Current World Environment

Introduction

Estimation of runoff due to rainfall in an ungauged catchment is always an important issue for the researchers. A number of models have been developed to establish rainfall-runoff relationship in ungauged catchments. The Geomorphologic Instantaneous Unit Hydrograph (GIUH) theory was introduced by Rodriguez-Iturbeet al.,^1,2by relating the peak discharge and time to peak discharge with the geomorphologic characteristics of the catchment and a dynamic velocity parameter. The two parameters of the triangular Instantaneous Unit Hydrograph (IUH) are the time to peak t_p,and the peak discharge rate q_pwhich depend on the dynamic flow velocity parameter V. The velocity parameter varies from storm to storm and also during a given storm. Ignacio Rodriguez-Iturbe, Gustavo Devoto and Juan B. Valdes²试图探讨的问题estimation of peak discharge and time to peak from GIUH and their study concluded that the problem associated with the time-variant IUH due to variation of dynamic velocity parameter could be overcome by adopting the velocity at the time of peak discharge rate for a given rainfall-runoff event.

Valdeset al.,¹applied the GIUH in several real-world basins, catchment area from 3 Km²to 103 Km², in Venezuela and Puerto Rico. The geomorphologic IUHs were compared with those corresponding IUHs derived from the discharge hydrograph generated from the physical based rainfall-runoff model which are almost similar for each basin. The difficulty with GIUH is the dependence of peak discharge rate q_pand time to peak t_pon the peak velocity V.Rodriguez-Iturbeet al.,³rationalized the V as a function of the effective rainfall intensity and duration proposed a Geomorpho-climatic Instantaneous Unit Hydrograph (GcIUH) as a link between climate, geomorphologic structure and hydrologic response of a basin which was the stochastic reinterpretation of GIUH. Rosso⁴related the Nash model parameters shape factor n & scale factor k with the Horton's bifurcation ratio, area ratio and length ratio. The shape factor is found to be dependent on Hortan’s ratio hence on the geomorphology of the basin, whereas the scale factor was found to be time-variant as it depends on both geomorphology of the basin and average flow in the stream. Afterwards, numbers of scientist and researchers have parameterized the Nash model and Clark model by establishing the relationship with GIUH and GcIUH model. GIUH and GcIUH models are useful for ungauged basins as the unit hydrograph can be derived from the topographic information extracted from geographic information system (GIS) and digital elevation model (DEM). A GIS can provide the basis for hydrologic modelling of ungauged catchments and for studying the hydrologic impact of physical changes within a catchment. GIUH model could also be used to predict/forecast the temporal variation of surface runoff. Panigrahi⁵derived Nash model parameters from GIUH and applied on six flood events of Kolar Basin (catchment area 880 km²)检查方法的有效性。的approach was able to reproduce the computed hydrographs rising and recession limbs characteristics. Similarly, the time to peak and magnitude of peak discharges are closely reproduced by this approach. Kumaret al.,⁶pinpointed most sensitive model parameters of GIUH based Clark model. Furthermore, Kumaret al.,^7,8have also applied GIUH for flood estimation. Kumaret al.,⁹used the GIUH-Clark and GIUH-Nash models to simulate the direct surface runoff of Ajaya basin, considering as an ungauged basin. The resulting direct surface runoff (DSRO) from both the models were found to be comparable with the Clark IUH model of HEC-1 package and Nash IUH of the basin. Sarkaret al.,¹⁰used Nakagami-m distribution to compute Geomorphological Instantaneous Unit Hydrograph for Bhagirathi-Bhilangana River catchment. The study results show that the Nakagami-m distribution function well reproduces the shape of unit hydrograph and estimation of peak ordinates shows good resemblance with the observed values. Singhet al.,¹¹critically examined the development and recent advances in synthetic unit hydrograph (SUH) for flood hydrograph modelling in the ungauged basin. For systematic study they categorized the SUH model into four main classes: (a) traditional/empirical model, (b) conceptual model, (d) probabilistic model and (d) geomorphological models. The applicability of each class of model for Prediction in Ungauged Basins was considered. Khatri¹²performed geomorphological analysis of the Bhagirathi basin and its tributaries meeting directly to the Tehri dam and simulated the devastating flood of June 2013 at Tehri dam using the GIUHs and using HEC-HMS. In another study, geomorphological instantaneous unit hydrograph was developed for Koel basin and it was compared with the well-accepted synthetic unit hydrograph derivation approach¹³of Central Water Commission (CWC). National Institute of Hydrology, Roorkee has developed a GIUH based NASH model algorithm to determine the hydrograph^7,8shape. Thus, the GIUH based NASH model is helpful in simulating runoff from rainfall in ungaugesd basins. Thus, in this study GIUH based Nash model has been developed to model the runoff generated from intermediate ungauged catchments.

Study Area

Tehri is a multipurpose project, located at 145 Km downstream of Gangotri glacier on river Bhagirathi. Tehri project is important for power generation, irrigation and flood control. Tehri dam has got good flood space and has played a very vital role in moderating the 2010 and 2013 floods of Uttarakhand. Tehri dam is situated in the district Tehri of Uttarakhand state of India. Tehri dam catchment is bounded between longitude 78^o9’15’’E to79^o24’55’’E and latitude 30^o20’20’’N to 31^o27’30’’N (Fig. 1). The catchment area of the Tehri Dam is 7293 Km²out of which 2042 Km²is permanently snow-covered. The elevation of the catchment varies between 600 m at dam site and 7000 m at the peak of Gangotri glacier. The catchment receives most of the rainfall during southwest monsoon. Annual rainfall ranges from 1016 to 2630 mm. River Bhagirathi Bhilangana and Balganga are the three major rivers which contribute to Tehri reservoir. Bhagirathi River originates from Gangotri near Gomukh at an elevation of 4255 m and traverses a distance of about 168 Km to its confluence with river Bhilangana at 1.5 Km upstream of Tehri dam. River Bhilangana traverses a distance of 72 Km before meeting with river Bhagirathi. Some minor tributaries like Mangad, Nilapani, Jadganga, Garunganga, Ganeshganga, Asiganga, Dharshugad, Jalkurgad also meet with river Bhagirathi. River Balganga is a major tributary of river Bhilangana, and it meets at Ghansali, 3 Km downstream of Sarasgaon at EL 818m, falling directly into the reservoir. Different tributaries of Bhagirathi and Bhilangna are shown in Fig.2. The contour map of the Tehri catchment is shown in Fig. 3.

Physiographic Analysis

Climate

The study basin receives moisture-bearing winds mainly from the Arabian Sea and heavy rainfall during June to September. The annual rainfall of the catchment varies from 1000 mm to 2615 mm. During the period June to September, high flows and floods are experinced in the river. The climatic condition variations are high in the study basin and these are related to changes in elevations and aspect.

Geology and Soils

The rock at dam site consists of the Chandpur Phyllite. Based on lithological characteristics and engineering properties, this has been classified into broadly three grades viz. Grade I (Phyllite Quartize), Grade II (Quartzitic Phillite) and Grade III (Schistose Phyllite). Riverbed consists of large boulders. Average upstream slope of the river is 1:22.

图1:位置特赫里流域的地图 Click here to view Figure

Figure 2: Location map Major rivers and tributaries of Tehri Catchment Click here to view Figure

Figure 3: Contour map of the catchment with a contour interval of 1000m Click here to view Figure

Delineation of catchment and sub-catchments

To develop the inflow forecasting model, the Tehri catchment has been divided into four parts.

1. Bhagirathi up to Maneri Bhali II (Catchment area 4693 Km²)
2. Bhilangana up to Ghansali, (Catchment area 792 Km²)
3. Balganga up to Sarasgaon, (Catchment area 488 Km²)
4. Intermediate catchment. (Catchment area 1320 Km²)

Intermediate catchment contains 16 ungauged tributaries which are falling directly into the reservoir and the unaccounted area, i.e. reservoir area and the catchment of some very small tributaries falling directly into the reservoir. Intermediate catchment does not receive any snowfall and is rainfed only. To delineate the catchment (Figure 4) and sub-catchments SRTM DEM data of 30m resolution have been used. The catchment area and the area of each of sub-catchments along with the areas of smaller watersheds at different outlets are shown in Table 1. Sub-catchment maps of Bhilangana at Ghansali, Balganga at Sarasgaon, Bhagirathi at Maneri Bhali II and intermediate catchment are presented in Figs. 5, 6, 7 and 8 respectively. Catchment area between different elevation bands of Bhilangana, Balganga, Bhagirathi and intermediate catchments are presented in Table 2 to 5. The snow and non-snow areas during accumulation (24.3.2001 and 10.05.2001) and depletion period (10.10.2001 and 7.9.20014) of Bhagirathi catchment are shown in Figure 9 to 12.¹⁴

Figure 4: Sub catchments of Tehri Click here to view Figure

Table1: Catchment area details

SN.	Description of Catchment / Sub catchments	Area (Km2)
1	At Tehri dam	7293.0
2	Bhagirathi at Dam axis	5807.0
3	Bhilangana at Dam axis	1486.0
4	Bhagirathi Catchment at Maneri Bhali II	4693.0
5	Bhilangana Catchment at Ghansali	792.0
6	Balganga catchment at Sarasgaon (Ghansali)	488.0
7	Intermediate Catchment between MB II and Ghansali	1320
8	Area of 10 small streams falling directly into the reservoir, Bhagirathi side	943.0
9	Area of 6 small streams falling directly into the reservoir, Bhilangana side	189.0
10	Reservoir area at full reservoir level i.e. at 830m	42.0
11	Unaccounted area of other very small tributaries falling directly into the reservoir.	146.0

Figure 5: Bhilangana Catchment at Ghansali Click here to view figure

Figure 6: Balganga Catchment at Sarasgaon Click here to view Figure

Figure 7: Bhagirathi Catchment at Maneri II Click here to view Figure

Figure 8: Intermediate catchment between Maneri II and Ghansali Click here to view Figure

Table 2: Elevation band wise area of Bhilangana catchment up to Ghansali

Elevation Bands	Elevation Range (M)	Catchment Area (KM2)	Percentage (%)
1	Upto 2000	190	24
2	2000-2800	182	23
3	2800-4000	158	20
4	4000-4800	122	16
5	4800-5600	90	11
6	5600-6717	49	6

Table 3: Elevation band wise area of Balganga catchment up to Sarasgaon

Elevation Bands	Elevation Range (M)	Catchment Area (KM2)	Percentage (%)
1	Upto 1400	50	10
2	1400-2000	110	22
3	2000-2800	130	26
4	2800-4000	100	20
5	4000-4826	99	20

Table 4: Elevation band wise area of Bhagirathi catchment up to MBII

Elevation Bands	Elevation Range (M)	Catchment Area (km2)	Percentage (%)
1	Upto 2000	488	10.4
2	2000-2800	452	9.6
3	2800-4000	554	11.8
4	4000-4800	892	19.0
5	4800-6000	1607	34.2
6	6000-7085	700	14.9

Table5: Elevation band wise area of the intermediate catchment

Elevation Bands	Elevation Range (M)	Catchment Area (km2)	Percentage (%)
1	Upto 1200	312	23.7
2	1200-1600	340	25.8
3	1600-2000	196	14.9
4	2000-2400	243	18.4
5	2400-2826	229	17.4

Figure 9: Class image dated 24/3/2001 showing snow andnon-snow areas14 Click here to view Figure

Figure 10: Class image dated 10/10/2001 showing snow and non snow areas14 Click here to view figure

Figure 11: Class image dated 10/05/2004 showing snow and non snow areas14 Click here to view Figure

图12:类图像过时07/09/2004 snow and non-snow areas showing snow and non-snow areas14 Click here to view Figure

Approximately 28% catchment has permanent snow. Snow gets accumulated up to 55% of the catchment at the start of depletion period. As mentioned above, Bhagirathi river catchment has been divided into four parts, i.e. Bhagirathi up to MBII, Bhilangana up to Ghansali, Balganga up to Sarasgaon and Intermediate catchment. The catchment area of river Bhagirathi, Bhilangana and Balganga are divided into 6, 6 and 5 elevation bands respectively. The maximum elevation of these catchments are 7085 m, 6717 m and 4826 m respectively. Similarly the minimum elevation of these catchments at the outlet is 983m, 855m and 870m respectively. 2752 km²area of Bhagirathi catchment is above 2800m elevation. Primarily this area makes river Bhagirathi as perennial. The intermediate catchment is 1320 km²and is only rainfed. The major contribution in run-off from this area comes during monsoon season. Theungauged tributaries from this area are contributing directly into the reservoir. The physiographic analysis of these tributaries shows that bifurcation ratio of these 16 tributaries varies between 2.02 and 2.09. The area ratios vary between 2.65 and 5.2 and length ratios vary between 1.89 and 3.76.

Extraction of Geomorphological Characteristics

Geomorphological characteristics of the catchments of the ungauged tributaries have been extracted using Arc GIS 10.1. The method of quantitative analysis of channel networks presented by Horton¹⁵and later revised by Strahler¹⁶has been used for stream ordering as follows:

1. Channel that originates at a source is first order streams.
2. Once the streams of same order (ω) joins, a stream of next higher order (ω+1) is formed.
3. A stream below the confluence of two different order streams has the order same as the higher order stream.
4. After carrying out the stream ordering in the basin, the highest stream order Ω is defined as order of the basin.

The following set of laws suggested by Horton, for indicating the geomorphological characteristics of the watershed have been used.

Horton’s Law of Stream Number: According to it stream order and total number of streams falling under a specific stream order show inverse geometric relationship expressed as:.

N_ω= R_B^Ω-ω(1)

where Ω is the order of highest order stream in the network, ω is the order of interest and R_Bis a constant for a given river network called as bifurcation ratio.

Also;

where R_Land R_Aare the length and area ratio and L-_ωandA-_ωare the average stream length and stream area of the order ω.

The overall bifurcation ratio of the catchment, length ratio and area ratio can be calculated either by the arithmetic average method or graphical method. In the graphical method, the plot of the logarithm of N_ω,LworÄ€_ωversus order ω approximately fit a straight line. The magnitudes of the slope of the straight lines are logthe arithm of R_B,R_Land R_A. Stream order, length of the stream, maximum and minimum elevation of stream segments and the contributing area of each sub-catchment are extracted separately by analyzing the DEM in Arc-GIS.

The bifurcation ratio (R_B), the Area ratio (R_A) and Length ratio (R_L) are calculated for all the sixteen streams using the graphical method. The Horton’s ratios for all the 16 stream lie within limits given for the natural streams.

The physiographic features of 16 small streams falling directly into the reservoir are extracted using GIS. These geomorphologic details are tabulated in Tables 6 and 7 respectively.

Table 6: Extracted Physiographic features of small streams falling directly into the reservoir using GIS

Development of GIUH based Nash Model for 16 Ungauged Tributaries

GIUH based Nash Model

In an ungauged basin unit hydrograph’s complete shape is determined by connecting peak flow (q_p) and time to peak (t_p) of GIUH with Nash IUH parameters:

q_p* t_p= 0.576*(R_B/R_A)^0.55*R_L^0.05....... (7)

Nash IUH model is defined as:

u(t) = (1/(k*Гn)) (t/k)^n-1e^-t/k........ (8)

where, u(t) denotes IUH ordinates in hour^-1and t is sampling time interval in hour, k is scale parameter and n is shape parameter of the Nash IUH and Гn is the gama value of shape factor (n).

纳什IUH方程的一阶导数respect to t and equating it to zero:

At peak discharge t becomes t_p,then

Thus,

q_p= (1/(k* Гn)) (n-1)^n-1e^-(n-1)(11)

Multiplying q_pwith t_pwe get

q_p* t_p= (n-1)/ (Гn)* (n-1)^n-1e^-(n-1)(12)

Equating equations (4.3) and (4.8) we get;

Value of parameter n can be found by equation (13) through Newton- Rapson method. Value of parameter k for the known values of velocity V and parameter n is computed as:

From the geomorphologic characteristics and Horton’s ratio of each sub-catchment, the IUH parameters q_pand t_pfor GIUH-Nash model are calculated. The GIUH-Nash method gives the complete shape of IUH. The ordinates of IUH are multiplied by the watershed area to get the UH ordinates.

Contribution of Ungauged Tributaries Falling Directly into the Reservoir

A number of models are mentioned in the literature which are modelling rainfall-runoff process in a basin using SCS-CN method in a gauged basin.¹⁷Using the climate change projections,¹⁸one can use such models for predicting the behaviours of river flows. Furthermore, various modelling techniques e.g. linear transfer function, artificial neural networks, Fuzzy Logic, ANFIS have also been used in gauged catchments.^{19,20,21,22,23}However, for ungauged catchment rainfall-runoff process can be modelled through GIUH models. Therefore, runoff from the 16 ungauged tributaries has been computed using the GIUH-Nash model. The GIUH based Nash model is used to compute 1 h UH of each of the 16 tributaries. GIUH-Nash Model parameters n and k and q_pand t_pfor all the ungauged tributaries are presented in Table 8. The IUHs of the16 tributaries are presented in Fig 13. The UH ordinates are given in Table 9. To develop the DSRO, using GIUH-Nash model, hourly rainfall distribution of effective rainfall hyetograph is required. Hourly data of 4 stations namely Dharasu, Tehri, Lambgaon and Ghansali stations have been used in the convolution of rainfall to develop the DSRO of all the 16 tributaries. Uniform infiltration loss rate of 3mm per hour has been taken to prepare the ERH. The ERH of respective catchments of all the 16 tributaries is convoluted with the respective 1h unit hydrograph for computing surface runoff hydrographs. After convolution of effective rainfall, the direct surface runoff of each of the tributaries has been computed. Typical time series plots of the runoff of some of the tributaries are presented in Fig. 14.

Table 8: GIUH-Nash Model parameters n and k and q_pand t_pof the ungauged tributaries

S. No.	GIUH-Nash Model
	n	k	qp(m3/s/km2)	tp(hr)
1	3.12	1.32	0.187	3.5
2	3.10	1.27	0.208	2.67
3	2.90	1.12	0.23	2.87
4	2.85	0.50	0.559	0.93
5	2.55	0.42	0.720	0.65
6	2.60	0.50	0.608	0.79
7	3.05	1.04	0.257	2.12
8	3.15	1.68	0.156	3.61
9	3.00	0.53	0.514	1.05
10	2.95	0.65	0.422	1.27
11	2.75	0.38	0.752	0.67
12	2.85	0.20	1.133	0.37
13	3.00	0.38	0.707	0.77
14	2.40	0.35	0.895	0.50
15	3.00	0.57	0.477	1.14
16	3.05	0.44	0.611	0.90

Figure 13: IUH of tributary 1 to 16 (T1 to T16) developed by GIUH-NASH Model Click here to view Figure

Figure 14: Time Series plot of Runoff Contribution of (A) tributary number 2 for the year 016 (B) tributary number 3 for the year of 2017. Click here to view Figure

Figure 15: Time Series plot of Runoff Contribution of (A) tributary number 8 for the year 2018 and (B) tributary number 15 for the year 2018 Click here to view Figure

Table 9: 1H-UH for 16 Tributaries (GIUH-Nash Model)

Time	Small Streams
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
0	0.0	0.0	0.00	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
1	8.0	19.0	22.00	69.0	24.5	29.0	21.5	19.0	26.3	38.0	27.9	21.2	31.4	31.4	47.3	22.3
2	48.0	55.0	54.00	45.7	6.7	13.5	50.8	69.9	23.2	46.5	8.0	0.4	13.5	3.6	48.9	13.7
3	98.0	66.0	61.00	11.2	0.6	2.3	49.0	107.0	7.6	21.9	0.8	0.0	2.0	0.1	19.2	3.0
4	113.0	57.0	47.00	1.9	0.0	0.3	33.8	117.0	1.8	7.3	0.1		0.2	0.0	5.3	0.5
5	93.0	41.0	30.00	0.3		0.0	19.5	107.2	0.3	2.0	0.0		0.0		1.2	0.1
6	63.0	26.5	18.00	0.0			10.1	88.0	0.1	0.5					0.3	0.0
7	37.0	16.0	9.50				4.9	67.0	0.0	0.1					0.0
8	19.0	9.0	5.00				2.2	48.5		0.0
9	9.5	5.0	2.50				1.0	33.6
10	4.5	2.7	1.00				0.4	22.6
11	2.0	1.4	0.50				0.2	14.8
12	0.8	0.7	0.25				0.0	9.5
13	0.4	0.4	0.13					6.0
14	0.2	0.2	0.00					3.7
15	0.1	0.1						2.3
16	0.0	0.0						1.4
17								0.9
18								0.5
19								0.3
20								0.2
21								0.0