Quantitative morphometric analysis and prioritization of sub-watersheds for soil erosion susceptibility: A comparison between fuzzy analytical hierarchy process and compound parameter analysis method

Identi�cation of critical sub-watersheds susceptible to soil erosion risk is the preliminary step in any watershed management plan. To achieve this goal, the prioritization of sub-watersheds based on morphometric characteristics is of paramount necessity. This study was performed on the Upper Shimsha-1 watershed using DEM to quantify the morphometric parameters in a GIS environment. The stream network was extracted in ArcGIS software, and the watershed was delineated into 16 sub-watersheds (SW1 to SW16). Two approaches, viz., the fuzzy analytical hierarchy process (FAHP) and compound parameter analysis methods, were employed in prioritizing sub-watersheds using 18 parameters highly related to soil erodibility. The FAHP score ranged from 0.145 (lowest priority) to 0.794 (highest priority), prioritizing sub-watersheds into ‘high’, ‘medium’ and ‘low’ classes occupying 10.76%, 27.23% and 62.01% of the total area, respectively. The compound parameter values ranged from 6.05 (highest priority) to 10.77 (lowest priority), and the ‘high’, ‘medium’ and ‘low’ classes occupied 31.84%, 16.49% and 51.67% of the total area, respectively. The common sub-watersheds from both methods under the ‘high’ priority class were SW14 and SW15, accounting for 10.76%, and under the ‘low’ priority class, SW1, SW8, SW9, SW11, SW12 and SW16 accounted for 42.66% of the total area. Hence, eight sub-watersheds were common in both prioritization methods corresponding to their respective priority classes. The integration of GIS technology, morphometry and prioritization methods has proven to be indispensable in watershed management and soil conservation efforts through this investigation. It further emphasizes the need for swift attention from decision-makers toward critical sub-watersheds.


Introduction
In the modern epoch of science and technology, the scope of e cient watershed management using geospatial technology over traditional methods has concerned decision-makers seeking rapid and accurate solutions to soil and water conservation challenges.The watershed, considered the primary unit for land management, is de ned as the topographical expanse from which surface water runoff as a consequence of precipitation is accumulated and channelled towards a converging point (Rajasekhar et al. 2020;Endalew and Mulu 2023).It forms the basic unit of morphometric investigation, as all geomorphologic and hydrologic phenomenon takes place within the watershed (Horton 1945).Watershed management plans are systematically designed towards sustainable exploitation of soil and water resources through a course of action to meet speci c needs without causing adverse impacts on the environment (Nigam et al. 2017).A properly formulated watershed management plan embodies a scienti c approach to combat excessive surface runoff, poor in ltration rates, accelerated soil erosion, droughts and oods and aids in achieving irrigation e ciency, groundwater recharge, construction of soil and water conservation structures, etc. (Ratna Reddy et al. 2017; Choudhari et al. 2018).Therefore, to tackle water-related problems, heightened attention should be allocated to watershed management (Shekar et al. 2023;Gautam et al. 2023).
The prominence of analytical geomorphological assessment in the realm of water resource management was highlighted by Horton (1945).Morphometric analyses were pioneered during the mid-20th century based on manual investigation of topographic maps (Horton 1945;Strahler 1952Strahler , 1964;;Miller 1953;Schumm 1956;Hadley 1961;Leopold 1964).
The process of quantitative measurement and geometrical analysis of the earth's surface con guration in addition to the characteristics and magnitude of its geographical features is de ned as morphometric analysis (Clarke 1996;Agarwal 1998; Ghosh and Gope 2021).It precisely determines the quantitative geographical features to elucidate linear, relief and areal attributes of watersheds.These attributes are of great importance in various investigations speci cally in environmental risk evaluation, natural resource appraisal and conservation efforts (Charizopoulos et al. 2019).
A basic understanding of geology, geomorphology, lithology, land use/cover and hydrology is necessary for gaining insights into the drainage system (Bhattacharya et al. 2020).Morphometric analysis, in turn, provides a comprehensive overview of the form, structure and hydrographic network of watersheds and their geomorphological history (Strahler 1964).It also provides information on terrain aspects such as lithology, rock hardness, permeability, slope, relief, groundwater recharge, ood peak, soil characteristics and runoff intensity and further holds a key role in depicting the signi cant watershed characteristics (Sangma and  Since the conventional approach of morphometric analysis is extensive, challenging and laborious, the adoption of remotely sensed data and GIS technology for evaluating the terrain and morphometric characteristics of drainage basins have gained international acclaim because of its streamlined, cost-effective and accurate approach ( A sub-watershed approach is helpful in the context of integrated watershed management.In general, the action of planning for watershed management is unfeasible for the whole watershed at a time, as it is inaccessible and economically impractical.Hence, pinpointing critical sub-watersheds that confront soil erosion risk is necessary.The prioritization of watersheds is the systematic ranking of sub-watersheds for conservation based on susceptibility to soil and water erosion.It is the most important step for water resource modellers in pursuit of sustainable watershed development, planning and designing e cient water harvesting structures (Balasubramanian et al. 2017).The application of geospatial technology in extracting basin parameters with precision has encouraged many researchers to prioritize sub-watersheds in the context of vulnerability to soil erosion and sudden oods.Distinct studies in the literature have used morphometric parameters for the prioritization of watersheds (Rahmati et  The traditional method of prioritization is mainly based on compound values taken as averages of each parametric value of morphological analysis (Gopinath 2016; Abdeta et al. 2020; Bharath et al. 2021;Obeidat et al. 2021).However, the latest approach makes use of multi-criteria decision-making models (MCDM) to include varying degrees of importance of several criteria for prioritization, viz., analytic network process (ANP), analytical hierarchy process (AHP) (Jaiswal et al. 2014;Meshram et al. 2019;Balasubramani et al. 2019), technique for order preference by similarity to ideal solution (TOPSIS), Vlekriterijumsko KOmpromisno Rangiranje (VIKOR) (Ameri et al. 2018) and Principal component analysis (PCA) methods (Siddiqui et al. 2020).The fuzzy analytical hierarchy process (FAHP) renowned for its novelty and superior accuracy is advantageous over AHP as it tolerates elements of fuzziness and ambiguity, which occur commonly in numerous decision-making instances (Mikhailov and Tsvetinov 2004).FAHP has been used in several studies for the prioritization of subwatersheds (Jaiswal et  The Shimsha River is among the tributaries of the Cauvery River, a major watercourse located in the southern region of India.This study is focused on the Upper Shimsha-1 watershed, herein referred to as US-1, which is present in the middle Cauvery basin as a part of the Shimsha subbasin.The study area under investigation has undergone signi cant alterations in its land use land cover over the past three decades primarily due to urbanization and industrialization. Nonetheless, the scienti c hydrological studies have remained scant in the literature review.Out of the limited studies mentioned above, Arulbalaji and Padmalal (2020) prioritized the entire Cauvery basin using compound parameter analysis, whereas Bharath et al. (2023) conducted a morphometric analysis of the Shimsha subbasin.However, they did not prioritize the sub-watersheds within this context.
Hence, a compelling need arises for prioritization of the US-1 watershed, which has remained unexamined thus far via compound parameter analysis or the FAHP method.Therefore, in light of the momentousness of morphometric analysis in watershed management planning and development, the main purpose of the current investigation is to perform quantitative morphometric analysis of the US-1 watershed adopting remote sensing and GIS technology.Secondly, we prioritized the critical sub-watersheds for soil erosion management using compound parameter analysis and FAHP followed by differentiation of the resulting outcomes.The ndings of this study can provide decisive inputs to authorities and policymakers to scale up and propose appropriate measures for soil erosion mitigation within the framework of watershed management.Furthermore, it helps researchers to conduct analogous studies in similar watershed areas.

Study area
The Upper Shimsha-1 (US-1) watershed is located between 13°33´27´´ N and 13°8´26´´ N latitudes and 77°5´7´´ E and 76°50´33´´ E longitudes with an area of 1261.91 km 2 .It occurs in the northern part of the Shimsha subbasin, which is a part of the Cauvery basin situated in the southern region of India (Fig. 1).It is ooded by the Shimsha River, among the many tributaries of Cauvery, originates in the Devarayanadurga hills in Tumkur taluk and runs for approximately 221 km before joining the Cauvery River.The greatest and lowest elevations are 1185 m and 666 m above mean sea level, respectively.The US-1 watershed lies predominantly in the Tumakuru and Gubbi taluks of the Tumakuru district and falls under Zone 5, i.e., the Eastern dry agroclimatic zone.The average normal rainfall of the Tumakuru and Gubbi taluks is 830 mm and 809 mm, respectively.The warmest and coolest months are May and December, with mean daily maximum and minimum temperatures of 38.1°C and 18.30°C, respectively.It falls under the rain shadow region of peninsular India and practices dry land agriculture.The rock formations belong to the Archaean complex and are dominated by migmatite gneiss, grey granite and granite.It has clay loam and loam textured soils.The major land use/cover type is cultivated lands with ragi, paddy, maize, minor millets, groundnut, coconut, areca nut, banana, tur, moong, etc., as major crops are grown in the current study area.
3 Materials and methods

Data acquisition
The primary data used for delineation of the watershed and generation of the stream network is the Advanced Land Observing Satellite (ALOS) PALSAR DEM.

Extraction of the stream network
All the geoprocessing steps, i.e., image processing, watershed delineation and stream network extraction, were carried out using ArcGIS 10.8.1 software.In ArcToolbox, the hydrology tool under the spatial analyst tool has consecutive steps to generate a stream network.The two ALOS PALSAR DEMs were rst mosaiced, and the errors present in the raw DEM were removed using the ' ll' tool.The next step involves the creation of a ow direction raster using the 'D8' approach that takes into account the elevation data of eight neighbouring cells in order to ll the depression cells followed by the creation of a ow accumulation raster (Thomas et al. 2014;Kumari et al. 2021).Then, by using a raster calculator, the drainage pattern was derived by de ning a threshold value and further used to create stream order by the Strahler method (Mark 1983;Odiji et al. 2021).In the next step, the pour points (outlets) were created and snapped at suitable locations on the ow accumulation raster, and the watershed tool was run to create the desired sub-watersheds.The corresponding raster layers were converted to vector format to determine the basic parameters of sub-watersheds using spatial data.It was further used to calculate linear, aerial and relief components by making use of the mathematical equations stated in Table 1.The methodological ow chart elucidates the stream network extraction and subsequent prioritization steps (Fig. 2).

Prioritization of sub-watersheds
Several methods, namely quantitative logic, fuzzy logic, statistical methods, ANP, AHP, TOPSIS and VIKOR, have been employed in various studies to prioritize sub-watersheds.In this study, two methods were employed for the prioritization of sub-watersheds, viz., the fuzzy analytical hierarchy process and compound parameter analysis.
A fuzzy set A denoted as {(x, (x))/x X} is comprised of ordered pairs.Further, X represents a subset of the real number R, wherein µ A (x) is denoted as the membership function.This membership function designates a grade of membership that varies between zero and one for each object "x".A triangular fuzzy number (TFN) is a real number that is expressed in a triplet form (l, m, u).It represents the 'lower', 'middle' and 'upper' values of a fuzzy number.The TFN is extensively used to ascertain fuzzy weights.The relative importance of each pair of criteria has been quanti ed through TFN with numerical values ranging from 0 to 9, as proposed by Saaty (1980).It is also stated by (Jaiswal et al. 2014;Mishra et al. 2019).
The rst step in the fuzzy AHP methodology involves deciding the relative signi cance of each pair of criteria within the same level of hierarchy (Chang 1996; Ghosh and Gope 2021).Each morphometric criterion being assessed via a pairwise comparison matrix relied on the weight scale resulting from normalized fuzzy calculations (Table 2).In the FAHP method, the fuzzi cation of the pairwise comparison matrix of the 'n' criteria is performed by a triangular membership function (Kordi 2008), which is denoted as = [ã ij ] in the subsequent matrix form: 1 where ã ij is a triangular fuzzy number, ã ij = (l ij , m ij , u ij ), and ã ij −1 =1/a ij .For each triangular fuzzy numerical value, ã ij or Z = l, and m, which is its membership function x), is a continuous mapping of real number −∝ ≤ x ≤ ∝ to the close interval (0, 1) and is de ned by the equation: It is important to note that the operations on triangular fuzzy numbers can be additional, multiplication and inverse.Supposing and are two TFNs wherein = ( , , ), and = ( , , ); then, After building a pairwise comparison matrix based on all judgments, the matrices were then amalgamated employing the fuzzy geometric mean method as outlined by Buckley (1985) as per the following equations: Furthermore, the fuzzy membership function that describes the weights of various parameters was calculated by employing the following mathematical equation: In the next step, to convert the membership function into a crisp and non-fuzzy form, the centre of area (COA) approach was used.This phase results in crisp numeric weights for all the parameters, and the formula is given below: In fuzzy AHP, the relative importance between the members is idiosyncratic and depends on one's comprehension of the subjects and response from various sources.Consequently, to gauge the uniformity of verdicts in FAHP analysis, a measure known as the consistency ratio (CR) was determined accordingly: where CI stands for the consistency index and RI stands for the random consistency index.The CI relies on the matrix size, i.e., the quantity of parameters considered.Further, the CI was determined using the following formula: wherein λ max is the principal eigenvector (Han and Tsay 1998; Malczewski 1999) which was calculated as a multiplicative result of the pairwise comparison matrix and weight vectors, defuzzifying the matrix and then summing all components of the resultant vector (Jaiswal et al. 2014;Mishra et al. 2019).As per Saaty (1980), a unitless prede ned value i.e., the random consistency index (RI) is based on the size of the matrix (n) after creating reciprocal matrices of different sizes.The judgment is considered consistent if CR is < 0.1.
In this study, a total of 18 morphometric parameters or erosion hazard parameters were considered whose range may vary.Hence, the values were subjected to normalization to t on a scale of zero to one as per the following equation: wherein W ij represents the normalized value of the i th morphometric parameter (P) of the j th watershed and OLB i and OUB i represent the original lower and upper bound of the i th morphometric parameter (P), respectively.P ij represents the original/actual value of the i th morphometric parameter (P) of the j th subwatershed.The nal priority value (F j ) of the sub-watershed using the FAHP is derived by summing up the product of the normalized value of each morphometric parameter and its respective weights resulting from the FAHP analysis using the following equation: Lastly, after calculating the nal priority values of all sub-watersheds, they are ranked accordingly in descending order of priority values as ranks 1, 2, 3 and so on.Rank 1 represents the highest priority for the urgency of soil conservation measures.Subsequently, all the sub-watersheds were grouped into different priority classes.

Prioritization using Compound Parameter Analysis
Numerous studies have used compound parameter analysis for the prioritization of susceptible watersheds to soil erosion (Patel et  parameters of watershed morphometry have a positive correlation with runoff and soil erodibility, whereas areal parameters have a negative correlation (Sangma and Guru 2020).Consequently, the sub-watersheds having higher values of linear and relief aspects as well as lower values of areal aspects were ranked highest (rank 1) and vice versa.After ranking all the sub-watersheds based on each parameter, the compound parameter value was determined by summing all the ranks of each sub-watershed and dividing it by the number of parameters considered.Lastly, all the sub-watersheds are ranked accordingly in ascending order of compound parameter value as ranks 1, 2, 3 and so on.Rank 1 represents the highest priority in terms of urgency of soil conservation measures, and all the sub-watersheds were systematically grouped into different priority classes.In both methods, the highest priority sub-watersheds, i.e., rank 1, signify the most pronounced instances of runoff and soil erosion risks demanding immediate attention and vice versa.

Results and discussion
Remote sensing and GIS techniques were executed on DEM to analyze the morphometric characteristics of the US-1 watershed, which was subsequently delineated into 16 sub-watersheds named SW1 to SW16.The computed results of the linear, areal and relief aspects of US-1 and its sub-watersheds are discussed below.The stream network map of the US-1 watershed is depicted in Fig. 3.

Basic parameters
The basin area (A) is a vital hydrological parameter of the watershed, as it receives rainfall directly and determines the total volume of water from rainfall.It is the totality of the physical landmass within the watershed boundary.In this study, the US-1 watershed has a total basin area of 1261.91 km 2 .SW1 (118.2 km 2 ) and SW5 (29.04 km 2 ) are the largest and smallest sub-watersheds in terms of area, respectively (Table 3).The basin perimeter (P) is the cumulative length of

Linear aspects
The linear aspects represent one-dimensional characteristics of a watershed in any morphometric evaluation (Table 3).Stream order (U) denotes the hierarchical rank of stream segments according to their position/occurrence in the tributary system.Morphometric analysis begins with a primary step of stream ordering based on the delineated stream network using DEM.In this study, the Strahler (1952) method was adopted for designating the stream order wherein each ngertip segment of the drainage network having no tributaries was assigned as rst order and a couple of rst-order streams converge to derive a second-order stream and this pattern continues successively; when streams of varying order join, the resulting stream is assigned with a higher order value (Asfaw and Workineh 2019).The stream order of a watershed, i.e., the highest stream order, receives the maximum discharge, runoff and sediment (Al-Saady et al. 2016).US-1 is a 6th-order stream depicting a dendritic pattern, and sub-watersheds are assigned a stream order ranging from 3 to 6 (Fig. 3).Soni (2017) opined that watersheds having such dendritic patterns develop over uniform resistant rocks and igneous rocks, leading to increased stream ow.
The stream number (N u ) signi es the number of segments within each stream order.There exists an inverse geometric series relationship between stream order and stream number (Horton 1945).A higher stream number in a watershed indicates a higher in ltration rate, permeability and erodible topography (Abdeta et al. 2020).In this study, the US-1 watershed has a total of 1522 streams.SW10 has the highest rst-order stream (103), and SW5 has the lowest (25) rst-order stream (Table 4).The surface runoff characteristics in a watershed are explained by Stream length (L u ).It is the sum of the total stream length within each order, which is in uenced by the slope, topography and rock formations.Generally, a longer stream length results in higher runoff and less in ltration, and it has an inverse relation with stream order (Obeidat et al. 2021).This further shows the variation in the in ltration capacity of the watershed ρ Page 10/30 with the rank of stream order.The US-I watershed has a total stream length of 1621.9 km, with SW10 and SW5 having the highest (187 km) and lowest (32.6 km) stream lengths, respectively.The mean stream length (L sm ) is associated with components of the drainage network and the nature of basin surfaces (Strahler 1964).It is conversely related to stream order and exhibits a signi cant relationship with surface runoff and the erosional status of the basin, where lower values mean higher surface runoff and soil erosion.According to Strahler (1964), a higher L sm indicates a higher average annual runoff.The L sm of US-1 is 1.07 km, and SW11 has the highest (1.87 km), whereas SW1 has the lowest (0.79 km) mean stream length.The stream length ratio (R l ) is obtained as the ratio between the stream length of a certain order and the stream length of its succeeding lower order as suggested by Potter (1957) The Rho coe cient is derived as the proportion between the stream length ratio and the mean bifurcation ratio.The Rho coe cient is an indicator of watershed physiographic development concerning drainage systems and quanti es the storage capacity of stream networks (Potter 1957).The Rho value is higher in SW8, SW11 and SW12, which possess good storage capacity during oods.The sinuosity index (Si) is a valuable tool for geologists and geomorphologists as it signi es the in uence of drainage patterns on the formation of landforms and aids as a good indicator of tectonic activity.In accordance with Leopold (1964), Si values > 1.5 are considered meandering, Si values from 1.25 to 1.5 as windy, Si values between 1.05 and 1.25 as twisty and values < 1.05 as straight.US-1 has a Si value of 1.34, indicating windy conditions.Much of the sub-watersheds are twisty followed by windy except SW14, which is meandering in nature.

Areal aspects
Drainage density (Dd) is quanti ed by dividing the total stream length of all orders by the drainage area of the watershed as explained by Horton (1932).It is a prominent morphometric parameter that shows the density/nearness of a branched channel network, thus offering a quanti able measure of basin average stream length, dissected landforms and runoff (Horton 1932;Strahler 1964).Dd is mainly dependent upon climatic conditions, soil type, vegetation, in ltration capacity, runoff intensity, and landscape evolution processes (Asfaw and Workineh 2019; Arulbalaji and Padmalal 2020).Fine textured impermeable subsurface soil, high relief and sparse vegetation are the typical characteristics of watersheds with higher Dd values where erosion and runoff potential are high (Farhan 2016; Asfaw and Workineh 2019).Similarly, coarse-textured subsoil, low relief and dense vegetation prevail in low Dd areas.In this study, the Dd of the US-1 watershed is 1.29, and among sub-watersheds, it ranges from 1 to 1.54; hence, SW4, SW14 and SW15 are prone to relatively higher soil erosion than the other sub-watersheds (Table 5).indicating high runoff from these areas compared to others.The circularity ratio (Rc) is the proportion of watershed area to that of circles with the same circumference as the watershed perimeter (Strahler 1964).Its value is impacted by the frequency of streams, geology, land use land cover, slope, relief and climate (Melton 1957).Rc ranges from 0 to 1, with lower values indicating an elongated basin and 1 indicating a perfect circle shape of the basin.The subwatersheds ranged from 0.16 to 0.5, and those having values between 0.4 and 0.5 possessed highly permeable and homogenous rocks.
The watershed shape is represented by the elongation ratio (Re) which usually varies from 0.6 to 1, and the basin shape nears a circle as Re approaches 1.
Higher Re values, i.e., closer to 1, typically exhibit much lower relief.On the other hand, elongation ratio (Re) values between 0.6 and 0.8 have higher relief and very steep slopes.As per Obeidat et al. ( 2021), watersheds are grouped as circular (Re > 0.9), oval if Re ranges from 0.8 to 0.9 and less elongated (Re < 0.7).
Accordingly, SW1, SW12 and SW13 have Re > 0.9, indicating a circular shape; ve of them are oval (5, 8, 9, 10 and 14), and the rest are less elongated.The form factor (Ff) is the ratio of watershed area and the square of its length as per Horton (1932)

Relief aspects
The relief aspect of a watershed is a three-dimensional picture expressed by taking into account the area, volume and elevation of the watershed.It quanti es the vertical descent from the inception of a stream segment to its joining point with a higher-order stream (Schumm 1956; Asfaw and Workineh 2019).
The US-1 watershed has a mean elevation of 925 m above mean sea level (msl), and its highest and lowest elevations are shown in Table 6.The respective elevations of individual sub-watersheds are also presented, wherein SW14 has the highest mean elevation (957 m), followed by SW15 (933 m), and SW1 has the lowest mean elevation of 702 m.Basin relief (Bh) is derived as the difference of the maximum and minimum elevation of a basin and in uences topographic land formations, drainage systems and, consequently, the surface ow, in ltration, permeability and erosion characteristics of watersheds (Magesh et al. 2011).An increase in Bh value results in heightened surface runoff and reduced in ltration rate.The highest Bh among sub-watersheds of US-1 was found to be in SW14 and SW15 (455 m), and the lowest Bh was in SW8 (60 m).The Relief Ratio (Rh) is a measure of the general steepness and the extent of erosional processes on the slopes of the watershed.It is the ratio of basin relief to the maximum length of the watershed running parallel to the main stream (Obeidat et al. 2021).Low Rh values indicate low relief and vice versa.It ranged from 0.005 to 0.04 among sub-watersheds.The relative relief ratio (Rhp) is a function of basin relief to the perimeter.Its value ranged from 0.1 in SW1 and SW16 to 1.04 in SW14.The stream gradient (Sg) is expressed as the ratio of the elevation difference between the source and mouth of a stream to the total stream length.It is associated with the energy of stream water to transport material and features of bedrock that resist ow (Hack 1957; Ghosh and Gope 2021).Its value ranged from 0.72 in SW16 to 5.61 in SW15.The ruggedness number (Rn) is an important relief parameter to determine the smoothness and/or roughness of watershed terrain; in other words, it is referred to as surface unevenness.The Rn value is between 0 and 1, where 0 indicates comparatively smoother terrain and 1 indicates more rugged terrain features.As per Strahler (1965), the Rn tends to become high when drainage density and basin relief are enormously high and indicate steep as well as long slopes.The Rn value of the US-1 watershed was found to be 0.67, and among sub-watersheds, SW1 had the lowest value (0.07), and SW10, SW13, SW14 and SW15 had higher Rn values, showing rugged terrain.The Melton ruggedness number ranged from 6.35 to 55.2 among sub-watersheds.
Hypsometric analysis is the measurement of elevation distribution across land surfaces, which is important in understanding the geomorphic evolution of land surfaces.It examines the relationship between the size and altitude of watersheds and identi es the phase of basin development, extent of dissection and erosion stages (Strahler 1952;Bharath et al. 2023).Hypsometry is the graphical representation of hypsometric analysis.Langbein (1947)  The hypsometric curve is the graphical representation of the relative area (a/A) and relative height (h/H) of the watershed depicting the portion of surface area at various heights over and underneath a datum.The shape and form of the hypsometric curve indicate major geomorphic processes at play in a watershed.A convex curve designates the youthful stage of the basin wherein much of the basin area is held relatively high, and a concave curve shows an old or monadnock stage with much of the basin area at lower altitudes.The equilibrium stage of the basin is shown in the form of an S-shaped curve, and the US-1 watershed belongs to the equilibrium stage with a sigmoid curve, as shown in Fig. 4.

FAHP method
The prioritization of sub-watersheds based on negative effects such as the severity of soil erosion is vital for any watershed management plan since the whole area cannot be looked into simultaneously.The sub-watersheds are hydrological units that possess unique morphometric characteristics, and the identi cation of crucial sub-watersheds is necessary.
In the present study, after computing all the morphometric parameters of each sub-watershed, the FAHP technique along with chosen morphometric parameters that in uence soil erodibility was used for prioritization of the US- stream length ratio (R lm ), mean bifurcation ratio (R bm ), drainage texture ratio (T), length of overland ow (Lof), in ltration number (Ifn), hypsometric integral (HI), stream gradient (Sg), ruggedness number (Rn), basin relief (Bh), relief ratio (Rh) and relative relief ratio (Rhp) are directly related to erodibility.Conversely, the compactness coe cient (Cc), form factor (Ff), elongation ratio (Re), shape factor (Sf) and circularity ratio (Rc) which are inversely related to soil erodibility, were utilized for prioritization.
A triangular fuzzy number (TFN) was used to overcome uncertainty in judging the parameters, and a pairwise comparison matrix was built to evaluate 18 morphometric parameters (Table 7).Subsequently, nal crisp numeric weights (x i ) were calculated for each parameter using the geometric mean method and centre of area (COA) method to defuzzify the weight matrix.Furthermore, the computed values of morphometric parameters were normalized (Table 8).The nal FAHP score (F j ) was obtained by summing the product of the crisp numeric weight and normalized values (W ij ) of the respective criteria, which ranged from 0.795 to 0.145 (Table 9).The sub-watersheds were ranked in descending order of the FAHP scores, meaning that a higher FAHP score corresponded to a higher rank and priority.The categorization of sub-watersheds based on FAHP into different priority classes is shown in Table 11.The map depicting the ranking and prioritized classes of sub-watersheds using the FAHP is shown in Fig. 5a and 5b.

Compound parameter analysis method
In the present study, the second method adopted for the prioritization of sub-watersheds is compound parameter analysis.The same eighteen parameters used in the FAHP method were considered for this method.The computed values of morphometric parameters that are inversely proportional to soil erodibility, i.e., compactness coe cient, elongation ratio, circularity ratio, form factor and shape factor, were ranked in ascending order of values.In other words, the smallest value was assigned the rst rank, the next smallest value was assigned the second rank, and so forth, until the largest value was allocated the sixteenth rank.This is because, as the values of these parameters increase, soil erosion tends to decrease.Furthermore, the values of those morphometric measures which are directly correlated to soil erodibility were ranked in descending order of their values.As a result, the rst rank was assigned to the highest value, and the last rank was assigned to the lowest value.This approach was adopted due to the positive relationship between these parameters and erosional susceptibility.After this, the compound value of each sub-watershed was calculated by averaging the ranks of all the parameters under individual sub-watersheds, and the results are shown in Table 10.The map depicting the ranking and prioritized classes of sub-watersheds using compound values is shown in Fig. 6a and 6b.Footnotes: Dd-drainage density, Fs-stream frequency, R lm -mean stream length ratio, R bm -mean Bifurcation ratio, T-drainage texture ratio, Lof-length of Overlan in ltration number, HI-hypsometric integral, Sg-stream gradient, Rn-ruggedness number, Bh-basin relief, Rh-relief ratio, Rhp-relative relief ratio, Cc-compactness Ff-form factor, Re-elongation ratio, Sf-shape factor, Rc-circularity ratio.
The compound value ranged from 6.056 to 10.778, and the sub-watershed having the least compound value was considered as having the utmost priority and vice versa.Consequently, SW4 was ranked 1 and was most susceptible to soil erosion, whereas SW12 was ranked 16 and had the least soil erosion according to compound parameter analysis.A total of ve sub-watersheds are categorized as 'high' priority occupying an area of 31.84%,another four of them are 'medium' priority occupying an area of 16.49%, and the remaining seven sub-watersheds are categorized as 'low' with an area of 51.67% (Table 11).

Comparison between FAHP and compound parameter analysis
The sub-watersheds of US-1 were prioritized using FAHP, which is a multi-criteria decision-making technique and compound parameter analysis approach.The comparison of results obtained from both methods is presented in Table 12.The common sub-watersheds under the 'high' priority class were SW14 and SW15; no common sub-watersheds were found under the 'medium' priority class, and six sub-watersheds viz., SW1, SW8, SW9, SW11, SW12 and SW16 were found to be common under the 'low' priority class in both methods.Hence, a total of eight out of sixteen sub-watersheds were categorized under the same priority class by both methods.The rest of the sub-watersheds differed in their priority classes, wherein SW2 was classi ed under an opposite priority class, i.e., both 'high' and 'low'.A study conducted by Hembram and Saha (2020) prioritized sub-watersheds in the Jainti River basin using fuzzy inference-based AHP and compound factors.In both methods, sub-watersheds 6 and 13 were common under the 'very high' priority class, sub-watersheds 4 and 8 were common under the 'high' priority class, and the outcome displayed good e ciency in the prioritization of erosion-prone areas at the subbasin scale.In this study, SW14 and SW15 as per FAHP along with SW2, SW4 and SW10 as per compound factor are highly susceptible to soil erosion risks and need immediate attention toward effective watershed management and planning.

Conclusion
A study was conducted on the Upper Shimsha-1 watershed to quantify the morphometric characteristics using remote sensing and GIS techniques and to prioritize the critical sub-watersheds susceptible to soil erosion using two approaches: FAHP and the compound parameter analysis method.The results revealed that US-1 is a 6th -order watershed with a dendritic stream network and is elongated in nature.Hypsometric analysis revealed that US-1 is in the equilibrium stage.It was delineated into 16 sub-watersheds, each of which displayed unique and varied morphometric characteristics and hence possessed varying degrees of soil erosion risks.A comprehensive set of eighteen parameters related to soil erosion were used to prioritize the sub-watersheds.It is noteworthy that SW14 and SW15 were identi ed as high priority; SW1, SW8, SW9, SW11, SW12 and SW16 were classi ed as low priority in both methodologies, highlighting that half of the total sub-watersheds of US-1 shared congruence in both prioritization methods corresponding with their respective priority classes.Although some sub-watersheds were categorized under different classes in both methods, this variance implies the effectiveness of these methods in prioritizing sub-watersheds.Since both FAHP, which is considered more advanced, and compound parameter analysis are being widely used by researchers to prioritize sub-watersheds, this experiment tries to cast light on the comparison between the two methods and to decide on the combined use of the same.Although land use land cover, sediment yield index, runoff potential and socioeconomic factors that were not incorporated within the scope of this study, indeed provide supplementary information on sub-watersheds.Nevertheless, morphometric analysis using geospatial technology forms the paramount for watershed prioritization in providing rapid and accurate solutions to soil and water conservation challenges.As this happens to be the inaugural study in prioritizing the sub-watersheds in the US-1 watershed area, the results of this paper strongly suggest that governing authorities and decision-makers endorse physical and biological soil conservation measures in highly critical sub-watersheds for the timely mitigation of soil erosion.Finally, the present study deduces the importance of morphometric analysis combined with FAHP and compound parameter analysis in watershed prioritization.This study is anticipated to guide researchers conducting studies in similar watershed areas by including supplementary information in future investigations.

Declarations Figures
Page 26/ Guru 2020; Sarkar et al. 2020; Gonçalves et al. 2023; Şener and Arslanoğlu 2023).Hence, morphometric analysis is a decisive tool for decisionmakers in watershed delineation and modelling, mitigation of soil erosion, groundwater potential zone mapping, landslide susceptibility mapping, river basin evaluation and prioritization of sub-watersheds for long-term watershed management plans (Mangan et al. 2019; Nitheshnirmal et al. 2019; Iacobucci et al. 2023).
A study was conducted by Bharath et al. (2023) investigating the drainage morphology of the Shimsha River subbasin adopting remotely sensed data, toposheets and GIS tools to gauge soil erosion and runoff in the basin.Another study by Arulbalaji and Padmalal (2020) carried out a morphometric analysis of the entire Cauvery basin and prioritized 17 sub-watersheds using compound parameter analysis.Furthermore, Harsha et al. (2020) and Chandrashekar et al. (2015) studied the morphometry of neighbouring Arkavathy subbasins using geospatial technology.
the boundary line of the watershed.The total length of the perimeter of US-1 is 242 km.The basin length (L b ) is the longest segment of the basin that aligns parallel to the main drainage stream(Schumm 1956).It greatly in uences the surface runoff characteristics of a watershed where longer streams mean more atter ground(Taha et al. 2017).The basin length of US-1 is 54 km, and among sub-watersheds, it is 20.8 km for SW3 and 7.49 km for SW5.The basin width (W b ) is the proportion of basin area to length and runs perpendicular to basin length.The results show that SW1 has a width of 11.4 km and SW2 has a width of 2.6 km.
.Pande and Moharir (2017) suggested that the changes in the ratio between succeeding stream orders rely on variations of slope and topography in uencing discharge as well as the erosional phase of the basin.SW11 has the highest R l of 4.27, and SW9 has the lowest R l (1.03).The mean stream length ratio (R lm ) of US-1 is 0.53, where SW9 has the lowest value of 0.34 and SW11 has the highest value of 1.07.A dimensionless parameter, the bifurcation ratio (R b ), is a principal linear aspect that relates the hydrological character of watersheds with geological structure as well as climatic conditions (Kabite and Gessesse 2018; Asfaw and Workineh 2019).It was introduced by Horton to show the degree of integration of streams belonging to different orders.Strahler (1964) opined that in watersheds having R b values from 3 to 5, the drainage patterns will not be affected by the geological structures.Lower values of R b indicate structurally less disturbed at lands with owing drainage patterns, whereas higher values indicate high runoff potential, soil erosion and overland ow.In the current study, the mean bifurcation ratio ranged from 2.79 to 6.28 among sub-watersheds, and US-1 had an R bm of 4.27.Sub-watersheds 2, 5, 6 and 16 had R bm values greater than 5, exhibiting geological and lithological in uences.
rst introduced it in watershed morphometry to describe the overall slope and forms existing in drainage basins.Hypsometric integral (HI) is expressed as the function of the partition of watershed topography.In tectonically active regions, the HI provides intuitions about the uplift rate as well as recent uplift anticlines, lithology and erosion (Sangma and Guru 2020; Obeidat et al. 2021).The HI values between 0.35 and 0.6 specify watersheds as being in equilibrium or the maturity stage, HI values lesser than 0.35 signi es the old stage, and HI > 0.6 signi es the young stage of watershed.In this study, HI ranged from 0.49 to 0.52 in SW13 and SW1, respectively.

Figure 1 Study
Figure 1 Study area map of Upper Shimsha-1 watershed descriptive caption: The state of Karnataka is highlighted within the shape le of India showing the location of study area.The North-eastern part of US-1 watershed exhibits higher elevation and decreases towards south-west direction.

Figure 2 Flowchart
Figure 2 Flowchart of methodology descriptive caption: The overall methodology is shown in the form of owchart starting with GIS analysis at the top and the successive steps are shown in rectangle boxes.At the end, the two approaches of prioritization being compared are depicted at the end of the owchart.

Figure 3 Drainage
Figure 3 Drainage map of Upper Shimsha-1 watershed descriptive caption: This gure comprises the branched network of streams similar to branches of a tree.The smallest nger like streams (1 st order streams)cover much of the study area and meet up to form a bigger stream (2 nd order stream) and further these streams converge to form higher order stream.The 6 th order stream originates at the center and ends at the south-eastern tip of the study area.

Figure 4 Hypsometric
Figure 4 Hypsometric curve of Upper Shimsha-1 watershed descriptive caption: this graph shows relative height on the Y-axis and relative area on X-axis.The S-shaped sigmoid curve origins at middle of graph on left side and ends at right bottom explaining the equilibrium stage of the watershed.

Figure 5 Ranking
Figure 5 Ranking (a) and priority classes (b) of sub watersheds based on FAHP descriptive caption: Fig 5a.The entire study area is divided into 16 sub-watersheds of various size and shapes.The FAHP ranks of each sub-watershed is assigned different colors for interpretation.Fig 5b.The 16 sub-watersheds are grouped into three classes as 'high', 'medium' and 'low' priority class based on FAHP.Each priority class is represented by different colors.

Figure 6
Figure 6 Ranking (a) and priority classes (b) of sub watersheds based on Compound parameter analysis method descriptive caption: Fig 6a.The entire study area is divided into 16 sub-watersheds of various size and shapes.The compound parameter ranks of each subwatershed is assigned different colors for interpretation.Fig 6b.The 16 sub-watersheds are grouped into three classes as 'high', 'medium' and 'low' priority class based on compound parameter method.Each priority class is represented by different colors.

Table 3
Basic and linear aspect results of Upper Shimsha-1 and its sub-watersheds

Table 4
Stream ordering of Upper Shimsha-1 and its sub-watersheds

Table 5
Areal aspect results of Upper Shimsha-1 and its sub-watersheds (Chorley et al. 1957<0.45)areelongated in nature(Strahler 1964).SW1, SW12 and SW13 exhibit circular shapes that are in agreement with Re and, as a result, experience peak ows of short duration.Sub-watersheds(2, 3, 4, 6, 7, 15 and 16) exhibit elongated shapes.The shape factor(Sf)is inversely related to the form factor, wherein lower Sf values indicate more erosion risk.The shape index (Sw) is the reciprocal form of the stream frequency, and the values range from 0.68 (SW8) to 1.55 (SW12).The drainage texture ratio (T) signi es the relative spacing of drainage channels, which can be categorized as 'very coarse' (T < 2), 'coarse' when T ranges from 2 to 4, 'medium' textured (4 to 6), ' ne' textured (6 to 8) and 'very ne' textured (T > 8)(Smith 1950;   Sreelakshmy et al. 2021).In this study, SW1, SW8 and SW10 have coarse-textured drainage, and the rest exhibit very coarse drainage.A compactness coe cient (Cc) closer to 1 indicates a circular shape of the basin, and a Cc less than 2 indicates an elongated shape.In the US-1 watershed, it ranged from 1.41 in SW13 to 2.52 in SW16.It is not in uenced by watershed size but by the slope of the watershed.The tness ratio (Rf) is the degree of topographic tness obtained by dividing the main stream length of the watershed by its perimeter.The Rf of the US-1 watershed in this study is 0.29, where SW1 has the lowest Rf (0.19) and SW2 has the highest Rf (0.4).The wandering ratio (Rw) is the proportion of the main stream length to the basin length and ranges from 1.05 (SW6) to 1.38 (SW14).The length of overland ow(Lof)and constant of channel maintenance (Cm) can be viewed as a function of density and greatly in uences the development of catchments(Mallick et al. 2022).The length of overland ow(Lof)is the distance covered by water on the ground surface before reaching a de ned stream network(Horton 1945).It is characterized by slope, relief, vegetation, soil pro le, rock formations, and climate and further helps to analyze the physiographical development of watersheds.Dd can also be used as a reciprocal to estimate Lof.It ranges from 0.32 km in SW4 to 0.5 km in SW1.The constant of channel maintenance (Cm) is estimated as the reciprocal of the drainage density as opined bySchumm (1956).It de nes the drainage area required for sustaining the unit length of the vertical stream.A lower value of Cm indicates low permeability and in ltration rates.US-1 had a low value of 0.78.The in ltration number (Ifn) is obtained as a multiplicative result of Dd and Fs, which indicates the surface runoff and in ltration rate and identi es impervious bedrock and high-relief areas.The sub-watersheds had Ifn values ranging from 0.78 (SW11) to 2.23 (SW4).A higher Ifn indicates high runoff and a low in ltration rate.Drainage intensity (Di) is the ratio of stream frequency (Fs) to drainage density (Dd), which represents the effectiveness of both parameters on surface denudation (Singh et al. 2021).It was found to be 0.94 for US-1, and SW11 had the lowest value (0.53), while SW1 had the highest value (1.26).The Rc indicates the shape of the basin, which becomes circular as the value approaches unity.In this study, SW13 and SW1 had values less than 1, and US-1 had an Rc of 1.82.The Lemniscate ratio (K) provides insights into the gradient of watersheds(Chorley et al. 1957).K values ranged from 0.22 in SW13 to 1.33 in SW2.
. Ff > 0.78 tend to have a circular shape that experiences high peak ows,

Table 6
Relief aspect results of Upper Shimsha-1 and its sub-watersheds

Table 8
Normalized values (W ij ) of morphometric parameters

Table 9
Among the 16 sub-watersheds, SW14 had the highest FAHP score of 0.795, followed by SW15 (0.766), and was designated under the 'high' class, occupying 10.76% of the US-1 watershed.Sub-watersheds SW4, SW10 and SW13 were categorized as having 'medium' priority and occupied 27.23%.The rest of the subwatersheds were of low priority, making 62.01% of the watershed with SW16 the least prioritized watershed.

Table 12
Common sub-watersheds to both FAHP and compound parameter analysis methods Priority class Common sub-watersheds Area affected in km 2 (%)