45.743 40.627 32.818 44.523 57.274 189.914 53.818 42.331 103.796 80.864 45.863 59.072 40.838 55.801 64.412 106.727 92.870 175.435 97.268 46.707

39.722 28.816 25.594 20.674 28.047 36.080 119.638 33.903 26.667 65.387 50.941 28.892 37.213 25.726 35.153 40.577 67.234 58.504 110.517 61.275 29.424

25.023 18.153 16.123 13.024 17.669 22.729 75.368 21.358 16.799 41.191 32.091 18.201 23.443 16.206 22.145 25.562 42.355 36.855 69.621 38.601 18.536

7.578 5.498 4.883 3.944 5.351 6.884 22.825 6.468 5.088 12.475 9.719 5.512 7.100 4.908 6.707 7.742 12.827 11.162 21.085 11.690 5.614

4.774 3.463 3.076 2.485 3.371 4.336 14.379 4.075 3.205 7.859 6.122 3.472 4.473 3.092 4.225 4.877 8.081 7.031 13.283 7.364 3.536

120

720

1440

27.270 17.886 29.426

8.259 5.417 8.912

5.203 3.412 5.614

Table 7 Rainfall Intensity in mm/hr for 75 years return period

Sl No 1 2 3

Raingauge Station Arehalli Arkalgud Attigundi

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10

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226.891 148.815 244.837

142.933 93.748 154.238

109.078 71.543 117.706

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68.715 45.069 74.150

43.288 28.392 46.712

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Basavapatna Balagodu Belur Bettadapura Bilur Channenahally Chikkamangalore Doddabemmatti Galibeedu Gonibeedu Gorur Hagare Halekote Hallibailu Hallimysore Harangi Hassan Hosakere Hunsur Javali Kenchammana hoskote Krishnarajpet Kushalnagar Malalur Mallipatna Melkote Naladi Nuggehalli Periyapatna Poonampet Sakleshpura Salagame Shantebachahalli Shantigrama Shravanabelagola Siddapura Srimangala Sukravarashante Talakavery Virajpet Yelawala

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140.155 189.499 168.382 137.108 383.201 154.604 143.908 109.546 364.906 263.483 146.739 144.809 148.047 330.016 138.048 154.108 162.698 487.507 151.164 325.738

88.292 119.377 106.074 86.373 241.402 97.394 90.656 69.010 229.877 165.984 92.440 91.224 93.264 207.898 86.965 97.082 102.494 307.111 95.228 205.203

67.379 91.102 80.950 65.915 184.224 74.326 69.184 52.664 175.429 126.670 70.545 69.617 71.174 158.655 66.367 74.087 78.217 234.369 72.672 156.599

42.446 57.390 50.995 41.524 116.054 46.822 43.583 33.176 110.513 79.797 44.440 43.856 44.837 99.947 41.809 46.672 49.274 147.643 45.781 98.651

26.740 36.154 32.125 26.158 73.109 29.496 27.456 20.900 69.619 50.269 27.996 27.628 28.245 62.962 26.338 29.402 31.041 93.010 28.840 62.146

16.845 22.775 20.237 16.479 46.056 18.581 17.296 13.166 43.857 31.667 17.636 17.404 17.793 39.664 16.592 18.522 19.554 58.592 18.168 39.150

5.102 6.898 6.129 4.991 13.948 5.627 5.238 3.987 13.282 9.591 5.341 5.271 5.389 12.012 5.025 5.609 5.922 17.745 5.502 11.857

3.214 4.345 3.861 3.144 8.787 3.545 3.300 2.512 8.367 6.042 3.365 3.320 3.395 7.567 3.165 3.534 3.731 11.179 3.466 7.469

208.296 151.096 134.201 108.404 147.058 189.213 627.418 177.816 139.833 342.989 267.142 151.520 195.214 134.914 184.373 212.791 352.598 306.765 579.548 321.355 154.293

131.219 95.185 84.542 68.291 92.641 119.197 395.249 112.017 88.089 216.070 168.290 95.452 122.978 84.991 116.148 134.051 222.124 193.250 365.093 202.441 97.199

100.139 72.640 64.517 52.115 70.698 90.964 301.632 85.485 67.225 164.892 128.429 72.843 93.849 64.860 88.637 102.300 169.512 147.478 278.618 154.491 74.176

63.083 45.760 40.643 32.831 44.537 57.304 190.016 53.852 42.349 103.875 80.905 45.888 59.121 40.859 55.838 64.445 106.786 92.905 175.518 97.323 46.728

39.740 28.827 25.604 20.682 28.057 36.099 119.703 33.925 26.678 65.437 50.967 28.908 37.244 25.740 35.176 40.598 67.271 58.527 110.570 61.310 29.437

25.035 18.160 16.129 13.029 17.675 22.741 75.408 21.371 16.806 41.223 32.107 18.211 23.462 16.215 22.159 25.575 42.378 36.869 69.654 38.623 18.544

7.582 5.500 4.885 3.946 5.353 6.887 22.838 6.472 5.090 12.485 9.724 5.515 7.106 4.911 6.711 7.745 12.834 11.166 21.095 11.697 5.616

4.776 3.465 3.077 2.486 3.372 4.339 14.387 4.077 3.206 7.865 6.126 3.474 4.476 3.094 4.228 4.879 8.085 7.034 13.289 7.369 3.538

120

720

1440

27.277 17.890 29.435 16.849 22.782 20.243 16.483 46.071 18.587 17.299 13.169 43.865 31.676 17.640 17.409 17.799 39.671

8.261 5.418 8.914 5.103 6.900 6.131 4.992 13.953 5.629 5.239 3.988 13.285 9.593 5.342 5.272 5.390 12.015

5.204 3.413 5.616 3.215 4.347 3.862 3.145 8.790 3.546 3.300 2.512 8.369 6.043 3.365 3.321 3.396 7.569

Table 8 Rainfall Intensity in mm/hr for 100 years return period

Sl No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Raingauge Station Arehalli Arkalgud Attigundi Basavapatna Balagodu Belur Bettadapura Bilur Channenahally Chikkamangalore Doddabemmatti Galibeedu Gonibeedu Gorur Hagare Halekote Hallibailu

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Time (t )in minutes 30 60

5

10

15

226.953 148.853 244.905 140.188 189.556 168.430 137.140 383.324 154.647 143.934 109.566 364.975 263.558 146.771 144.845 148.094 330.079

142.971 93.772 154.281 88.313 119.413 106.104 86.393 241.480 97.422 90.673 69.023 229.920 166.032 92.460 91.247 93.293 207.937

109.108 71.561 117.738 67.396 91.129 80.973 65.930 184.283 74.347 69.196 52.674 175.462 126.706 70.560 69.634 71.196 158.686

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68.733 45.081 74.170 42.457 57.408 51.010 41.533 116.091 46.835 43.591 33.183 110.534 79.820 44.450 43.867 44.851 99.966

43.299 28.399 46.724 26.746 36.165 32.134 26.164 73.133 29.504 27.461 20.904 69.632 50.283 28.002 27.634 28.254 62.974

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Hallimysore Harangi Hassan Hosakere Hunsur Javali Kenchammana hoskote Krishnarajpet Kushalnagar Malalur Mallipatna Melkote Naladi Nuggehalli Periyapatna Poonampet Sakleshpura Salagame Shantebachahalli Shantigrama Shravanabelagola Siddapura Srimangala Sukravarashante Talakavery Virajpet Yelawala

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138.072 154.150 162.736 487.601 151.204 325.801

86.980 97.108 102.517 307.170 95.253 205.242

66.378 74.108 78.235 234.415 72.691 156.629

41.816 46.685 49.285 147.672 45.793 98.670

26.342 29.410 31.048 93.027 28.848 62.158

16.595 18.527 19.559 58.604 18.173 39.157

5.026 5.611 5.923 17.748 5.504 11.859

3.166 3.535 3.732 11.181 3.467 7.471

208.344 151.125 134.228 108.425 147.082 189.262 627.584 177.873 139.861 343.119 267.210 151.562 195.296 134.949 184.433 212.844 352.694 306.823 579.684 321.445 154.327

131.249 95.203 84.558 68.303 92.656 119.228 395.354 112.053 88.107 216.152 168.332 95.478 123.029 85.013 116.186 134.084 222.184 193.287 365.179 202.498 97.220

100.161 72.653 64.530 52.125 70.710 90.988 301.711 85.512 67.238 164.955 128.461 72.864 93.888 64.877 88.666 102.325 169.558 147.505 278.683 154.535 74.193

63.098 45.769 40.651 32.837 44.544 57.319 190.066 53.869 42.358 103.915 80.926 45.901 59.146 40.870 55.856 64.461 106.815 92.922 175.560 97.351 46.738

39.749 28.832 25.609 20.686 28.061 36.109 119.734 33.936 26.684 65.462 50.980 28.916 37.260 25.746 35.187 40.608 67.289 58.537 110.596 61.327 29.443

25.040 18.163 16.133 13.031 17.677 22.747 75.428 21.378 16.810 41.239 32.115 18.216 23.472 16.219 22.167 25.581 42.389 36.876 69.671 38.634 18.548

7.584 5.501 4.886 3.947 5.354 6.889 22.844 6.474 5.091 12.489 9.726 5.517 7.109 4.912 6.713 7.747 12.838 11.168 21.100 11.700 5.617

4.777 3.465 3.078 2.486 3.373 4.340 14.391 4.079 3.207 7.868 6.127 3.475 4.478 3.094 4.229 4.881 8.087 7.035 13.292 7.371 3.539

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Figure 4; Isopluvial Maps for different duration and frequency

4 CONCLUSIONS Hydrologists and engineers require Intensity-duration-frequency data in the planning and design of water resources projects. Historical rainfall records are needed to obtain design estimates for both small and large projects. This study has attempted to provide much needed and useful design charts for water resources planning and development in Upper Cauvery. The results from the IDF analysis showed that the Log-Normal distribution method was successfully used to derive the rainfall intensity, duration and frequency at each of the 44 selected synoptic stations in Upper Cauvery. Isopluvial maps were also produce for Upper Cauvery for various duration and frequencies. The results obtained should serve to meet the need for rainfall intensity-duration-frequency relationships and estimates in various parts of Upper Cauvery, both for short and longer recurrence intervals. The use of the results of this study to calculate design floods could be done with greater easy for most parts of Upper Cauvery. Village maps can be overlayed with isopluvial maps to find the rainfall intensity at any particular point. It is hoped that as more precipitation data at required time scale are available the analysis could also be refined and applied to individual station series to obtain improved estimates of the IDF parameters and more precise maps.

Reference 1.

Bell F. C., 1969, “Generalized rainfall-duration-frequency relationship”, ASCE J. Hydraulic Eng., 95, 311–327.

2.

Bernard, M. M., (1932), “Formulas for rainfall intensities of long durations”. Trans. ASCE 6:592 - 624.

3.

Bhaskar, N. R.; Parida, B. P.; Nayak, A. K. 1997. Flood Estimation for Ungauged Catchments Using the GIUH. Journal of Water Resources Planning and Management., ASCE 123(4): 228-238.

4.

Chow V.T., D.R. Maidment and L.W.Mays, 1988, “Applied Hydrology”, McGraw- Hill, Chapter 10 – Probability, Risk and Uncertainty Analysis for Hydrologic and Hydraulic Design: 361 – 398.

5.

M. M. Rashid, 1 S. B. Faruque and 2 J. B. Alam 2012, “Modeling of Short Duration Rainfall Intensity Duration Frequency (SDRIDF) Equation for Sylhet City in Bangladesh.

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Mohammed Badiuddin Parvez, M Inayathulla “Generation Of Intensity Duration Frequency Curves For Different Return Period Using Short Duration Rainfall For Manvi Taluk Raichur District Karnataka”, International Research Journal of Engineering and Management Studies (IRJEMS), Volume: 03 Issue: 04 | April -2019.

7.

Mohammed Badiuddin Parvez, M Inayathulla “Prioritization Of Subwatersheds of Cauvery Region Based on Morphometric Analysis Using GIS”, International Journal for Research in Engineering Application & Management (IJREAM), Volume: 05 Issue: 01, April -2019.

8.

Mohammed Badiuddin Parvez, M Inayathulla “Modelling of Short Duration Isopluvial Map For Raichur District Karnataka”, International Journal for Science and Advance Research in Technology (IJSART), Volume: 05 Issue: 4, April -2019.

9.

Mohammed Badiuddin Parvez, M Inayathulla, "Rainfall Analysis for Modelling of IDF Curves for Bangalore Rural, Karnataka", International Journal of Scientific Research in Multidisciplinary Studies , Vol.5, Issue.8, pp.114-132, 2019 10. Mohammed Badiuddin Parvez, and M Inayathulla. "Generation of Short Duration Isohyetal Maps For Raichur District Karnataka" International Journal Of Advance Research And Innovative Ideas In Education Volume 5 Issue 2 2019 Page 3234-3242 11. Mohammed Badiuddin Parvez, and M Inayathulla. " Derivation Of Intensity Duration Frequency Curves Using Short Duration Rainfall For Yermarus Raingauge Station Raichur District Karnataka" International Journal of Innovative Research in Technology Volume 6 Issue 2 July 2019 Page 1-7 12. Sherman, C. W. (1931). Frequency and intensity of excessive rainfall at Boston, Massachusetts, Transactions of the American Society of Civil Engineers, 95, pp.951– 960. AUTHORS PROFILE

Mohammed Badiuddin Parvez* Is a life member of Indian Water Resources Society, ASCE Born in Karnataka, India Obtained his BE in Civil Engineering in the year 2009-2013 from UVCE, Bangalore and M.E with specialization in Water Resources Engineering during 2013-2015 from UVCE, Bangalore University and Pursuing Ph.D from Bangalore University. And has 3 years of teaching experience. Till date, has presented and published several technical papers in many National and International seminars, Journals and conferences.

Amritha Thankachan, born in Kerala, obtained her B.Tech in Civil Engineering in the year 2008-2012 from Amal Jyothi College of Engineering, Kanjirappally, Kottayam and M.Tech with specialization on Integrated Water Resources Management during 2012-2014 from Karunya University, Coimbatore. Presently pursuing Ph.D from Bangalore University. She is having more than 4 years of teaching experience. Till date, has presented and published several technical papers in many National and International Seminars and Conferences.

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Chalapathi k Is a life member of Indian Water Resources Society. Born in Karnataka, Obtained his BE in Civil Engineering in the year 20082012 from GSKSJTI, Bangalore. and M.E with specialization on Water Resources Engineering during 2012-2014 from UVCE, Bangalore University and Pursuing Ph.D from Bangalore University. And has 3 years of teaching experience. Till date, has presented and published several technical papers in many National and International seminars and conferences.

M Inayathulla Is a life member of Environmental and Water Resources Engineering (EWRI), ASCE, WWI, ASTEE, ASFPM. Born in Karnataka, Obtained his BE in Civil Engineering in the year 1987-1991 from UBDT, Davanagere and M.E with specialization on Water Resources Engineering during 1992-1994 from UVCE, Bangalore University and got Doctorate from Bangalore University in the year 1990-1995. Presently working as Professor at UVCE, Bangalore University, India. And has more than 25 years of teaching experience. Till date, has presented and published several technical papers in many National and International seminars and conferences

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Profile for mbadiuddinparvez34

Isopluvial Maps of Daily Maximum Precipitation for Different Frequency for Upper Cauvery Karnataka  

Probable maximum precipitation (PMP) is widely used by hydrologists for appraisal of probable maximum flood (PMF) used for soil and water co...

Isopluvial Maps of Daily Maximum Precipitation for Different Frequency for Upper Cauvery Karnataka  

Probable maximum precipitation (PMP) is widely used by hydrologists for appraisal of probable maximum flood (PMF) used for soil and water co...

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