Impact of geomorphometric parameters on landslide occurrence and distribution in Yamuna River Basin, North-Western Himalaya, India

Landscape evolution is a dynamic process controlled by several geomorphic parameters along with geology, tectonics and climatic condition of the area. The Himalayan mountain belt is highly geodynamic with immature topography which offer one of the best places to study the impact of geomorphotectonic characteristics on the occurrence and distribution of landslides along with tectonically modied geomorphic features. The morphotectonic study of the drainage basin is extensively utilized to analyze the landscape evolution in the study area along with impact of neotectonic activity in landscape evolution. The study shows that the Yamuna River, originating from the mighty Himalayas, ows downslope by adjusting its course due to ongoing tectonic activities, underlying structures, and climatic factors. Active tectonics play important role in modifying the landscape and impacting the occurrence and distribution of landslides. The characteristics of rainfall induced landslides have been studied in relation to morphotectonic parameters. The analysis shows that the probability density of landslides was highest in the range of 25 o -30 o and that landslide size increased up to 20 o -25 o slope angle, decreasing on further increase in slope angle. The study also shows that slope angle merely controls number of landslides rather than size of the landslides. Landslides were mostly restricted to South facing slopes. About 91% of the landslide occur in the drainage density range of 1.2 to 2.1 km/km 2 while landslides show very low occurrence in either lower (< 1.2) or higher (> 2.1) drainage density. The present analysis can be very helpful in landslide risk reduction and landslide hazard zonation and probably to plan critical locations for installation of early warning signals.


Introduction
Landscape evolution is a dynamic process controlled by several geomorphic parameters along with geology, tectonics and climatic condition of the area (Bishop 2013). They are very sensitive to natural and arti cial infringement such as a tectonic event, rainfall and earthquake in addition to anthropogenic activities that disturb the natural progression of erosional episodes and, in the process, creates large number of landforms (Sharp 1982). Landslide is the result of these erosional episodes and their occurrence and distribution are interrelated with the geomorphometric parameters such as relief, slope, slope direction, drainage basin etc. along with an associated natural or anthropogenic event (Korup 2005;Cerri 2018). Thus, identi cation of right parameters controlling landslide distribution in an area is of prime importance.
In very simple terms, a landslide is the movement of the rock mass, earth, or debris down a slope (Cruden 1991). It is a very complex phenomenon and can be easily characterized as one of the most devastating erosional processes in mountainous areas (Bennett et al. 2012). In particular, rainfall-induced landslides occur almost every year worldwide (Li et al. 2011). Landslides are associated with the transportation of large volume of material and have continuously led to the evolution of the landscapes through a variety of slope movement processes such as ows, slides, falls, topples, spread, and other complex types (Varnes 1978;Cruden and Varnes 1996;Hungr et al. 2014). A triggering event such as rainfall, earthquake, snowmelt is commonly associated with a landslide (Guthrie and Evans 2004;Malamud et al. 2004;Guzzetti et al. 2009;Florsheim and Nichols 2013;Tanyas et al. 2019).
In addition, the neotectonic activities also play a key role in the development of modern landform through deformation in the lithospheric crust (Rana et al. 2016). The preexisting drainage networks and consequently the drainage basin is very much sensitive, and are the rst element that responds to sudden geomorphic change, resulting from ongoing tectonic activities (Goldsworthy & Jackson, 2000, Queiroz et al., 2015. The evolution of geomorphic architecture resulting from neotectonic activities in a region can also be effectively assessed through the morphotectonic analysis (Das and Gupta, 2019). Nowadays, the GIS technologies in association with eld investigations have the potential to provide synoptic view and multi-temporal data of a drainage basin (Rai et al., 2017).
The Himalaya is amongst the youngest mountain chains in the world and geodynamically active in nature exhibiting complex geological settings and immature topography (Awasthi andPrakash, 2001, Valdiya, 2016). Therefore, the Himalayan region offer one of the best places to study the impact of geomorphotectonic characteristics on the occurrence and distribution of landslides along with tectonically modi ed geomorphic features. In this study, an attempt has been made to assess the geomorphometric characteristics of the Yamuna river basin, North Western Himalaya, India and further identi cation of causative factors responsible for large number of landslide associated with rainfall event (Fig. 1).

Regional Setting
The basin mainly constitutes parts of Higher Himalaya, Lesser Himalaya, Siwalik Group of rocks, as well as the foreland basin. The extreme northeastern portion of the basin depicts lithologies of Higher Himalaya (Vaikrita Group) which is strongly metamorphosed in nature. The Main Central Thrust (MCT) marks the southern limit of the Higher Himalaya litho-unit. In the present study area, the MCT zone is con ned between the Vaikrita Thrust (VT) in the north and the Munsiari Thrust (MT) in the south (Yin, 2006). Further, the Munsiari Almora nappe is also sandwiched between Vaikrita Thrust in the north and Munsiari Thrust (MT) in the south and formed due to tectonic transport of the rocks from Higher Himalaya to the Lesser Himalaya over the Main Central Thrust during Eocene-Oligocene (Ahmad et al.,2000). The Munsiari Almora nappe is the largest nappes distributed along the Himalayan arc. The Munsiari Thrust is a highly tectonised and signi cantly condensed litho-unit representing the root zone of the Lesser Himalayan crystalline nappes (Kumar, 2016). Due to the lithological and petrological similarity of Munsiari and Almora Formations, Valdiya (1980), refers to them as the same litho-stratigraphic unit.
The Ramgarh Group of rocks are present as a klippe and exposed in imbrication under the Munsiari Almora nappe in the basin. After the Munsiari Thrust, there lies a thick pile of unmetamorphosed to lowgrade metamorphosed Proterozoic metasedimentary litho-unit of the Lesser Himalayan (LH) zone. The Ton Thrust (TT) striking over 100 km, divides this region into the Inner (older) and Outer (younger) Lesser Himalayan litho-units at the western edge of the Munsiari Almora Nappes. The base of the Inner Lesser Himalayan contains Berinag quartzite. This litho-unit is overlain by Neoproterozoic Deoban dolomites.
The Outer Lesser Himalaya is comprised of 850 Ma Chandpur Formation. The Main Boundary Thrust (MBT) marks the southern limit of Lesser Himalaya. The variation in geomorphological, geological, and geophysical signature along the Main Boundary Thrust suggests the active nature of the thrust (Valdiya, et al., 1984) After MBT; rocks of the Siwalik Formation are deposited and runs almost parallel to the Lesser Himalaya (LH). The rocks of the Siwalik Formation have been formed by the deposition of sediments by ancient Himalayan rivers during the last 16 Ma to 1.5 Ma (Valdiya, 2010). The Main Frontal Thrust (MFT) is situated at the southern boundary of Siwalik rocks and followed by the foreland basin. The foreland basin has been formed by the exure of the Indian plate through the weight of Himalaya Mountain. The foreland basin is comprised of a thick cover (~ 6 km) of quaternary sediments deposited over the Paleozoic basement platform. The detailed regional setting has been shown in Fig. 2.

Materials And Methods
The ongoing collisional event between the Indian and Eurasian plate has resulted in tremendous stress generation and tectonic activities in the Himalayan zone. The Himalaya is considered as one of the youngest and dynamic mountain belt in the world. Due to enduring stress generation geomorphological characteristics of Himalayan basins keeps on modifying within short span of time. Keeping this in view, the methodology of present study has been sub-divided into three parts which includes (1) Assessment of geomorphological parameter of the basin; (2) Evaluation of Neotectonic impacts on the assessed geomorphological parameters and, (3) Statistical analysis of associated landslide

Geomorphological Parameters
The geomorphological characteristics have been evaluated utilizing the Advanced Spaceborne Thermal Emission and Re ection Radiometer Digital Elevation Map (ASTER DEM) of the basin having a spatial resolution of 30 m. The ASTER-DEM has been processed in the GIS environment using ARC GIS v.10.2.
The drainage basin has been extracted using Arc-hydro tool and further processed to extract drainage network map, slope map, aspect map, drainage density map. In addition, some important basin geometry viz., Form Factor (Ff) and Circulatory ratio (Rc) have also been calculated for the Yamuna River basin.

Impact of Neotectonics
The impact of Neotectonics on the evaluated geomorphological parameters have been assessed with the help of different geomorphic indices. The geomorphic indices of the basin are calibrated with the help of different tools such as Valley morph tool and 3D Analyst tool that works on GIS platform. Further, some calculations have been carried in the Global Mapper-13 software package. The signi cant geomorphic indices mainly comprised of Stream Length-Gradient Index (SL), Asymmetry factor (AF), Transverse Topography Symmetry (T), Mountain Front Sinuosity (Smf). The indices have been brie y discussed below and their mathematical expressions are presented in Table 2. The indices have been calculated for ten 5th order sub-basins which covers the maximum part of the Yamuna basin in the study area.

Stream Length-Gradient Index (SL)
The Stream gradient index is one of the indices to evaluate active tectonics concerning the shape of stream channels (Hack, 1973). The higher value of this index indicates that the river is owing over active uplift or resistant lithology whereas, the lower value indicates stream owing parallel to the crushed zones due to strike-slip faulting (Keller and Printer, 2002). Therefore, the anomaly in SL value indicates activities of geological structures that disrupt the bedrock (Guarnieri and Pirrotta, 2007). The active vertical uplift gives rise to sharp knick points in the river longitudinal pro le. In the present study, the main streams of each 5th order drainage sub-basins are segmented at succeeding equal contour intervals to measure the elevation difference. The calculated SL distribution patterns are analyzed along with the longitudinal pro le of the river to understand the lithological and tectonic interactions.

Asymmetry factor (AF)
The drainage basin asymmetry factor is helpful in identifying the neotectonic activity by determining the asymmetry and the lateral tilting nature of drainage basins concerning the main river course. The tilting may be linked with the activity of active fault in the basin (Hare and Gardner, 1985;Cox, 1994). Therefore, the Value of AF tells about the asymmetry of the basin and the in uence of active tectonics or lithological control. It is a ratio of the basin area laying on the right (Facing downstream) to the total area of the drainage basin.

Transverse Topography Symmetry (T)
The Transverse Topography Symmetry is a very signi cant quantitative parameter for evaluating tectonic tilt of the basin resulting from active tectonics. The variation in this index indicates differential upliftment rates in basins. These upliftment causes by active tectonics lead to the change in channel slope and consequently shift in the river channel (Jain and Sinha, 2005). This factor varies within the range of 0 (minimum tilting) to 1 (maximum tilting). The Valley morph tool under Arc-GIS environment (After Dexaberger et al., 2014) have been processed and the measurements were taken at the interval of every 150 m. Further, the mean value of T has been obtained from the several values of T calculated from the Valleymorph tool.

The Mountain Front Sinuosity (Smf)
The index of mountain front sinuosity (Smf) is used to determine the degree of active tectonics in a mountainous region. The Sinuosity of the mountain front (Smf) can be described as the ratio of the mountain front's length along the mountain foot which is also known as the break-in topography of the slope (Lmf) and the mountain front extension along a straight line (Ls) (after Bull, 1978). This index indicates the relationship between the behavior of rivers (erosive process) to produce an irregular front and vertical tectonic activity to produce a straight front on the mountain (Bull andMcFadden, 1977, Keller, 1986). If the ratio of this index is equal to 1, it indicates the activity of geotectonic processes and the young nature of mountains, and the increase of this value indicates lesser tectonic activities and the dominance of surface processes (Rockwell et al., 1985;Keller, 1986;Silva et al., 2003). The increase in Smf value indicates a reduced upliftment rate resulting from active tectonics and the predominance of erosive processes. Therefore, the higher Smf values (> 3) are generally linked with inactive mountain fronts. The data for Smf has been calculated at an interval of 500 meters in the basin from the lowest point up to an elevation of 5882 m

Landslide characteristics
For the landslide study in the region, landslide inventory was prepared from the available data on the Geological Survey of India Website (BHUKOSH). The downloaded data have been processed in a GIS environment and statistically analyzed (Table.1). It is well understood that the large-scale landslide is the most hazardous but a small-scale landslide event is very common therefore quanti cation of the frequency size distribution for landslides is important to assess landslide hazard and also for future land use planning (Malamud et al. 2004;Hurst et al. 2013). A large number of literature is available on the magnitude of area and volume of the landslide, all suggesting area of landslide may vary up to 8 orders of magnitude and volume around 12 orders of magnitude (Malamud et al. 2004;Guzzetti et al. 2009). To quantify the occurrence of the landslide in a particular area, frequency-size statistical analysis is generally performed on a large number of landslide data from landslide inventory. The probability density (P D ) of the total number of landslides in this study is estimated following Malamud et al. (2004) using Where, δN is the total number of landslides with areas between A L and A L + δA L , and N L is the total number of landslides in the inventory. The bin size is adjusted in such a way that bin width (δA L , km 2 ) varies in log scale.
It is interesting to note that despite large variations in landslide types, sizes, distribution, geology, and triggering mechanisms, evidence indicates that in many historical and fresh landslides, the frequencyarea distribution (FAD) of medium and large scale landslide decays following inverse power law of landslide area (Hovius et al. 1997;Stark and Hovius 2001;Guzzetti et al. 2002Guzzetti et al. , 2009Guthrie and Evans 2004;Malamud et al. 2004;Eeckhaut et al. 2007;Hurst et al. 2013). Experience from FAD plots of a large number of researches carried around the world suggests that two scaling regimes exist; an inverse power law exists only for landslide greater than a particular size and the minimum size will vary for different inventories, frequency of small landslide generally follow a positive power law. The transition from one to other is referred to as rollover by many researchers which can also be marked by the peak point of the FAD after which frequency density curve starts to decrease following positive power law (Guthrie and Evans 2004;Eeckhaut et al. 2007;Hurst et al. 2013;Tanyas et al. 2019). Many researchers believe that a rollover occurs in FAD of historical inventories where evidence of smaller landslide has been lost due to subsequent modi cation in the landscape by landslides, erosion, vegetation growth, anthropogenic in uence, etc. (Malamud et al. 2004;Eeckhaut et al. 2007;Hurst et al. 2013). The point in FAD where the curve begins to diverge has been referred to as cut-off point, visible in both cumulative and noncumulative FAD (Hovius et al. 1997;Stark and Hovius 2001;Tanyas et al. 2019

Geomorphological Parameters
The Yamuna river basin in the study area is mainly a 7th order drainage basin exhibiting sub-dendritic, trellis, and rectangular types of drainage patterns (Fig. 3). Along with these, the drainage pattern also shows sharp bending of the stream channel and channel straightening at places. These drainage patterns indicate that the basin is under several kinds of control, which mainly includes structural, topographic, and lithological. The drainage density map of the Yamuna river basin illustrates very low (< 1 km/sq km) to low (< 1.9 km/sq km) in a majority of the upper portion of the basin (Fig. 4). Whereas, moderate (2-2.8 km/sq km) to relatively higher drainage density (2.9-3.6 km/sq km) is chie y located in the lower part of the basin (Fig. 4). The drainage density is greatly in uenced by rainfall intensity, rock resistivity, mean annual runoff, and landslides, in many cases (Chorley 1957a, b;Chorley and Morgan 1962, Morisawa 1962, Zavoianu 1985Gardiner 1996). The parameter bears inverse relation with in ltration capacity of the basin, permeability of the subsoil, degree of development of drainage network, texture, and stream within the basin (Horton 1945, Strahler 1956, Melton 1957, Zavoianu 1985. The drainage density signi cantly affects the runoff pattern in a basin as the surface runoffs are removed rapidly in a region having higher drainage density (Chorley 1969). The lower drainage density in the present study attributes to the low mean annual runoff, higher in ltration capacity or permeability of subbasin, higher vegetation cover, and well-drained soil. Hasegawa et al, (2013) suggested that the basin having lower drainage density are prone to large-scale landslide whereas moderate to higher drainage density attributes to shallow seated landslide events. Smallest landslides seem to be concentrated in the drainage density range below 2.2 km per square km. The median landslide size is almost equal for drainage density till 2.2 km per square km but increases beyond this value. Some of the largest landslides albeit few in number are concentrated in the drainage density range of 2.2 to 2.5 km per square km. Interestingly, larger landslides are also concentrated in the drainage density range of 1 to 2.2 km per square km (Fig. 5). The data of recent landslide events, when studied along with the drainage density map of the basin, supports the nding of Hasegawa et al, (2013). Almost all the landslide events are characteristically con ned to the region having lower drainage density (0.16 km/sq km to 1.9 km/sq km). The Form Factor of the sub-basins ranges from 0.2 (sub-basins "E" and "G") to 0.53 for sub-basin "D". Amongst another watershed, the moderate value of form factor (0.25 < form factor < 0.4) have been observed as 0.29 for sub-basins "F" 0.29 for sub-basin "J" 0.32 for sub-basin "A"; 0.39 for sub-basin "B". The higher value (> 0.4) of form factor has been observed as; 0.41 for sub-basin "I" 0.48 for sub-basin "C" and 0.50 for sub-basin "H" (classi cation after Prabhakaran and Raj, 2018). The Form Factor is mainly controlled by drainage development in a basin because of neotectonic activities. In the initial phase of basin development, the tectonically undisturbed basins are pear-shaped which becomes elongated under the in uence of active tectonics and continuous erosion (Prabhakaran et al., 2018). It varies between 0 (highly elongated) to 1(circular). The Form Factor attributes to the peak discharge (Sreedevi, 2005) and ow intensity (Mesa, 2006) of the drainage network. The observation suggests that the majority of the drainage basin has a moderate to low form factor. This observation advocates that almost all sub-basins of the Yamuna river basin is elongated in shape having lower peak ow of longer duration. The circulatory ratio generally varies from 0 to 1. In present study, the Circulatory ratio of the sub-basins ranges from 0.16 (for sub-basins "G") to 0.53 for sub-basin "D". The other sub-basins possesses low to a moderate value of Circulatory ratio, which "comprises 0.26 for sub-basin "E", 0.27 for sub-basin "F", 0.31 for sub-basin "A", 0.32 for sub-basin "J", 0.36 for sub-basin "I", 0.38 for sub-basin "B", 0.42 for sub-basin "C", and 0.46 for sub-basin "H". The circulatory ratio is largely in uenced by basin slope, basin relief, structural features, stream length, etc. The ratio signi cantly indicates different stages of the life cycle of the sub-basin (Wilson et al. 2012). In present context, the circulatory ratio for sub-basins indicates the youth stage of the tributaries with moderately to strongly elongated sub-basin. The characteristics of low runoff of the basin facilitate the higher in ltration rate of water, which further makes the subsoil permeable.

Impact of Neotectonics
The river longitudinal pro le for fth-order streams of all sub-basins is observed to be the concave upward pattern which suggests tectonic instability in the region since the river pro les tend to be more strongly concave in tectonically active regions resulting from tectonically induced spatial variations in uplift rates (Kale and Shejwalkar, 2008;Seybold et al., 2020). The calculated SL index curve for all the fth-order sub-basins when plotted with the longitudinal pro le of the river presents a remarkable feature of the basin. The SL index shows characteristic higher values, steep rise and intersection with the river longitudinal pro le, in the region, where it encounters active faults which indicate tectonic control on the river development (sub-basins, 5 A, B, E, J). The major thrust like MBT, Munsiari thrust, Bearing thrust, Ton thrust is passing through the river pro le have higher SL index values (Fig. 6). The SL index and curve exhibit characteristics lower values for those sub-basins where stream channels are not traversed by major faults. Further, minor uctuations in the SL pro les also indicate recent active tectonics in the subbasins (Ramírez-Herrera and Gaidzik 2017; Shankar et al., 2020). The observed SL index for different subbasins indicates the characteristic increase in landslide events (in terms of frequency and area) with increase in SL anomaly. Similar observations have also been made by different researchers (viz., Hack, 1973;Troiani, 2014) while working in different neotectonically active region. This may be because of the fact that the vertical upliftment of sub-basins accelerates river incision producing over-steepened and unstable slopes, which enhances the landslide activities. The Asymmetry factors measured in our study ranged from 23 for sub-basin "F" to 64 for sub-basin "D" (Fig. 7) in which the AF > 50 indicates a tectonic tilt of the sub-basin towards left (viewing towards downstream side of the sub-basin) and therefore depicting the upliftment in the opposite direction. The observation suggests that almost all the subbasins are tilted towards their left bank (viewing downstream) and hence uplifted in their right bank. The average values of Transverse Topography symmetry of the sub-basins range from 0.17 (in case of subbasin C) to a maximum of 0.58 (for sub-basin F). The values of T is also supporting the results of AF values. The streams in all the sub-basin show remarkable shifting in the opposite direction of the upliftment (Fig. 7). The basin asymmetry is depicting a positive correlation with the T values. The Smf of the basin ranges from (1.02) in case of sub-basin e to maximum of (2.63) at some localities of sub-basin and average of (1.53) suggesting Active Mountain fronts for all the sub-basins (Fig. 8). The calculated Smf values of the sub-basins showing an active mountain front. In addition to these observations, various neotectonic structures such as sand dykes, lenses, triangular fault faces, and knick-points have been observed at an outcrop scale at different locations in the basin during the eld investigations ( Fig. 9).

Landslide Analysis
The hill slope is an important controlling factor for mass wasting processes (Larsen and Torres-sanchez 1998). From our general understanding of Mohr-Coulomb failure theory, shear stress of the mass has a direct relation to slope angle, which essentially means that more the slope angle more will be shear stress available for failure. In this regard, landslides can be expected on relatively steeper slopes. In this study, landslides originated on a wide range of slope angles however, the majority seems to have concentrated in the slope range of 40 o -70 o (Fig. 10). The percentage of the landslide (~ 78%) tends to increase with slope angle with a maximum in the range 50 o -70 o . Few landslides (~ 11%) were recorded on very gentle slopes (≤ 30 o ) while the frequency of landslide (2%) decays signi cantly towards a higher slope angle of ≥ 70 o (Fig. 11). Florsheim and Nichols (2013) analyzed shallow translational rainfall triggered historical landslides and concluded that the majority of the slides initiated on an average slope of ~ 22 o . Martin et al. (2002) analyzing shallow landslides highlights that most landslides tend to initiate on hill slopes of 25 o -30 o . The analyzed inventory in the present case is not limited to shallow landslides and therefore it becomes di cult to get similar threshold values. Shallow landslide such as debris slide and ow typically occurs in upper unconsolidated material where slight disturbance can initiate slope failure even on very gentle slopes. However, the failure of the individual slope is a complex mix of a variety of processes such as lithology, hydrology, structures, weathering rates, relief, slope angle, and its curvature. There seems to be no clear relation between landslide size and slope angle for rainfall-triggered landslides (Fig. 12). This points to an important understanding that either large or small landslide is not con ned to a particular range of slope angles. Kasai and Yamada (2019) working on FAD of earthquake-triggered landslides observed that the probability density of landslides was highest in the range of 25 o -30 o and that landslide size increased up to 20 o -25 o slope angle, decreasing on further increase in slope angle. It can be seen in Fig. 12 that the median landslide size is almost equal for all groups of slope angles and therefore slope angle merely controls the number of landslides rather than landslide size. Interestingly, a greater number of largest landslides were observed in the slope range of 30 o -70 o (larger landslides, 0.05km 2 are few) followed by a few larger landslides on a very gentle slope (< 20 o ). Steeper slopes (> 70 o ) and slope range between 20 o -30 o seem to be devoid of larger landslides. Around 89% of the landslide area lies between 30 o -70 o slope angles, which shows that these slope angles are the most vulnerable zones. Landslides are observed along all slope directions in the analyzed basin albeit in different proportions (data of slope angle extracted from Aspect Map pf the basin) (Fig. 13). The percentage of landslides in the north-facing slope (NW to NE) is less in comparison to other directions. Around 50% of the landslide occurred on the south-facing slope (SW to SE) while only ~ 24% on the north-facing slope, the remaining ~ 25% of landslide are con ned to E and W direction (Fig,14). Similarly, ~ 91% of the landslide occur in the drainage density range of 1.2 to 2.1 km/km 2 while landslides show very low occurrence in either lower (< 1.2) or higher (> 2.1) drainage density (Fig. 15). The total number of landslides analyzed is 2757 with a maximum, minimum, and average area of 0.24 km 2 , 4x10 − 6 km 2, and 3.4x10 − 3 km 2 , respectively. The landslide data superimposed over rainfall map clearly highlights the critical locations of landslides.
Rainfall triggered landslide are very frequent and most widespread across the world. It has been noted that majority of rainfall induced landslide start as small and shallow failures but may transform to debris ow on its way down slope and increase the ultimate volume of the failed mass resulting into severe loss and damage (Crosta and Frattini 2003). The shallow nature of rainfall induced landslides is mainly attributed to sudden increase in pore pressure of the unconsolidated overburden causing the failure surface to develop with the soil pro le or only in sur cial layers in case of bedrock (Singh et al. 2017, Crosta, 1998. The probability-size distribution for landslides is generally similar universally with major differences in the rollover, cutoff point, and scaling exponent. Globally, authors have either analyzed FAD for a single triggering event such as earthquake, rainfall, etc. or landslides have been analyzed for multiple events, and all follow a similar trend for medium and large-scale landslides with the tail showing inverse power law t. The scaling exponent of the tail for medium and large scale landslide is quite variable but a value of -2.3 ± 0.6 seems the best t for a large number of studies with a maximum reported over 3.0 (Brardinoni and Church 2004;Malamud et al. 2004;Catani et al. 2005;Eeckhaut et al. 2007). However, it is to be noted that smaller values have also been reported by many authors (Hovius et al. 1997;Stark and Hovius 2001;Martin et al. 2002;Hurst et al. 2013). The position of rollover (peak of FAD curve) in the FAD of this study is questionable as data of smaller landslide seems to be missing from the inventory but from the visual inspection, the peak seems to be achieved for the analyzed landslide data at around 50m 2 . The cutoff point for the analyzed inventory is around 3000m 2 , a point beyond which most of the data of medium and large landslide decays following an inverse power law with a scaling exponent of ~ 2.3 (Fig. 16). Guthrie and Evans (2004) analyzing the magnitude-frequency relationship of a landslide triggered by a storm event suggested that proper characterization of magnitude-frequency of a landslide is necessary for the determination of impact, landscape denudation, and assessment of total risk.

Conclusions
The characteristic drainage patterns, observations from morphotectonic analysis, seismic activities in the Yamuna river basin con rms neotectonic activities in the basin. The ongoing upliftment of the basin, tilting, Active Mountain fronts, V-shaped valleys along with strong eld evidences are some of the prominent signatures which con rm the ongoing active tectonics. The observation of the morphotectonic analysis landslide activities in the region suggests the role of active tectonics in modifying the landscape and shows good correlation with analysed landslide. Landslide characteristics were studied with the help of statistical analysis in the form of FAD plots and controls of different geomorphological parameters such as slope angle, slope direction, drainage density on the frequency of landslides. larger landslides are not observed in drainage density below 1 but smaller landslides seem to be concentrated in the drainage density below 2.2 km per square km.The analysis reveals that landslides occur on a wide range of slope angles but the frequency of landslide (~ 78%) is greatest in the range of 40-70. Interestingly, the slope angle merely controls the frequency of landslide, the size of landslide seems to have no clear relation with slope angle as the median size of landslide area shows only slight variation with slope angle. Both frequency and large landslides are either very less or absent at higher slope angles (> 70). Landslides can be seen in all slope directions but the south-facing slope (SW to SE) seems to have around 50% of the landslide in the basin and therefore most critical. For the analyzed rainfall-induced landslide inventory, the cutoff point is found at 3000 m 2 beyond which inverse power law ts well for medium and large scale landslides with a scaling exponent of -2.3. From further analysis of FAD plots, it seems the data of small landslides is not complete in the inventory and therefore it becomes di cult to obtain the rollover. But from visual inspection, it seems that the peak of the FAD plot is at 50 m 2 , which can possibly be the rollover after which small landslides follow a positive power-law relationship.  Cox (1994) 7. Mountain Front Sinuosity (S mf ) S mf = L mf /L s L mf = The topographic break in the slope Ls = Length of the mountain front measured along the straight line (Bull and McFadden 1977 Figures Figure 1 The ASTER DEM of the Yamuna River basin showing elevations and major locations, highways and railways. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. The regional map of Yamuna River basin along with major geological Formations (Modi ed after Valdiya 1980) (white lines indicates sub-basin boundary). Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. The SL curve (dotted line) for the 5th-order drainage basins (A to J) of the Yamuna river basin, North Western Himalaya, India (longitudinal river pro le represented by the solid line).

Declarations
concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 8
The Smf map of the Yamuna River basin North Western Himalaya, India. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.

Figure 11
Landslide frequency versus slope angle plot of Yamuna River basin North Western Himalaya, India.

Figure 12
Landslide area versus slope angle plot of Yamuna River basin North Western Himalaya, India Figure 13 The Aspect map of the Yamuna River basin North Western Himalaya, India. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors. Landslide probability density distribution versus area plot of Yamuna River basin North Western Himalaya, India