Current World Environment

Introduction

Flood, a natural disaster is responsible for loss of life and property world over. Floods damage property and endanger the lives of humans and animals and also affect the environment and aquatic life negatively. Floods have been occurring repeatedly in India. Approximately 40 million ha area (12%) in India has been identified as flood prone.¹⁸For mitigating the flood disasters, various structural and non-structural measures are adopted. Structural measures include protection works and flood embankments while non-structural measures include flood forecasting, flood warning and flood plain zoning. Design flood estimates are required for the design of various hydraulic structures such as weirs, barrages, dams, embankment etc. and flood protection / relief schemes.^5,14Flood forecasts are required for operation of various flood control structures, for taking emergency measures such as maintenance of flood levees, evacuating the people to safe localities etc. Whenever rainfall or river flow records are not available at or near the site of interest, it is difficult for hydrologists or engineers to derive reliable flood estimates directly. In such situation, flood formulae developed for the region are one of the alternative methods for estimation of design floods, particularly for small-to-medium catchments. The conventional flood formulae developed for different regions of India are empirical in nature and do not provide estimates for a desired return period.

A number of studies have been carried out for estimation of design floods for various structures by different Indian organizations. Among these the prominent studies are carried out jointly by the Central Water Commission (CWC), Research Designs and Standards Organization (RDSO), and India Meteorological Department (IMD) using the method based on synthetic unit hydrograph and design rainfall, considering physiographic and meteorological characteristics for estimation of design floods³and regional flood frequency studies carried out by RDSO using the USGS and pooled curve methods¹²for various hydro-meteorological subzones of India. The concept of the geomorphologic instantaneous unit hydrograph (GIUH) was introduced by Rodriguez-Iturbe and Valdes.¹⁷The topographic and geometric properties of the watershed and its drainage channel network are reflected by geomorphology.⁶Snyder (1938) proposed synthetic unit hydrograph approach (SUH) for ungauged basin.²¹A desirable method should satisfy the requirements of universal acceptability; ease in use with a minimum of data; robustness in nature; and reliability.¹⁴Now a days GIS and remote sensing techniques are being used extensively to monitor the disasters like droughts and floods.⁷

Practically in the design of all hydrologic structures the peak flow that can be expected with an assigned frequency (say 1 in 100 years) is of primary importance to adequately design the structure to accommodate its effect. The design of bridges, culvert waterways and spillways for dams and estimation of scour at a hydraulic structure are some examples wherein flood-peak values are required. To estimate the magnitude of a flood peak the following methods are available: (1) Rational method; (2) Empirical method; (3) Unit-hydrograph technique and (4) Flood-frequency studies.¹⁰The use of a particular method depends upon (i) the desired objective, (ii) the available data and (iii) the importance of the project. Further, the rational method is applicable only to small-size (<50 km²) catchments and the unit-hydrograph method is normally restricted to moderate-size catchments with areas less than 5000 (km²).^13,15

In present study, design floods for various structures in the 9 river basins namely Wadhavan-Bhogavo, Limbdi-bhogavo, Sukhbhadar, Utavali, Padalio, Khalkhalia, Ghelo, Keri and Kalubhar have been estimated. Deterministic approach based on unit hydrograph theory developed by CWC⁴and statistical approaches based on frequency analysis has been used for the design flood estimation.

Study Area and Data Availability

Saurashtra basin is a region of western India, located on the Arabian Sea coast of state of Gujarat. Saurashtra is bounded on three sides by waters of sea, namely in the north by the Gulf of Kutch with some part by the little Rann, in the west and south by the Arabian Sea and in the South-East by the Gulf of Khambhat; while in the east is the Mainland of Gujarat and are shown in Figure.^1,8,9,19The area covered by Saurashtra region is 59,360 sq. km. of which 9000 sq. Km. area is under study.²⁰Suarashtra basin lies between latitude 20ËšN to 24ËšN and longitude 69ËšE to 73ËšE. The rivers of Saurashtra region under study are: Wadhavan-Bhogavo, Limbdi-Bhogavo, Sukhbhadar, Utavali, Khalkhalia, Padalio, Keri, Ghelo and Kalubhar. There are 20 dams situated in these river basins. Details of river basins and dam situated in these river basins are shown in Table 1 and 4. Basin maps with dam site are shown in Figure 3 to 10.

There are 13 rain gauge stations and 9 G&D stations in these river basins which are shown in Figure 2. The rainfall data are collected from IMD as well as Kalpasar Department and G&D data are collected from Kalpasar Department of Gujarat. Details of G&D stations and raingauge stations are shown in Table 2 and 3.For Synthetic Unit Hydrograph analysis, data related to catchment like river length, catchment area and equivalent slope are required and the same are computed using SWAT model and Arc-GIS. SRTM data of 90 m resolution are used for this purpose.

Figure 1: Location map of study area a) Subzone 3 (a) of India b) River map of Gujarat (Source: Gujarat State Disaster Management Authority) Click here to View figure

Figure 2: Location of G&D sites and rain-gauge in river basin map Click here to View figure

Figure 3: Basin map of Wadhavan-Bhogav Click here to View figure

Figure 4: Basin map of Limbdi-Bhogavo Click here to View figure

Figure 5: Basin map of Sukhbhadar Click here to View figure

Figure 6: Basin map of Utavali Click here to View figure

Figure 7: Basinmap of Padalio and Khalkhalia Click here to View figure

Figure 8: Basin map of Keri Click here to View figure

Figure 9: Basin map of Ghelo Click here to View figure

Figure 10: Basin map of Kalubhar Click here to View figure

Table 1: Details of River Basins

Sr.No.	Basin Name	Area (km2)	Length (km)	Eq. Slope (m/km)
1	Wadhavan-Bhogavo	1517	128	1.19
2	Limbdi-Bhogavo	915	118	1.4
3	Sukhbhadar	1774	145	0.997
4	Utavali	1206	98	0.751
5	Padalio	311	50	0.779
6	Khalkhalia	436	47	0.779
7	Keri	556	110	1.537
8	Ghelo	626	94	1.565
9	Kalubhar	2047	90	1.42

Table 2:Details ofG&D stations of Saurashtra region

Sr. No.	Station Name	Longitude	Latitude	Type	Data Availability (Years)	River Basin
1	Limbdi	71Ëš43'8.39"	22Ëš33'28.79"	Daily	1991-2011	Limbdi
2	Ranpur	71Ëš43'29.99"	22Ëš 21' 18"	Daily	1991-2010	Sukhbhadar
3	Bhimnnath	72Ëš 5' 59.99"	22Ëš 13' 1.2"	Daily	1999-2010	Utavali
4	Barwala	71Ëš 46' 8.4"	22Ëš12'10.79"	Daily	1991-2009	Utavali
5	Keria	71Ëš 52' 33.6"	22Ëš 6' 7.2"	Daily	1991-2010	Padalio
6	Muldharoi	71Ëš55'51.59"	22Ëš3'14.39"	Daily	1997-2010	Padalio
7	Goradka	71Ëš 28' 26.4"	22Ëš 5'20.39"	Daily	1991-2010	Keri
8	Vallabhipur	71Ëš 52' 22.8"	21Ëš 53'9.59"	Daily	1991-2010	Ghelo
9	Umrala	71Ëš 47' 56.4"	21Ëš 50'56.4"	Daily	1991-2008	Kalubhar

Table 3: Details ofRain gauge stations of Saurashtra region

Sr.No.	Station Name	Longitude	Latitude	Type of Data	Data Availability (Years)	River Basin
1	WB II	71Ëš31' 58.8"	22Ëš43' 55.19"	Hourly	1906-2003	WB
2	Sayla	71Ëš27' 21.6"	22Ëš32' 42"	Hourly	1969-2003	WB
3	Chotila	71Ëš12' 46.79"	22Ëš25' 15.59"	Hourly	1968-2003	WB
4	Limbdi	71Ëš43' 19.19"	22Ëš34' 15.6"	Hourly	1991-2010	Limbdi
5	Dhandhuka	71Ëš 58'29.99"	22Ëš 23'27.59"	Hourly	1901-2006	Sukhbhadar
6	Chorvira	71Ëš 45'28.79"	22Ëš 20' 45.6"	Hourly	1991-2010	Sukhbhadar
7	Lakhavad	71Ëš 31'55.19"	22Ëš 19' 12"	Hourly	1982-2010	Sukhbhadar
8	Dholera	72Ëš11'41.99''	22Ëš15'7.19"	Hourly	1901-2006	Sukhbhadar
9	Bhavnagar	72Ëš 8' 13.2"	21Ëš 46' 55.2"	Hourly	1901-2006	Kalubhar
10	Vallavipur	71Ëš52'44.4"	21Ëš53'27.59"	Hourly	1960-2003	Ghelo
11	Umrala	71Ëš48' 21.59"	21Ëš 50' 38.4"	Hourly	1961-2007	Kalubhar
12	Dedava	71Ëš21' 18"	21Ëš53' 45.6"	Hourly	1982-2010	Kalubhar
13	Pipardi	71Ëš20' 9.59"	21Ëš50' 9.59"	Hourly	1983-2007	Kalubhar

Table 4: Details of Dam with river-wise

Sr. No.	Name of River	Name of the Dam	Location		Area (km2)	River Length (km)	Eq. Slope (m/km)
			Longitude	Latitude
1	Wadhwan-Bhogavo	WB I	71°28’57.7”	22°40’49.6”	389	50	1.86
		WB II	71°36’26.8”	22°43’17.2”	159	14	1.22
		WB III	71°48’50.0”	22°39’45.6”	303	24	1.81
2	Limbdi-Bhogavo	LB I	71°27' 21.6"	22°28' 48"	329	33	1.727
		LB II	71°36“39.6”	22°32' 34.8"	201	19	2.142
		LB III	71°56' 45.6"	22°33' 17.9"	192	36	1.504
3	Sukhbhadar	Sukhbhadar	71°32' 13.2"	22°20' 45.6"	591	45	1.937
		Goma	71°30' 3.6"	22°14' 23.9"	165	24	3.211
4	Utavali	Khambhada	71°50' 41.9"	22°10' 22.8"	255	40	2.431
		Senthali	71°44' 27.6"	22°9' 43.2"	62	18	3.332
5	Keri	Bhimdad	71°34“37.2”	22°4' 51.6"	126	24	2.931
		Gala	71°34' 22.8"	22°2' 45.6"	169	26	3.892
6	Ghelo	GheloSomnath	71°24' 7.2"	22°3' 10.8"	56	12	5.662
		GheloItaria	71°23' 49.2"	21°58' 4.8"	111	16	3.681
		Limbali	71°31' 48"	21°58' 8.4"	142	27	3.427
		Navagam	71°47' 24"	21°56' 20.4"	60	15	1.988
7	Kalubhar	Kalubhar	71°38' 27.6"	21°51' 28.8"	592	46	3.139
		Rangholi	71°39' 35.9"	21°45' 36"	397	31	2.570
		Malpara	71°32' 56.4"	21°51' 39.6"	114	23	2.470
8	Padalio	Bhambhan	71°41' 6"	22°6' 0"	66	14	3.66

Methodology

In this study, deterministic approach based on unit hydrograph theory and statistical approaches based on frequency analysis are used for design flood estimation.

1 Deterministic Approach

Due to paucity of data, regional approach based on synthetic unit hydrograph developed by Central Water Commission (CWC), 1987 has been used.²The study area falls under the subzone 3(a).

• Synthetic Unit Hydrograph (SUH) method

The following relationship for SUH method has been developed by CWC (1987):

t_p= 0.433(L/S_c)^0.704(1)
q_p=1.161/(t_p)^0.635(2)
T_B= 8.3758(t_p)^0.512(3)
W₅₀= 2.284/(q_p)^1.00(4)
Q_p=q_p* A (5)
W₇₅=1.331/(q_p)^0.991(6)
WR₅₀= 0.827/(q_p)^1.023(7)
WR₇₅= 0.561/(q_p)^1.037(8)
T_m=t_p+ 0.5 (9)

Where,

A = Total catchment area in km²
L = Length of longest main stream along the river course in km
S_c= Equivalent stream slope in m/km
t_p=时间从有效降雨durat的中心ion to the peak in hr.
q_p= Peak rate of discharge in cumec per sq. km.
Q_p= Peak discharge of U.G. in m³/s
T_B= Base width of U.G. in hr.
T_m= time from the start of rise to the peak of U.G. in hr.
W₅₀= Width of U.G. measured at 50% of peak discharge ordinate in hr.
W₇₅= Width of U.G. measured at 75% of peak discharge ordinate in hr.
W_R50= Width of rising limb of U.G. measured at 50% of peak discharge ordinate in hr.
W_R75=宽肢的ug以75%的增长peak discharge ordinate in hr.

Regional flood formulae method

The regional flood formulae have been developed by CWC to estimate 25, 50 and 100 year return period flood values. The meteorological variability has been accounted from region to region in these formulae. The others factors such as shape of the catchment, slope of the stream etc, which have influence on the peak, have also been included in these formulae thereby improving over most of the limitations of the empirical / rational formula. Thus to estimate design flood for sub-zone 3(a), Regional flood formula is given as²:

Where,

a, b, c, d and e are coefficient and the value of this coefficient is provided in CWC report.
Q_T= Design flood for a desired return period T in m³/s
A = Catchment Area in km²
S = Equivalent slope of main stream in m/km
R_t= Storm depth of return period t in cm
L = Longest length of main stream in km

Thus,

Qâ‚‚â‚… = 1.005 * A^(0.978)* S^(0.25)* R_t^(1.19)/ L^(0.618)(11)
Qâ‚…â‚€ = 1.164* A^(0.947)* S^(0.242)* R_t^(1.143)/ L^(0.566)(12)
Q₁₀₀ = 1.161* A^(0.96)* S^(0.241)* R_t^(1.126)/ L^(0.568)(13)

Statistical Approach

The statistical approach, otherwise also called frequency analysis, may be performed on the past recorded data of annual peak data series. Frequency analysis is carried out on the available record of annual flood peak discharge or annual rainfall events of the region.

Frequency Analysis for individual gauged sites

Frequency analysis study interprets a past record of events to predict the future probabilities of occurrence and estimate the magnitude of an event corresponding to a specific return period.¹If the event records are of sufficient length and reliability, they may yield satisfactory estimates. The method, however, does not provide a hydrograph shape but gives only a peak discharge of known frequency. The processed data series are to be analysed to ensure that the fundamental assumption of frequency analysis are satisfied. The data series is to be checked for randomness, presence of trend and outliers. The presence of trend is tested by using Kendall’s rank correlation test and Turning point test. The presence of randomness and outliers is tested by Anderson’s correlogram test and Chow test respectively. Detailed at site flood frequency analysis is carried out by using various distributions like Normal, Log-Normal, Pearson type III, Log-Pearson type III, Gumbel’s Extreme value distribution.⁹Gumbel EV1 is the commonly used distributions and the details about these distributions are given below.^1,15,16

Gumbel EV-1 type distribution

It is one of the most commonly used distributions in flood frequency analysis and was introduced by Gumbel in 1941. It is widely used for extreme values in hydrologic and meteorological studies for prediction of flood peaks, maximum rainfalls, maximum wind speed, etc. It is the double exponential distribution (known as Gumbel’s distribution or extreme value type 1 or Gumbel’s EV-1 distribution). The CDF of EV-1 distribution is defined as

F (x) = exp [-exp(-(x-u)/α (14)

Where, u and a are the location and scale parameters of the distribution.
Using method of moments, u and a are obtained by following equation:

Where, and S_Xare mean and standard deviation of the variate X.
Equation (16) can be written in the reduced variate form as

F(y) =exp (-exp (-Y_T)) (17)

Where,

The reduced variateY_Tcan be written in terms of return period, T, by replacing F(x) by 1-1/T as

Regional flood frequency analysis

Kumar (2009), developed the Regional flood frequency relationship using L-moment approach for ungauged catchments for 17 Subzones hydro-meteorologically homogeneous. Out of 17 subzones, Saurashtra region falls under Subzone 3(a) and the relationship for this subzone developed by Kumar (2009) is given as follows¹¹:

Q_T= C_T* A^b(22)

Where,

Q_T= Flood estimate for an ungauged catchment in m³/s for T year return period
C_T= a regional coefficient
A = Catchment area in km²
b = a regional coefficient, for subzone 3(a) this value is 0.383.
Value of C_Tfor Various return period for Subzone 3(a) are shown in Table 5.

Table 5: Value of C_Tfor Various return period for Subzone 3(a)

Coeff. (b)	CTfor Subzone 3(a)
	Return Period (Years)
	2	10	25	50	100
0.383	23.283	68.862	94.629	114.058	133.488

Results and Discussion

In this study initially the above approach are used for 20 dams as well as for 9 river basins on the basis of 24 hour rainfall for T year return period given in the iso-pluvial map. After rainfall frequency analysis, it is revised only for dams because these basins are heavily affected by dams situated on upstream. The result obtained by the above approach by the use of 24 hour rainfall for a T year return period given in the iso-pluvial map (IMD, Pune) are shown in Table 6 and 7 as well as developed by rainfall frequency analysis for basin wise are shown in Table 8 and 9.From Table 6, it can be seen that design flood estimates for return period of 25, 50 and 100 years for dams namely Wadhavan-Bhogavo, Limbdi-Bhogavo, Sukhbhadar, Utavali, Khalkhalia, Padalio, Keri and Kalubhar are underestimating except Ghelo which is overestimating when compares with the result obtained from Table 8. The reason behind this variation in result is the use of value T year return period 24 hour rainfall. By rainfall frequency analysis it has been found that the river basins namely Wadhavan-Bhogavo, Limbdi-Bhogavo, Sukhbhadar and Kalubhar have higher value of rainfall from what recommended by IMD Pune while Ghelo river basin has lower value. T year return period 24 hour rainfall recommended by IMD Pune for these river basinsis: R₂₅= 20 cm, R₅₀= 24 cm and R₁₀₀= 28cm. Since only 5 basins namely Wadhavan-Bhogavo, Limbdi-Bhogavo, Sukhbhadar, Ghelo and Kalubhar have sufficient rainfall data availability so by using Gumbel EV1 distribution T year return period 24 hour rainfall are estimated for 5 river basins and are shown in Table 8. Thus this estimated value of 24 hour rainfall for return period of 25, 50 and 100 years is used to revise design floods for the dams present in these river basins. Revised design floods for dams in these river basins for return period of 25, 50 and 100 years are computed and tabulated in Table 9 and from Table 9 it is found that the % difference is very less between revised SUH and revised RFF method.

By using the relationship developed by Kumar (2009), the design flood estimates for return period of 25, 50 and 100 years for dams and rivers are computed below in Table 10 and 11. From Table 10 and 11 it is found that the % difference is very large between L-moment and revised SUH method. L-moment method underestimates the design floods for dams as well as river basins.

The annual flood data for the nine river sites are heavily affected by the storage dams in the upstream. Hence these data violate the basic principle of virgin flow. Hence the flood frequency analysis of these data was not attempted further.

表6:设计洪水(立方米秒)20水坝

Basin Name	Dam	SUH Method			RFF method
		Q₂₅	Q₅₀	Q₁₀₀	Q₂₅	Q₅₀	Q₁₀₀
Wadavan-Bhogavo	WB I	1345.53	1676.05	1868.75	1261.18	1566.76	1882.22
	WB II	754.02	929.89	1105.27	1039.06	1290.82	1550.72
	WB III	1348.32	1666.65	2029.65	1544.16	1918.30	2304.54
Limbdi-Bhogavo	LB I	1303.96	1503.09	1929.6	1384.68	1720.19	2066.53
	LB II	1140.6	1389.58	1658.26	1293.99	1607.52	1931.18
	LB III	749.15	926.93	1103.8	734.48	912.44	1096.15
Suhkbhadar	Goma	1034.31	1204.52	1497.79	983.51	1221.82	1467.82
	Sukhbhadar	1789.9	2550.71	3050.28	2046.92	2542.89	3054.88
Utavali	Senthali	437.17	533.07	630.93	455.27	565.58	679.46
	Khambhada	1118.01	1380.51	1642.09	906.15	1125.71	1352.36
Padalio	Bhambhan	510.88	623.08	735.27	578.64	718.84	863.58
Keri	Bhimdad	745.08	914.13	1082.44	738.48	917.41	1102.12
	Gala	1057.66	1294.23	1531.72	1005.44	1249.05	1500.54
Ghelo	Somnath	562.15	683.43	804.03	604.54	751.02	902.24
	Itaria	830.22	1013.49	1197.47	887.28	1102.27	1324.21
	Limbali	895.08	1094.84	1251.58	802.56	997.01	1197.75
	Navagam	388.78	475.89	562.89	433.71	538.80	647.29
Kalubhar	Malpara	721.43	882.32	1044.39	699.35	868.80	1043.73
	Rangholi	1871.56	2307.04	2744.37	1874.26	2328.39	2797.20
	Kalubhar	1904.34	2370.23	2843.88	2149.38	2670.16	3207.78

Table 7: Design flood (Cumec) for 9 river basins

Sr. No.	Basin Name	SUH Method			RFF method
		Q₂₅	Q₅₀	Q₁₀₀	Q₂₅	Q₅₀	Q₁₀₀
1	Wadhavan-Bhogavo	2710.72	3472.33	4228.19	2473.45	3129.90	3832.12
2	Limbdi-Bhogavo	1832.21	2326.2	2821.62	1638.00	2095.30	2548.53
3	Sukhbhadar	3192.12	4068.33	4947.0	2519.04	3200.88	3926.56
4	Utavali	2208.94	2686.26	3101.49	2085.64	2630.09	3213.83
5	Padalio	754.38	952.94	1149.27	1178.52	1480.72	1787.92
6	Khalkhalia	1032.13	1319.2	1572.23	815.14	1038.28	1248.04
7	Keri	1306.05	1635.35	1971.73	1237.48	1581.81	1912.50
8	Ghelo	1413.24	1791.38	2170.07	1337.6	1709.47	2069.72
9	Kalubhar	3862.14	4952.84	5334.61	4274.00	5256.78	6464.61

Table 8: 24 hour Rainfall (cm) for T year return period for river basins

Sr. No.	Basin Name	R25		R50		R100
		After analysis	As per Iso-pluvial map	After analysis	As per Isopluvial map	After analysis	As per Isopluvial map
1	Wadhavan-Bhogavo	25	20	28	24	32	28
2	Limbdi-Bhogavo	34	20	38	24	41	28
3	Sukhbhadar	21	20	25	24	28	28
4	Ghelo	18	20	21	24	23	28
5	Kalubhar	21	20	24	24	27	28

Table 9: Revised design flood for T year return period by SUH and RFF methods for dams Click here to View table

Table 10: Design flood for T year return period by L-moment method for dams Click here to View table

Table 11: Design flood for T year return period for river basins

Basin Name	Area (km2)	Return Period (years)
		25		PD	50		PD	100		PD
		L-moment	SUH		L-moment	SUH		L-moment	SUH
WB	1517	1564.38	2710.72	36	1885.57	3472.33	40	2206.78	4228.19	42
LB	915	1288.99	1832.21	21	1553.64	2326.20	25	1818.30	2821.62	29
Sukhbhadar	1774	1661.01	3192.12	34	2002.05	4068.33	37	2343.10	4947.0	40
Utavali	1206	1432.78	2208.94	31	1726.96	2686.26	34	2021.15	3101.49	37
Padalio	311	852.61	754.38	0	1027.67	952.94	1	1202.73	1149.27	3.6
Khalkhalia	436	970.39	1032.13	17	1169.63	1319.20	21	1368.88	1572.23	23
Keri	556	1065.09	1306.05	13	1283.78	1635.35	18	1502.47	1971.73	21
Ghelo	626	1114.58	1413.24	17	1343.43	1791.38	21	1572.28	2170.07	24
Kalubhar	2047	1754.62	3862.14	59	2114.87	4952.84	59	2475.14	5334.61	60

[Note:PD- % Difference]

Conclusions

After the analysis of these river basins and dams situated on it, the following conclusions are drawn:

• For the study area, 24 hr rainfall for the return period of 25, 50 and 100 years are different for 9 river basins which also differs from iso-pluvial map recommended by IMD, Pune for this region.
• Revised design floods using SUH and RFF method on the basis of estimated rainfall indicates over-estimated and under-estimated design floods.
• Due to construction of number of dams in 9 river basins, design flood estimation on each dam by using deterministic approach is more feasible.
• The percentage difference is very less between revised SUH and revised RFF method. So, for safety purpose one with higher value will be used.
• Regional flood frequency relationship based on L-moment under-estimates the design floods with average percentage difference of 32.023% for dams and 28.28% for river basins.
• 大的平均百分比差异的原因was investigated and the data analysis reveals that there are large storages in these basins and hence application of either RFF or L-moment based methods may not be applicable.

Acknowledgement

We acknowledge the IMD, Pune as well as Kalpasar Department of Gujarat, India, for providing hydro-meteorological data of the Saurashtra region of Gujarat.

References

1. Chow, V.T., Maidment, D.R. and Mays, L.W. ‘Applied Hydrology’,McGraw-Hill, New York, (2010).
2. CWC, ‘Flood estimation report for Mahi and Sabarmati (Sub-zone-3(a))’,Directorate of Hydrology, New Delhi, (1987).
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