_{1}

^{*}

Major peninsular rivers debouching into the Bay of Bengal through 2729 km long east coast of India, carry enormous inland flow and sediment from their alluvial basins. Present climate changes, storm irregularities and tsunamis have changed the hydrology of the coastal rivers. The hydrologic interventions for human need have reduced the sediment flow of the rivers resulting in sinking the deltas. Twelve important river basins in the east coast of India were identified. Linear and nonlinear regression equations were developed by stochastic approach of their annual flow (1986-2011) and yearly sediment influx (1993-2012) for the 12 rivers at their delta head. As results, the annual flow of the rivers from Subarnarekha to Godavari followed rational curves except the Brahmani River and Gaussian models for rivers from the Godavari to south except the river Vaigai. Similarly, the curve fitting models of time series for sediment had shown a change in curve pattern, the river Godavari being the line of demarcation. Gumbel II and Log Pearson type III methods were used to predict the flow and the sediment at various probabilities. Sediment prediction by Gumbel method had shown lower values than Log Pearson Type III methods for planning and design of hydraulic structures. The disparities in geologic formation of the central India and Deccan Plateau can be emphasized based on the statistical interpretations.

The Central Water Commission (CWC) of India has classified rivers in India based on their Catchment area as major (>20,000 sqkm), medium (2000 - 20,000 sqkm) and minor (<2000 sqkm). India has 12 major, 46 medium and 14 minor and desert flowing river basins comprising of areas 252.8 MH, 24.6 MH and 110 MH respectively (CWC Hand Book 2005) [

Sl | State | Name of drainage channels (d/c’s) joining BOB via a lagoon | Name of the rivers and distributaries directly joining Bay of Bengal |
---|---|---|---|

1 | West Bengal | - | Haladi, Rupnarain, Damodar, Rasulpur, Mandarmani |

2 | Odisha | Chilika lake: Daya, Bhargovi, Salia (Four inlets) | Subarnarekha, Jambhira, Budhabalanga, Baitarani (Dhamara), Bramhani, Mahanadi, Devi, Kusha-bhadra, Rushikulya, Bahuda |

3 | Andhra Pradesh | Kolleru: Budameru, Tamileru, Gaderu (connected by 68 drains bet. Krishna and Godavari, Iskapalli, Vallederu (T. I. one) Kuratipalem) | Vamsdhra, Nagavai, Peddagedda, Kandivalasa, Nelhmaria, Gosiani, Narayagida, Sarada, Varaha, Tandava, Eluru, Godavari, Krishna, Gundlakamma, Musi, Palleru, Manneru, Penneru, Upputeru, Swarnamukhi |

4 | Tamilnadu | Pulikat: Arani, Kalangi and swarnmukhi rivers (T.I.: Tupilipalem, Rayadoruvu and Pulicat villages) | Arni, Cooum, Adyar, Palar, Chunnambar, Uppar, Vellar, Kollidam (Coleroon), Kaveri, Varshalee, Manimuttar, Vaigai, Vaippar Chittar, Thamarparani |

5 | Puduchery | Arya Kupam, Mallatar, Ginjer, Ponnaiyar, Godilam |

The Subarnarekha, the northern most east flowing peninsular river, is originating from rifts of the Chota Nagpur Hills (lat 23˚18'E and long 85˚11'N). The small river, Thamarparani in extreme south starts from the Western Ghats (lat 8˚46'E and long 77˚15'N) near Vana-theertham waterfalls near Agastyarkoodam peak of Western Ghats in Ambasamudram district.

The east flowing rivers originate from eastern side of the Western Ghats range and flow through the basalts of the Deccan plateau. They take course along the Deccan traps and crosses through the gorges of the Eastern Ghats belt to join the Bay of Bengal.

The lengths of east flowing ephemeral rivers are long and catchment areas of these basins are large with wide deltas than that of West Coast Rivers. The east coast is emergent whereas the west coast submerging. They carry huge sediment to form large deltas. The longest river is the Godavari (1465 km) of catchment area 312,812 km^{2} (

East coast of India is extending from Kanya Kumari in south to Haladia port in north with a continental shelf of area 22,411 sqkm up to 50 m., Kulkarni et al., (1985) [^{9} km^{3}

River No | Name of River | Length Km/Basin catchment (sqkm) | (G & D site) | Catchment upto delta head (sqkm) | Years of flow Obsn. | Av. annual disch. (Bcum) | Years of sediment Obsn. | Av sed (MMT) |
---|---|---|---|---|---|---|---|---|

1 | Subarnrekha | 446/19,277 | Ghatsila | 14,176 | 1986-2011 | 13.875 | 1993-2012 | 2.64 |

2 | Baitarani | 365/14,218 | Anandpur | 8570 | 1991-2011 | 4.79 | 1993-2012 | 2.24 |

3 | Brahmani | 799/39,116 | Jenapur | 33,955 | 1986-2011 | 17.433 | 1993-2012 | 5.23 |

4 | Mahanadi | 891/141,589 | Tikarpada | 124,450 | 1986-2011 | 46.969 | 1993-2012 | 11.02 |

5 | Vans-dhara | 254/10,830 | Kasinagar | 7820 | 1986-2011 | 2.896 | 1993-2012 | 3.087 |

6 | Godavari | 1465/312,812 | Pollavaram | 307,800 | 1985-2011 | 83.942 | 1993-2012 | 45.57 |

7 | Krishna | 1400/258,948 | Agraharam/Vijaywada | 251,360 | 1985-2011 | 26.048 | 1993-2012 | 5.145 |

8 | Pennar | 597/55,213 | Nellore (Musiri) | 50,800 | 1989-2011 | 1.299 | 1991-2012 | 1.157 |

9 | Ponnaiyar | 400/16,019 | Gumanur | 4620 | 1989-1998 | 0.653 | 1991-2012 | 0.357 |

10 | Cauvery | 765/81,155 | Kodumudi | 66,243 | 1989-2011 | 8.185 | 1993-2012 | 0.326 |

11 | Vaigai | 240/7741 | Ambasamudram | 3721 | 1989-1999 2007-2011 | 0.053 | 2003-2012 | 0.073 |

12 | Thambar parani | 130/5482 | Murapandu | 4380 | 1989-1999 2007-2011 | 0.551 | 1991-2012 | 0.044 |

of water with huge quantities of sediment in average 1.2 × 10^{12} kg to sea which is one tenth of sediment flux of the globe Chandra Mohan et al. (2001) [

The climate of the region is subtropical to tropical. The temperature of the basin area is in average 18˚C to 45˚C with rainfall ranging from 1400 - 1500 mm in northern part and 900 - 1000 mm in the southern region of EC of India. The South West monsoon (JJAS months) and North East monsoon (Nov. and Dec.) influence the quantity of rainfall of the area. The rivers in south of the Godavari basin receives rainfall from both the south west monsoon and north east monsoon. The east flowing rivers to the north of the Godavari basin receives rainfall from the south west monsoon. The Bay of Bengal disturbances through the Odisha coast (48.2%), West Bengal coast (25.5%, Andhra coast (19.3%) and Tamilnadu coast (6.7%) Mohapatra et al., 2010 [

The East coast of India and the adjoining Bay of Bengal was rifted from Antarctica during the early Cretaceous period (65.5 Mya BP). The conjugate oceanic crust of the Bay of Bengal was assumed to be between Ender Bay basin and East Antarctica. Fuloria et al. 2014 [

Tandon et al., 2007 [

The suspended sediment (coarse, medium and silt loads) are 90% of the total annual sediment load which is carried by the flood flow d/s to Bay retaining only 10% behind the water resources structures. Dams (Major, Medium and minor) and BWA’s (barrages, weirs and anicuts) in Odisha constructed along these rivers are 180 and 43 respectively (INDIA-WRIS WIKI-2014) [

The deltas of rivers are sinking, shrinking and under subsidence due to anthropologic interventions like dams and BWA’s. Sediment studies have been done by various authors like Gamage et al. (2009) [

Sanil Ku. V. et al., 2006 [

Nnaji et al. 2014 [

Less research work have been done on the sediment flow of small river basin. This paper is an attempt to study the water and the sediment flow in 12 major rivers flowing into the Bay of Bengal along east coast of India at their delta head.

Spatiotemporal trends of annual discharge of (monsoon + non-monsoon) flow and sediment were collected from Integrated Hydrological data book (non-classified basins), 2005, 2006, 2009, 2012 and 2015 of Central Water Commission, Government of India [

sediment discharge against annual flow and their trend with time were studied. The linear and nonlinear regression equations of the twelve rivers were developed using different curves such as polynomial, sigmoid, peak, power, logarithm, rational and wave form by the statistical tools and EXCEL methods and others. The equations that had highest R^{2} value (>60%) were considered as the fitted curve.

Flood and sediment modeling and prediction were done by deterministic modeling by using a long data series. Different models used are deterministic, stochastic, statistical or soft computing. Attempt has been made in this paper to predict the annual flow and corresponding sediment at various recurrence intervals though the time series length is short. The common statistical probability density functions used were Gumble, Log Pearson Type III (LPT III) and compared the results with their present trend.

The annual time series data were collected to find a trend in the annual flow and the sediment influx and used to predict future values of the time series. Regression equations both linear and nonlinear equations used were polynomials, peak, sigmoid, wave form, power, exponential and rational etc. Correlation is done to test how closely the experimental data (Variables) are interdependent. The correlation coefficient and coefficient of determination were found to verify the reliability of the data.

Correlation Coefficient (R)

It is the data in a time series are linearly related the correlation coefficient (r) is calculated by formulae

r = [ ∑ d x d y ] / [ ∑ d x 2 ∑ d y 2 ]

It is the ratio of standard deviation to covariance and how a time series close to the mean value of data series,

where

∑ d x 2 = ∑ x 2 − ( ∑ x 2 ) n , ∑ d y 2 = ∑ y 2 − ( ∑ y 2 ) n

and

∑ d x d y = ∑ x y − ( ∑ x ∑ y ) n

where “d” represents as the deviation from the mean. R values lies between −1 < R < 1. When R is zero or near zero there is almost zero correlation, +1 is a perfect fit with same slope and the time series is positively and linearly related. For R-values to be negative it indicates perfect negative fit with opposite slope and the series is not related. OR, the other form can be: The

CorrelationCoefficient = R = ( 1 − SSE SST )

where SSE is the sum of squares due to error and

SST = ∑ squaredtotals = ∑ ( y i − y ¯ ) 2

where, y ¯ = mean value of the series y.

Coefficient of determination (R^{2})

In a regression model the ratio of the variance of the fitted values to the observed values are called coefficient of determination. If y i is the observed value, y ¯ = mean value of the series y and y ^ i is the fitted value then the coefficient of

determination = R 2 = ∑ ( y ^ i − y ¯ ) 2 ∑ ( y i − y ¯ ) 2 where, R^{2} has values lies between 0 and 1.

Higher the R^{2 }values better the result of the model and hence the prediction and the curve fitting. It indicates about % of data lies close to best fit line. Negative values of R^{2} indicate the regression equation does not fit the data.

The dimensions like shape, size, and flow parameters differ. The regression equations that fit the curve with highest R^{2} values also differ from river to river. The common used statistical projections for annual flow and sediment were made by using Gumbel II or Log Pearson Type III methods for recurrence intervals 1.11, 2, 5, 10, 20, 25, 50, 100 ∙∙∙ upto 10,000 years for 12 major rivers in Odisha, Andhra Pradesh, Puducherry and Tamil Nadu.

The rivers, their length, the location of the gauge and discharge site, the average annual flow and the average annual sediment of the twelve rivers are given in

The total catchment area for the peninsular east flowing rivers debouching the Bay of Bengal upto their delta head found to be 0.97 million sqkm. The average annual flow, the corresponding average annual sediment flowing at the delta head of the rivers found to be 227.3 Billon Cum and 84.6 MMT respectively (About 10% allowances provided for the small rivers and lagoons which are not considered).

The annual flow for the largest and the longest 12small and large rivers in East coast of India were taken for the years 1986 to 2011. Various stochastic models tried and the curve fitting equations having highest R^{2} values are given in

Using methods of both linear and nonlinear regression techniques, fitted curves were tried. The equation of the curve considered to be the best fit whose coefficient of determination values (R^{2}) found to be the highest. From time series of annual flow for the northern east flowing rivers in India (the Subarnarekha to the Godavari) supports rational function whereas the small southern rivers (Krishna to Thambarparani) follows Gaussian or Lognormal distribution except the river Vaigai, The fittest distribution have high R^{2} values for the southern rivers than the northern rivers

The annual sediment flow for the largest and the longest 12small and large rivers in East coast of India were taken for the years 1993 to 2012. Various stochastic models tried and the curve fitting equations having highest R^{2 }values for the quantum of sediment flow in the rivers are given in

On linear and nonlinear curve fitting, the annual sediment flow exhibit nonlinear correlation of Gaussian type and the coefficient of determination values have shown higher values 50% - 99% except rivers Brahmani and Godavari. Maximum numbers of large dams in the sub- basins of the river Godavari might not be giving R^{2}-value <50% (

Return period or recurrence interval (Tr) is the average interval of any event in the years equaling or exceeding a given magnitude. Probability exceedence (p) is

Number of river | Equation | Parameters for Equations | R^{2} in % | ||||||
---|---|---|---|---|---|---|---|---|---|

y_{0} | a | b | c | d | x_{0} | ||||

Subarnarekha | Rational (7P) | Y = a + b x + c x 2 + d x 3 1 + e x + f x 2 + g x 3 | 6.434 | −1.33 | 0.081 | d = −1.5E−7 e = −0.20 | f = −0.012 g = −2.2E−4 | 54 | |

Baitarani | Log Normal | Y = y 0 + a x e [ − 0.5 ln x x 0 b ] 2 | 2.88 | 42.2 | 0.05 | .17.3 | 38 | ||

Brahmani | Sine (4P) | Y = y 0 + a sin ( 2 π x b + c ) | 1.79 | 4.22 | 2.23 | 0.601 | 30 | ||

Mahanadi | Rational (6P) | Y = a + b x + c x 2 1 + d x + e x 2 + f x 3 | 39.6 | −6.67 | −0.25 | d = −0.177 e = 0.008 | f = −4.88E−5 | 60 | |

Vansadhara | Damped Sine | Y = y 0 + a e − x d sin [ 2 π ( x ) b + c ] | 2.76 | 1.52 | 1463 | 4.85 | 117.1 | 36 | |

Nagavali | Rational (5P) | Y = a + b x + c x 2 1 + d x + e x 2 | 2.47 | −0.34 | 0.01 | d = −0.138 e = 0.0042 | 43 | ||

Godavari | Rational (6P) | Y = a + b x + c x 2 1 + d x + e x 2 + f x 3 | 108 | −17.7 | 0.52 | d = −0.139 e = 8.04E−5 | 32 | ||

Krishna | Gaussian(mod) | Y = y 0 + a e 0.5 ( x − x 0 b ) c | 21.9 | 35.2 | 1.495 | 18.4 | 21.47 | 50 | |

Pennar | Gaussian(4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 1.01 | 17.5 | 22.38 | 8.321 | 55 | ||

Ponniayar | Weilbull (5P) | Y = y 0 + ⋯ + c − 1 c | 0.38 | 5.7 | 1.35 | 4.87 | 7.609 | 69 | |

Cauvery | Gaussian(4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 9.05 | −7.8 | 1.013 | 14.6 | 4.11 | 46 | |

Vaigai | Rational (8P) | Y = a + b x + c x 2 + d x 3 1 + e x + f x 2 + g x 3 + h x 4 | 0.02 | −8E−2 | 9E−4 | d = 2.77E−5 e = −0.446 | f = 0.068 g = −0.003 h = 5.15E−5 | 92 | |

Tambarparani | Log Normal | Y = y 0 + a x e [ − 0.5 ln x x 0 b ] 2 | 4.66 | 4.57 | 0.12 | 4.64 | 61 |

River | Equation | Parameters for Equations | R^{2} (%)^{ } | ||||||
---|---|---|---|---|---|---|---|---|---|

y_{0 } | a | b | c | d | x_{0 } | ||||

Subarnarekha | Mod Gaussian | Y = y 0 + a e 0.5 ( x − x 0 b ) c | 1.97 | 1.09 | 0.52 | 3.93 | 1.561 | 54% | |

Budha balanga | Mod damped Sine | Y = a e − x c sin π ( x − x 0 ) b | 1.99 | 8.96 | 1.37E6 | −0.18 | 92% | ||

Brahmani | Inverse 3^{rd} order | Y = y 0 + a x + b x 2 + c x 3 | 5.24 | 23.5 | 139 | −114.1 | 37% | ||

Mahanadi | Damped Sine | Y = y 0 a e − x d sin [ 2 π ( x ) b + c ] | 8.69 | 977 | 4.16 | 4.77 | 0.66 | 86% |

Rushikulya | Mod Gaussian | Y = y 0 + a e 0.5 ( x − x 0 b ) c | 1.26 | 4.23 | 1.11 | 8.026 | 8.84 | 80% | |
---|---|---|---|---|---|---|---|---|---|

Vansadhara | Lorenzian (4P) | Y = y 0 + a 1 + [ x − x 0 b ] 2 | 2.15 | 13.3 | 0.49 | 15.34 | 58% | ||

Nagavali | Lorenzian (4P) | Y = y 0 + a 1 + [ x − x 0 b ] 2 | 0.54 | 9.96 | 0.86 | 1.347 | 7.222 | 93% | |

Godavari | Rational (10P) | Y = a + b x + c x 2 + d x 3 1 + f x + g x 2 + h x 3 + i x 4 | 73.87 | −43.7 | 7.51 | d = −0.49 e = 0.011 f = −0.50 | 43% | ||

Krishna | Gaussian (4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 11.5 | 177.2 | 0.37 | 4.11 | 73% | ||

Pennar | Gaussian (4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 0.84 | 20.14 | 0.22 | 4.39 | 99% | ||

Ponniayar | Gaussian (3P) | Y = a e 0.5 ( x − x 0 b ) 2 | 7.17 | 0.34 | 16.18 | 99% | |||

Cauvery | Gaussian (4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 0.26 | 0.706 | 0.77 | 4.11 | 58% | ||

Vaigai | Gaussian (5P) | Y = y 0 + a e 0.5 ( x − x 0 b ) c | 0.04 | 0.082 | 2.26 | 209.3 | 4.628 | 57% | |

Tambarparani | Gaussian (4P) | Y = y 0 + a e 0.5 ( x − x 0 b ) 2 | 0.02 | 0.362 | 0.51 | 3.342 | 94% |

(T_{r}) (yr) | Subarnarekha | Baitarani | Bramhani | Mahanadi | Vansadhara | Godavari | Krishna | Pennar | Ponniyar | Cauvery | Vaigai | Tambarparani |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | |

1.05 | 1.47 | 1.62 | 6.8 | 14.55 | 0.56 | 28.77 | 3.73 | −1.46 | −0.55 | 3.58 | 0.04 | 0.1 |

1.11 | 2.43 | 2.15 | 8.48 | 19.98 | 0.95 | 38.19 | 7.47 | −0.99 | −0.37 | 4.35 | 0.04 | 0.18 |

1.25 | 3.69 | 2.85 | 10.7 | 27.12 | 1.46 | 50.58 | 12.38 | −0.38 | −0.13 | 5.37 | 0.05 | 0.28 |

2 | 6.63 | 4.47 | 15.85 | 43.72 | 2.66 | 79.39 | 23.8 | 1.03 | 0.42 | 7.73 | 0.08 | 0.51 |

5 | 10.59 | 6.66 | 22.78 | 66.07 | 4.28 | 118.16 | 39.17 | 2.93 | 1.17 | 10.92 | 0.11 | 0.82 |

10 | 13.21 | 8.11 | 27.37 | 80.86 | 5.34 | 143.83 | 49.34 | 4.2 | 1.66 | 13.02 | 0.13 | 1.03 |

25 | 16.52 | 9.94 | 33.16 | 99.55 | 6.69 | 176.26 | 62.2 | 5.79 | 2.28 | 15.69 | 0.16 | 1.29 |

50 | 18.97 | 11.29 | 37.46 | 113.42 | 7.69 | 200.32 | 71.73 | 6.97 | 2.75 | 17.66 | 0.18 | 1.48 |

100 | 21.41 | 12.64 | 41.73 | 127.19 | 8.69 | 224.2 | 81.2 | 8.14 | 3.2 | 19.62 | 0.20 | 1.67 |

200 | 23.84 | 13.98 | 45.99 | 140.90 | 9.68 | 248.00 | 90.63 | 9.31 | 3.66 | 21.58 | 0.22 | 1.87 |

500 | 27.04 | 15.75 | 51.6 | 158.99 | 10.99 | 279.39 | 103.07 | 10.85 | 4.26 | 24.15 | 0.24 | 2.12 |

1000 | 29.47 | 17.09 | 55.84 | 172.67 | 11.97 | 303.12 | 112.48 | 12.02 | 4.72 | 26.1 | 0.26 | 2.31 |

2000 | 31.89 | 18.43 | 60.08 | 186.34 | 12.96 | 326.84 | 121.88 | 13.18 | 5.18 | 28.05 | 0.28 | 2.5 |

5000 | 35.09 | 20.19 | 65.68 | 204.41 | 14.26 | 358.18 | 134.31 | 14.72 | 5.78 | 30.62 | 0.31 | 2.75 |

10,000 | 37.5 | 21.53 | 69.92 | 218.07 | 15.25 | 381.89 | 143.7 | 15.89 | 6.23 | 32.57 | 0.33 | 2.94 |

the chance that the annual event of any year will equal or exceed some given value. The probability (P) of an event with recurrence interval T is P = 1/T.

Gumbel method is one of the oldest methods for prediction of hydrologic data Al-Mashidani et al. 1978 [

K = − 6 / π ( λ − ln ( ln T − ln ( T − 1 ) ) )

where λ is Euler’s constant = 0.5772. To test the goodness of fit χ^{2} test is conducted with hypothesis that the data fits Gumbel distribution and vice versa. (Never Mujere 2011) [

From the future estimation of quantity of flow by Gumble II method in 12 major rivers in east coast of India at various recurrence intervals are observed. It is found that total annual discharge of the major rivers shall increase proportionately at higher return periods. There shall be years ahead when the monsoon shall be erratic and the rainfall/runoff shall have increasing tendency as flow prediction indicate irregularity

Prediction of the annual sediment against various recurrence interval of the east flowing rivers in the east coast, it is ascertained that the sediment concentration/Bcum of inland inflow shall increase gradually and the delta building process shall be emerging

Ret. period (yr) | Subarnarekha | Baitarani | Bramhani | Mahanadi | Vansadhara | Godavari | Krishna | Pennar | Ponniyar | Cauvery | Vaigai | Tparani |
---|---|---|---|---|---|---|---|---|---|---|---|---|

MMT | MMT | MMT | MMT | MMT | MMT | MMT | MMT | MMT | MMT | MMT | MMT | |

2 | 2.20 | 1.77 | 4.66 | 9.33 | 2.10 | 41.98 | 4.44 | 0.98 | 0.05 | 0.27 | 0.05 | 0.02 |

5 | 5.41 | 3.63 | 8.74 | 21.51 | 4.87 | 63.77 | 11.11 | 2.36 | 0.17 | 0.50 | 0.10 | 0.05 |

10 | 7.54 | 4.94 | 11.43 | 29.58 | 7.26 | 77.47 | 15.52 | 3.27 | 0.24 | 0.66 | 0.15 | 0.09 |

25 | 10.23 | 6.53 | 14.84 | 39.77 | 10.80 | 93.74 | 21.10 | 4.43 | 0.34 | 0.87 | 0.24 | 0.21 |

50 | 12.23 | 7.63 | 17.37 | 47.33 | 13.74 | 105.07 | 25.23 | 5.28 | 0.41 | 1.02 | 0.32 | 0.35 |

100 | 14.21 | 8.66 | 19.88 | 54.84 | 16.87 | 115.72 | 29.34 | 6.13 | 0.47 | 1.17 | 0.42 | 0.59 |

200 | 16.18 | 9.59 | 22.38 | 62.31 | 20.21 | 125.84 | 33.43 | 6.98 | 0.54 | 1.31 | 0.54 | 0.96 |

500 | 18.79 | 10.70 | 25.68 | 72.18 | 24.88 | 138.44 | 38.83 | 8.10 | 0.64 | 1.48 | 0.73 | 1.78 |

1000 | 20.76 | 11.46 | 28.17 | 79.63 | 28.62 | 147.56 | 42.91 | 8.94 | 0.70 | 1.62 | 0.91 | 2.79 |

2000 | 22.72 | 12.15 | 30.66 | 87.09 | 32.48 | 156.19 | 46.99 | 9.79 | 0.77 | 1.74 | 1.12 | 4.35 |

5000 | 25.32 | 12.82 | 33.96 | 96.94 | 36.88 | 165.29 | 52.38 | 10.9 | 0.87 | 1.87 | 1.40 | 7.14 |

10,000 | 27.29 | 13.51 | 36.45 | 104.4 | 41.92 | 174.97 | 56.46 | 11.75 | 0.93 | 2.01 | 1.76 | 11.7 |

Return period (yr) | Subarnarekha | Baitarani | Bramhani | Mahanadi | Vansadhara | Godavari | Krishna | Pennar | Ponniyar | Cauvery | Vaigai | Thamarparani |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | Bcum | |

1.05 | 2.56 | 1.78 | 0.67 | 23.79 | 0.87 | 39.09 | 6.71 | 0.02 | 0.04 | 2.98 | 0 | 0.23 |

1.11 | 3.14 | 2.24 | 3.05 | 26.59 | 1.14 | 45.45 | 9.2 | 0.04 | 0.06 | 3.98 | 0 | 0.27 |

1.25 | 4.02 | 2.91 | 10.76 | 30.72 | 1.55 | 54.6 | 13.07 | 0.09 | 0.1 | 5.39 | 0.01 | 0.32 |

2 | 6.37 | 4.52 | 24.94 | 41.9 | 2.63 | 77.8 | 23.53 | 0.45 | 0.27 | 8.37 | 0.04 | 0.48 |

5 | 9.93 | 6.57 | 22.33 | 59.82 | 4.13 | 111.25 | 38.04 | 1.97 | 0.73 | 11.09 | 0.1 | 0.74 |

10 | 12.46 | 7.79 | 20 | 73.45 | 5.07 | 134.32 | 46.99 | 4.01 | 1.25 | 12.2 | 0.16 | 0.93 |

25 | 15.79 | 9.16 | 19.23 | 92.8 | 6.17 | 164.4 | 57.24 | 8.22 | 2.24 | 13.07 | 0.24 | 1.2 |

50 | 18.35 | 10.08 | 18.76 | 108.84 | 6.93 | 187.42 | 64.1 | 12.78 | 3.28 | 13.49 | 0.31 | 1.43 |

100 | 20.98 | 10.91 | 18.89 | 126.35 | 7.64 | 210.94 | 70.32 | 18.73 | 4.63 | 13.76 | 0.37 | 1.67 |

200 | 23.69 | 11.68 | 18.88 | 145.52 | 8.3 | 235.2 | 75.99 | 26.29 | 6.37 | 13.95 | 0.44 | 1.93 |

500 | 27.39 | 12.6 | 18.87 | 173.79 | 9.11 | 268.41 | 82.71 | 39.02 | 9.41 | 14.12 | 0.53 | 2.32 |

1000 | 30.3 | 13.25 | 18.87 | 197.61 | 9.69 | 294.59 | 87.34 | 51.06 | 12.4 | 14.2 | 0.6 | 2.64 |

2000 | 33.3 | 13.84 | 18.87 | 223.79 | 10.23 | 321.79 | 91.58 | 65.26 | 16.2 | 14.26 | 0.66 | 2.99 |

5000 | 36.79 | 14.45 | 18.87 | 256.95 | 10.79 | 353.7 | 95.77 | 83.87 | 21.5 | 14.29 | 0.73 | 3.42 |

10,000 | 40.64 | 15.08 | 18.87 | 295.09 | 11.37 | 388.77 | 100.1 | 107.9 | 28.5 | 14.33 | 0.8 | 3.92 |

Skewness | −0.12 | −0.59 | −4.62 | 0.49 | −0.57 | 0.04 | −0.7 | −0.34 | 0.11 | −1.46 | −0.7 | 0.25 |

LPT III method is one of the commonly used method hydrologic frequency analysis. The method is extremely flexible Nnaji G. A. et al., 2014 [

log x = log x ¯ + K σ lg x

where x is taken as annual flow or yearly sediment flow. log x ¯ arithmetic mean of logarithm values of the variables x and K is the frequency factor found from the Log Pearson frequency factor table, and is the standard deviation of the

logarithm values given by σ log x = [ ∑ ( log x − log x ¯ ) ] n − 1 and the results are shown in

On analysis of annual flow series of major rivers in the east coast falling Bay of Bengal by LPT III it is observed that at 50 years return period Godavari shall increase in flow and shall have 108.84 Bcum whereas present annual average discharge was 83.942 Bcum. The river Brahmani shall show a constant average annual flow for the coming 10,000 years

R. period (yr) | Srekha | Baitarani | Bramhani | Mahanadi | Vansadhara | Godavari | Krishna | Pennar | Ponniyar | Cauvery | Vaigai | Tparani |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2 | 1.44 | 1.77 | 4.64 | 7.81 | 2.10 | 41.98 | 2.58 | 0.72 | 0.02 | 0.27 | 0.05 | 0.02 |

5 | 4.36 | 3.63 | 8.13 | 14.83 | 4.87 | 63.77 | 8.19 | 1.60 | 0.08 | 0.50 | 0.10 | 0.05 |

10 | 7.20 | 4.94 | 10.10 | 21.51 | 7.26 | 77.47 | 14.55 | 2.54 | 0.17 | 0.66 | 0.15 | 0.09 |

25 | 11.60 | 6.53 | 12.11 | 32.90 | 10.80 | 93.74 | 26.33 | 4.28 | 0.40 | 0.87 | 0.24 | 0.21 |

50 | 15.33 | 7.63 | 13.30 | 43.99 | 13.74 | 105.1 | 38.17 | 6.10 | 0.73 | 1.02 | 0.32 | 0.35 |

100 | 19.33 | 8.66 | 14.26 | 57.77 | 16.87 | 115.72 | 52.87 | 8.48 | 1.27 | 1.17 | 0.42 | 0.59 |

200 | 23.53 | 9.59 | 15.04 | 74.81 | 20.21 | 125.84 | 70.88 | 11.58 | 2.16 | 1.31 | 0.54 | 0.96 |

500 | 29.31 | 10.70 | 15.86 | 103.59 | 24.88 | 138.44 | 100.27 | 17.12 | 4.19 | 1.48 | 0.73 | 1.78 |

1000 | 33.85 | 11.46 | 16.34 | 131.14 | 28.62 | 147.56 | 127.21 | 22.69 | 6.79 | 1.62 | 0.91 | 2.79 |

2000 | 38.37 | 12.15 | 16.73 | 164.83 | 32.48 | 156.19 | 158.63 | 29.80 | 10.8 | 1.74 | 1.12 | 4.35 |

5000 | 43.34 | 12.82 | 17.05 | 212.60 | 36.88 | 165.29 | 199.64 | 40.30 | 18.2 | 1.87 | 1.40 | 7.14 |

10000 | 48.96 | 13.51 | 17.39 | 274.30 | 41.92 | 175.09 | 251.29 | 54.54 | 30.6 | 2.01 | 1.76 | 11.72 |

Skew | −0.61 | −0.80 | −1.10 | 0.52 | −0.42 | −0.49 | −0.22 | 0.44 | 0.51 | −0.6 | 0.14 | −0.69 |

On comparison of predicted values at various recurrence intervals of total annual flow through the major rivers along east coast falling in the Bay of Bengal it is observed that Gumbel II method had lower values than LPT III method towards tail end. The forecasted values are almost same upto 4000 years of forecast

On comparison of the projected values of total annual sediment influx from the inland rivers along east coast, it is found Gumbel II method predict lower values of sediment at lower probabilities whereas LPT III method very high values. For design purposes of hydraulic structures Gumbel method may be accepted as projected sediment

On study of major east flowing rivers along east coast of India and falling in Bay of Bengal, the following conclusions may be drawn:

1) All the east flowing rivers are emerging below the rift of Narmada valley and falling in Bay of Bengal forming large coastal plains, number of distributaries and encouraging huge sediment flow to the Bay of Bengal. The average annual flow and sediment at the delta head of the rivers are found to be 227.3 Billon Cum and 84.6 MMT respectively.

2) Erratic monsoon and hydrologic interventions have reduced sediment concentration of the rivers reaching delta head.

3) Regression analysis results of annual flow and sediment series had made a distinct division of peninsula Indian rivers above and below the Godavari River. The rivers flowing south of the river Godavari followed Gaussian model and the rivers above towards North East followed rational equations. The flow and the sediment influx are monsoon dependent.

4) Regression analysis of sediment influx time series follows Gaussian pattern towards south of Godavari river, but to the north, the sediment pattern does not obey any curve pattern, and 60% follow peak type equations except sediment flow of the Brahmani river.

5) The flow and sediment were projected by Gumbel II and Log Pearson III methods and observed both the methods gave almost equal predicted values for flow but for sediment forecast Gumbel II method gave lower values at various return periods.

From the above results, it can be inferred that for any structural design purposes, the Gumbel method projected values can be used for hydrologic study.

Mishra, S.P. (2017) Stochastic Modeling of Flow and Sediment of the Rivers at Delta Head, East Coast of India. American Journal of Operations Research, 7, 331-347. https://doi.org/10.4236/ajor.2017.76025