Analysis of geo-morphometric and topo-hydrological indices using COP-DEM: a case study of Betwa River Basin, Central India

ABSTRACT

The open source 30 m Copernicus DEM (COP-DEM)   has been used to derive the geo-morphometric and topo-hydrological characteristics of Betwa River Basin. Drainage network with 7^th order stream and mostly dendritic pattern has been delineated using the Strahler’s method. The drainage density, stream frequency, form factor, length of overland flow and circulatory ratio of the basin were computed as 0.38 Km/Km², 0.08 Km⁻², 0.23, 1.31, and 0.20, respectively. These outcomes suggest less available surface flow, lesser relative relief, poor drainage network, and nearly elongated shape of the basin. The mean bifurcation ratio for entire basin was calculated as 4.0 that signifies gradient dependent drainage network of the basin. The ruggedness number was computed as 0.24, which reflects the geology dominated (granite–gneiss) rocky and undulated topography of the basin. The dissection index ranges from 0.06 to 0.3, which implies less degree of dissection and mature stage of the basin. The topographic wetness index (TWI), stream power index (SPI), terrain ruggedness index (TRI), and sediment transport index (STI) ranges from 3.13 to 26.35; 0 to 6; 0 to 30; and 0 to 121.4, respectively. It implies that the lower basin is less susceptible towards erosion as compared to upper basin.

KEYWORDS:

• Copernicus DEM
• geo-morphometric parameters
• topo-hydrological indices
• Betwa River Basin
• coefficient of line correspondence (CLC)

1. Introduction

The river basins of semi-arid and arid regions, where surface water is scarce and in some places completely unavailable, are facing more severe challenges as compare to other regions of the world (Dubey et al., 2020; Sreedevi et al., 2013). Over exploitation of water resources in semi-arid and arid basins aggravate the water availability in the basins and alter the river flows and sediment load which in turn affects the morphology of that basin (Desai et al., 2021; Singh et al., 2021; Sreedevi et al., 2013). The relationships of different hydro-meteorological phenomena with the physiographic features of the drainage basins have been extensively studied by researchers (Bryndal et al., 2020; Kanhaiya et al., 2018, 2019; Magesh et al., 2013; Obeidat et al., 2021; Singh, Kanhaiya, et al., 2019; Rai et al., 2017; Singh, Kanhaiya et al., 2019). Quantification of geo-morphometric parameters such as basin area, perimeter, length, stream order, bifurcation ratio, stream length, stream frequency, drainage density, elongation ratio, circularity ratio, form factor ratio, texture ratio etc. of any basin gives detail about the geological, physiological, and hydrological dynamics of a basin (Shreve, 1966; Sreedevi et al., 2013; Singh & Kanhaiya, 2015; Prakash et al., 2017; Kumar et al.,; Singh, Kanhaiya et al., 2019; Kanhaiya et al., 2019; Kumar & Singh, 2021a; Kumar et al., 2021b). The hydro-morphological aspects of basins have also been investigated widely by assessing the topo-hydrological parameters viz. Topographic Wetness Index (TWI); Stream Power Index (SPI); Terrain Roughness Index (TRI) and Sediment Transport Index (STI) etc. (Alilou et al., 2019). Both, the geo-morphometric and topo-hydrological analysis is essential to unearth the geological, physiological and hydrological characteristics of river basins and help in river basin management (Alilou et al., 2019). It also helps in identification of structural and tectonic events associated with the evolutionary processes of a basin (Resmi et al., 2019). Nowadays, digital elevation models (DEM; Burrough et al., 2015; Lakshmi & Yarrakula, 2018; Polidori & El Hage, 2020) in conjunction with geospatial techniques (Smith & Clark, 2005) are being widely used by the researchers for various scientific analysis including studies pertinent to the topography, geomorphology, hydrology, tectonic activities, morphometric analysis, and so on (Dubey et al., 2015; Banerjee et al., 2017; Singh, Kanhaiya et al., 2019; Kumar et al., 2021b; Jothimani et al., 2021). Details of open source and commercial DEMs are outlined in Table 1.

Table 1. Details of open source and commercial DEMs.

	Dataset	Coverage	Sensor/Satellite	Resolution (m)	Vertical Accuracy using GPS ground-control points	Reference
Open Source/Classified	ALOS AW3D30	82^°S-82^°N	Optical	30	4.4m(RSME)	Tadono et al. (2014), Eorc (2021)
	ASTER GDEM	83^°S-83^°N	Optical	30	17m (95% conf.)	Tachikawa et al. (2011); Abrams et al. (2020)
	Bare Earth DEM	56^°S-60^°N	SRTM	90	5.9m (RMSE)	O’Loughlin et al. (2016)
	EarthEnv	60^°S-83^°N	ASTER & SRTM	90	4.15m (RMSE)	Robinson et al. (2014)
	GMTED2010	worldwide coverage	SRTM & 10 Others Sources	250,500 & 1000	26m (RSME)	Danielson and Gesch (2011)
	MERIT	worldwide coverage	AW3D30, SRTM & Viewfinder Panorama	90	5m (LE90)	Yamazaki et al. (2017)
	SRTM	60^°N-56^°S	SAR C-Band	30 & 90	6m(MAE)	Farr et al. (2007)
	TanDEM-X	worldwide coverage	SAR X-Band	30 & 90	3.10m to 13.11 m (RSME) by Vaka et al. (2019)	Rizzoli et al. (2017); Hawker et al. (2019); Zink et al. (2021)
	Viewfinder Panorama	worldwide coverage	ASTER,SRTM & Other sources	90	-	De Ferranti (2014)
	Carto DEM	Indiansubcontinent	Optical	30	8 m (LE90)	Muralikrishnan et al. (2013); Bhardwaj (2019)
	NASADEM	60^°N-56^°S	SAR C-band	30	Reported between 5 m to 7.5 m (RSME) by Vaka et al. (2019)	Buckley et al. (2020)
	Copernicus DEM	worldwide coverage	TanDEM-X and World DEM^TM	30 & 90	< 4m(LE90)	Leister-Taylor et al. (2020); Fahrland et al. (2020)
Classified/ Commercial Global DEMs	ALOS AW3D	82^°S-82^°N	Optical	5	2.7m (RMSE)	Takaku et al. (2014)
	PlanetDEM 30 Plus	worldwide coverage	SRTM	30	Not Reported	Observer (2017)
	NEXTMap World 10	worldwide coverage	Not Reported	10	10m (LE95)	InterMap (2018)
	World DEM	worldwide coverage	Optical	12	<1.4m (RMSE)	Rizzoli et al. (2017)

Majority of the recent DEM based studies have been performed using Shuttle Radar Topography Mission (SRTM) DEMs (Guth, 2011; Singh et al., 2020; Patel et al., 2022), DEM generated from topographic contours (TOPO) DEMs (Chopra et al., 2005; Prasannakumar et al., 2013), Cartosat DEMs (Pandule, 2019; Sharma & Mahajan, 2020; Yadav et al., 2014 Yadav et al., 2018 Yadav et al., 2020) and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) DEMs (Farhan, 2017; Sujatha et al., 2015), Advanced Land Observation System (ALOS) DEMs (Caglar et al., 2018; Tesema, 2021). Recently, an improved DEM data product namely Copernicus DEM GLO-30 has been released by the European Space Agency (ESA) for the academic, scien2017tific research and civil applications. As per ESA, improvements such as flattening of water bodies with assured hydrological consistency and editing of other man made special features and implausible structures gives Copernicus DEM GLO-30 an edge over other DEMs.

In accordance with the recent progresses and researches as detailed above the present study aims to extract geo-morphometric and topo-hydrological characteristics of BRB using Copernicus DEM GLO-30 and geospatial techniques as an maiden attempt. It is a maiden attempt to explore the geo-morphometric characteristics together with topo-hydrological aspects of BRB using fine resolution (30 meter) Copernicus DEM GLO-30. Being located in the semi arid to humid subtropical region of Central India, BRB has also experienced considerable change over the years (Singh et al., 2022 Kumar et al., 2017; Singh & Sharma, 2022). It covers major portion of India’s water scarce Bundelkhand region within its diverse geological, hydrological, and physiographic setups. Recently, Government of India has announced interlinking of Ken River with Betwa River to bring the “surplus” waters of Ken river basin into water “deficit” Betwa river basin, under the national river interlinking project namely Ken-Betwa Link Project (KBLP; Avtar et al., 2010). Hence, this study will be a reference work in future for analyzing and monitoring the landform changes in the basin after completion of the proposed river interlinking project (KBLP). Further the study will signify the suitability and potentials of Copernicus DEM GLO-30 as an alternative DEM for studying topo-hydrological and geo-morphometric characteristics of drainage basins. This study will also prove to be vital for the better management, planning, decision making, and conservation of the basin as well as for future strategies to be implemented in the BRB.

2. Study area

The Betwa River Basin (BRB), a sub-basin of the Yamuna River Basin, is situated between longitudes 23°5′ to 25°55′E and latitudes 77°15′ to 79°45′N in Central India (Figure 1). The strike ridges of Vindhyan hills and Malwa plateau along the south and southwest margin of Betwa River Basin separates it from Narmada valley. The ravines of Chambal-Sindh and basin area of Ken River reside to the west and east margins of the BRB respectively. Betwa River, a major cratonic tributary of Yamuna River, is main stream of the BRB. Betwa River rises at an elevation of about 576 m above mean sea level (a.m.s.l.) from Jhiri perennial spring at the foot of Dhondi Dant hills (Vindhyan Range) near Barkhera village in Raisen district of Madhya Pradesh, India. It flows in SW to NE direction for 590 Km to join river Yamuna at the village Merapur Daria (about 106 m a.m.s.l.) in Hamirpur district of Uttar Pradesh, India. The major sub tributaries that join the Betwa River in the BRB are Kaliasot, Halali, Sagar, and Bina in upstream, Narain, Orr, and Jamni in midstream, and Dhasan, and Birma in downstream. It drains a total catchment area of about 43,346.11 km² between the two states viz. Madhya Pradesh (68.84% of the total area) and Uttar Pradesh (32.16% of the total area). The Basin has an average population density of 295.9 people per kilometer with a total population of 20.20 million people (Ahlawat, 2010; Chandramouli, 2011). Majority of the population living in the basin is agrarian, rural poor, economically deprived, and prone to nature induced distresses like frequent drought (Pandey et al., 2008; Singh & Sharma, 2022) and disastrous floods (Avtar et al., 2010).The basin receives average annual rainfall of about 918 mm, mostly (80%) from south-west monsoon system (Chaube et al., 2011). More rainfall occurs in the upper and middle portion of the basin as compare to the lower portion of the basin (Singhai et al., 2019). Basin is also characterized by average minimum and maximum temperatures of 06.7°C (mild winter) and 44.2°C (hot summer) respectively (Suryavanshi et al., 2014). The National Bureau of Soil Survey and Land Use Planning (NBSSLUP), Nagpur, India, has identified major soil types in the basin as clay, silty clay, clay loam and sandy loam soil (Suryavanshi et al., 2017). The basin is pervaded by extremely jagged, rocky and undulating surface topography, having dispersed elongated hills, steep forest-covered hills, scattered bushes, flat plateaus, and parallel linear ridges with land slopes varying from 0 degree to 57 degree.

Figure 1. The location map of Betwa River Basin, India is showing topographic variability, river network with gauge stations and major cities.

3. Geology

Geologically, the basin is underlain with the litho-assemblages of various age groups from Archaean to Quaternary period. The geological map of the basin (Figure 2) is based on the geological data of BRB obtained from the Bhukosh (https://bhukosh.gsi.gov.in/Bhukosh/Public) gateway of Geological Survey of India (GSI). The Deccan trap (66 million years), the Vindhyan Supergroup (1.4–0.9 billion years), the Bijawar group (2.6–2.4 billion years) and Bundelkhand complex (older than 2.6 billion years) are the major group of rocks with high uncertain ages that collectively underlain the Betwa River basin (Venkatesh & Anshumali, 2019). The basaltic rocks of Deccan trap extends over 42% area basically in upper portion of the basin; Bundelkhand massif covers 41% area basically in upper and middle parts of the basin; Alluvial plain envelopes 9% area in lower regions of the basin; Vindhyan Supergroup occupies about 6% basin area and Bijawar Group is extended over 2% area of the BRB. Vindhyan Supergroup in BRB includes rocks of Bhander group, Kaimur group, Rewa group, and Semri group.

Figure 2. Stratigraphic horizons of the Betwa River Basin, India.

Betwa river and its tributaries in the basin drain basically through the terrains comprises of coarse, medium and fine grained granite, porphyritic granite, basalt, sandstone, shale, silt, and clay with kankar, red quartizofelpathic, sand and grey micaceous sand, alluvium, laterite, limestone, dolomite, dolerite, amphibolites, migmatite, calc-silicate rocks, granitoids, granite gneisses, syenites, tonalite–trondhjemite–granodiorite (TTG), basaltic metasediments, quartz veins, and other terrigenous sediments and rocks (Malviya et al., 2006; Pati et al., 2007). Major portion of the basin is underlined by granite followed by basalt, sandstone, and alluvium respectively. These terrains have relatively low primary porosity and permeability except alluvium; hence does not permit sufficient groundwater recharge that produce ground water scarcity in different parts of the basin. There are small patches of alluvium or highly fractured/ jointed rocks which stores and provides water for drinking and irrigation purposes.

4. Materials and methods

In the present study, an integrated approach of using Topographical maps and Digital Elevation Model (DEM) for quantifying different drainage dimensions have been employed. Copernicus DEM with spatial resolution 30 m (Table 3) and Survey of India’s (SOI) toposheets with scale of 1:50,000 have been used in a geo-processing framework to build database, extraction of drainage parameters and generation of thematic maps. Table 4, Shows details of the data sets used in present study. The steps and procedures opted for this study has been shown in Figure 3.

Figure 3. The flowchart of methodology is showing the steps and procedures employed in the study.

Table 2. Formulae and methods applied for computing geo-morphometric parameters of Betwa River Basin.

Sr. No.	Name and notation of parameters	Formulae/Methods	Units	References
(A) Basic aspects
1	Total Basin area	Total area enclosed by basin boundary	Km^2	(Schumm 1956)
2	Total Basin perimeter	Length of horizontal projection of basin water divide	Km	Schumm (1956)
3	Basin length	Straight line distance from basin’s mouth point to its outlet point	Km	Horton (1932)
(B) Linear Aspects
1	Stream order (μ)	Hierarchy based ranking of streams.	Dimensionless	Strahler (1952a)
2	Stream number (Nμ)	Nμ = Nμ1+ Nμ2+ Nμ3+ … … Nμn	Dimensionless	Horton (1945)
3	Stream Length (Lμ)	Length of the stream. Lμ = Lμ1+ Lμ2+ Lμ3+ … … Lμn	Km	Horton (1945)
4	Mean stream length (Lsm)	Average of stream length of all orders. Lsm = Lμ/Nμ; Where, Lμ represents mean stream length of a given order and Nμ denotes stream segment number	Km	Horton (1945)
5	Bifurcation Ratio (Rb)	Rb = Nμ/Nμ +1 Where, Nμ denotes number of stream segments, present in the given order and Nμ+1 implies number of segments of the next higher order	Dimensionless	Schumm (1956)
6	Stream length ratio (RL)	RL = Lμ/Lμ-1 Where, Lμ stands for total stream length of order (μ), and Lμ-1 indicates the total stream length of its next lower order	Dimensionless	Horton (1945)
7	Hydrological storage coefficient (Rho)	Rho = RL/Rb Where, RL denotes stream length ratio and Rb refers to bifurcation ratio	Dimensionless	Horton (1945)
7	Sinuosity Index (SI)	SI = AL/EL Where, AL represents actual length of stream and EL stands for expected straight path of the stream	Dimensionless	Schumm (1956)
(C) Areal Aspects
8	Stream frequency (Fs)	Fs = N/A Where, N stands for total number of streams and A symbolize area of basin	Km^−2	(Horton 1945)
9	Drainage density (Dd)	Dd = L/A Where, L denotes total length of stream and A indicates area of basin.	Km^−1	(Horton 1945)
10	Texture ratio (T)	T = N1/P Where, N1 represents total number of first order stream and P denotes perimeter of basin.	Km^−1	(Horton 1945)
12	Elongation ratio (Re)	Re = √(Au/π)/ Lb Where, A indicates area of basin, Lb represents basin length and π value equals to 3.14,	Dimensionless	Schumm (1956)
11	Form factor (Rf)	Rf = A/(Lb)^2 Where, A implies area of basin and Lb stands for basin length	Dimensionless	Horton (1945)
14	Length of overland flow (Lg)	Lg = 1/2Dd Where, Dd refers to drainage density	Km	Horton (1945)
13	Circulatory ratio (Rc)	Rc = 4πA/P^2 Where A denotes Area of basin, π value equals to 3.14 and P denotes perimeter of basin.	Dimensionless	Miller (1953)
15	Constant channel maintenance(C)	C = 1/Dd Where, Dd denotes drainage density	-	Horton (1945)
(D) Relief Aspects
16	Basin relief (R)	Vertical distance between the lowest and highest points of basin.	Km	Schumm (1956)
18	Ruggedness Number (Rn)	Rn = Bh×Dd Where, Bh refers to basin relief and Dd stands for drainage density	Dimensionless	Schumm (1956)
17	Relief Ratio (Rh)	Rh = Bh/Lb Where, Bh represents basin relief and Lb denotes basin length	Dimensionless	Schumm (1956)
19	Dissection index	Dis = R/Rh Where R denotes basin relief and Rh implies relief ratio	Dimensionless	Schumm (1956)
20	Hypsometric Curve	Area and elevation are plotted as functions of total area and total elevation of basin in horizontal axis and vertical axis.	-	Strahler (1964)

Table 3. Major specifications of Copernicus DEM.

Specifications	Copernicus DEM GLO 30
Acquisition technique	RADAR
Data format	GeoTIFF
Horizontal Reference Datum	WGS84-G1150 (EPSG 4326)
Vertical Datum	EGM2008 (EPSG 3855)
Spatial resolution	30 m
Projection system	Geographic Coordinates
Absolute horizontal accuracy (CE90)	Less than 4 m
Absolute vertical accuracy (LE90)	Less than 6 m
Relative vertical accuracy for slopes at or below 20%	Less than 2 m
Relative vertical accuracy for slopes above 20%	Less than 4 m

Table 4. Details of SOI toposheets and DEM used in the study.

Sr. no.	Topo sheet numbers/DEM tiles numbers	Source	Scale/Resolution	Website
1	54E/3, 54 H/15, 54 H/16, 54 K/4, 54 K/8, 54 K/10, 54 K/11, 54 K/12, 54 K/13, 54 K/14, 54 L/2, 54 L/4, 54 L/5, 54 L/6, 54 L/8, 54 L/9, 54 L/11, 54 L/12, 54 L/13, 54 L/16, 54 L/2, 54O/1, 54O/2, 54O/5, 54O/6, 54P/2, 54P/4, 54P/5, 54Q/3, 54Q/4, 54Q/7, 54Q/8, 55E/2,55E/3, 55E/4, 55E/5, 55E/6, 55E/7, 55E/9, 55E/10, 55E/11, 55E/12, 55E/13, 55E/14, 55E/15, 55E/16, 55 F/1, 55 F/5, 55 F/9, 55 F/13, 55I/1,55I/2, 55I/3, 55I/4, 55I/5, 55I/6, 55I/7, 55I/8, 55I/9 & 55I/10	Survey of India (SOI), Dehradun, India	1:50,000	https://surveyofindia.gov.in/
2	N22/E077,N23/E077,N23/E078,N24/E078,N24/E079,N25/E077,N25/E078,N25/E079,N25/E080,N26/E079 & N26/E080	European Space Agency (Copernicus DEM)	1 ARC (30 m)	https://panda.copernicus.eu/web/cds-catalogue/panda

Geocoding of SOI toposheets have been done by geometrically rectifying and geo-referencing each of them using ground control points (GCPs) and projection system Universal Transverse Mercator (UTM), Zone 43, datum World Geodetic System (WGS) 1984 in Arc GIS software. The Drainage network of the basin has been derived by defining threshold values during each the steps viz. pits or sinks fill, flow direction, and accumulation, stream order extraction, and drainage network delineation. Appropriate threshold values determine the level of pairing between actual ground based drainage network and drainage network extracted from DEM (Arulbalaji & Padmalal, 2020). A larger threshold value will provide sparse drainage network and vice versa (Anish et al., 2021). The sinks have been filled to eliminate drainage network discontinuity by the higher values of surrounding elevations. Eight-direction flow model has been used on the filled DEM for deriving flow direction from each pixel (Fairfield & Leymarie, 1991). Further, flow direction was used for generating drainage system by taking the pixels having a threshold value of more than 100 into consideration using a trial-and-error approach (Mark, 1983). The boundary polygon of Betwa River basin was extracted from Copernicus DEM and SOI toposheets using pour point (Magesh et al., 2013). The cross verification of Copernicus DEM based drainage system was performed using a mosaiced map derived from the geocoded toposheets of SOI. The stream network present in toposheet has been validated with the extracted stream network from Copernicus DEM by visually as well as using Coefficient of Line Correspondence (CLC) analysis method (Stanislawski et al., 2015). CLC automatically differentiates matching and non matching linear features from two separate drainage networks. The CLC value ranges from 0 to 1 where zero denotes no match between features and 1 represents perfect match between features. The expression of CLC is as follows (Equation. 1)(1) $\mathrm{CLC}=\mathrm{\Sigma }\left(\mathrm{Lm}/\mathrm{La}\right)$(1) :

(1) $\mathrm{CLC}=\mathrm{\Sigma }\left(\mathrm{Lm}/\mathrm{La}\right)$(1)

Where, Lm denotes the sum of the length of the matching lines and La represents the sum of the length of all lines in both datasets.

Only matching stream networks of both datasets were taken for the study. The unmatched extracted stream networks were reprocessed again and again by altering the threshold values until the acceptable result obtained (Harsha et al., 2020). The assessment of geo-morphometric and topo-hydrological parameters of the BRB have been quantified using well established formulae and methods mentioned in Table 21.

5. Results and discussion

In this study, COP-DEM with 30 m pixel size has been used for deriving the geo-morphometric and topo-hydrological attributes of the BRB. The drainage basin parameters such as basin size, slope, shape, drainage density, and stream length etc. of the basin have been computed using ArcGIS software. The CLC method based drainage delineation accuracy was calculated as 0.92, which denotes high match between extracted drainage networks with delineated drainage networks. Total 3522 numbers of streams of all orders mostly with NE and SW orientation has been calculated in the basin. An inverse relation has been observed between stream number (Nμ) and increasing order of the streams (μ). The 1^st order streams shares about 80% of the total streams and number of successive higher-order streams from the 2^nd order to 7^th order decreases with inconsistency and abruptly. Higher number of streams in 1^st order especially in the upper reaches of the basin reflects semi-permeable lithology and low infiltration rate of the terrain. The river basins are natural, unique, hydrologically self-contained, and fundamental entities of the water resource planning and management (Moore et al., 1991). They are very sensitive and dynamic component of the fluvial landscape that naturally keeps changing their state (Brunsden, 2001; Fryirs, 2017). Hence, an assessment of both geo-morphometric and topo-hydrological parameters of a drainage basin gives essential information about three-dimensional geometry of the basin, which helps in planning and management of that basin (Bryndal et al., 2020; Rajasekhar et al., 2020). The COP-DEM based basic morphometric parameters of the basin viz. elevation, relative relief ,slope and aspect has been shown in Figure 4. The results of the linear, areal and relief aspects of present study are as follows.

Figure 4. Showing (a) Elevation map, (b) Relative relief map, (c) Slope map, and (d) Aspect map.

5.1. Linear morphometric parameters

A linear aspect reflects details about one-dimensional morphometric parameter such as stream order, stream number, stream length, bifurcation ratio, and sinuosity index etc. It indicates topological characteristics of the stream segments and channel patterns of the drainage system. Linear aspects of a drainage basin exhibit spatio-temporal variations, hence influences hydrological behavior of a basin (Soni, 2017). The result of linear morphometric parameters are given in the Table 5.

Table 5. Results of linear geo-morphometric parameters.

Parameters	Stream order (μ)							Mean	Standard deviation (SD)	Co-efficient of variation (CV)
	1^st	2^nd	3^rd	4^th	5^th	6^th	7^th
Number of the streams (Nμ)	2766	598	122	28	5	2	1	503.14	1020.78	202.88
Total stream number of all orders (ΣNμ)	3522	-	-	-	-	-	-	-	-	-
Order-wise total stream length in Km (Lμ)	8182.59	4353.80	1909.24	972.65	767.92	183.08	124.00	2356.18	2951.81	125.28
Total streams length of all order in Km (ΣLμ)	16,493.28	-	-	-	-	-	-	-	-	-
Order wise mean streams length in Km (Lμ)	2.95828	7.2806	15.65	34.74	153.58	91.54	124.00	61.39	61.20	99.69
Bifurcation ratio (Rb)	-	4.63	4.90	4.36	5.6	2.5	2	4.00	1.42	35.63
Stream length ratio (RL)	-	0.53	0.44	0.51	0.79	0.24	0.68	0.53	0.19	36.02
Hydrological storage coefficient (Rho)	-	0.12	0.09	0.12	0.14	0.10	0.34	0.15	0.09	63.24
Sinuosity index	1.53	-	-	-	-	-	-	-	-	-

5.1.1. Stream order (μ)

The first step towards drainage basin analysis is stream ordering. It is a measure of stream branching extent in a basin. Stream ordering is performed by designating a rank to a stream in the hierarchy of tributaries (Leopold et al., 2020). It provides an idea about the size of drainage basin and approximate index of stream flow. The stream order is generally controlled by the tectonic and physiographic set-up of the basins (Yadav et al., 2018; Kanhaiya et al., 2019). The smallest, fingertip stream that has no tributaries are designated as first-order streams; the confluence of two first-order streams forms a second-order stream and so on. Therefore, with the increase of stream order, decrease in number of stream is obvious. The order and size of the streams in a basin generally depends on its physiographic and structural terrain properties (Haghipour & Burg, 2014). Our analysis shows that BRB is a seventh-order drainage basin with 78.53% and 16.98% streams of first and second-order respectively (Figure 5). Venkatesh and Anshumali (2019) have used SRTM-DEM with 90 m pixels for morphometric analysis of BRB and reported it as sixth-order drainage basin. The stream order difference can be attributed to the fine resolution of COP-DEM used for the study. The drainage pattern of the BRB is mostly sub-dendritic to rectilinear in nature, which represents the plateau–plain sub-humid environment and reflects terrain gradient based river channels of the basin (Wakode et al., 2013). The numbers of higher order streams (4^th, 5^th, 6^th order) in the basin are less in number due to dominance of alluvial plain course in lower reaches.

Figure 5. Map showing different stream orders of Betwa River Basin.

5.1.2. Stream number (Nμ)

The order wise cumulative measurement of stream segment gives stream number (Yadav et al., 2014). It signifies hydrological character of a basin especially factors like surface runoff. Stream number provides substantial information about the surface runoff features i.e., a higher number of first-order streams indicate higher permeability and erodible topography. According to Horton (1945), stream number shows reciprocal geometric sequence with the order unit, i.e., with increase in stream order the stream number decreases. The streams in the BRB are supporting the Horton’s principle and total number of streams computed in the study area is 3522. Higher number of headwater streams indicates highly erodible topography with erosional landform in upper reaches and affects surface runoff characteristics in lower reaches of basin (Singh & Awasthi, 2011). Figure 6 depicting inverse relation between stream order and stream number of BRB.

Figure 6. Graph showing number of stream, mean stream length, bifurcation ratio, and hydrological storage coefficient with respect to the stream order in the basin.

5.1.3. Stream length (Lμ)

Stream length is the total length of a stream measured from its genesis upto its outlet and depicts development stages of successive stream segments (Allan et al., 2020). It expresses the hydrological characteristics such as surface runoff and sediment properties as well as contributing area of a basin (Magesh et al., 2011). Generally, 1^st order streams have higher combined stream length and better distribution than that of next higher orders (Rai et al., 2018). Such type of stream arrangement represents the chronological evolution of the rivers. The shorter stream lengths indicate areas with larger slopes and finer textures whereas longer stream lengths are normally indicative of flatter gradient. The number of streams in different order in the basin was counted along with their lengths measurement from origin to drainage divide. The calculated stream length for each stream order is listed in Table 5. The result shows that the 5^th and 7^th order streams have relatively longer length of 153.58 Km and 124.00 Km respectively than their lower order streams. It was unexpected outcome and probably corresponds to the unique geophysical characteristics of the BRB. The cumulative length of all order streams in the basin is 16,493.279 Km. The first order stream which shares half of the total stream length of the BRB is ephemeral in dry season and perennial during rest of the seasons. The perennial length of first order stream in BRB decreases during dry seasons especially in upstream regions of the basin. The higher mean stream length (153.58 km) of 5^th order streams indicates comparatively higher hydraulic conductivity by this order of streams than the streams of other orders in the basin. Further, slightly steeper slope of hilly regions in upper middle reaches of the basin have produced shorter stream length while low slope in lower reaches have generated longer stream length in the basin.

5.1.4. Stream length ratio (R_L)

The stream length ratio denotes ratio between total stream lengths of a particular order and total stream length of its subsequent previous order (Horton, 1945). Stream length ratio, to extent, corresponds to the hydrological characteristics of a basin (Kabite & Gessesse, 2018). Variation of stream length ratio between successive orders of stream corresponds to the differences in topographic and slope characteristics of the basin and hence relates with surface flow discharge and different stages of erosion in the basin (Horton, 1945; Magesh & Chandrasekar, 2014). An increasing trend in stream length ratio from lower order to higher orders depicts attainment of geomorphic maturity (Thomas et al., 2010) while a deviation in trend corresponds to the delayed youth stage of stream’s geomorphic development (Sreedevi et al., 2009). The highest stream length ratio belongs to 5^th order stream (0.79) whereas the lowest is of 6^th order (0.24; Table 5).

The inconsistencies in stream length ratio between successive stream orders represent uneven topography and spatial variation in infiltration rate in the basin. The calculated stream length ratio values of BRB are indicative of its mature geomorphic developments and low water regimes. The relatively higher stream length ratio of lowest order streams correspond the areas with low permeable formations basically the upper and middle regions of BRB.

5.1.5. Mean stream length ratio (L_sm)

The mean stream length represents the drainage network characteristics and properties with respect to basin surface features (Horton, 1945; Strahler, 1964). It has been derived by dividing the sum of calculated stream lengths ratios by total of stream segment number. The computed mean stream length ratio of BRB is 0.531. Generally, lower mean stream length ratio value corresponds to mountain environment and plateau or plain morphology is associated with higher value of mean stream length ratio (Rai et al., 2017). Normally, with the increase in streams order, the mean stream length also increases (Shrestha et al., 2017) but in this study, mean stream length depicts anomalies with respect to increasing order of streams. The higher value of mean stream length of 5^th order streams in BRB represents that the streams of this order have continued their channel lengthening processes while successive order streams have aborted their channel lengthening. These abnormalities in mean stream length of BRB, corresponds to the variations in terrain gradient, uneven topography, coarse drainage pattern, and mature stages of geological developments of the basin. It has also brought discrepancies in stream length ratio and affects surface runoff characteristics of the basin.

5.1.6. Bifurcation ratio (R_b)

Bifurcation ratio is highly linked with the stream segmentation pattern and degree of stream distribution within the drainage network, hence signifies the hydro-morphological characteristics of a river basin. Bifurcation ratio in a drainage system is a proportion of the total numbers of stream segments of a specified order to the total number of stream of the subsequent higher order (Schumm, 1956). It reflects the level of integration among tributaries of various stream orders in a basin. Normally the bifurcation ratio value varies between 2 to 5 (Joji et al., 2013). Chow (1964) stated that the bifurcation ratio values ranges from 3 to 5 reflect independency of drainage pattern from the basin’s geologic structures. Low mean bifurcation ratio values denote well-dissected, elongated drainage basins having high overland flow, high infiltration rate, high structural complexity, extended peak of discharge, and less chances of soil erosion and flood risk (Strahler, 1957; Thomas et al., 2010). The high mean values of bifurcation ratio imply circular drainage system with low infiltration rate, sharp peak flow, less groundwater recharge, higher chances of soil erosion, and flood risk (Reddy et al., 2004). Bifurcation ratio values (Table 5) in BRB shows significant variation from 2 to 5.6, for different stream orders depicting it as a natural drainage system with dendritic drainage pattern (Joji et al., 2013). The higher bifurcation ratio between 1^st and 2^nd order streams than their successive higher orders represents accelerated state of erosion due to higher overland flow. The higher values of bifurcation ratio represent mature topographic regions of BRB while lower values imply plans regions of the basin (Magesh & Chandrasekar, 2014). The computed value of mean bifurcation ratio of entire BRB is 4.0. The result also signifies that the drainage network pattern in the basin is more or less gradient dependent rather than structurally controlled (Chow, 1964). The higher number of first-order streams and low bifurcation ratio in the BRB reflects its semi-elongated shape (Choudhari et al., 2018; Magesh et al., 2012). The low bifurcation ratio values between 5^th to 6^th and 6^th to 7^th order streams depicts the lower reaches of the basin having less number of streams of these orders under water stressed conditions. The higher bifurcation ratio values between 4^th to 5^th order streams in BRB indicate variation of terrain gradient and collection of bounteous water in upper basin area. The low mean bifurcation ratio of the BRB indicates that the Betwa drainage system is slope dependent with low water carrying capacity, low flood susceptibility and high water scarcity.

5.1.7. Sinuosity index (SI)

Sinuosity index or meander ratio is a factor which explains deviation of a river form its expected straight path (Schumm, 1956). It is calculated as proportion of the straight distance measured between the end points against actual length by the side of river meandering. Sinuosity index of a straight river will be 01. The sinuosity index value from 1 to 1.5 represents the river course as sinuous and sinuosity index value from 1.5 to 4 denotes river course as meandering (Leopold & Wolman, 1957). In this study, the calculated sinuosity index for the highest order of stream i.e., 7^th order stream was 1.53. Hence, the stream course is basically in between sinuous and meandering typology.

5.1.8. Hydrological storage coefficient (Rho)

The hydrological storage coefficient or “Rho” coefficient (ρ) reflects storage potential of the drainage system (Horton, 1945). It correspond degree of drainage development with respect to the physiographic growth of the basin. The ratio of stream length to the bifurcation ratio is defined as “Rho” coefficient and it is influenced by geological, climatic, geo-morphological, and biological factors of the basin (Horton, 1945). Mean “Rho” coefficient of BRB is 0.15 which signifies that the basin has lower hydrological storage capacity.

5.2. Areal Aspects of River Basin Morphometry

Areal aspects deals with two-dimensional quantitative morphometric parameters such as basin area and shape, drainage texture, elongation ratio, circularity ratio, drainage density, stream frequency, and form factor. These factors more or less depend on the lithology and hydro-geomorphic conditions of the basins and relates with overland flow in different stream orders (Veeranna et al., 2017). Basin area implies a horizontal plane enclosed within water divides or ridgelines and encompasses streams of all orders of a basin, flowing to a common outlet. Discharge per unit area inversely relates with the size of the basin (Chorley, 1957). Perimeter denotes length of entire boundary stretch of a Basin. It illustrates shape and size of a drainage system and influences parameters like elongation ratio and circulatory ratio. Table 6 shows that the computed basin length of the BRB is 437.93 Km. The total areal extension of the BRB is computed as 43,346.11 Km² while (the outer boundary of the BRB that encloses its area) is calculated as 1643.74 Km.

Table 6. Results of areal geo-morphometric parameters.

Parameters	Unit	Value
Basin area (A)	Km^2	43,346.11
Perimeter	Km	1643.74
Basin length	Km	437.93
Drainage density (Dd)	Km/Km^2	0.38
Stream frequency (Fs)	Km^2	0.08
Drainage texture (Dt)	Km^−1	0.03
Form factor (Ff)	-	0.23
Elongation ratio (Re)	-	0.61
Circularity ratio (Rc)	-	0.20
Length of overland flow (Lg)	Km^−1	1.31
Constant of channel maintenance (C)	Km^2/Km	2.63

5.2.1. Drainage density (Dd)

Drainage density (Dd) represents the ratio of cumulated length of streams of all orders within the basin to the total area of the drainage basin (; Horton, 1945). It is an expression of intricacy of stream arrangement in a drainage basin (Horton, 1932) and denoted in terms of Km/Km². Generally, drainage density value in humid region ranges between 0.55 to 2.09 Km/Km² (Joji et al., 2013). It is influenced by the climate, rock types, soil, terrain relief, permeability, runoff intensity, and vegetation cover of the basin (Bhat et al., 2019). Drainage density also reveals susceptibility of basins towards hydrological hazards, especially in areas where hydro-meteorological data are scared or absent (Obeidat et al., 2021). Generally, drainage density is categorize into four classes i.e., very high > 6 Km/Km², high 4–6 Km/Km², moderate 2–4 Km/Km², low < 2 Km/Km² (Gregory & Walling, 1968). Low drainage density value implies an area having coarse drainage texture, low relief, permeable sub-soil, compact vegetation cover, high infiltration capacity, less surface runoff, and higher potential of ground water whereas high drainage density values is characterized with fine drainage texture, elevated relief, impermeable sub-soil, peak runoff, low infiltration capacity, and sparse vegetation cover (Choudhari et al., 2018; Sahu et al., 2017). Drainage texture represents relative spacing of streams in a basin and depends on precipitation, soil type, vegetation, lithology, stage of development, and infiltration capacity . The underlying lithology and hard rock structure of BRB strongly influences the drainage network in the basin. The drainage density value of the basin is 0.38 Km/Km² which reflect presence of poor and coarse drainage texture, lower relief with variation in vegetation coverage and to some extent permeable subsoil in the basin (Figure 8a).

5.2.3. Stream frequency (Fs)

Stream frequency (Fs) of a basin represents the ratio between cumulative stream segment number irrespective of their orders and basin area (Horton, 1945). Generally, drainage density and stream frequency exhibit a positive correlation, although it is also possible to have different stream frequencies with same drainage density. The climatic conditions, rock and soil types, vegetation thickness, terrain relief, infiltration capacity, permeability, and other runoff processes of a basin play vital role in controlling stream frequency distribution (Bali et al., 2012). Low value of stream frequency represents flat terrain and high infiltration or penetrability of the basin surface (Farhan, 2017). Greater stream frequency value of a basin indicates faster runoff and risk of flooding. The calculated stream frequency value for the BRB is 0.08 per Km² (Figure 8b) which indicates poor drainage network, plateau–plain, semi-humid environment, low permeability of rock, lesser relative relief and less available surface flow (Bali et al., 2012; Thomas et al., 2010).

5.2.4. Drainage texture (Dt)

Drainage texture is the ratio of the total number of stream sections of all orders per unit perimeter of a basin (Horton, 1945). It describes relative arrangement of drainage network in a basin. Drainage network arrangement generally depends on climate, slope, soil type, vegetation, rainfall, lithology and infiltration capacity of the basin (Horton, 1945; Smith and Clark, 1950; Soni, 2017). The regions having soft rock unprotected by vegetation bear finer texture, while resistant rocks results coarse drainage texture (Fenta et al., 2017). Finer the texture higher will be the dissection and erosion. As per the drainage texture classification of Smith and Clark, (1950), drainage texture value less or equal to 02 Km⁻¹ represents very coarse texture, between 02 to 04 Km⁻¹ denotes coarse texture, between 04 to 06 Km⁻¹ implies moderate texture, between 06 to 08 Km⁻¹indicates fine texture and values greater than 08 Km⁻¹ shows ultra fine texture (Rai et al., 2018). The drainage texture value of BRB is 0.03 Km⁻¹ which is less than 02 Km⁻¹; hence the basin encompasses coarse drainage texture formed on basalt and granitic rocks spread in the form of mounds, ridges and plains having moderate degree of slopes (Figure 8d).

5.2.5. Form factor (Rf)

Form factor ratio is a dimensionless proportion between basin area and the square of the basin length (Horton, 1945). It indicates the flow intensity of a basin on a defined scale (Sreedevi et al., 2013). The form factor varies between zero to unity where value “0” indicates strongly elongated shape of basin and “1” suggests near-circular shape of basin. The form factor also depicts the runoff characteristics of a basin. Smaller form factor value with elongated basin shape will generate low runoff with long runoff duration whereas higher form factor value with circular basin, will produce high runoff for short duration leading floods (Bali et al., 2012). Elongated basin is generally associated with plateau–plain front where flood management is easier than that of circular basin of Mountain–plains front. The form factor value for a perfectly circular basin will always be less than the maximum threshold value of 0.7854 (Waikar & Nilawar, 2014). The estimated form factor value for the BRB is 0.23, which indicates elongated shape of the basin and slightly narrow rather than circular and thus it will generate low peak flow for longer duration.

5.2.6. Elongation ratio (Re)

Elongation ratio (Re) denotes the proportion of the diameter of a circle, whose area is identical with the area of the drainage basin to the maximum length of the basin (Schumm, 1956). Elongation ratio is dimensionless and represents the basin shape and hydrological characteristics. The value of elongation ratio generally ranges between “0” to “1” where zero depicts highly elongated basin shape and one represents highly circular shape of basin (Strahler, 1964). Generally, elongation ratio value near “1” is attained by the geo-morphologically controlled, sub-humid, mountainous, circular river basins (Magesh et al., 2013). Strahler (1964) classified elongation ratio values and associated basin shape as circular (0.9–0.10), oval (0.8–0.9), less elongated (0.7–0.8), elongated (0.5–0.7) and more elongated (< 0.5) whereas Kumar et al. (2015) have categorized elongation ratio value and related basin shape as circular (> 0.9), oval (0.9 to 0.8) and elongated (< 0.7). A circular basin is more vulnerable to flooding due to inflated runoff and short time of concentration than an elongated basin. The elongation ratio value of the BRB is 0.61 which infers that the basin have nearly elongated shape. Though, it is not entirely elongated but slightly elliptical in middle reaches due to the heterogeneous lithology in this portion of the basin. Elongation dominates upper and lower reaches of the basin. Elongation ratio also depicts that the basin have low terrain relief, gentle gradient with low peak discharge and plateau–plain front river basin.

5.2.7. Circulatory ratio (Rc)

Circularity ratio (Rc) is defined as dimensionless proportion of basin area with respect to a circle area having identical circumference to the basin perimeter (Miller, 1953; Pareta & Pareta, 2011; Strahler, 1964). The drainage density, stream frequency, geological structure, climatic conditions, relief, slope, land use/land cover etc. of any basin directly influences value of Circularity ratio. Miller (1953) had classified basin shape on the basis of circulatory ratio varies between 0 (highly elongated) to 1 (highly circular). High, medium and low, values of the circularity ratio represent the older, mature and younger stages of basin development respectively. Generally, river basin having mountainous origin tends to form circular basins (high value of circularity ratio). They used to have young morphological profile and generate peak discharge during high rainfall seasons. Contrary to that elongated basin are generally found in plateau–plains (low value of circularity ratio) representing mature morphological adjustment and low discharge properties of the basin (Shaikh et al., 2022; Thomas et al., 2010). The calculated circularity ratio value of BRB is 0.20, which indicates low discharge of runoff, less prone to floods because excess water takes long time to reach at basin outlet. The low circularity ratio of BRB indicates near elongated characteristics of the basin with early to late mature landforms showing active denudational process in basin.

5.2.8. Length of overland flow (Lg)

The length of overland flow (Lg) is horizontally projected non-channel length of flow path of water on the ground, before it gets concentrated into certain stream channels (Horton, 1945). Length of overland flow shows inverse relation with terrain gradient hence low relief results a higher overland flow and vice versa (Kumar et al., 2015). Infiltration (exfiltration) and percolation properties of basin soil, average slope of the channel and basin drainage density significantly affects length of overland flow (Schmid, 1997). Higher length of overland flow value, in a basin represents longer distance covered by the water before getting accumulated into the stream channels. The length of overland flow in BRB is computed as 1.31 Km⁻¹, which indicates low relief and rainfall has to add substantial amount of water to generate surface runoff in the region (Figure 7).

Figure 7. Map depicting length overland flow in Betwa River Basin.

5.2.9. Constant channel maintenance(C)

The reciprocal of drainage density is termed as Constant of channel maintenance (C; Schumm, 1956). It denotes the number of sq. unit of drainage area required to carry, maintain and develop one linear unit length of drainage channel and expressed in units of km²/km (Rekha et al., 2011). It informs about the infiltration and runoff characteristics of a basin. Dimensionally it is length and hence increases in magnitude with the increases in the scale of the landform unit. Higher constant of channel maintenance value represents the basin area dominated with lower order drainages, sparse vegetation cover, higher flood potentiality and young geo-morphological adjustment and vice-versa (Samal et al., 2015). The calculated constant channel maintenance of the BRB is 2.63 Km²/Km. It shows that on an average 2.63 Km² basin surface area are needed for the development and maintenance of one Km long linear stream channel. Constant channel maintenance value of the BRB characterizes basin as plateau–plain environment with moderate permeability, moderate gradient, low drainage density, moderate bare soil infiltration and moderate surface runoff.

5.3. Relief morphometric parameters

Relief is an important aspect of any drainage system. It denotes the difference of elevation between lowest and highest point in any region. It represents three-dimensional morphometric parameters like basin relief, ruggedness number, relief ratio, gradient ratio, slope, river profile, and hypsometric curve. Figure 8 (a-d) shows the drainage density, stream frequency, dissection index and drainage texture of the BRB.

5.3.1. Basin relief (R)

Basin relief reflects actual elevation difference from the highest point (divide ridge) of the basin surface to the lowest point (basin outlet) on common basin surface. It represents basin’s denudational characteristics and significantly influences the landforms development, development of drainage, permeability, surface and subsurface water flow, flood patterns, erosional properties, sediment amount that can be transported and erosional stages of any river basin (Raux et al., 2011). Basin relief maintains the drainage channel gradient and hence represents basin’s potential energy of the draining.

An increase in basin relief leads steeper slopes, higher stream gradients, high erosion, low infiltration, high runoff conditions, and less time of concentration thereby increase in flood peak (Patton & Baker, 1976). The highest elevation of the BRB is 717 m which corresponds basically to the upper hilly regions of the basin and the lowest is 86 m. The total relative relief of the whole BRB is 631 m (Table 7). The basin relief value of BRB indicates dissected and erosional landforms, moderate stream gradient, moderate runoff and geo-morphologically mature stages of the basin development (Rai et al., 2017).

Table 7. Results of relief aspects and respective unit.

Parameters	Unit	Value
Basin relief (R)	Meter	631
Relief ratio (Rr)	-	0.0014
Ruggedness number (Rn)	-	0.24
Dissection index	-	0.06 to 0.3

5.3.2. Relief ratio (Rh)

Relief ratio (Rh) denotes the dimensionless proportion of basin relief to the longest parallel length along the principle drainage channel towards the outlet (Schumm, 1956). It basically refracts the slope scenario of the basin which affects hydro-geomorphic characteristics of a basin (Rajasekhar et al., 2020). Higher value of relief ratio represents steeper slope, high basin discharges, faster runoff, greater erosive power and vice-versa. Generally, the value of relief ratio decreases with increase in the area and size of the basin. Mountainous river basins having circular basin shape, high basin relief and small basin area generates high value of relief ratio while low values of relief ratio are associated with the plateau river basin having ridges and mounds with moderate degree of slope (Thomas et al., 2010). The calculated relief ratio value of the BRB is 0.0014, which is very low and represents nearly elongated shape of the basin, moderate basin relief and maximum denudation stages of geomorphic developments (Table 7).

5.3.3. Ruggedness number (Rn)

Ruggedness number is calculated by multiplying drainage density with relative relief of basin. It is a dimensionless unit which depicts the structural complexity and unevenness of the terrain. High drainage density and high relative relief results high ruggedness number (Ansari et al., 2012). The Rn value depends on climate, slope, steepness, geology, geomorphology, vegetation cover, etc., of a region. It affects stream energy, surface storage capacity, runoff velocity, and routing at the basin scale. High Rn reflects extremely uneven topography, increased peak discharge, primary stage of denudation activities and vice-versa (Ozdemir & Bird, 2009). Mountainous basins have usually higher ruggedness number value than that of plateau river basin. The calculated Rn value for BRB is 0.24, which indicates maximum denudation and mature stages of the basin (Table 7). It is also characterized by the granite–gneiss dominated geology and rolling plateau fringe landforms.

5.3.4. Dissection index (Dis)

Dissection index of any physiographic region attributes phases of its landform development, degree of vertical erosion and magnitude of terrain dissection in the region (Schumm, 1956). The proportion of maximum relative relief to the maximum absolute relief of the basin gives dissection index. It represents ratio of actual dissection created by the rivers to the potential dissection up to base levels. Dissection index value ranges between 0 to 1, where 0 implies presence of flat terrain, less degree of dissection, absence of vertical erosion and old stage of the basin while 1 indicates undulated terrain, hill slope escarpments, cliffs or at seashore. The value of dissection index of BRB is ranges from 0.06 to 0.3 (Figure 8c), which reflects less degree of dissection and mature stage of the basin (Table 7).

Figure 8. Maps showing values of (a) Drainage density, (b) Stream frequency, (c) Dissection index, and (d) Drainage texture of Betwa River Basin.

5.3.4. Hypsometric curve

A graphical plot derived using relative basin area along abscissa and relative altitudes along ordinate represents hypsometric curve. It is performed to examine the connection between horizontal cross-sectional areas of a basin with its elevation and has also been known as drainage-basin relief graph. It reveals information pertinent to the stages of geological successions and susceptibility of basin towards erosion (Singh & Singh, 2018). It is strongly influenced by the climate, tectonics, lithology and other geological conditions of a basin. The hypsometric curve reflects stages of erodibility in different parts of the basin. It tells about the regions in the basin which are more or less eroded or denuded in comparison to other regions. Strahler (1952a) stated that, the convex hypsometric curve represents non-equilibrium youth stage of a basin i.e., the basin is highly susceptibility towards erosion. An S-shape hypsometric curve which is concave upwards at higher altitudes and convex downwards at lower elevations represents mature stage of basin (Strahler, 1952b). A basin at mature stage shows less susceptibility towards erosion (Sharma & Mahajan, 2020). A concave hypsometric curve indicates that the basin is in monadnock phase, i.e., highly matured stage which is least susceptible to erosion. A more mature river basin produces more concave hypsometric curve. We have performed hypsometric curve analysis of BRB using formula of Ritter et al. (2002). The S-shape curve of BRB shown in Figure 9 indicates that the upper portion of the basin is in equilibrium stage and less prone to erosion while the lower portion of the basin is in an in-equilibrium young stage and more susceptible for erosion. Figure 10 shows longitudinal profile of BRB along Betwa River and corresponds to the differences in altitude from origin to the confluence with Yamuna River. It also depicts that the upper to middle portion of the basin have moderate stream gradient compare to the steeper stream gradient of lower portion of the basin.

Figure 9. Map showing hypsometric curve of Betwa River Basin.

Figure 10. Map showing river basin profile of Betwa River Basin.

5.4. The topo-hydrological aspects

To assess the overland flow, erosion risk and sediment transport in the basin topographic indices were computed (Equations. 2(2) $\mathrm{TWI}=\ln \left(\mathrm{As}/\tan \mathit{\beta }\right)$(2) –5(5) $\mathrm{STI}=\left(\mathrm{m}+1\right)\times {\left(\mathrm{As}/22:13\right)}^{\mathrm{m}}\times \sin {\left(\mathit{\beta }/0:0896\right)}^{\mathrm{n}}$(5) ). The topo-hydrological features of BRB have been extracted from COP DEM. Figure 11, Maps showing the values of the topo-hydrological factors within the study area. (a) topographic wetness index (TWI), (b) stream power index (SPI), (c) terrain ruggedness index (TRI), (d) sediment transport index (STI).

Figure 11. Maps showing the values of the topo-hydrological indices within the study area, (a) topographic wetness index (TWI), (b) stream power index (SPI), (c) terrain ruggedness index (TRI), and (d) sediment transport index (STI).

5.4.1. Topographic wetness index (TWI)

It is a topo-hydrological factor introduced by Beven et al. (1984). It represents the effects of topography on hydrological processes e.g., over land flow generation and accumulation; identification of hydrological flow paths; spatial patterns of soil moisture etc. in the river basin (Gallant & Wilson, 1996; Sørensen & Seibert, 2007). Areas having higher value of TWI represent wetter & gentle slope areas, having greater potential to be saturated by water before the surrounding areas and vice versa. It indicates area with higher propensity to water accumulation and runoff-generation in the basin. Moore et al. (1991) have introduced following equation for TWI computation assuming uniform soil properties and steady state conditions in the study area:

(2) $\mathrm{TWI}=\ln \left(\mathrm{As}/\tan \mathit{\beta }\right)$(2)

Where, “ln” denotes the natural logarithm, “As” represents specific basin area (m²m⁻¹) i.e., the upslope contributing area per unit contour length and “β” stands for the slope gradient in degree.

The computed TWI value in BRB ranges from 3.13 to 26.25, where higher value spread along the flat plains in the basin and lower values are associated with rocky high lands and hills of the basin (Figure 11(a)).

5.4.2. Stream power index (SPI)

It represents the interconnection between stream’s energy expenditure with time and quantity of sediment transported by the stream (Bagnold, 1966). It is a product of tangent of the slope in degrees and area of the basin. SPI is an important parameter in sediment transport studies and reflects stream’s power to transport water and sediment per unit of flow length. It is an important factor which initiates channel development in a river basin (Barman et al., 2021). It is closely related with TWI and escalates with the increase in slope steepness and size of the basin. It reflects potential erosive power of over land flow and influenced by the soil quality, soil profile, vegetation types, coverage and distribution, precipitation and climate (Moore et al., 1991). A positive SPI value indicates potential erosive areas while negative SPI value shows topographic areas having potential for depositional. Moore et al. (1991) had provided following equation for SPI calculation with an assumption that the discharge is proportional to the basin area.

(3) $\mathrm{SPI}=\mathrm{As}\tan \mathit{\beta }$(3)

Where, “As” denotes specific basin area (m²m⁻¹) i.e., the upslope contributing area per unit contour length and “β” refers to the slope gradient in degree.

The SPI value in BRB varies from 0 to 6 (Figure 11(b)). The low range of SPI value reflects old stage of the basin and shows that the overland flow in the basin has lower erosive power. Most of the area in BRB showed SPI value zero that is less susceptibility towards erosion while few regions with high flow accumulation potential (river bed) have shown value 6.

5.4.3. Terrain roughness index (TRI)

The TRI factor influence stream energy, runoff velocity, surface storage capacity, and routing at the basin scale. It reflects the amount of elevation difference between neighboring cells and calculated by measuring the elevation differences between the focal cell and eight neighboring cells. It reflects average elevation change between any point on a grid and its surrounding areas.

(4) $\mathrm{TRI}=\sqrt{\mathrm{Abs}({max}^2-{min}^2)}$(4)

Where, Abs means absolute and max and min are elevation in meter,

TRI value in BRB ranged from 0 to 30 (Figure 11(c)). TRI value zero corresponds to the flat plains of the basin while 30 indicate hills and ridges of the basin.

5.4.4. Sediment transport index (STI)

It has been introduced by Moore and Burch (1986) for characterization of erosion and deposition processes. It is correlated with soil erosion as it demonstrates the convergence and divergence of sediments flow from the region of higher elevation to the lower elevation region which are susceptible for inundation and sediment accumulation.

(5) $\mathrm{STI}=\left(\mathrm{m}+1\right)\times {\left(\mathrm{As}/22:13\right)}^{\mathrm{m}}\times \sin {\left(\mathit{\beta }/0:0896\right)}^{\mathrm{n}}$(5)

Where, “As” is the specific basin area (m²m⁻¹) i.e., the upslope contributing area per unit contour length, “β” denotes the local slope gradient in degrees, “m” is area exponent and “n” is slope exponent.

STI value in BRB ranged from 0 to 121.4 (Figure 11(d)). Larger value of STI generally belongs to areas dominated by steep slopes, ravines and water streams, and corresponding areas having higher susceptibility to soil erosion and degradation.

The appendix (field photographs, 1–4) depicting the intermittent nature of river in upper reaches, geological formations, vegetations and erosive and depositional characteristics of Betwa River Basin.

6. Conclusion

The present study demonstrates that the newly released COP-DEM is an efficient DEM for geo-morphometric and topo-hydrological analysis. The CLC analysis showed that the drainage networks delineation was performed with better accuracy. Our analysis suggests that the BRB falls under seventh order basin with high number of headwater streams. High number of headwater streams dominates upper to middle reaches of the BRB and infers relatively higher relief with steeper slopes, rocky outcrops, dissected plateau and hills. The drainage basin have mostly dendritic to sub-dendritic (parallel) drainage pattern while at some places radial and trellised patterns also co- exists which implies that the river channel is following the terrain gradient. The slope map of the basin also affirms that the basin have mostly east facing and relatively gentle slope gradient. However, due to local geological factors such as rugged terrain, moderately dissected topography with underlain rocks of Archaean–Proterozoic age and Deccan Trap rocks of Cretaceous age at few places the river shows sinuous and meandering phenomenon. Lower mean bifurcation ratio, less circularity ratio, low elongation ratio, very low overall drainage density, low stream frequency and small drainage texture ratio of BRB infers well-dissected, slope dependent, near elongated drainage basin having high overland flow, low infiltration rate and high structural complexity. A high stream frequency and drainage density have been noticed in Deccan Trap part of the Betwa River basin as compare to those of Vindhyan Supergroup and Bundelkhand complex.

Conspicuously coarse drainage texture is characteristically present in Bundelkhand massif which is due to presence of sub-surface jointed and fractured lithology of granite dominated terrain. Further, the basin relief, ruggedness number, relief ratio and hypsometric curve depict less erosion intensity in lower parts of the basin due to attainment of mature and maximum denudation stages of erosion in this region and low terrain relief of the basin. In addition to that the values of topo-hydrological indices viz. TWI, SPI, TRI and STI also infer that the upper portion of the BRB have less soil moisture content, high overland flow, high ruggedness and higher erosion potential. We recommend special attention towards the upper part of the Betwa River Basin which needs immediate basin conservation interventions to ensure sustainability of BRB.

Acknowledgments

The first author wishes to acknowledge the support received from the University Grants Commission (UGC), New Delhi, India for providing grant under UGC NET-JRF fellowship (Ref no. 3622/(NET-JUNE 2014). Authors also express thanks to DST-FIST, New Delhi, India for providing necessary facilities for the research and development activities at our Centre.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the University Grants Commission [3622/(NET-JUNE 2014)].

Appendix

Photograph 1. A site from upper reaches of Betwa River Basin.

Photograph 2. Betwa River flowing in North East direction on Bundelkhand plateau.

Photograph 3. Erosional plain developed by Betwa River in lower reaches.

Photograph 4. Confluence of Betwa River (red arrow) with Yamuna (blue arrow) at Merapur Daria, Hamirpur, U.P., India.