journal of applied hydrology

ISSN 0971 - 670X Vol. XXVII, No. 1 to 4, Jan. - Dec., 2014

JOURNAL OF APPLIED HYDROLOGY

Published by

ASSOCIATION OF HYDROLOGISTS OF INDIA AND

ANDHRA UNIVERSITY VISAKHAPATNAM - 530 003. INDIA

JOURNAL OF APPLIED HYDROLOGY Patron Vice-Chancellor, Andhra University Editor V.V. Jagannadha Sarma P. Rajendra Prasad

Associate Editors C. Subba Rao

N.V.B.S.S. Prasad

EDITORIAL BOARD Nani G. Bhowmik, Illinois State Water Survey, U.S.A. S.M. Rao, Former Head Istope Division, BARC, Bombay, India. B.S.R. Reddy, Retd. Professor, Andhra University, Visakhapatnam, India. V.R.R.M. Babu, Retd. Professor, Andhra University, Visakhapatnam, India. L.R. Khan, Bangladesh Agricultural University, Mymensingh, Bangladesh. A. Narayana Swamy, Andhra University, Visakhapatnam, India. S.K. Gupta, Physical Research Laboratory, Ahmedabad. Director, Andhra Pradesh Groundwater Department, Hyderabad. H.J. Kumpel, University of Bonn, Germany. Dai Shen Sheng, Xiamen, China. EDITORIAL ADVISORY BOARD Pierre Hubert, UMR Sisyphe, Ecole des Mines de Paris, France. C. Voute, Sofia, Bulgaria. George Matthess, Kiel University, Kiel, F.R. Germany. J. Zschau, Geoforeshungs, Zentrum, Potsdam, Germany. Publication Subscriptions

: : :

Quarterly For institutions (Annual)

Rs. 2000 (within India) US$150 (outside India inclusive of surface mail) add $ 15 for air mail : For Individuals Rs. 500 (within India) (Single copy) $ 30 (outside India inclusive of surface mail) add $ 5 for air mail For members of the Association of Hydrologists of India : Free

All Subscriptions Addressed to

Advertisements and Enquiries Addressed to

Association of Hydrologists of India C/o Dept. of Geophysics Andhra University Visakhapatnam - 530 003. India. Phone/Fax: 0891-2575500 e-mail: [email protected]

The Editor Journal of Applied Hydrology C/o Dept. of Geophysics Andhra University Visakhapatnam - 530 003, India. vi

JOURNAL OF APPLIED HYDROLOGY

Vol. XXVII, No. 1 to 4, Jan. - Dec., 2014

Published by

ASSOCIATION OF HYDROLOGISTS OF INDIA AND ANDHRA UNIVERSITY VISAKHAPATNAM - 530 003, INDIA.

JOURNAL OF APPLIED HYDROLOGY Vol. XXVII, No. 1 to 4, Jan. - Dec., 2014

CONTENTS Irrigation planning for Ponnaniyar reservoir using water balance model C.R.Suribabu and S.Suryanarayanan

1

Daily rainfall forecast of Patna gauge station by using Wavelet Neural Network R. Venkata Ramana, B. Krishna, N. G. Pandey and B. Chakravorty

15

Analysis of daily maximum rainfall for Hydrological Design of small scale water harvestig structure B. Panigrahi and Kajal Panigrahi

28

Spatial distribution of ground water quality parameters using Geographic Information System (GIS) in and around Rajahmundry, A.P. Ch.Venkateswara Rao, M.Ravi Sankar and Ch.Vasudeva Rao

42

A GIS based morphometric analysis and associated landuse study of Dakshina Pinakini river basin, Chikkaballapura and Bangalore Districts, Karnataka N.K. Narayanaswamy, S. Shivanna, S.B. Bramhananada and H.C. Vajrappa

52

Groundwater quality assessment studies in Sheri Nala Basin, Sangli District, Maharashtra, India A.S.Yadav and P.T. Sawant

63

Numerical simulation of a tropical cyclone with an Axisymmetric model using a real time thermodynamic sounding A.Sravani, G. Papa Rao, N. Nanaji Rao, Roshmitha Panda and S.S.V.S. Ramakrishna

76

Flood hazard in Murshidabad District : A river basin approach Swati Mollah

97

N.A.Mayaja and C.V. Srinivasa

111

Flood characteristics of Pampa river, Kerala : A regression based rainfall – runoff modeling and analysis

Stable isotope Characterization of Various types of waters in Y-drain system of Errakalva Basin in Andhra Pradesh S. V. Vijaya Kumar, Y. R. Satyaji Rao, J. V. Tyagi, T. Vijaya, U. V. N. Rao and P. R. Rao

119

JOURNAL OF APPLIED HYDROLOGY Vol. XXVII No. 1 to 4, Jan to Dec, 2014, pp. 1 - 14

IRRIGATION PLANNING FOR PONNANIYAR RESERVOIR USING WATER BALANCE MODEL C.R.Suribabu and S.Suryanarayanan Centre for Advanced Research in Environment, School of Civil Engineering, SASTRA University Thanjavur 613 401 E-mail: [email protected] ABSTRACT The growing demand of food production needs efficient operation and management of irrigation system. Most of the approaches followed aim at meeting the crop demand with available water to get maximum production. Scheduling of water delivery is one among them and it is a core activity that has more influence on the performance of the system compared to other irrigation activities. Irrigation scheduling deals with two questions, when and how much to irrigate. A reservoir operation policy is a sequence of release decisions in operational periods, specified as a function of the available storage at the beginning of the period and the inflow to the reservoir during the period. Developing appropriate operating policy will be helpful to the reservoir operator to provide supply during normal and abnormal periods. In the present work, Ponnaniar reservoir located at Manapparai in Tiruchirappalli district is considered to study the performance of the system. A water balance model is developed and supply demand ratio is evaluated for irrigated groundnut crop. Introduction The ever increasing demand of food production needs sustainable and efficient planning, operation and management of irrigation system. Scheduling of water delivery is one among them and it is a core activity that has more influence on the performance of the system compared to other irrigation activities (Chambers, 1988). Irrigation scheduling deals with two questions, when and how much to irrigate. Before starting a crop, the availability of water in the reservoir, chances of rainfall during the crop growth periods, groundwater potential etc, are to be checked. In developing countries like India, more scientific approach is needed for utilizing the resources effectively. In water deficit prone irrigation systems, attempts can be made to utilize rainfall to the maximum extent for crop growth. A major research focus of the past five decades in water resources engineering has been on developing and adapting system analysis techniques for application in reservoir management and operations. A primary emphasis of systems analysis related to reservoir problems is the application of mathematical simulation and optimization models to provide an improved basis for decisionmaking. Yeh (1985) provides a state of the art review of theories and applications of system analysis techniques to the reservoir problems. Algorithms and methods surveyed in this research include linear programming, dynamic programming, non-linear programming, and simulation. Many of these methods are included in textbooks like Loucks et al (1981). Simonovic (1992) provides short reviews of the mathematical models used in reservoir management and operations in support of previous state of the art and provide two ideas for closing gap between theory and practice. A simple simulation – optimization model for reservoir sizing and knowledge-based technology with regard to single-multiple reservoir analysis had illustrated with examples. Recently, Labadie (2004) presented state of art review on optimal operation of multi reservoir systems. Labadie (2004) viewed reservoir system optimization problem in two general perspectives as traditional methods and non1

C.R.Suribabu et al

traditional methods of optimization. Algorithms and methods surveyed in this research include implicit stochastic optimization (ISO), explicit stochastic optimization models (ESO), multi-objective optimization models and heuristic optimization model. The review highlights the need of application of heuristic methods to overcome computational challenges of explicit stochastic optimization, use of fuzzy rule based systems and neural networks to alleviate problem encountering to derive operating policies through implicit stochastic optimization models and ability of genetic algorithms to get into with simulation models. Dynamic programming(DP) has been the popular techniques in the past for optimal operation (Stedinger et al, 1984; Gygier and Stedinger, 1985; Tejada-Guibert et al, 1995). Advantages of DP are its ability to address the non-linearity’s in the problem formulation, and to decompose complex problems. Use of genetic algorithm in determining the optimal reservoir operating policy has not received significant attention from water resources engineers, though Oliveira and Loucks (1997) and Wardlaw and sharif (1999) explored the potential of GA in reservoir operation. Huang (2001) has proposed Ant colony system based optimization approach for the enhancement of hydroelectric generation scheduling. This paper present a simple water balance model for irrigation planning for Ponnaniar Reservoir. Ponnaniar reservoir Ponnaniar reservoir is situated in Mogavanur village of Manapparai Taluk across Ponnaniar River. The site of the reservoir is located in between Semmalai hills and Perumal Malai hills. The jungle stream originated from Kadavoor hills and traverses through east in Manapparai Taluk for a distance of 32 Km and joins the River Ariyar. The river finally in-falls into the River Cauvery. Ponnaniar dam has been constructed across Ponnaniar river, a tributary to Cauvery at longitudinal 78o16’20"E and latitude 10o34’55"N in Manapparai Taluk in Trichy district during the period 1970-1974. The Cantonment boundary of the Ponnaniar sub-basin has an elongated shape for a maximum length of 85 km in the south west by north east direction and an average width of 34 km in the north west to south east direction. The main Ponnaniar River has a total length of 85 Kms and the total catchment area of Ponnaniar upto the reservoir site is 87.02 Sq.Km. The total dependable yield had been worked out as 10.26 M.Cum (362 Mcft) at dam site taking in to consideration Manapparai town as the nearest Rainfall station where yield has been worked out to be 0.305 M.um (10.773 M.Cft) as per Dry Damp Wet Method. The reservoir has a water spread area of 126.72 Hectares (313 Acres) and a capacity of 3.40 M.Cum (120 M.Cft) at F.R.L The dam is 247 m long including a Masonry dam of 52 m and an earth dam of 195 m. The masonry portion consists of a spillway 27.00 m long (88’8") with a pier of 6.10m (20’0") width accommodating the river sluice. The canal sluice is provided in the earth dam portion with all sill at +234.70 m (+770’0"). 1830 acres of new ayacuts and 231 acres of existing ayacuts are benefited in Mugavanur Village. This is the first scheme in Tamilnadu wherein polythene lining is used in canal distributary system to prevent losses due to seepage in black cotton soil completely. The scheme was taken in 1970 and completed in 1974. Salient Features of Ponnaniar dam Location Longitude Latitude

_ _

78o 16’ 20" 10o 34’ 55"

General River/Basin

_

Ponnaniar/Cauvery Basin

2

Irrigation Planning for Ponnaniyar Reservoir Using Water balance Model

Nearest City District

_ _

Trichy Trichy

Reservoir Catchment Area Design Flood FRL/MWL Capacity of FRL

_ _ _ _

87.02 Sq.Km 199 Cumecs (7028 Cusecs) + 250.24 m (+821.00 ft.) 3.40 M.cum (120 Mcft)

Dam Type Top of the Dam Maximum height Length of the Earth Dam Length of the Masonry Dam

_ _ _ _ _

TE/PG +253.29 m (+831.00 ft) 24.80 m 195 m 52 m

Spillway Crest Level Number of Gate & Type Size of Vent Discharge

_ _ _ _

+ 247.19 m (+811.00 cft) 2 Nos – Vertical lift gate 9.45 x 3.05 m (31’x10’) 199 Cumecs (7028 Cusecs)

River Sluice Sill Level Vent Discharge

_ _ _

234.70 m 1 No 1.52 x 1.83 m 29.45 Cumecs

Canal Sluice Sill Level Vent Discharge Ayacut

_ _ _ _

+ 234.70 m 1 No 1.52 x 1.83 m 1.50 Cumecs 740 ha

Water balance simulation model The basic dynamics of Ponnaniar reservoir system can be described by the following flow or equation at every time period (t):

S (t ) = S (t - 1) + In(t ) - [ IR(t ) + Spill (t )] - L(t )

(1)

where S(t) is the storage volume of reservoir at the end of period t, IR(t) is the gross irrigation water release volume from the reservoir during the period t, In(t) is the total net inflow volume to reservoir during the period t, Spill (t) is the spilled release volume from reservoir during the period t, and L(t) is the total loss due to evaporation from the reservoir during period t.

3

C.R.Suribabu et al

Simple bounds on variables

S min (t ) £ S (t ) ³ S max (t )

(2)

IR(t ) ³ Demand (t )

(3)

where Smin(t) is the dead storage volume at the end of period (t), S(t) is the storage volume at the end of period t and S max (t) is the maximum storage volume at the end of period t. The release into the canals should be greater than or equal to the irrigation demand. The computational process of water balance equation is carried out as follows using Microsoft Excel. Step 1: Balance Storage = End Storage + Inflow Step 2: Storage available = Balance storage - evaporation loss Step 3: Release = Storage available - demand (if storage available >= Demand, else release = storage available) Step 4: Total storage = Storage available - Release Step 5: Spill = Total storage - reservoir capacity, (if total storage >= reservoir capacity, else spill = zero) Step 6: Deficit = Demand - Release Step 7: End storage = Total storage - spill Model Input Table 1 provides the monthly depth of evaporation. This data is obtained from PWD report for Ponnaniar reservoir. Table 1 Monthly Evaporation at Dam site (m)

July

Depth of Evaporation in m 0.1524

0.1016

August

0.1524

March

0.1778

September

0.1524

April

0.2286

October

0.127

May

0.254

November

0.1016

June

0.1778

December

0.1016

January

Depth of Evaporation in m 0.1016

February

Month

Month

4


Table 2 present the data pertaining to the reservoir elevation, water spread area and capacity. Using this data, a graph is plotted between water spread area and capacity and a linear relation is established between them. Fig. 1 shows the monthly evaporation in metre. Fig. 2 shows the water spread area vs. capacity curve. Table 3 and 4 provide the details on main channel and distributaries in the system with the length of channel, command area in acres and hectares. It can seen from the Table 5 that the normal data of opening of reservoir for irrigation fall in the month of September. In some years the data of opening is reported January. Table 6 presents the net irrigation requirement for irrigated dry groundnut staring from 1st sep. Similarly the net irrigation requirement for paddy both Samba and Thaladi are presented from Table 7 to 11. The depth of water requirement for each month is obtained from PWD (2002) report for water management studies in Agniar river basin. Table 8 gives the annual rainfall at the dam site and inflow to the reservoir. The mean annual rainfall at the site is found out from the data as 888.85 mm. Fig. 3 shows the annual rainfall at dam site. Fig 4 presents the annual inflow for year 1975 – 2007. Table 2: Elevation – Water Spread Area – Capacity Details Sl.No

Elevation (m)

Water Spread Area 2

Capacity

234.7

(Million m ) 0.0028

(M.Cum)

1 2

236

0.1631

0.01631

3

237

0.04093

0.04093

0.00384

4

238

0.06616

0.06616

5

239

0.08751

0.10916

6

240

0.10916

0.10916

7

241

0.1345

0.1345

8

242

0.1652

0.1652

9

243

0.1965

0.1965

10

244

0.227

0.227

11

245

0.26735

0.26735

12

246

0.32595

0.32595

13

247

0.3927

0.3927

14

248

0.50995

0.50995

15

249

0.66315

0.66315

16

250

0.66315

0.66315

17

250

0.7061

0.18242

TOTAL

3.38863 Mm Or

3

119.80 Mcft.

5

C.R.Suribabu et al

Fig. 1: Monthly Evaporation in metre

Fig. 2: Water spread area versus capacity relation

6


Table 3: Details of channel for new command area Sl. No

Length of the channel in (m)

Type

Area in Acres

Area in Hectares 313.42

1

Distributory No. I

3500.00

774.47

2

Distributory No. II

720.00

87.08

35.24

3

Branch Distributory

1440.00

187.36

75.82

4

Sub Branch Distributory

330.00

102.88

41.63

5

Field Bothy No. 1

1335.00

106.41

43.06

6

Field Bothy No. 2

360.00

67.82

27.45

7

Field Bothy No. 3

740.00

47.13

19.07

8

Field Bothy No.4

720.00

60.72

24.57

9

Field Bothy No. 5

1260.00

160.77

65.06

10

Field Bothy No. 6

1260.00

135.19

54.71

11

Field Bothy No. 7

420.00

90.47

36.61

340.00

9.70

3.93

3500.00

-

12

Field Bothy No. 8

13

Main Canal Total

1830.00

740.58

Table 4 : Details of Channel for Old command area Sl. No

Type

Length of the channel in (m)

Area in Acres

Area in Hectares

1

Mudal Madai channel

NA

127.00

51.40

2

Karugulam

NA

128.00

51.80

3

Kalsanthappankulam

NA

16.00

6.48

Results and Discussion Ponnaniar reservoir is a multipurpose reservoir. The main purpose of the reservoir is to supply water for irrigation. The other purpose is to control the flood. The main crops cultivated in the command area are groundnut, paddy, jasmine flower and pulses. For the present study, 33 years of rainfall and inflow data are collected from PWD, Ponnaniar. The monthly evaporation and other hydraulic details are also collected from them. The effective rainfall is calculated using rational method. If the monthly rainfall is less than 50 mm, then 60 % of rainfall is considered as effective. Otherwise 25 mm is considered as effective rainfall. Using daily data of inflow, the monthly inflow for each year is found out. Similarly, the monthly rainfall all 33 years are found out. The average rainfall is found out by taking the average of 33 years of rainfall. And it is found as 888.85 mm. The rain gauge station is located at the dam site. As there is no rain gauge station at command area, this rainfall data is used for the calculation of effective rainfall. It can be seen from the Table 8 that year 1978 received a maximum rainfall of 1180 mm and year 2001 received a minimum rainfall of 554 mm. Out 33 years of annual rainfall, 11 years received more than 1000 mm rainfall and remaining years received less than 1000 mm. Only in two years, the rainfall is less than 600 mm. The inflow in the years 1998 and 1999 are recorded with highest value. During that period dam experienced more spill. These spilled water could not utilized for irrigation purposes. The net irrigation requirements for ground net and paddy are calculated and presented in the Table 6 and 7. The depth of water required for each month is obtained from PWD report (2002) and same is used for finding NIR. To 7

C.R.Suribabu et al

account conveyance and other losses, the actual water required is taken as 1.3 times the estimated value. The water balance model is developed and analysis has been carried out for all 33 years of data. The water balance model is carried out using MS-Excel sheet. Two cases are formulated in which first case aimed to supply water for groundnut crop for both old and new zones. In the second case zone 1 allotted for paddy and zone 2 is allotted for groundnut. The normal date of opening of this reservoir is in the first week of September. Keeping this, the water balancing is carried out with ground net water requirement as outflow. Table 9 shows the net irrigation demand for both the cases. The supply and demand ratio for groundnut (alone) is worked out and presented in Table 10. It can be seen from the Table 10 that the supply demand ratio is one for 20 years out of 33 years of analysis. If supply demand ratio is greater than 80 %, generally it is considered that the deficit less supply. Three more years fall between 80 % and 99.99 %. Hence 23 years provided satisfactory supply to groundnut crop if it is started first week of September. Two years experienced too severe shortage of supply. The performance for years 1985 and 1988 are less than 20%. It can be seen from the Table 11 that the supply demand ratio is one for 16 years out of 33 years of analysis for case II. The supply demand ratio for three years namely 1984, 1997 and 2002 are between 80 % and 99.99%. Hence 19 years provided satisfactory supply to the paddy (Zone I) and groundnut (Zone II). Table 5 :Details Showing Year-wise water opening and closing Date of opening Sl. No

Date of closing

Date

M

M.Cum

Date

1

01.09.1975

12.440

52.270

31.01.1976

4.240

5.960

2

15.09.1976

10.310

32.090

15.02.1977

5.400

12.070

3

15.09.1977

10.530

49.640

15.02.1978

10.100

45.035

M

M.Cum

4

01.09.1978

11.740

64.750

28.02.1979

14.320

114.643

5

01.10.1979

11.170

45.198

27.02.1980

12.300

57.946

6

25.09.1980

12.250

57.370

31.08.1981

4.470

5.018

7

08.10.1981

12.230

57.139

29.01.1982

5.000

6.656

8

04.11.1982

12.510

60.858

25.01.1983

5.150

7.119 9.087

9

01.09.1983

13.700

79.020

23.11.1984

5.690

10

20.12.1986

11.440

48.039

04.03.1987

4.800

6.038

11

04.01.1988

14.410

92.400

09.04.1988

8.540

23.689 10.861

12

02.01.1989

10.460

38.492

07.03.1990

6.150

13

26.01.1991

6.570

12.721

15.02.1991

5.700

9.125

14

01.09.1991

13.390

73.436

30.01.1992

6.800

13.814

15

06.02.1993

10.795

41.655

09.04.1993

6.830

13.957

16

02.12.1993

15.540

119.700

14.04.1994

9.820

33.133

17

02.12.1994

15.440

114.149

30.03.1995

6.070

10.533

18

15.09.1996

14.160

87.303

31.01.1997

8.540

23.690

19

14.12.1998

15.250

112.074

27.03.1999

11.700

51.034

20

31.03.1999

11.520

48.960

17.04.1999

10.840

38.681

21

27.10.1999

15.250

11.074

13.02.2000

14.100

86.212

22

17.02.2000

14.100

86.212

26.03.2000

12.970

67.239

23

16.11.2001

13.580

76.858

17.02.2002

7.780

18.991

8


Table 6 : Net Irrigation requirement for Irrigated dry crop groundnut

NIR Demand for Groundnut Mm3 Zone

Area

Number

ID

Hectare

Sep

Sq. m

Oct

90 mm

Nov

Dec

150 mm

145 mm

109.68

1096800

0.0987

0.1645

0.1590

0.0768

Area 1

313.42

3134200

0.2821

0.4701

0.4545

0.2194

Area 2

35.24

352400

0.0317

0.0529

0.0511

0.0247

Area 3

75.82

758200

0.0682

0.1137

0.1099

0.0531

Area 4

41.63

416300

0.0375

0.0624

0.0604

0.0291

Area 5

43.06

430600

0.0388

0.0646

0.0624

0.0301

Area 6

27.45

274500

0.0247

0.0412

0.0398

0.0192

Area 7

19.07

190700

0.0172

0.0286

0.0277

0.0133

Area 8

24.57

245700

0.0221

0.0369

0.0356

0.0172

Area 9

65.06

650600

0.0586

0.0976

0.0943

0.0455

Area 10

54.71

547100

0.0492

0.0821

0.0793

0.0383

Area 11

36.61

366100

0.0329

0.0549

0.0531

0.0256

Area 12

3.93

39300

0.0035

0.0059

0.0057

0.0028

Zone 1 Zone 2

Command Area

70 mm

Table 7: Net Irrigation requirement for Paddy (Samba – (Sep-Jan)) NIR Demand for Samba (Sep-Jan) in Mm3 Zone

Area

Number

ID

Sep

Oct

Nov

Dec

Jan

Hectare

Sq. m

620 mm

270 mm

230 mm

200 mm

180 mm

109.68

1096800

0.6800

0.2413

0.2523

0.2194

0.1974

Area 1

313.42

3134200

1.9432

0.6895

0.7209

0.6268

0.5642

Area 2

35.24

352400

0.2185

0.0775

0.0811

0.0705

0.0634

Zone 1 Zone 2

Command Area

Area 3

75.82

758200

0.4701

0.1668

0.1744

0.1516

0.1365

Area 4

41.63

416300

0.2581

0.0916

0.0957

0.0833

0.0749

Area 5

43.06

430600

0.2670

0.0947

0.0990

0.0861

0.0775

Area 6

27.45

274500

0.1702

0.0604

0.0631

0.0549

0.0494

Area 7

19.07

190700

0.1182

0.0420

0.0439

0.0381

0.0343

Area 8

24.57

245700

0.1523

0.0541

0.0565

0.0491

0.0442

Area 9

65.06

650600

0.4034

0.1431

0.1496

0.1301

0.1171

Area 10

54.71

547100

0.3392

0.1204

0.1258

0.1094

0.0985

Area 11

36.61

366100

0.2270

0.0805

0.0842

0.0732

0.0659

Area 12

3.93

39300

0.0244

0.0086

0.0090

0.0079

0.0071

9

C.R.Suribabu et al

Table 8: Annual rainfall and inflow for Ponnaniar reservoir Sl. No

Year

Annual rainfall in mm

Annual inflow in 3

1

1975

906.93

Mm 5.48

2

1976

805.52

6.34

3

1977

1136.15

22

4

1978

1180.39

12.09

5

1979

959.15

15.76

6

1980

557.4

6.41

7

1981

916.27

4.23

8

1982

895.81

3.6

9

1983

1039.29

1.96

10

1984

786.84

6.97

11

1985

673.86

0.88

12

1986

757.14

1.69

13

1987

1040.37

2.89

14

1988

715.58

0.93

15

1989

1019.2

5.46

16

1990

511.7

0.69

17

1991

984.8

4.65

18

1992

949.2

1.3

19

1993

1064

6.24

20

1994

902.3

5.14

21

1995

811.8

1.35

22

1996

1060.8

2.87

23

1997

1009.5

10.23

24

1998

1164.6

130.32

25

1999

907.6

164.53

26

2000

804.9

35.18

27

2001

554.1

27.2

28

2002

696.2

13.35

29

2003

546.8

2.62

30

2004

1106.2

14.36

31

2005

1106

8.4

32

2006

730.9

11.32

33

2007

971,20

18.53

Mean rainfall in mm

888.85

10


Table 9 : Net irrigation demand in (Mm3) for case I and II Sl No. 1 2

Cases Groundnut for both zones Paddy for zone 1 and Groundnut for zone 2

September

October

November December

January

0.7652

1.2754

1.2329

0.5952

-

1.3465

1.3522

1.3261

0.7378

0.1974

Table 10 : Supply demand ratio for ground nut crop for 33 years

Mm

Mm

2001

3.75900

3.75900

Supply demand Ratio 1.00

1.00

2002

3.77980

3.53270

0.93

1.00

2003

3.77980

3.77980

1.00

3.78300

3.78300

1.00

Mm

Mm

1975

3.75902

3.75902


1976

3.76437

3.76437

1977

3.77061

3.77061

Year

Demand in Supply in 3

3

Year


3

1978

3.75902

3.75902

1.00

2004

1979

3.75501

3.75501

1.00

2005

3.75900

3.75900

1.00

1980

3.75902

3.75902

1.00

1981

3.75539

3.75539

1.00

2006 2007

3.77520 3.77300

3.77520 3.77300

1.00 1.00

1982

3.75902

3.75902

1.00

1983

3.77000

2.01573

0.54

1984

3.75900

3.24600

0.86

1985

3.77220

0.71540

0.19

1986

3.76400

1.53400

0.41

1987

3.75900

2.75000

0.73

1988

3.77100

0.75050

0.20

1989

3.76060

3.76060

1.00

1990

3.76810

1.46600

0.39

1991

3.76350

3.76350

1.00

1992

3.75902

1.66390

0.44

1993

3.75902

2.40843

0.64

1994

3.77590

3.77590

1.00

1995

3.78407

2.10640

0.56

1996

3.75902

2.63800

0.70

1997

3.75902

3.16400

0.84

1998

3.75902

3.75902

1.00

1999

3.78180

3.78180

1.00

2000

3.75900

3.75900

1.00

11

C.R.Suribabu et al

Table 11 : Supply demand ratio for Paddy (Old command) ground nut crop (New command) for 33 years

Mm

Mm

1975

4.85032

4.85032


1976

4.85567

4.85567

1.00

1993

4.85032

2.48163

0.59

4.86721

4.86721

1.00

Year


3

Year


1992

3

Mm

Mm

4.85032

1.32986


1977

4.86191

4.86191

1.00

1994

1978

4.85032

4.85032

1.00

1995

4.87531

1.39000

0.29

1979

4.84631

4.84631

1.00

1996

4.85032

2.67000

0.55

1980

4.85015

4.85015

1.00

1997

4.85032

3.57329

0.74

4.85032

4.85032

1.00

1981

4.84500

4.84500

1.00

1998

1982

4.85032

3.69415

0.76

1999

4.85470

4.85470

1.00

1983

4.85339

1.46198

0.30

2000

4.82290

4.82290

1.00

1984

4.82290

3.41248

0.70

2001

4.84900

4.84900

1.00

4.86918

4.86918

1.00

1985

4.83611

0.73035

0.15

2002

1986

4.85537

1.19022

0.30

2003

4.87115

3.55962

0.73

1987

4.85032

2.76815

0.57

2004

4.87168

4.87168

1.00

1988

4.86218

0.92922

0.19

2005

4.84479

4.84479

1.00

4.86553

4.86553

1.00

4.85681

4.66690

0.96

1989

4.82452

4.82452

1.00

2006

1990

4.85510

0.61151

0.13

2007

1991

4.85484

4.34611

0.89

Fig. 3. Annual Rainfall in mm at Dam site

12


Fig. 4. Annual inflow to the reservoir (1975-2007) Conclusion Ponnanaiar reservoir is a multipurpose reservoir. The reservoir is situated across the river Ponnaniar. This reservoir water is used to cultivate paddy, groundnut, pulses, corn and jasmine. This reservoir also acts as flood controller for the river Ponnaniar. For the present study, 33 years of rainfall and inflow data are collected from PWD, Ponnaniar in addition to the monthly depth of evaporation. A water balance model is developed using MS-Excel sheet. The gross irrigation requirements for paddy and groundnut are calculated. The depth water required for each month is taken and volume of water required per month is calculated for each crop. The total area is divided into two zones. The zone I belongs to an old command area and zone II belongs to the new command area. Two cases are formulated in which first case aimed to supply water for groundnut crop for both old and new zones. In the second case zone 1 allotted for paddy and zone 2 is allotted for groundnut. The normal date of opening of this reservoir is in the first week of September. Keeping this, the water balance model is carried out with gross water requirement as demand. The supply demand ratio is evaluated for both the cases. It is found that the supplying water for groundnut crop gives more reliable than supplying water for paddy and groundnut. Since this reservoir is operated at the end of south east monsoon season, the storage available at the end of southwest monsoon helps the reservoir operator to take appropriate decision. The water balance model shows that 23 years provided satisfactory supply to groundnut crop if it is started first week of September. Two years experienced too severe shortage of supply. The performance for years 1985 and 1988 are less than 20%. Incase of case II, 19 years provided satisfactory supply to the paddy (Zone I) and groundnut (Zone II).

13

C.R.Suribabu et al

Reference Chambers, R (Ed.), 1988. Managing canal irrigation: practical analysis from South Asia, Oxford Publishing, New Delhi, pp. 20-25. Gygier, J.C., and Stedinger, J.R., 1985, Algorithms for optimising hydropower system operation, Water Resources Research, 21(1), 1-10. Huang S.J., 200, Enhancement of hydroelectric generation scheduling using ant colony system based optimization approaches, IEEE Transactions on Energy Conversion, 16(3),296-301. Labadie, 2004, Optimal operation of multi reservoir systems: State of the art review, Journal of water resources planning and management, ASCE, 130(2),93-111. Loucks, D.P., Stedinger, J.R., and Haith, D.A., 1981, Water resources systems planning and analysis. Prentice-Hall Inc., Englewood Cliffs, N.J. Oliveira and Loucks 1997, Operating rules for Multireservoir systems, Water Resources Research, 33(4), 839-852. PWD, 2002, Water Management studies in Agniar river basin, Institute for Water studies, WRO, PWD. Simonovic, 1992, Reservoir systems analysis: closing gap between theory and practice, Journal of water resources planning and management, ASCE, 118(3), 262-280. Stedinger, J.R., Sule, B.F., and Loucks, D.P., 1984, Stochastic dynamic programming models for reservoir operation optimisation, Water Resources Research, 20(11), 1499-1505. Tejada-Guibert, J.A., Johnson, S.A., and Stedinger, J.R., 1995, The value of hydrologic information in stochastic dynamic programming models of a multireservoir system, Water Resources Research, 31(10), 2571-2579. Wardlaw, R., and Sharif, M., 1999, Evaluation of genetic algorithms for optimal reservoir system operation, Journal Water Resources planning and management, ASCE, 125(1), 25-33. Yeh, W., 1985, Reservoir management and operations models: A state of the art review, Water Resources Research, 21(12), 1797-1818.

14


DAILY RAINFALL FORECAST OF PATNA GAUGE STATION BY USING WAVELET NEURAL NETWORK R. Venkata Ramana1, B. Krishna2, N. G. Pandey1 and B. Chakravorty1 Centeres for Flood Management Studies, National Institute of Hydrology, Patna 2 Deltaic Regional Centre, National Institute of Hydrology, Kakinada

1

ABSTRACT Rainfall is one of the most significant parameters in a hydrological model, several models have been developed to analyze and predict the rainfall forecast. In recent years, wavelet techniques have been widely applied to various water resources research because of their time-frequency representation. In this paper an attempt has been made to find an alternative method for rainfall prediction by combining the wavelet technique with Artificial Neural Network (ANN). The wavelet and ANN models have been applied to daily rainfall data series of IMD Patna rain gauge station. The calibration and validation performance of the models is evaluated with appropriate statistical methods. The results of daily rainfall series modeling indicate that the performances of wavelet models are more effective than the ANN models. Introduction Rainfall is a complex atmospheric process, which is space and time dependent and it is not easy to predict. Due to the apparent random characteristics of rainfall series, they are often described by a stochastic process. For water resources planning purposes, a long-term rainfall series is required in hydrological and simulation models. There have been many attempts to find the most appropriate method for rainfall prediction for example, coupling physical, marine, and meteorological or satellite data with a forecasting model, or even applying several techniques such as the artificial neural network or fuzzy logic as a forecasting approach. In recent years, several numerical weather forecasts have been proposed for weather prediction but most of these models are limited to short period forecasts. This paper introduces a new approach for prediction of rainfall series. Several time series models have been proposed for modeling annual rainfall series such as the autoregressive model (AR) (Yevjevich,1972), the fractional Guassian noise model (Matalas and Wallis, 1971), autoregressive moving-average models (ARMA) (Carlson et al., 1970) and the disaggregation multivariate model (Valencia and Schaake, 1973). In the past decade, wavelet theory has been introduced to signal processing analysis. In recent years, the wavelet transform has been successfully applied to wave data analysis and other ocean engineering applications (Massel, 2001; Teisseire et al., 2002; Huang, 2004). The time-frequency character of long-term climatic data is investigated using the continuous wavelet transform technique (Lau and Weng, 1995; Torrence and Compo, 1997; Mallat, 1998) and wavelet analysis of wind wave measurements obtained from a coastal observation tower (Huang, 2004). Combination of neural networks and wavelet methods to predict ground water levels (Wu et al., 2004). Dynamical Recurrent Neural Network (DRNN) on each resolution scale of the sunspot time series resulting from the wavelet decomposed series with the Temporal Recurrent Back propagation (TRBP) algorithm (Aussem, 1997). Wavelet transforms were also applied to time series prediction preprocessed for multistep prediction (Tsui et al., 1997). By coupling the wavelet method with the traditional AR model, the Wavelet-Autoregressive model (WARM) is developed for annual rainfall prediction. 15

R. Venkata Ramana et al

In this paper, a Wavelet Neural Network (WNN) model, which is the combination of wavelet analysis and ANN, has been proposed for rainfall forecast modeling of IMD, Patna station. Wavelet Analysis The wavelet analysis is an advanced tool in signal processing that has attracted much attention since its theoretical development (Grossmann and Morlet, 1984). Its use has increased rapidly in communications, image processing and optical engineering applications as an alternative to the Fourier transform in preserving local, non-periodic and multiscaled phenomena. The difference between wavelets and Fourier transforms is that wavelets can provide the exact locality of any changes in the dynamical patterns of the sequence, whereas the Fourier transforms concentrate mainly on their frequency. Moreover, Fourier transform assume infinite length signals, whereas wavelet transforms can be applied to any kind and any size of time series, even when these sequences are not homogeneously sampled in time (Antonios and Constantine, 2003). In general, wavelet transforms can be used to explore, denoise and smoothen time series which aid in forecasting and other empirical analysis. Wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (or mother) wavelet. In wavelet analysis, the use of a fully scalable modulated window solves the signal-cutting problem. The window is shifted along the signal and for every position the spectrum is calculated. Then this process is repeated many times with a slightly shorter (or longer) window for every new cycle. In the end, the result will be a collection of time-frequency representations of the signal, all with different resolutions. Because of this collection of representations we can speak of a multiresolution analysis. By decomposing a time series into time-frequency-space, one is able to determine both the dominant modes of variability and how those modes vary in time. Wavelets have proven to be a powerful tool for the analysis and synthesis of data from long memory processes. Wavelets are strongly connected to such processes in that the same shapes repeat at different orders of magnitude. The ability of the wavelets to simultaneously localize a process in time and scale domain results in representing many dense matrices in a sparse form. Discrete Wavelet Transform (DWT) The basic aim of wavelet analysis is to determine the frequency (or scale) content of a signal and then it assess and determine the temporal variation of this frequency content. This property is in complete contrast to the Fourier analysis, which allows for the determination of the frequency content of a signal but fails to determine frequency-time dependence. Therefore, the wavelet transform is the tool of choice when signals are characterized by localized high frequency events or when signals are characterized by a large numbers of scale variable processes. Because of its localization properties in both time and scale, the wavelet transform allows for tracking the time evolution of processes at different scales in the signal. The wavelet transform of a time series f(t) is defined as

f ( a, b ) =

1 a

¥

æt -bö ÷dt a ø

ò f (t )j çè

-¥

(1)

where j (t) is the basic wavelet with effective length (t) that is usually much shorter than the target time series f(t). The variables ‘a’ is the scale or dilation factor that determines the characteristic 16

Daily rainfall forecast of Patna gauge station by using Wavelet Neural Network

frequency so that its variation gives rise to a spectrum and ‘b’ is the translation in time so that its variation represents the ‘sliding’ of the wavelet over f(t). The wavelet spectrum is thus customarily displayed in time-frequency domain. For low scales i.e. when |a|1, the wavelet is stretched and contains mostly low frequencies. For small scales, we obtain thus a more detailed view of the signal (also known as a “higher resolution”) whereas for larger scales we obtain a more general view of the signal structure. The original signal X(n) (Fig. 1) passes through two complementary filters (low pass and high pass filters) and emerges as two signals as Approximations (A) and Details (D). The approximations are the high-scale, low frequency components of the signal. The details are the low-scale, high frequency components. Normally, the low frequency content of the signal (approximation, A) is the most important part. It demonstrates the signal identity. The high-frequency component (detail, D) is nuance. The decomposition process can be iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components (Fig. 1).

Fig. 1. Diagram of multiresolution analysis of signal Mother Wavelet The choice of the mother wavelet depends on the data to be analyzed. The Daubechies and Morlet wavelet transforms are the commonly used “Mother” wavelets. Daubechies wavelets exhibit good trade-off between parsimony and information richness, it produces the identical events across the observed time series and appears in so many different fashions that most prediction models are unable to recognize them well (Benaouda et al., 2006). Morlet wavelets, on the other hand, have a more consistent response to similar events but have the weakness of generating many more inputs than the Daubechies wavelets for the prediction models. An ANN, can be defined as a system or mathematical model consisting of many nonlinear artificial neurons running in parallel, which can be generated, as one or multiple layered. Although the concept of artificial neurons was first introduced by McCulloch and Pitts, the major applications of ANN’s have arisen only since the development of the back-propagation method of training by Rumelhart (Rumelhart et al., 1986). Following this development, ANN research has resulted in the successful solution of some complicated problems not easily solved by traditional modeling methods when the quality/quantity of data is very limited. ANN models are ‘black box’ models with particular properties, which are greatly suited to dynamic nonlinear system modeling. The main advantage of this approach over traditional methods is that it does not require the complex nature of the underlying process under consideration to be explicitly described in mathematical form. ANN applications in hydrology vary, from real time to event based modeling. 17


The most popular ANN architecture in hydrologic modeling is the multilayer perceptron (MLP) trained with BP algorithm (ASCE 2000(a) &(b)). A multilayer perceptron network consists of an input layer, one or more hidden layers of computation nodes, and an output layer. The number of input and output nodes is determined by the nature of the actual input and output variables. The number of hidden nodes, however, depends on the complexity of the mathematical nature of the problem, and is determined by the modeler, often by trial and error. The input signal propagates through the network in a forward direction, layer by layer. Each hidden and output node processes its input by multiplying each of its input values by a weight, summing the product and then passing the sum through a nonlinear transfer function to produce a result. For the training process, where weights are selected, the neural network uses the gradient descent method to modify the randomly selected weights of the nodes in response to the errors between the actual output values and the target values. This process is referred to as training or learning. It stops when the errors are minimized or another stopping criterion is met. The Back Propagation Neural Network (BPNN) can be expressed as (2) Y=f WX - q

(å

)

where, X = input or hidden node value; Y = output value of the hidden or output node; f (.) = transfer function; W = weights connecting the input to hidden, or hidden to output nodes; and

q = bias (or threshold) for each node. Method of Network Training Levenberg-Marquardt method (LM) was used for training of the given network. It is a modification of the classic Newton algorithm for finding an optimum solution to a minimization problem. In practice, LM is faster and finds better optima for a variety of problems than most other methods (Hagan, 2004). The method also takes advantage of the internal recurrence to dynamically incorporate past experience in the training process (Coulibaly et al., 2000). The Levenberg-Marquardt algorithm (LMA) is given by

(

X k +1 = X k - J T J + mI

)

-1

J te

(3)

where, X is the weights of neural network; J is the Jacobian matrix of the performance criteria to be minimized; µ is a learning rate that controls the learning process; and e is residual error vector. If scalar µ is very large, the above expression approximates gradient descent with a small step size, while if it is very small; the above expression becomes Gauss-Newton method using the approximate Hessian matrix. The Gauss-Newton method is faster and more accurate near an error minimum. 18


Hence we decrease µ after each successful step and increase only when a step increases the error. LMA has great computational and memory requirements, and thus it can only be used in small networks. It is faster and less easily trapped in local minima than other optimization algorithms. Selection of Network Architecture Increasing the number of training patterns provide more information about the shape of the solution surface, and thus increases the potential level of accuracy that can be achieved by the network. A large training pattern set, however can sometimes overwhelm certain training algorithms, thereby increasing the likelihood of an algorithm becoming stuck in a local error minimum. Consequently, there is no guarantee that adding more training patterns leads to improve solution. Moreover, there is a limit to the amount of information that can be modeled by a network that comprises a fixed number of hidden neurons. The time required to train a network increases with the number of patterns in the training set. The critical aspect is the choice of the number of nodes in the hidden layer and hence the number of connection weights. Based on the physical knowledge of the problem and statistical analysis, different combinations of antecedent values of the time series were considered as input nodes. The output node is the time series data to be predicted in one step ahead. Time series data was standardized for zero mean and unit variation, and then normalized into 0 to 1. The activation function used for the hidden and output layer was logarithmic sigmoidal and pure linear function respectively. For deciding the optimal hidden neurons, a trial and error procedure started with two hidden neurons initially, and the number of hidden neurons was increased up to 10 with a step size of 1 in each trial. For each set of hidden neurons, the network was trained in batch mode to minimize the mean square error at the output layer. In order to check any over fitting during training, a cross validation was performed by keeping track of the efficiency of the fitted model. The training was stopped when there was no significant improvement in the efficiency, and the model was then tested for its generalization properties. Fig. 2 shows the multilayer perceptron (MLP) neural network architecture when the original signal taken as input of the neural network architecture.

Fig. 2. Signal data based Multi Layer Perceptron (MLP) neural network structure. 19


Method of Combining Wavelet Analysis with ANN The decomposed details (D) and approximation (A) were taken as inputs to neural network structure as shown in Fig. 3, where ‘i’ is the level of decomposition varying from 1 to I and j is the number of antecedent values varying from 0 to J and N is the length of the time series. To obtain the optimal weights (parameters) of the neural network structure, LM back propagation algorithm was used to train the network. A standard MLP with a logarithmic sigmoidal transfer function for the hidden layer and linear transfer function for the output layer were used in the analysis. The number of hidden nodes was determined by trial and error procedure. The output node will be the original value at one step ahead.

Fig. 3. Wavelet based Multi Layer perceptron (MLP) neural network structure. Linear Auto-Regressive (AR) Modeling A common approach for modeling univariate time series is the autoregressive (AR) model:

X t = d + f1 X t -1 + f2 X t - 2+......... + f p X t - p+ At

(4)

where, Xt is the time series; At is white noise, and p ö æ d = çç1 - å fi ÷÷ m è i =1 ø

(5)

where ‘µ’ is the mean of the time series. An autoregressive model is simply a linear regression of the current value of the series against one or more prior values. AR models can be analyzed with linear least squares technique. They also have a straightforward interpretation. The determination of the model order can be estimated by examining the plots of Auto Correlation Function (ACF) and Partial Auto Correlation Function 20


(PACF). The number of non-zero terms (i.e. outside confidence bands) in PACF suggests the order of the AR model. An AR (k) model will be implied by a sample PACF with k non-zero terms, and the terms in the sample ACF will decay slowly towards zero. From ACF and PACF analysis for rainfall, the order of the AR model is selected as 1. Performance Criteria The performance of various models during calibration and validation were evaluated by using the statistical indices: the Root Mean Squared Error (RMSE), Correlation Coefficient (R) and Coefficient of Efficiency. Study Area Patna, capital of Bihar state is situated on the bank of river Ganga with latitude 250 37’ and longitude 850 10¢’ and has a mean elevation of 49.68m above the MSL. Patna and its upland is sandwiched between the high Himalayan ranges in the far north and the high tracts of Chhotanagpur in the south. Due to its location with relation to latitude and other features, Patna has a humid subtropical climate with hot summers from late March to early June, the monsoon season from late June to late October and a mild winter from November to February. Highest temperature ever recorded is 46.6 0C (in 1966) lowest ever is 2.30C (in 2003) and highest daily rainfall was 250.8 mm (in 1987). Patna has a temperate climate, suitable for urban living. Patna is a linear city and is about 30 Km long from east to west and 5-7 Km from north to south. The city is situated between the river Ganga in the north, river Punpun in the south and river Sone in the west (Fig. 4).

Fig. 4. Study area and location of IMD station of Patna

21


Development of Wavelet Neural Network Model The original time series was decomposed into Details and Approximations to certain number of sub-time series {D1, D2…. Dp, Ap} by wavelet transform algorithm. These play different role in the original time series and the behavior of each sub-time series is distinct (Wang and Ding, 2003). So the contribution to original time series varies from each successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components, tested using different scales from 1 to 10 with different sliding window amplitudes. In this context, dealing with a very irregular signal shape, an irregular wavelet, the Daubechies wavelet of order 5 (DB5), has been used at level 3. Consequently, D1, D2, D3 were detail time series, and A3 was the approximation time series. An ANN was constructed in which the sub-series {D1, D2, D3, A3} at time t are input of ANN and the original time series at t + T time are output of ANN, where T is the length of time to forecast. The input nodes are the antecedent values of the time series and were presented in Table 1. The Wavelet Neural Network model (WNN) was formed in which the weights are learned with Feed forward neural network with Back Propagation algorithm. The number of hidden neurons for BPNN was deter-mined by trial and error procedure. Table 1: Model Inputs

Model I

X (t) = f (x [t-1])

Model II

X (t) = f (x [t-1], x [t-2])

Model III

X (t) = f (x [t-1], x [t-2], x [t-3])

Model IV

X (t) = f (x [t-1], x [t-2], x [t-3], x [t-4])

Model V

X (t) = f (x [t-1], x [t-2], x [t-3], x [t-4], x [t-5])

Results and Discussion To forecast the rainfall at Patna gauging station of IMD Patna (Fig. 4), the daily rainfall data of 20 years was used. The first fourteen years (1973-86) data were used for training of the model, and the remaining six years (1986-93) data were used for calibration and validation. The model inputs (Table 1) were decomposed by wavelets and decomposed sub-series were taken as input to ANN. ANN was trained using back propagation with LM algorithm. The optimal number of hidden neurons was determined as six by trial and error procedure. The performance of various models estimated to forecast the rainfall was presented in Table 2. From Table 2, it is found that low RMSE values (3.593 to 9.279 mm) for WNN models when compared to ANN and AR models. It has been observed that WNN models estimated the peak values of rainfall to a reasonable accuracy (peak rainfall in the data series is 250 mm). Further, it is observed that the WNN model having four antecedent values of the time series, estimated minimum RMSE (3.593mm), high correlation coefficient (0.944) and highest efficiency (>88%) during the validation period. The model IV of WNN was selected as the best fit model to forecast the rainfall one-day in advance.

22


Table 2: Goodness of fit statistics of the calibration and validation the forecasted rainfall. ANN Calibration Model

RMSE

R

Validation COE(%)

RMSE

R

COE(%)

Model I

12.514

0.397

14.433

10.333

0.367

11.266

Model II

12.314

0.377

14.233

10.133

0.357

12.266

Model III

12.244

0.39

15.208

10.305

0.324

9.314

Model IV

12.167

0.403

16.274

10.245

0.338

10.41

Model V

11.989

0.432

18.695

10.424

0.316

7.282

Model VI

12.205

0.397

15.744

10.306

0.325

9.416

Model I

11.265

0.531

9.279

0.514

26.401

WNN 28.226

Model II

8.034

0.797

63.491

7.368

0.736

53.615

Model III

4.442

0.943

88.841

4.178

0.923

85.093

Model IV

3.707

0.96

92.23

3.593

0.944

88.979

Model V

3.859

0.957

91.578

3.757

0.938

87.96

Model VI

3.714

0.961

92.197

3.811

0.937

87.615

12.664

0.342

10.23

0.357

10.506

AR 9.286

Fig’s 5 and 6, shows the observed and modeled graphs for ANN and WNN models respectively. It is found that values modeled from WNN model properly matched with the observed values, whereas ANN model underestimated the observed values. From this analysis, it is evident that the performance of WNN was much better than ANN and AR models in forecasting the rainfall.

Fig. 5(a). Plot of observed and modeled rainfall for ANN model during calibration 23


Fig. 5(b). Plot of observed and modeled rainfall for ANN model during validation.

Fig. 6(a). Plot of observed and modeled rainfall for WNN model during calibration

24


Fig. 6(b). Plot of observed and modeled rainfall for WNN model during validation Conclusions This paper reports a hybrid model called wavelet based neural network model for time series modeling of rainfall. The proposed model is a combination of wavelet analysis and artificial neural network (WNN). Wavelet decomposes the time series into multilevels of details and it can adopt multiresolution analysis and effectively diagnose the main frequency component of the signal and abstract local information of the time series. The proposed WNN model has been applied to daily rainfall of Patna gauging station, IMD Patna India. The time series data of rainfall was decomposed into sub series by DWT. Each of the sub-series plays distinct role in original time series. Appropriate sub-series of the variable used as inputs to the ANN model and original time series of the variable as output. From the current study it is found that the proposed wavelet neural network model is better in forecasting rainfall of Patna gauging station. In the analysis, original signals are represented in different resolution by discrete wavelet transformation; therefore, the WNN forecasts are more accurate than that obtained directly by original signals. References Antonios, A. and Constantine, E. V. “Wavelet Exploratory Analysis of the FTSE ALL SHARE Index,” Preprint submitted to Economics Letters University of Durham, Durham, 2003. ASCE Task Committee, “Artificial Neural Networks in hydrology-I: Preliminary Concepts,” Journal of Hydrolo- gic Engineering, Vol. 5, No. 2, 2000(a), pp. 115-123. ASCE Task Committee, “Artificial Neural Networks in Hydrology-II: Hydrologic Applications,” Journal of Hy-drologic Engineering, Vol. 5, No. 2, 2000(b), pp. 124- 137.

25


Aussem, A. and Murtagh, F. “Combining Neural Network Forecasts on Wavelet Transformed Series,” Connection Science, Vol. 9, No. 1, 1997, pp. 113-121. Benaouda, D., Murtagh, F,.. Starck, J. L. and Renaud, O. “Wavelet-Based Nonlinear Multiscale Decomposition M- odel for Electricity Load Forecasting,” Neurocomputing, Vol. 70, No. 13, 2006, pp. 139-154. Box, G.E., and G. Jenkins. 1970. Time series analysis, forecasting and control, Holden-Day Inc., San Francisco. Burrus, C.S., R.A. Gopinath, and H. Gao. 1998. Introduction to wavelet and wavelet transform, Prentice-Hall International, Inc. Carlson, R.F., A.J.A. MacCormick, and D.G. Watts. 1970. Application of linear models to four annual streamflowseries, Water Resour. Res., 6,4, pp 1070-1078 Coulibaly, P., Anctil, F.., Rasmussen, P.and Bobee, B. “A Recurrent Neural Networks Approach Using Indices of Low-Frequency Climatic Variability to Forecast Regional Annual Runoff,” Hydrological Processes, Vol. 14, No. 15, 2000, pp. 2755-2777. Feiring, M.B., and B.B. Jackson. 1971. Synthetic hydrology monograph No.1, American geophysical Union,Washington D.C. Grossmann, A., and Morlet, J. “Decomposition of Hardy Functions into Square Integrable Wavelets of Constant shape,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 723736. Hagan, M. T., and Menhaj, M. B. “Training Feed forward Networks with Marquardt Algorithm,” IEEE Transac-tions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989- 993. Huang, M.C. 2004. Wave parameters and functions in wavelet analysis, Ocean Engineering 31:1, pp 111-125 Jury, M.R., and J.L. Melice. 2000. Analysis of Durban rainfall and Nile river flow 1871-1999, Theor. Appl.Climatol. 67, pp 161-169 Lau, K.M., and H.Y. Weng. 1995. Climate signal detection using wavelet transform: how to make a time seriessing, Bull. Amer. Meteor. Soc. 76, pp 2391-2402 Mallat, S. 1998. A wavelet tour of signal processing, San Diego, CA: Academic Press. Massel, S.R. 2001. Wavelet analysis for processing of ocean surface wave records, Ocean Engineering 28, pp 957-987 Matalas, N.C., and J.R. Wallis. 1971. Statistical properties of multivariate fractional noise process, Water Resour.Res., 7, pp 1460-1468 Rumelhart, D. E., Hinton G. E. and Williams, R. J. “Lear- ning Representations by Back-Propagating Errors,” Na-ture, Vol. 323, No. 9, 1986, pp. 533-536

26


Salas, J.D., J.W. Delleur, V. Yevjevich, and W.L. Lane. 1985. Applied modeling of hydrological time series, BookCrafters, Inc. Michigan. Teisseire, L.M., M.G. Delafoy, D.A. Jordan , R.W. Miksad, and D.C. Weggel. 2002.Measurement of theinstantaneous characteristics of natural response modes of a spar platform subjected to irregular wave loading,International Journal of Offshore and Polar Engineering 12:1, pp 1624 Torrence, C., and G.P. Compo. 1997. A practical guide to wavelet analysis, Bull. Amer. Meteor. Soc. 79:1, pp 61-78 Transforms in time series prediction, Proc. IEEE Int. Conf. Syst. Man. Cybern. Vol. 2, pp. 17911796 Tsui, F.C., C.C. Li, M. Sun, and R.J. Sclabassi. 1997. A comparative study of two biorthogonal wavelet Valencia, D.R., and J.C. Schaake, Jr. 1973. Disaggregation processes in stochastic hydrology, Water Resour. Res.9:3, pp 580-585 Wang, D. and Ding, J. “Wavelet Network Model and Its Application to the Prediction of Hydrology,” Nature and Science, Vol. 1, No. 1, 2003, pp. 67-71. Wu, D. J., Wang, J and Teng, Y. “Prediction of Under-ground Water Levels Using Wavelet Decompositions and Transforms,” Journal of Hydro-Engineering, Vol. 5, 2004, pp. 34-39. Yevjevich, V. 1972. Stochastic processes in hydrology, Water Resources Publications, Colorado.

27


ANALYSIS OF DAILY MAXIMUM RAINFALL FOR HYDROLOGICAL DESIGN OF SMALL SCALE WATER HARVESTIG STRUCTURE *B. Panigrahi1 and Kajal Panigrahi2 Dept. of Soil and Water Conservation Engineering, Orissa University of Agril. & Tech., Bhubaneswar-751003, Odisha. 2 Dept. of Civil Engineering, National Institute of Technology, Rourkela, Odisha. *E- mail: [email protected]

1

ABSTRACT In the present study, annual daily maximum rainfall data of 29 years (1985-2013) for Balijore Nallah watershed of Sambalpur district of Odisha, India were analysed to find out the best fit probability distribution function to them. Total 12 numbers of probability distribution functions i.e. (i) Normal, (ii) Log Normal (2-p), (iii) Log Normal (3-p), (iv) Gamma (v) Extreme value (maximum), (vi) Extreme value (minimum), (vii) Exponential, (viii) Pearson, (ix) Log Pearson, (x) Extreme value type III, (xi) Generalised extreme value and (xii) Generalised Pareto distribution were considered to find out the best fit probability distribution function to the hydrologic values of annual daily maximum rainfall data. The 12 probability distribution functions as cited above were analysed through software “FLOOD” and the values of daily maximum rainfall were predicted at different probability of exceedences (PE) ranging from 10 to 90 percent. Statistical test of Chi-square, mean absolute relative error (MARE), model efficiency (ME), root mean square error (RMSE) and coefficient of determination (CD) were employed to ascertain the best fit distribution function. Statistical analyses indicated that Generalised Pareto distribution was the best to predict annual maximum daily rainfall at different probability levels. Accordingly, annual daily maximum rainfall at 10 to 90 percent PE levels was predicted by Generalised Pareto distribution. Since small water harvesting structures are designed for 5 years recurrence interval (20% PE level), one day maximum rainfall at this return period was predicted by the above mentioned best fit distribution (180.3 mm). This predicted one day maximum rainfall was used to forecast surface runoff from the watershed by Soil Conservation Service –Curve Number (SCS-CN) method for upland and medium land condition of the watershed. The values of the surface runoff for upland and medium land of the study watershed were predicted as 137.4 and 124.8 mm, respectively which can be used for effective design of small scale water harvesting structures Introduction The two vital natural resources required for agricultural production of any country are soil and water. The net productivity of crops depends on the proper management and utilisation of these two resources. Rainfall is a highly spatial and temporarily stochastic factor. Due to uneven as well as erratic distribution of rainfall and absence of suitable water conservation structures, the upland of a watershed faces water scarcity. At the same time, there is stagnation of excess rainwater in the lowland and thus both the situations hamper crop production and productivity. Moreover, crop production in the rainfed farming system suffers much due to water scarcity during winter (rabi) and summer seasons. In the absence of water harvesting structures, farmers in the rainfed farming system are not able to grow any second crop in winter. Even in the rainy season, sometimes some dry spells of 10 to 15 days duration are common which hampers crop production in the absence of supplemental irrigation through some suitable water harvesting structures (Panigrahi, 2001). Effective hydrologic design of soil and water conservation structures including small scale water harvesting structures require accurate prediction of one day maximum rainfall by a best fit probability 28

Analysis of Daily Maximum Rainfall for Hydrological Design of Small Scale Water Harvestig Structure

distribution function and corresponding expected surface runoff for the design return period. Otherwise these soil and water conservation structures constructed with huge investments and labour will fail during the flash floods because of under as well as inaccurate design. Rainfall data can be analysed in different ways depending on the problem under consideration. For hydrologic design of soil and water conservation structures like water harvesting structures, spillways of different water harvesting structures, check dam etc., analysis of one day maximum rainfall is of great importance (Ravi Babu et al., 2006). The analysis of rainfall data for the prediction of expected rainfall at a given return period is commonly done by utilising different probability distribution functions. Probability analysis is a common tool to predict the occurrence of any stochastic event like occurrence of rainfall event based on the past behaviour of rainfall. Based on the theoretical probability distribution functions, it would be possible to forecast the amount of rainfall for any desired return period (Kumar and Kumar, 1989; Panigrahi, 1998). Several studies have been conducted at different parts of the world on rainfall analysis to predict the magnitude of rainfall by studying different probability distribution functions. Agarwal et al. (1988) and Bhatt et al. (1996) reported Log Pearson Type III distribution to be most suitable for prediction of daily maximum rainfall for two regions of Uttar Pradesh. Kumar (1999) used Gumbel, Log Pearson Type III and Log Normal distribution and found the Log Normal distribution to be the best fit distribution for predicting annual daily maximum rainfall for Pantnagar. Ravi Babu et al. (2006) reported that Log Pearson Type III was the best fit distribution for prediction of annual daily maximum rainfall for Bankura district of West Bengal. They found out annual daily maximum rainfall for Bankura district by the above mentioned distribution to be 116, 155, 165, 185 and 207 mm for 5, 10, 15, 25 and 50 year return periods, respectively. Surface runoff is an important component of hydrological cycle. However, it is a complex parameter since its generation depends on a number of factors including rainfall and various watershed physiographic factors. For design of water conservation structures, reliable estimate of surface runoff from a watered is very much essential (Singh et al., 1994). Soil Conservation Service-Curve Number (SCS-CN) method also called as Hydrologic Soil Cover Complex Method is accepted these days as a reliable method for estimation of runoff from a small agricultural watersheds (Panigrahi, 2013; Singh, 2001). Mishra et al. (2005) investigated the applicability of SCS-CN method for the estimation of runoff in laterite zone of West Bengal based on daily total rainfall of two watersheds. Their observations revealed that SCS-CN method was the best to predict runoff from a watershed which could be used in accurate design of soil and water conservation structures. Panigrahi (2011) also advocated the same method for runoff estimation for design of on-farm reservoirs in rainfed farming systems of eastern India. Runoff harvesting and recycling through various forms of water harvesting structures including farm pond is a common method used by the farmers in the region. However, design of most of the water harvesting structures in watersheds are based on thumb rule by considering either the highest value of the maximum daily rainfall or considering the maximum daily rainfall at 50 percent PE level by a suitable probability distribution function. This makes the structure either over estimated or under estimated. From the design point of view, both methods are unacceptable. An over estimated structure, though can accommodate all the runoff but makes the structure costly and also cause wastage of a lot of area towards the construction of the structures. . On the other hand, an under estimated structure cannot accommodate all the runoff and thus during flash floods causes havoc. 29

B. Panigrahi et al

From effective hydrological design point of view, the water harvesting structures should be designed at 5 years return period i.e. at 20% PE level (Mishra et al., 2006; Panigrahi, 2011; Shrivastava, 1996). Hence it is felt necessary to design the structure scientifically at a particular return period (5 years considered in the study) by a suitable best fitting probability distribution function. Keeping the above mentioned points in view, the present study was undertaken to predict daily maximum rainfall by fitting 12 probability distribution functions i.e. (i) Normal, (ii) Log Normal (2-p), (iii) Log Normal (3-p), (iv) Gamma (v) Extreme value (maximum), (vi) Extreme value (minimum), (vii) Exponential, (viii) Pearson, (ix) Log Pearson, (x) Extreme value type III, (xi) Generalised extreme value and (xii) Generalised Pareto distribution and predicting the event by a best fit distribution by statistical tests conducting Chi-square, mean absolute relative error (MARE), model efficiency (ME, root mean square error (RMSE) and coefficient of determination (CD). The values of one day maximum rainfall by this best fit distribution was predicted at 10 to 90 % PE level. But for estimation of runoff for hydrological design of small water harvesting structures, maximum one day rainfall at 20 % PE level (5 years return period) was considered. The so predicted rainfall was used to compute the runoff for upland and medium land condition of the watershed by SCS-CN method in Balijore Nallah watershed, Odisha.. Materials and Methods Watershed and Data Collection The present study was undertaken in Balijore Nallah watershed of Sambalpur district of Odisha. The latitude, longitude and altitude of the watershed area are 210 38’N - 210 40’N, 840 5’ E - 840 8’ E and 178.8 m above the mean sea level, respectively. The area falls under the sub-humid climatic condition in the eastern part of the country. The area is characterised by hot summer, wet rainy and cold winter. The watershed is situated at a distance of 6 km from the National Highway. The average annual rainfall of the watershed is 1788 mm. Average maximum and minimum temperatures are 45.3 and 11.80C, respectively. Relative humidity ranges from 72 to 82% in rainy season and 38 to 70% in remaining months. Crops grown in the area are mainly rice followed by pulses like black gram and green gram and oilseeds like groundnut and sunflower. The lands are generally monocropped. The watershed has total area of 1551.72 ha. It covers two villages i.e. Katarbaga and Ludhapali. Total agricultural land of Katarbaga is 926.46 ha out of which up, medium and low land covers 574.37 ha, 291.25 ha and 60.84 ha, respectively. Similarly, total agricultural land of Ludhapali is 203.96 ha out of which up, medium and low land covers 111.58 ha, 77.44 ha and 14.94 ha, respectively (Anonymous, 1997). Detail land uses of the watershed are presented in Figs. 1 (a) and (b).

Fig. 1 (a). Present land use of watershed

Fig. 1 (b). Distribution of agricultural land 30


The major soil types of the study area red (alfisols), laterite and lateritic (ultisol and oxisol) with limited patches of forest humus soil. About 41% of soils are acidic, 47% are neutral and rest are alkaline in reaction. Soil slopes in the upland are more than 6%, whereas that in medium land is about 3%. The soil texture of the study area is sandy loam with sand, silt and clay percentage of 77.8, 11.8 and 10.4, respectively. Average values of bulk density, volumetric moisture content at field capacity and permanent welting point are 1.58 gm/cc, 28% and 10%, respectively. Average pH, EC and organic carbon were 6.4, 0.08 dS/m and 0.57%, respectively (Anonymous, 1997). The watershed comes under West Central Table Land Agroclimatic Zone of Odisha. The area is composed of undulating topography of high ridges and low vallies. The watershed is surrounded by hillocks and forest area which contributes to the internal drainage system of the project area. The general drainage pattern is dendrites. It is the principal tributary of river Ib which drains to the Hirakud reservoir. Soil erosion in the watershed is moderate to high. The forest lands are found to be severely eroded whereas the arable up lands are subjected to moderate to severe erosion. The medium lands located on the slopes are susceptible to moderate erosion whereas the low lands located mostly on the valley bottom and drainage channel are subjected to over flooding during the rainy season. The water resources in the watershed are not fully used. The scope for use of water by different sources is limited. The village Katarbaga has only 3 water harvesting structures, 68 dug wells, 6 tanks and 3 tube wells. Similarly, village Ludhapali has only one water harvesting structure, 10 dug wells, 2 tanks and 2 tube wells. Water from these sources are mainly used for domestic purposes and sometimes used as life saving supplemental irrigation during dry spells over a limited patch. The average groundwater level lies 7 to 8 m below the ground level and the scope for ground water recharge is limited. As such the best alternative to have better groundwater recharge is through constructions of water harvesting structures including farm ponds in the drainage channels (Anonymous, 1997). Crop production in the watershed is entirely dependent on rainfall. Rainfall distribution in the area is very much erratic and uneven which causes drastic yield reduction of crops. At times, there is insitu drought and flood which also hampers crop production. High velocity of water flowing over the sloppy land in the watershed also causes severe soil and water erosion. The problem is more aggressive in the low land where accumulation of water in the crop field during high rainfall causes submergence of crops. There is no scope of irrigation except conservation and management of excess rainfall in different soil and water conservation structures. Prediction of Daily Maximum Rainfall Daily rainfall data of 29 years (1985-2013) were collected from the meteorological station of Regional Research and Technology Transfer Station, Chiplima located at the vicinity of the watershed. From the daily rainfall data, one day maximum rainfall data of each year were obtained. Fig. 2 represents the variation of one day maximum rainfall of different year. These one day maximum rainfall values were statistically analysed by software called “FLOOD”. Total 12 probability distribution functions were studies. They are (i) Normal (ii) Log Normal (2-p), (iii) Log Normal (3-p), (iv) Gamma (v) Extreme value (maximum), (vi) Extreme value (minimum), (vii) Exponential, (viii) Pearson, (ix) Log Pearson, (x) Extreme value type III, (xi) Generalised extreme value and (xii) Generalised Pareto distribution. One day maximum rainfall values by these different distributions were predicted and the values at different probability distributions ranging from 10 to 90% PE levels are shown in Table 1. Since at a given PE level, each distribution gives 31

B. Panigrahi et al

different values of rainfall, it is suggested to use a best fit distribution to forecast the event. In the present study five statistical criteria are used to find out the best fit distribution. They are (i) Chisquare test, (ii) Mean absolute relative error (MARE), (iii) Model efficiency (ME), (iv) Root mean square error (RMSE) and (v) Coefficient of determination (CD). The value of the Chi-square is given as: 9

c2 = å i =1

(Oi - Pi ) 2 Pi

(1)

where, c2 = Value of Chi-square, O = Observed value and P = Predicted value and summation is done from i = 1 to 9 i.e. 10 to 90% PE.

Fig. 2: Variation of one day maximum rainfall in different years The value of mean absolute relative error (MARE) is given as: 9

MARE =

å

i =1

Oi - Pi Pi

(2)

n where, O and P are as defined earlier. Summation is done from i = 1 to 9 i.e. 10 to 90% PE and n = Number of data point i.e. 9.

32


Table 1: One day maximum rainfall at different probability of exceedance by various distributions Types of Distribution Normal distribution Log normal (2-p) distribution Log normal (3-p) distribution Gamma distribution Extreme value (max) distribution Extreme value (min.) distribution Exponential distribution Extreme value (Type III) dist. Log Pearson distribution Pearson distribution GEV distribution Generalized Pareto distribution

Probability,% 60 50

10

20

30

40

70

80

194.0 204.7

172.3 172.9

158.3 154.7

146.6 137.9

135.7 130.4

124.7 117.1

109.9 104.0

94.0 92.9

75.4 77.5

197.1

174.5

159.8

144.7

133.7

121.9

108.7

95.7

74.8

197.9 198.0

172.8 170.5

157.8 153.3

141.2 138.1

128.2 128.9

119.9 118.7

107.6 106.1

95.3 96.0

78.0 82.1

188.4

173.3

163.6

152.6

146.4

130.2

118.0

101.8

72.3

190.6

171.2

158.0

143.3

132.6

122.8

110.3

100.5

75.5

197.1

174.9

159.9

145.3

132.7

121.3

107.4

93.9

75.2

201.1

175.6

157.9

143.8

130.3

118.6

102.5

92.3

76.6

197.1 197.9 201.8

174.6 174.9 180.3

156.8 158.1 165.3

146.7 145.5 150.8

133.7 132.7 132.5

121.9 120.2 118.5

108.6 107.9 100.7

94.6 93.9 87.0

75.9 76.7 71.5

Model efficiency is defined as (Nash and Sutcliffe, 1970): 9

ME = 1 -

å (O - P )

2

å (O - O )

2

i

i =1 9

i

(3) i

i =1

-

where, O is the mean of the observed data and other parameters are defined as earlier.. Value of root mean square error is given as (Laogue and Green, 1991): 9

å

RMSE =

(Oi

- Pi ) n

i =1

2

(4)

Coefficient of determination (CD) is defined as (Laogue and Green, 1991): 9

CD =

å ( P - O) i =1 9

2

i

å (O - O)

(5) 2

i

i =1

33

90

B. Panigrahi et al

The RMSE, MARE and Chi-square values indicate the extent to which the simulations are overestimating or underestimating the observed values. The smaller the RMSE, MARE and Chisquare, the closer are the simulated values to the observed values. The CD statistics describe the ratio of the scatter of the simulated values to that of the observed values. A CD value of 1 indicates that the simulated values perfectly match the observed values. The model efficiency (ME) can have the highest value of 1. A value closer to 1 indicates that ME is perfect and predictions are better. Observed values of daily maximum rainfall at 10 to 90% PE levels were predicted by Weibull’s distribution. The value predicted at 50% PE level by Weibull’s distribution is considered as the mean of the observed data. Values of Chi-square, MARE, ME, RMSE and CD calculated for each distribution is presented in Table 2. The observed values of daily maximum rainfall predicted by Weibull’s distribution are presented in Table 2: Statistical parameters for best fit probability distribution function Distribution

Chi-square

MARE

ME

RMSE

CD

Normal distribution

3.41

0.044

0.969

7.47

0.71

Log normal (2-p) distribution Log normal (3-p) distribution Gamma distribution

2.65

0.045

0.980

6.05

0.80

2.63

0.039

0.977

6.38

0.75

3.39

0.051

0.972

7.05

0.73

Extreme value (max) distribution Extreme value (min.) distribution Exponential distribution Extreme value (Type III) dist. Log Pearson distribution Pearson distribution

5.08

0.063

0.960

8.43

0.68

9.28

0.074

0.919

12.09

0.69

5.32

0.053

0.953

9.21

0.65

2.22

0.035

0.980

5.96

0.76

2.58

0.039

0.978

6.30

0.74

1.56

0.034

0.987

4.78

0.81

GEV distribution

2.43

0.039

0.980

6.03

0.76

Generalized Pareto distribution

0.85

0.021

0.991

3.94

0.95

Fig. 3 also depicts the predicted values of daily maximum rainfall at 10 to 90% PE level which is obtained by the best fit distribution.

As suggested by Shrivastava (1996), Mishra et al., (2006) and Panigrahi, (2011) daily maximum rainfall value predicted by the best fit distribution at 5 years return period (20% PE levels) was considered for computation of runoff for subsequent use in hydrological design of water harvesting structures.

34


Fig. 3. Variation of one day maximum observed and predicted rainfall at different probability of exceedance Prediction of Daily Surface Runoff Daily surface runoff was estimated by SCS-CN method as described below. SCS-CN method is also called as Hydrologic Soil Cover Complex Number method or US Soil Conservation Service (SCS) method. It is based on the recharge capacity of the watershed. The recharge capacity is determined by the antecedent moisture condition (AMC) and by the physical characteristics of the watershed. Let Ia be the initial quantity of interception, depression storage and infiltration that must be satisfied by any rainfall before runoff can occur. It is assumed that the ratio of the direct runoff Q and the rainfall minus initial losses (P – Ia) and the storage capacity Sr are related by:

Q P - Q - Ia = P - Ia Sr

(6)

Ia is assumed to be certain percentage of Sr. For Indian condition for all types of soils except black cotton soil the value of Ia is assumed to be 0.3 Sr (Bhattacharya and Patil, 2008; Panigrahi, 2011; Patanaik, 2013). Accordingly the runoff is given as:

Q=

( P - 0.3Sr ) 2 ( P + 0.7 Sr )

Q=0

if P>0.3 Sr

(7)

if P