1 Introduction

The science of morphometry is concerned with the quantitative measurement and generalization of land surface geometry. Since the drainage basin (watershed) is considered as a basic unit of landform analysis, the geometric characters of master channel and its tributary network is important to understand and predict processes like floods, sediment dynamics and erosional patterns (Ritter et al. 1995). Fluvial morphometry embodies these geometric characters that define the linear, areal and relief aspects of the river basin and those of its tributary basins and their interrelationships. They reflect respectively the one-, two- and three-dimensional components of the basin. The hydrological characters and response of a river basin is intimately related to its geometric dimensions. Hence morphometric analysis is important for conservation and management of watersheds including flood control measures, which is in turn related to topographical components like relief, gradient, aspect, soil, vegetation, nature of rocks and tectonic and climatic factors like precipitation (Chorley et al. 1984; Ritter et al. 1995).

The introduction of remote sensing and GIS techniques has led to the rapid and precise estimation of morphometric parameters (Lillesand and Kiefer 1994, Biswas et al. 1999; Nookaratnam et al. 2005). The differentiation of a river basin into its constituent sub-water sheds and subsequent estimation of their morphometric parameters ensures effective and representational coverage of the basin. The influence of topographic and precipitation characters on the morphometric components is thus ensured. This leads to effective planning and development of basin and chalking out strategies for water and soil conservation (Kumar et al., 2011; Ahmed and Rao 2015; Choudhari et al. 2018), flood control (Youssef et al. 2011) and soil conservation (Biswas et al. 1999; Nookaratnam et al. 2005; Gadallah and Siddig 2024) practices.

The success of water or soil management studies of a basin depends on the effective delineation of the degree of susceptibility to hydrological processes in the different parts of the basin. Towards this end, prioritization of sub-basins (sub-watersheds) based on morphometric factors is carried out to understand the vulnerability of different sub-watersheds to hazards like flooding, soil erosion and groundwater storage. The common approach consists of ranking the sub-basins based on the calculation of a compound amount of the ranks given to each morphometric parameter considered for each sub-basin (Biswas et al. 1999; Nookaratnam et al. 2005; Ahmed and Rao 2015; Sengupta et al. 2022, Arulbalaji and Padmalal 2020; Bharath et al. 2021; Shekar and Mathew 2022). However, this method suffer from statical deficiencies in that the interdependence between the morphometric values are not considered. Also, the average values do have significance only when the standard deviations of the values of each parameter is low, which seldom happens in natural conditions.

Multi Criteria Decision Analysis (MCDA) is found to be a valuable tool in overcoming these deficits. MCDA techniques have been found to be advantageous in problems which involve uncertainties, conflicting criteria and where the criteria have different units of measurement. Various methods of MCDA have been applied to understand and prioritize in various applications like flood potential, soil erosion and delineation of groundwater potential. Komaragiri et al. (2018) have used entropy method for assigning weights for morphometric criteria and Fuzzy VIKOR is found to be effective for prioritization of sub-watersheds in Mahanadi River for implementation of soil and water conservation measures. Analytical Hierarchical Process (AHP) and a Fuzzy Analytical Hierarchical process (FAHP) technique have been adopted by Meshram et al., (2019) to rank sub-basins of two rivers for watershed management and FAHP is found to be more useful. Fuzzy based Best Worse Multi-Criteria Decision-Making (F-BWM) and Fuzzy Logic (FL), Interval Rough-Analytical Hierarchy Process (IR-AHP) has also been found to be useful in ranking soil erosion in Gusru river, India (Meshram et al. 2022a, b). Various MCDA methods (AHP, ANP, and ELECTRE I, VIKOR, TOPSIS) coupled with hydrograph concept were utilised by Akay and Koçyigit (2020) to study flood potential and for grading sub-watersheds of ungauged basins. They argue that MCDA methods are superior to traditional methods like hazard degree (HD), compound factor (CF) approaches and a statistical method (SM) adopted by Kocyigit and Akay (2018). Komaragiri et al. (2018) has applied Fuzzy Logic (FL), Interval Rough-Analytical Hierarchy Process (IR-AHP) methods to priortise erosion susceptibility of Gusru river. Results of Fuzzy AHP and Compound Parameter approaches give similar results for sub-watersheds of the Tenughat (Sengupta et al. 2022), unlike previously mentioned studies. They have used Sediment delivery ratio (SDR) model to explain the variance of soil erosion in the basin. Sridhar and Ganapuram (2021) have operated FAHP and Universal Soil Loss Equation (USLE) to calculate the erosion susceptibility of sub-watersheds of a river, and their outcomes were comparable. Principal Component Analysis (PCA) have been used in the prioritization of sub-basins to select the most significant morphometric parameters to be used. These have been combined with Normalised Difference Vegetation Index (NDVI) to rank Huehuetan river based on soil erosion by López-Pérez and Fernández-Reynoso (2021). They contend that this method suit areas with heavy rainfall and useful to decide on suitable management strategies. Rahman et al. (2022) conducted a similar study using not only PCA, but also PCA adopted weighted sum model (PCA-WSM) to select suitable morphometric variables of Darla basin in Bangladesh. Four most significant variables are identified by both the methods and they yield similar results. Prioritisation of sub-basins of Alaknanda River, India have been attempted using the approaches of Principal Component Analysis (PCA), compounding method (CM), Geomorphological Instantaneous Unit Hydrograph (GIUH), and Revised Universal Soil Loss Equations (RUSLE) by Singh and Kansal (2023). These gave different vulnerability rankings which they attribute to the distinct aspects that influence the basin. The final prioritization was estimated based on weighted average score.

These techniques have been applied in the various facets of hydrological studies. Razavi Toosi and Samani (2017) implemented DEMATEL (fuzzy DEcision-Making Trial and Evaluation Laboratory) model to provide a visual understanding among interdependencies of social, economic, environmental, managerial and technical criteria in five watersheds in Iran and fuzzy VIKOR process for ranking sub-basins. They argue that this model can help to consider weights of policymaking norms by considering intricate relationships among different decision levels and adopting suitable watershed management strategies. Asl-Rousta and Mousavi (2018) have simulated discharge of Sirwan River in Iran by means of SWAT model and have investigated the impacts of the number and location of sites, parameter set, and calibration method on the performance of the model. The twelve calibration settings built are discriminated using TOPSIS approach. Liu et al., (2019) argue that since ecological operation of reservoirs and balancing of traditional benefits like irrigation and flood control involve multi-objective optimization, fuzzy evaluation is a worthy method. Golfam et al., (2019) opine that best scenario to adapting to climate change on agriculture based on data for a thirty-year period on Gharanghu basin, Iran. Eight reservoir efficiency criteria are used as evaluation indices and five scenarios created by reducing water demand amounts. The prioritization studies using AHP and TOPSIS throw out different results regarding the best scenario for agricultural water management.

However, there are only limited efforts in most of these studies, to understand and discuss the topographical, structural and lithological controls that influence the morphometric factors and their interrelationship in individual sub-basins. These, in turn have a bearing on the total river basin that help in the prioritization of their sub-basins vis-à-vis any given hydrological hazards like flooding or soil erosion. It is felt that such an attempt, as in this study, would enhance the efficacy in selection of water and soil management and remedial practices for which prioritization is done in the first place. This is the primary objective of the present work.

In this study, the VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje in Serbian) method is the multi criteria analysis used. This method is characterized by its employment of aggregating functions; it focuses on compromising solutions for a prioritization problem with conflicting criteria as is commonly seen in natural systems, which can help decision makers obtain final solutions (Opricovic and Tzeng, 2004). The relative weights for the factors are obtained using SMARTER method. The salient details of how VIKOR was applied in combination with SMARTER method in the present study are discussed in the following section.

This work is part of our ongoing studies on the accuracy, sensitivity and resolution aspects of digital elevation models derived from different satellite data. Here, the prioritization is attempted on the sub-watersheds of Mahe river basin based on their susceptibility to flooding. The river experiences frequent phases of overflow during the monsoon seasons that last for about seven to eight months of a year. The unusually destructive flooding of 2018 (mortality of > 440; economic damage exceeding $3 billion) and 2019 in northern districts of Kerala (Mishra et al. 2018), gave impetus to the present work. The return periods of the then widely prevalent extreme rainfall events (≥ 204.5 mm), range from 75 to 500 years. Also, the inundated area could increase by about 16, 25, 37 and 40% for 5-, 25-, 50- and 100-year return periods of floods (CWC 2018). It is expected that the present work would help in evolving effective water control and conservation strategies.

2 Study Area

The Mahe river basin (MRB) falls between coordinates N11°35′ 16′, E75°30′ 07′′ in the south-west and N11°49′ 00′′, E75° 50′ 07′′ in the north-east in the State of Kerala, India (Fig. 1). The state of Kerala is located in the south western margin of the India, with a coastal length of 600 km and width ranging from 35 to 120 km (CWRDM 1995; Soman 2002). The extent of the state roughly resembles a scalene triangle, framed by mountains of Western Ghats (> 800 m) along the eastern fringe and the Arabian sea to the west. This unique physiography gives rise to relatively short rivers (< 244 km) but with high gradients. These ensure them a youthful nature with disproportionally high erosive power (Soman 2002).

Fig. 1
figure 1

Sub-watersheds of Mahe River Basin. The main stream is shown in red in the inset at the top

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Kerala supports the highest density of population (860/km2) among the states of India (382/km2) as per 2011 census (https://knowindia.india.gov.in), most of which are concentrated in the coastal plains in the lower reaches of forty-one rivers of the state. The state enjoys a humid tropical climate with an average annual precipitation of 3266 mm, where about 65% of the rainfall is contributed by the southwest monsoon (Srinivasan et al. 1972).

The Mahe river originates from Wynad Hills at an elevation of about 910 m and flows for 54 km before draining into the Arabian Sea. The area of the basin is about 402 km2. The average annual discharge of the river is about 248 Mm3 (CWRDM 1995).The average temperature ranges between 25 to 28 °C.

The rock types in this area are dominantly hornblende biotite gneiss, charnockite, quartzo-feldspathic gneiss, pyroxene granulite, banded magnetite quartzite, younger granite, gabbro and mafic intrusives of different generations along with recent sedimentary deposits and laterites. The major set of fault lineaments trend (1) NW–SE to WNW–ESE, (2) NNW–SSE to N– S, and (3) ENE–WSW (Nair 1990). The influence of these is reflected in the rectangular drainage pattern of the Mahe, particularly in the upper courses and the sharp veering of its channels. The major geomorphic components in the area are denudational plateaus, denudational hills and valleys, denudational slopes, flood plain, and valley flat (GSI 2002). The coastal belt with alluvial and beach deposit underlain by laterite, yields abundant yield of water. Open dug wells meet the domestic needs of water. (CGWB 2022).

3 Materials and Methods

The study is based on data derived from Survey of India topographical maps (1:50,000) and Digital Elevation Models of Shuttle Radar Topographic Mission (SRTM) with a pixel size of 90 m. The thematic layers required for the study has been generated using Arc GIS 10 and ERDAS IMAGINE 2011 software. Mahe river basin is divided into thirteen sub-watersheds (Fig. 1), based on analysis from DEM and topographic sheets, and designated as SW 1 to SW 13. Computation of basin parameters required for morphometric analysis, ordering, lengths, area, etc. are derived in a GIS platform. These are later used to calculate other morphometric parameters using established mathematical equations (Table 1).

Table 1 Description of morphometric parameters used in prioritisation of sub-watersheds
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Stream order, or classification of streams based on the number and type of tributary junctions, has proven to be a useful indicator of stream size, discharge, and drainage area (Strahler 1957). Essentially it is a method to quantify the hierarchy of linkage in a river network. One of the most accepted is the Strahler method (1964), whereby all the streams of the river network that does not have any tributary is designated as of order one. Two first streams join to form a stream segment of second order, two second order segments join to form a third order segment and so on. Mahe river is of sixth order with two fifth order tributary basins. The details are presented in Fig. 2 and Table 2. The higher number of lower order streams (like first and second), act as feeder channels contributing more water yield to the total basin as a whole.

Fig. 2
figure 2

Slope map of Mahe River Basin

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Table 2 Morphometric parameters of the sub-watersheds of Mahe basin
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Thirteen morphometric factors are identified to be significant for MCDA in this work which is further discussed in Table 1. Those are selected based on those parameters which factor in the basic topographic components like relief, slope, basin area, perimeter, length and number of streams etc. the basic morphometric parameters used to calculate each of them. Care has been taken, as far possible to avoid repetition of the same set of factors used as ratios or products. For example, drainage texture (which is product of drainage density and stream frequency) is not considered, since both parameters are separately taken into account. Similarly, form factor, Ff and compactness coefficient, Cc are also left out in the study. They are essentially of ratios of areas between basin lengths and perimeters, respectively. These proportions are represented in elongation ratio and circularity ratios, which are discussed here.

VIKOR method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. VIKOR methodology has been applied to different engineering domains. Fallahpour and Moghassem (2012) have applied for parameter selection problem in rotor spinning. Arif et al. (2020) has addressed the prioritization of the goods sellers in e- market place by integrating VIKOR with the SMARTER method. Mohsen and Fereshteh (2017) have used this method to rank and prioritize the failure modes in a geothermal power plant. Kuo and Liang (2011) have used the method to evaluate service quality of airports. The method offers a variety of advantages:

  • The method uses a linear method of normalizing.

  • The method uses an aggregating function representing the distance from ideal solution, considering the relative importance of all criteria, and a balance between total and individual satisfaction (Fallahpour and Moghassem 2012).

The general steps involved in the VIKOR method are:

  • Step 1: Establish a matrix of criteria and different alternatives.

  • Step 2: Determine the weights for each factor.

  • Step 3: Determine the best and worst values of all factor functions.

  • Step 4: Calculate the utility measure and regret measure for each alternative

  • Step 5: Calculate the value of VIKOR index

  • Step 6: Rank the preference order

4 Discussion

The relationship between parameters and flood potential is given in Table 1. Higher the values for certain parameters, greater the potential for discharge with high peak flows with shorter lag times for water from upper part of the basin to reach the outlet. These in turn enhance the rate and pace of occurrence of floods. However, the correlation of each of these parameters with the flooding potential is not in the same proportion for each sub-basin (for instance, the highest values of these factors are not exhibited by the same sub-basin). This also holds true for the geometric factors that correlate inversely with discharge and flooding potential. The flooding potential of each basin and its sub-basins are governed by the collective influence of morphometric factors with each other and topographic elements (such as slope, relief, rock and soil characters), tectonics, climatic aspects like temperature and precipitation in a steady state equilibrium (Ritter et al. 1995).This is attested by their conformity to Horton’s laws (r > 0.98) which contend that the total length and number of streams decrease with increasing order in a geometric series (Horton 1932). On the other hand, the mean stream length shows a positive correlation with stream orders.

SW 12 is the smallest basin (area < 1 km2), partially bounded by hillocks and topographic rises, where the river flows over less than 1 km. The small area and perimeter give rise to high drainage density and stream frequency, texture ratio and low TWI and SPI values. Since the first order streams directly join the main fifth order river, its bifurcation and stream length ratios could not be estimated. Its rather peculiar morphometric characters and low spatial extent have induced us to consider it as an ‘aberrance’ and exclude this sub-basin from further discussions.

The morphometric parameters of Mahe river (Table 2) reveals it to be a sixth order basin with moderately high runoff as attested by its moderate slope (2.31°), gradient ratio (0.03), bifurcation ratio (4.21), density, stream frequency and consequently lower base flow, percolation rate. The varying nature of slope, relief and other topographic factors, lithological components and tectonic elements account for the fluctuating values of bifurcation ratios (Fig. 1; Table 2). This is in contrast to the theoretical concept that bifurcation ratios decrease with increase of stream orders (Chorley et al. 1984). The relatively high values of length of overland flow (0.24) indicate the appreciable span of flow before it is channelized, reflecting the overall gradient of the basin. The shape parameters of the river identify it to be an elongated basin (low Rc < 0.4; Re < 0.7) as per Makrari et al. 2022 with flatter flows with longer lag times. The development of the basin is influenced by topography and terrain than tectonic elements (as Rb is between 3 and 5 (Strahler 1957). Thus, the Mahe is revealed to possess lower potential for flooding and inundation. This is underscored by the significant wetness index (> 8.3, Thomas et al. 2012) and lower stream power index highlighting the appreciable groundwater storage and moderate erosion potential (Table 2). This is further underscored by the Melton ruggedness of 0.07, indicating Mahe to be a water flood basin, since MRn < 0.3 (Wilford et al. 2004; Makrari et al. 2022), rather than one where debris flood occurs.

The VIKOR method is implemented for the morphometric factors related to sub-watersheds of Mahe river basin. The steps mentioned above as motivated by Fallahpour and Moghassem (2012) has been applied here and is presented hereunder:

  • Step 1: The thirteen key morphometric factors (MF) pertaining to thirteen sub-watersheds of Mahe river basin are summarized in Table 3. This is considered for the application of VIKOR methodology.

Table 3 Morphometric factors values for thirteen sub-watersheds of Mahe River Basin
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  • Step 2: The determination of weights (W) for each factor is obtained by using Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER) method. The method is prompted by Arif et al. (2020), wherein it determines the weight of each factor based on Rank Order Centroid (ROC).

Determination of priority factor based on the relative importance of the factor can be written C1 ≥ C2 ≥ C3 ≥ … ≥ Cj, to determine its weight. Weighting with the ROC technique, can be formulated as \({W}_{j}=\left(\frac{1}{J}\right)\sum_{i=j}^{J}(\frac{1}{i}).\) where J is expressed as the number of factors, j as j-th factor, and I expressed as order of the factor (i = 1,2,3, …, j). Here thirteen factors are rank ordered based on their importance and subsequently factor weights are calculated with the ROC formulation and are given in Table 4.

Table 4 Factor weights determined using SMARTER method
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  • Step 3: Determine the best \({f}_{j}^{*}\) and the worst \({f}_{j}^{-}\) values of all factor functions. If the factor contributes lesser to the floods, then use the function \({f}_{j}^{*}= {max}_{j}{f}_{ij}\) and\({f}_{j}^{-}= {min}_{j}{f}_{ij}\). If the factor contribute more to the floods, then use the function \({f}_{j}^{*}= {min}_{j}{f}_{ij}\) and\({f}_{j}^{-}= {max}_{j}{f}_{ij}\), where I expressed as order of water shed basins (i = 1,2,3,…,n), and j expressed as order of factors (j = 1,2,3, …., m).. Accordingly, the best \({f}_{j}^{*}\) and the worst \({f}_{j}^{-}\) values of all thirteen factor functions are calculated and are presented in Table 5.

    Table 5 Best \({f}_{j}^{*}\) and the Worst \({f}_{j}^{-}\) values for the morphometric factors
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  • Step 4: The utility measure or the value of alternative distance to the positive ideal solution (Si) and the regret measure or the value of alternative distance to the negative ideal solution (Ri) are calculated for each of the thirteen sub-watersheds using the following formula:

    $${S}_{i}={\sum }_{j=1}^{n}{W}_{j}\frac{({f}^{*}-{f}_{ij})}{({f}_{j}^{*}-{f}_{j}^{-})}$$
    $${R}_{i}={max}_{j}\left[{W}_{j}\frac{({f}^{*}-{f}_{ij})}{({f}_{j}^{*}-{f}_{j}^{-})}\right]$$

    Where Wj is the weight of factor obtained in step 2 using SMARTER method. The calculated values of Si and Rj for each of the thirteen sub-watersheds are presented in Table 6.

    Table 6 Si and Rj values for Sub-watersheds
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  • Step 5: VIKOR index (Qi) is calculated for each of the thirteen sub-watersheds using the following formula:

    $${Q}_{i}=v\left[\frac{({S}_{i}-{S}^{*})}{({S}^{*}-{S}^{-})}\right]+(1-v)\left[\frac{({R}_{i}-{R}^{*})}{({R}^{*}-{R}^{-})}\right]$$

    Where S* = miniSi; S− = maxiSi; R* = miniRi; R− = maxiRi and v is given as a weight for the strategy of maximum group utility and (1-v) is the weight of the individual regret v can take any value ranging from 0 to 1; normally the value of v is taken as 0.5 (Cristobal 2011). The calculated value of VIKOR index for the sub-watersheds are presented in Table 7.

    Table 7 Qi and Rank order values for Sub-watersheds
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  • Step 6: Rank the sub-watersheds after sorting by the values of Qi in deceasing order. In the present study the priority ranks of the sub-watersheds were determined by the Q value so as to compromise the S and R values (Lee et al. 2014). The ranks of the sub-watersheds are presented in Table 6. Higher the rank, more vulnerable the sub-watershed for the floods. Consequently, sub-watersheds SW 3-8 are found to most prone to inundation, while SW 9-13 is found to be least susceptible. These findings are further analysed in terms of topographical, structural and lithological framework.

The spatial analysis of constituent subbasins presents marked contrasting characters from those of Mahe basin, reflecting the difference in terrain, properties of soil, rock and gradient characters within the basin (Ramasamy et al. 2021). VIKOR analysis have recognized SW 3–8 as the sub-watersheds, most vulnerable to flooding. These comprises about 23.2% of the total basin area and are disposed in the crystalline rock terrain of Western Ghats (GSI 2002; Soman 2002). They are characterized by, in general, low areal values, higher relief and gradient ratios >  ~ 0.10, i.e. 5.71° (Figs. 1 and 2). SW 3–8 are also distinguished by very fine texture (> 26), the highest number of first order streams, slope (> 7.5°), Melton ruggedness number (> 0.21) and texture number (> 6). These are indicative of the high gradient and impermeable rocky terrain exposed in parts of these sub basins. The lowest Lo values (0.15) reveal the short flow paths before concentrating into distinct stream channels. In addition, the steep drainage divides (Fig. 2) of sub-basins with their high relief, funnels water from lower orders into the main streams catalyzing narrow high peak flows with shorter flow duration (Avci 2023). Such tributaries ensure highest discharge per unit area in a basin, though their individual total discharge would be much diminished than the main stream (Ritter et al. 1995). The general circularity and elongation ratios are less than 0.4 and 0.6 indicate their elongated nature, as observed in basins with high gradients (Schumm 1956; Manu and Anirudhan 2008; Kumar et al. 2011). These, thereby reflect their substantial infiltration capacities. These basins are covered by thick tropical ever green forests and attendant thick humus, which is known to encourage water infiltration of the terrain and thus subdues discharge and flooding potential (Chorley et al. 1984; Charlton 2007). However, in SW 3–8, morphometric characters discussed previously seem to have offset the effects of vegetation and their elongated nature. TWI, a negating parameter of discharge exhibits the lowest values, pointing to the lower base flow and groundwater storage. The Melton ruggedness ratios indicates basins SW 4,6 and 7 belong to the upper grade of water flood category (< 0.3), while the rest are capable of debris rich floods (as high as 0.43 in SW 8),). The relation between stream number and drainage density (r = -0.77) indicates marked influence of headward erosion for these sub-basins. Such trends were noted for the Mahe by Ramasamy et al., (2021) and has also been observed elsewhere (Hack 1957; Mulder and Syvitski 1996; Thomas et al. 2010; Choudhari et al. 2018). On the other hand, in rest of the sub-watersheds this relation is very explicit (r = 0.99), along expected lines.

The terrain of SW 1 (ranked 5 in MCDM) includes topography of moderate elevation (790 m), relief (776 m.), slope (3.22°), bifurcation ratio (4.66) but with its considerable gradient (712 m.), low Dd (1.68) and elongated nature (Fig. 1; Table 2). These combined with the physiographic unit of laterite uplands (Ramasamy et al. 2021), the porous nature of which encourages infiltration and has a subduing influence on surface runoff. In this sub-basin, the high runoff benefitted from its high relief, gradient and resistant impermeable rocks (Schumm 1956; Ritter et al. 1995) in its upper reaches are to a limit muffled by the lateritic components further downstream. This is further influenced by its considerable areas and elongated nature, resulting in flatter peaks with longer lag times than expected leading to reduced threat of flooding. The medium values of Lo (0.30), underscore the significant base flow and infiltration nature of the terrain. The lower order stream networks coalesce and spreads out in the lower part of the sub-basin where the lower relief, and slope result in flatter topography, relatively unimpeded by restrictions imposed by mountain divides and tectonic lineaments.

SW 2, in contrast is of less steepness (1.17°), gradient ratio (0.001), relief (128 m.), compared to SW1 (Fig. 2). However, the similar values are seen in texture and drainage ratios, wetness index, shape factors, mean stream lengths (Table 2). The bifurcation ratios of first order streams indicate the significant structural control and more importantly, the substantial contribution to runoff from these feeder channels for this rather small subbasin (~ 11 km2). Small basins are known to enhance flooding potential (Ritter et al. 1995) with high peak flows and short lag times (Avci 2023). Further, the cumulative discharge from the upstream subbasins forming the fifth order SW 2 supply sizably to the runoff, that is not reflected in its morphometric values. The permeable laterite that is widespread in the terrain restrains the surface runoff to an extent, a scenario similar to that of SW 1. Thus, SW 1 and 2 constituting about 16.4% of MRB, offer restrained susceptibility (ranked 5 and 6) to flooding, compared to SW3-8.

Such characteristics are more pronounced in SW 10, 11 and 13 that constitute about 38% of the Mahe basin area that virtually comprises the coastal plains (Figs. 1 and 2). These are characterized by lateritic soil and alluvium (and the lateritic highlands in their upstream) that favour percolation of water to the water table where most of agriculture here is concentrated. This is confirmed by highest (mostly > 8) wetness indices, emphasizing the reduced susceptibility to flooding. The slight gradient (0.65–1.2°) likely spawns the low drainage density (< 2) and frequency (and attendant very coarse texture of < 2) and Melton number (0.02–0.04) and very high length of overland flow (0.30–0.35). This is also borne out by low elongation and circularity ratios of the sub-basins of lower relief (i.e., except SW 3–8), which do not display high values as expected in lower relief portions of a river (Schumm 1956). Obviously, the effect of the permeable thick soil and alluvial deposits and the underlying laterite affect the surface runoff (Rai et al. 2014; Aparna et al. 2015) accounting for the low to moderate ratios.

SW 9 with its steep upstream portions (> 20°), expresses a morphometric pattern comparable to SW 1 in many respects (Table 2) but is graded as the one which is second least prone to flooding (Fig. 3). However, the lower gradient ratio (as opposed to slope gradient), reflects the subdued potential energy of the discharge. Its elongated nature, and being the largest sub-watershed, translates to longer length of flow, lag time and consequently lower vulnerability to inundation. In addition, the billowing of its lower reaches and the laterite and lateritic and alluvial soil of landscape checks the energy of the stream, resulting in lower value (vis-à-vis its size) of SPI (5.81), with larger flow accumulation (TWI-7.21) and rate of soil infiltration.

Fig. 3
figure 3

Classification of sub-watersheds of the Mahe based on their flooding potential

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Thus, SW 9–13, that includes the largest sub-watersheds consists of 60.4% of the Mahe basin. As discussed above, the morphometric framework of these sub-basins ensure high infiltration rate of water (and greater base flow) and hence, as the least prone to flooding in Mahe. The VIKOR analysis too supports this trend. In fact, they form good aquifers as attested by the groundwater yield here (CGWB 2012; 2017). The flood plains and associated wet lands effect a flood controlling system that holds a large amount of water as part of the base flow. This checks the magnitude and height of peak flows that last over a longer duration (Chorley et al. 1984; Ritter et al. 1995). Again, the large swath of the basin encompassing the lower reaches of these sub-watersheds ensure that the flooding effects of the upper sub water sheds are curtailed to an extent, by promoting the broadening out of water.

SW 3–8, nestled at the heights of Western Ghats is benefitted by greater precipitation there (> 4000 mm) than the midland and coastal plains in Kerala (Rao and Ramamurti 1968; CWC 2018). Moreover, the orographic effect on precipitation ensures that rainfall increases with height in the Ghats (Tawde and Singh 2014; Halder et al. 2022). Consequently, it is a common observation that even moderate showers in the Ghats sometimes lead to inundation in the higher reaches of rivers (CWC 2018). The short lengths and high gradients of Kerala rivers (11.6° in the mountains to 3.67° at the onset of lowlands, in the case of the Mahe) along with their conducive morphometric factors and flatter topographic nature, ensure that the enhanced collective discharge in sub-basins SW 3–8 during rains, is rapidly emptied to the lower stretches of rivers. The heightened runoff thus produced, leads to broader peaks flows (as discussed earlier) in the coastal plains (i.e. in SW 9–13 in Mahe), that takes a longer time to recede. This is borne out by previous studies (CWC 2018; Das 2020) that reveal that risk of spiked runoff increases in the lower reaches of streams during monsoons, where the population density is highest (https://ecostat.kerala.gov.in/; Das 2020). Ponding up of water has been observed in many stretches of streams in the midland and coastal areas of Kerala, related to movements along fault zones (Valdiya and Narayana 2007). This probably augments the phases of high discharge during monsoons, adding to the impact of runoff from upstream. Another catalytic feature is the massive deforestation occurring in the Ghats (Padma 2018; Ramachandra and Bharath 2020). However, our ongoing studies reveal that unbridled and rampant constructive practices occurring over the past decades (and thus decreasing the permeability of the sub-basin) likely contributes to the destruction of the natural flood control system, leading to the gradual increase of frequency and extent of floods. This trend is in line with findings of previous studies in the state (George and Chattopadhyay 2001; John et al. 2020) and their effects on surface runoff (Dixit et al. 2022).

From the above discussions, it is seen that sub-watersheds of the Mahe may be categorized into three groups (Fig. 3), based on their flooding potential- Low (SW 9, 10, 11, 13), Moderate (SW 1,2) and High (SW 3, 4,5, 6, 7,8). Suitable control and management strategies could be planned and implemented based on proneness to flooding befitting each sub-watershed. The study highlights the efficacy of MCDA techniques like VIKOR to prioritise sub-basins with respect to any given hazard. However, multi-dimensional studies incorporating discharge and Land Use-Land Cover (LULC)patterns would further enhance the clarity runoff characteristics of a river basin and in consequence, the flooding potential.

Currently, no flood control structures exist in the Mahe. Construction of flood control measures like diversion dams and channelization methods (except resectioning or dredging) may not feasible when the high population density (as much as 4646/km2 in Mahe district, https://mahe.gov.in) and compact built-up patterns extending right to the edge of the river are considered. Implementation of Flood plain zonation based on the flood susceptibility would also be difficult for social and economic reasons. Also, they would involve resettling and rehabilitation of populace and large-scale modification/removal of existing construction structures. Dams in the sparsely populated mountainous terrain of the basin seem to be an effective and viable option considering the performance of these structures in controlling floods in other rivers of the state and elsewhere. The option of closed diversion canals needs to explored as they have been found to be theoretically operational in similar settings (Indrawati et al. 2018).

5 Conclusion

The disaggregation of river basins into their constituent sub-watersheds afford workable representative component units. This study has revealed the efficiency of MCDM techniques through SMARTER and VIKOR methods in prioritizing sub-basins based on their inclination to flooding considering conflicting factors. This would help in chalking out relevant protection and regulatory mechanism based on the probability of inundation for each sub-basin.

The morphometric measurements of Mahe river reveals it to be a sixth order basin with moderately high runoff, consequently appreciable percolation rate, base flow and groundwater potential, particularly in its lower reaches. SW 3–8 in the upstream of the Mahe, situated in the crystalline rock terrain was identified to be the sub-basins most prone to flooding. This is reflected in their highest values of relief, gradient, fine texture and texture ratios. These along with their small areal extents counteract the effects of dense foliage and elongated nature in regulating runoff, leading to high peak flows of shorter duration. They form 23% of the total river basin. SW 1 and 2, offers a moderate risk of flooding, since the advantage of prominent runoff in their upper reaches is inhibited by the laterite components of the downstream terrain. The sub-basins SW 10–13 virtually covers the coastal plains of the Mahe. The low measures of gradient and slope, coarse texture, along with thick soil and alluvium of their lateritic terrain regulate their discharge rendering them least vulnerable to flooding. The low gradient ratio, elongated nature and permeable terrain ensures the low susceptibility of the largest sub-basin SW 9 to inundation, though its morphometry mostly echoes that of ‘Moderate’ SW 1. Hence, SW 9–13, forming 60% of the Mahe basin fall in the ‘Low’ grade of flooding potential. However, the enhanced cumulative discharge from the higher reaches during monsoons leads to heightened runoff in these sub-basins, that diminishes only over a longer period of time. Construction of dams may be a feasible flood control measure in the Mahe.