Introduction

Watershed is important for the management of natural resources and natural hazards in long-term development (Khan et al. 2001; Aouragh and Essahlaoui 2018). Effective watershed management necessitates a thorough understanding of the hydrological behavior of the watershed (Gajbhiye et al. 2013). A detailed analysis of each watershed is required to establish a management plan. Morphometric analysis is a useful tool for assessing and understanding the behavior of hydrological systems (Bhattacharya et al. 2021). Hydrological and geomorphic processes that can be measured with morphometry include soil erosion, runoff, sedimentation, and drainage geometry (Arabameri et al. 2020). The watershed is the basic unit of morphometric analysis, which was developed by Miller (1953); Horton (1945); Schumm (1956); Strahler (1957); and Sameena et al. (2009).

Soil erosion risk mapping and soil conservation planning, which are normally done with the use of erosion models, are becoming increasingly important in a watershed for long-term agricultural and natural resource development (Singh 2009; Haokip et al. 2021; Novara et al. 2011). Prioritization of watersheds is a well-known scientific method for identifying places that are prone to soil erosion and flooding, as well as appropriate for groundwater exploration (Magesh and Chandrasekar 2012; Arabameri et al. 2018; Jothimani et al. 2020; Bhattacharya et al. 2021). The accelerated erosion can be reduced in a watershed by identifying and prioritizing soil erosion-prone areas (Prieto-Amparán et al. 2019; Nitheshnirmal et al. 2019).

There are numerous methods for prioritizing watersheds such as Universal Soil Loss Equation (USLE) and Sediment Yield Index (SYI), including the analytical hierarchy process (AHP) using morphometric analysis of the watershed (Anees et al. 2018; Arulbalaji et al. 2019). In situations, when the data is scarce, morphometric analysis can be quite useful (Javed et al. 2011; Pramanik 2016; Ameri et al. 2018). As the linear and shape parameters have a direct and indirect relationship with erodibility, morphometric analysis assists in the identification of sensitive zones that are susceptible to soil erosion (Farhan et al. 2017; Shivhare et al. 2018; Haokip et al. 2021). Furthermore, this factor is a useful tool for choosing sub-basins without having to examine the region's soil map (Pandey and Sharma 2017; Meshram et al. 2020). Assessing the soil erosion risk, particularly in mountainous areas, where it is difficult due to the variability of topography and the lack or insufficiency of essential data. The present study aims to identify the sensitive soil erosion-prone sub-watersheds in the upper catchment and lower undulating plain catchment of the Teesta basin based on morphometric characteristics using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS).

Study area

The study area is the sub-watersheds of the Teesta River basin, which is situated in Sikkim and West Bengal (Fig. 1). It is important to discuss the basin as a whole in the Indian part. The Teesta exhibits large variability in geography, the glacial, periglacial deposition, dissected valley, flood plain, and landslide slope (Mukhopadhyay 1984; Rudra 2008, Sarkar 2008). The lower section of the basin has a gentle slope intended for flat topography. The southern part of the Teesta River Basin has a 4° slope. The central part has an increased 23° to 51° slope, the northern part has 25°, and the extreme northern part has a high slope (Mukhopadhyay 1984; Mandal and Chakrabarty 2016; Pal et al. 2016; Karmokar and De 2020).

Fig. 1
figure 1

Location of the study area

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Methodology

The geospatial techniques were applied to delineate the soil erosion potential zones of the Teesta River basin using the morphometric parameter. The Aster DEM was used to define the drainage and watershed boundaries. Arc GIS tools were used to derive and calculate morphometric parameters of the watersheds. Morphometric parameters were calculated based on the mathematical equation illustrated in Table 1. The morphometric parameters were categorized into two categories. The parameter includes bifurcation ration (Rb), circulatory ration (Rc), basin length (L), stream frequency (Fs), drainage density (Dd), basin perimeter (P), basin width (W), shape factor (Bs), drainage texture (Dt), and elongation ratio (Re). Category-1 comprises all parameters that have a direct relationship with soil erodibility, while category-2 has an inverse relationship. The higher the values of linear parameters the greater erosion will be and the lower values of shape parameters indicate higher susceptibility to erosion (Arabameri et al. 2019; Nitheshnirmal et al. 2019; Amiri et al. 2019). After determining and computing the effective values of the morphometric parameters, prioritization was done using the AHP and the TOPSIS MCDM models. A methodological chart are shown in Fig. 2.

Table 1 Formulas adopted for computation of morphometric parameter
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Fig. 2
figure 2

Methodology chart

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AHP model

The weights of criteria can be determined in a variety of ways, in this study, the weights of each criterion were assigned to Saaty’s relative importance scale (Saaty 1990; Arulbalaji et al. 2019). A pairwise comparison matrix was used to compute the weights. Table is derived from a review of the literature and personal experience (Arabameri et al. 2020). First, using Saaty’s rating scale (Table 2), pairwise comparison matrices are constructed for criteria based on relative influence on soil erodibility (Nitheshnirmal et al. 2019). The pairwise comparison matrix was created by taking into account the information provided by the relevant literature (Ranjan et al. 2013; Jaiswal et al. 2015; Gaikwad and Bhagat 2018; Meshram et al. 2019; Arulbalaji et al. 2019; Saha et al. 2021).

Table 2 The comparison scale for the relative pairwise comparison matrix (Saaty 1977)
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The consistency ratio (CR) is the method through, which the validity of relative influence is measured after the comparison matrix has been constructed (Saaty 1990; Arabameri et al. 2020). A CR value < 0.1 is acceptable. Equations (1) to (2) were used to calculate CR (Novara et al. 2011).

$$\mathrm{CR}=\frac{CI}{RI}$$
(1)
$$\mathrm{CI}=\frac{{\lambda }_{\mathrm{max}-n}}{n-1}$$
(2)
$${\Lambda }_{\mathrm{max}}=\frac{\sum\uplambda }{n}$$
(3)
$$\lambda =\frac{wsv}{w}$$
(4)
$$\mathrm{wsv}=A\times W$$
(5)

where CR is the consistency ratio, CI is the consistency index, RI is a random index (Table 3), n is the number of criteria, λmax is the largest special matrix value, λ is the consistency vector, WSV is the weighted sum vector, A is pairwise comparison matrix, and W is the weight of criteria vector.

Table 3 Values of random index (RI)
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Technique for Order of Preference by Similarity to the Ideal Solution Model (TOPSIS)

The most well-known decision-making model, TOPSIS (Hwang and Yoon 1981), is one of the most technical schedules for prioritizing alternatives through the distance from the ideal and anti-ideal points. It is simple to find the best answer. A positive ideal indicator positive ideal solution (PIS) will provide the best value, while a negative ideal indicator negative ideal solution (NIS) will provide the poorest value, and a ranking will be determined accordingly (Behzadian et al. 2012; Chen 2000). The outcome of these two distances is expressed as a closeness coefficient, which is based on the fact that the option with a numerical value of a larger coefficient of attraction is known as the preferred option (Ustaoglu et al. 2021).

The TOPSIS procedure is as follows (Aouragh and Essahlaoui 2018).

  1. Step 1:

    In the matrix alternatives were used in rows and evaluation criteria were used in columns (Sadhasivam et al. 2020). In the study, the decision matrix D was created using 15 alternative sub-watersheds and 10 criteria (Fig. 3).

    (6)

where A1, A2…, Am are possible alternatives among, which decision-makers have to choose.

Fig. 3
figure 3

Decision tree

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C1, C2…, Cn are criteria with which alternative performance is measured; Xij is the rating of alternative Ai concerning criterion Cj.

  1. Step 2:

    The criteria are stated in various units, and the decision matrix should be normalized.

    $${\mathrm{n}}_{\mathrm{ij}}=\frac{Xij}{\sqrt{\sum_{i=1}^{m} {Xij}^{2}}}$$
    (7)

where nij is a normalized decision matrix element and \(Xij\) is the i-th alternative performance in j-th criteria.

  1. Step 3:

    Calculate the weighted normalized decision matrix as follows

    $${\mathrm{v}}_{\mathrm{ij}}={\mathrm{n}}_{\mathrm{ij}}\;{\mathrm{X\;w}}_{\mathrm{j}}, \mathrm{i}=1, . . ., \;\mathrm{m}; \;\mathrm{j}=1, . . ., \mathrm{n}.$$
    (8)

    where vij is the weighted normalized matrix element, nij is the normalized matrix element, wj is the weight of criteria j. The weights of the criteria were calculated using Saaty’s analytical hierarchy process. To compute weight, we employed the AHP method, which is widely used in the literature (Arulbalaji et al. 2019; Saha et al. 2021).

  2. Step 4:

    Identification of the positive ideal solution and negative ideal solution as given in reference (Strahler 1957) calculation of the positive-ideal (A+) and negative ideal (A.−) solutions respectively (Aouragh and Essahlaoui 2018)

    $${\mathrm{A}}^{+}=\left\{\left(\left({maxv}_{ij }/j\in J\right),\left({minv}_{ij} /j\in {J}^{^{\prime}}\right)\right)/i=\mathrm{1,2},\dots ,m\right\}={v}_{1}^{+},{v}_{2}^{+},\dots , {v}_{m}^{+}$$
    (9)
    $${\mathrm{A}}^{-}=\left\{\left(\left({maxv}_{ij }/j\in J\right),\left({minv}_{ij} /j\in {J}^{^{\prime}}\right)\right)/i=\mathrm{1,2},\dots ,m\right\}={v}_{1}^{-},{v}_{2}^{-},\dots , {v}_{m}^{-}$$
    (10)

    where J is associated with the positive criteria, and \({J}^{^{\prime}}\) is associated with the negative criteria.

  3. Step 5:

    Calculation of distances to positive ideal (S+) and negative ideal (S−) points by Eq. 11 and Eq. 12.

    $${S}_{i}^{+}=\sqrt{\sum\nolimits_{j=1}^{n}{\left({v}_{ij}-{v}_{ij}^{+}\right)}^{2}}$$
    (11)
    $${S}_{i}^{-}=\sqrt{\sum\nolimits_{j=1}^{n}{\left({v}_{ij}-{v}_{ij}^{-}\right)}^{2}}$$
    (12)
  4. Step 6:

    Final step is to calculate the relative closeness (Eq. 13) to the ideal solution.

    $${cl}_{i}^{+}=\frac{{S}_{i}^{-}}{{S}_{i}^{+}+{S}_{i}^{-}};0\le 1;\;\;i=\mathrm{1,2}\dots \dots ,$$
    (13)

    where \({\mathrm{cl}}_{\mathrm{i}}^{+}\) is closeness coefficient, \({\mathrm{S}}_{\mathrm{i}}^{+}\) is the positive ideal solution (PIS), and \({\mathrm{S}}_{\mathrm{i}}^{-}\) is the negative ideal solution (NIS). If \({\mathrm{cl}}_{\mathrm{i}}^{+}\)=0 the decision point is near the absolute negative ideal solution. If, \({\mathrm{cl}}_{\mathrm{i}}^{+}\)=1, the decision point/alternative is near the absolute positive ideal solution (Ustaoglu et al. 2021). In the final step of TOPSIS, alternatives (sub-watershed of the study area) were ranked according to calculated \({\mathrm{cl}}_{\mathrm{i}}^{+}\) values.

Result and discussion

The first stage in proper planning and management of natural resources, as well as the determination of soil and water conservation measures, is the identification and prioritization of sub-watersheds within a watershed. The Teesta River sub-watersheds have been segmented into 14 sub-watersheds for prioritizing purposes, namely; SW-1 to SW-14. The ranking of distinct sub-watersheds according to the order in which they must be taken for soil conservation measures is known as watershed prioritization (Nitheshnirmal et al. 2019). Morphometric analysis is an important tool for the prioritization of sub-watersheds (Meshram et al. 2020). The present study is used 10 erosion risk assessment morphometric parameters, i.e., bifurcation ratio (Rb), shape factor (Bs), drainage density (Dd), stream frequency (Fs), drainage texture (Dt), form factor (Rf), circularity ratio (Rc), and elongation ratio (Re), basin perimeter (P), shape factor (Bs), basin width (W), and basin length (L) for prioritizing sub-watersheds for treatment and conservation measure. Erodibility is directly related to linear parameters such as drainage density, stream frequency, bifurcation ratio, and drainage texture; the higher the value, the greater the erodibility. Erodibility is inversely proportional to shape parameters such as circularity ratio, basin shape, and compactness coefficient; the lower the value, the greater the erodibility (Arabameri et al. 2018; Aouragh and Essahlaoui 2018). The parameters Rb, Dd, Dt, Fs, P, L, and W were used as positive criteria in the study area, with maximum values indicating high erosion, and Rc, Re, and Bs were used as negative criteria, with minimum values indicating high erosion. In the study, the relative weights of each criterion were determined through AHP (Table 4), using Microsoft Excel, and the weights were used as input for TOPSIS to select the best alternatives.

Table 4 Selected criteria along with its type and weights (AHP)
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Based on TOPSIS greatest closeness (\({cl}_{i}^{+}\)) to ideal solution (Table 5), sub-watersheds were classified as very high (0.435–0.774), high (0.360–0.434), medium (0.307–0.359), less (0.229–0.306), and very less (0.199–0.228). Sub-watersheds (SW5, SW1, SW3, SW4, SW14) have been discovered in Fig. 4 to be particularly vulnerable to soil erosion, and conservation measures can be implemented in these micro watersheds as a priority to preserve the long-term sustainability of agriculture by preventing excessive soil loss through erosion.

Table 5 Values of morphometric parameters and closest coefficient to the ideal solution with ranking(R) and priority index of Teesta sub-watersheds
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Fig. 4
figure 4

Soil erosion prioritization using TOPSIS model in Teesta sub-watersheds

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Conclusion

Prioritization of sub-watersheds is the order in which sub-watersheds in a basin are ranked for soil conservation measures. The morphometric parameters play an important role in hydrological behavior, which identifies the locations that are sensitive to natural hazards such as soil erosion of a river basin. Without huge expenses and time, it is possible to claim that sub-watersheds may be prioritized based on morphometric criteria to execute conservation measures. The study demonstrated that the digital elevation model (DEM) with GIS is an effective tool for sub-watershed delineation and extraction of its morphometric factors, and the results of the TOPSIS technique in relation to erosion may strongly suggest that the necessary protection measures should be taken to minimize soil erosion. In order to ensure the sustainable growth of agricultural and natural resources, sub-watershed with very high (SW 5) and high (SW 1, SW 3, SW 4, SW 14) susceptibility to erosion should be taken care of for soil and water conservation measures. Our study also examines how decision-makers might use MCDM approaches (AHP and TOPSIS) with Microsoft Excel in the fields of soil and water resources. Lastly, where soil erosion is high and slope is steep, mechanical methods such as contour bunds may be advised for installation in very high and high priority sub-watersheds.