1 Introduction

Some extreme weather conditions such as the occurrences of heavy rainfall, floods, drought, heatwaves and hurricanes have increased in recent decades all over the world. Some research has shown that the appearance of these events is the outcome of potential changes in climate and the impact of climate change on floods is especially significant (Frei et al. 2000; Milly et al. 2002; van Aalst 2006). So, watershed management faces a substantial challenge from those flash floods. Moreover, management challenges such as the mitigation of flood hazards, installation of control structures and urbanization stress on the environment demand a thorough knowledge of the magnitude and frequency of flooding events and their change through time (Knuepfer and Montz 2008). Hence, watershed prioritization which is based on grading of different watersheds of a basin has become an important means for watershed management. Moreover, it might even become more crucial for ungauged basins where no or scarce flow data are available and the watershed is prone to flash floods. In the literature, different methods have been developed for prioritization of watersheds among which morphometric analysis is accepted to be the best approach (Sukristiyanti et al. 2018). Morphometric analysis depends on grading of various morphometric parameters of watershed. However, despite many approaches and researches conducted on the subject, there is still no specific accepted classification for morphometric parameters, their effects and ranges of their values, resulting in conflicting criteria which might challenge the judgment and conclusion of a decision-maker (Sukristiyanti et al. 2018; Iqbal and Sajjad 2014; Malekian and Azarnivand 2016). Therefore, it is crucial to adopt an approach for ranking of the morphometric parameters in which the decision-maker would be able to rank the alternatives for watershed prioritization and determine the sub-basin with the highest flood potential. Prioritization of watersheds can thus be regarded as a multi-criteria decision-making (MCDM) problem. In the last several decades, MCDM methods have found an extensive area of usage and have been implemented in different areas of business, groundwater, water resources and management, and water distribution networks (Srdjevic 2007; Geng and Wardlaw 2013; Azarnivand et al. 2014; Tecle and Duckstein 1994; Uzun and Kabak 2019). The MCDM is associated with the formation, definition and solution of problems which include conflicting criteria. Some of those methods of MCDM, which have been employed in water management, are technique for order of preference by similarity to ideal solution (TOPSIS), analytic network process (ANP), analytical hierarchy process (AHP), compromise programming (CP), elimination and Et choice translating reality (ELECTRE) and VlseKriterijumska optimizacija I Kompromisno Resenje (VIKOR).

The MCDM methods have been implemented to various areas of water management such as assessing flood management options, helping optimization of the allocation of available resources and assessing flood hazard potential (Yang et al. 2013; Guo et al. 2014; Roy and Blaschke 2015; Malekian and Azarnivand 2016). Some of the MCDM approaches such as ANP, AHP and TOPSIS have been implemented to integrate varying levels of significance of many criteria associated with the selection of sub-basins (Chang and Hsu 2009, 2011; Gopinath et al. 2016; Rahmati et al. 2016; Meshram et al. 2019). Meshram et al. (2019) investigated the sub-basins with regard to their potential in susceptibility with flash floods using morphological parameters of the sub-basins and identified the most critical ones, using geographical information systems (GIS) and remote sensing, AHP and fuzzy AHP. Chang and Hsu (2009, 2011) employed VIKOR to determine watershed vulnerability using five criteria for prioritization of the subdivisions of a watershed. Chung and Lee (2009) used ELECTRE II to spatially quantify the hydrological vulnerability of the watershed by means of AHP method to estimate the weights of the chosen factors denoting flood potential. Besides those applications, some studies were conducted for the assessment of the prediction capability of various MCDM approaches in prioritization of the sub-basins, their flood management activities and determination of spatial distribution of inundated areas (Chitsaz and Banihabib 2015; Arabameri et al. 2019). Extensive research has also been conducted to achieve theoretical and methodological improvements in the methods (Chen et al. 2016, 2019a, b; Deng et al. 2019a; Zhao et al. 2019, 2020a, b). For example, Chen et al. (2019a) developed a proportional interval type-two hesitant fuzzy TOPSIS approach to provide linguistic decision-making under uncertainty. Chen et al. (2019c) developed an integrated multi-criteria group decision-making approach combining proportional hesitant fuzzy linguistic term set and the TOPSIS to ideal solution to rank the alternatives for the transportation of hazardous materials and select the best one. Chen et al. (2019d) developed a novel hybrid multi-criteria group decision-making model for sustainable building material selection under uncertainty and verified their model by performing sensitive and comparative analysis. Deng et al. (2019b) developed an improved ant colony optimization algorithm to improve the optimization performance in solving large-scale optimization problem. Deng et al. (2017a) proposed a genetic and ant colony adaptive collaborative optimization algorithm avoiding falling into the local extreme, and taking on better search precision and faster convergence speed for solving complex optimization problems. In another study, Deng et al. (2017b) developed an improved adaptive particle swarm optimization algorithm and applied it to gate assignment at the airport in order to fast and effectively assign the gates to different flights in different times.

In the current research, the aim of the study is to adopt MCDM methods to overcome the aforementioned deficiency of traditional methods which is the lack of a standard classification of morphometric parameters. Hence, MCDM approaches were performed for watershed prioritization regarding the flood potential of the sub-basins. Akçay Basin sited in Turkey was chosen as study area, and 12 morphometric parameters were selected for morphometric analysis. Prioritization of the sub-basins was carried out (1) by using traditional methods such as hazard degree (HD), compound factor (CF) approach and a simple statistical method (SM) adopted by Baduna Kocyigit and Akay (2018) and (2) by employing AHP, ANP methods and then ELECTRE I, VIKOR, TOPSIS by using criteria weights obtained from ANP and AHP. Furthermore, effects of the variations in criteria weights on the alternatives were examined by sensitivity analysis. Since Akçay is an ungauged basin, the geomorphological instantaneous unit hydrograph (GIUH) which is a widely used method for estimation of flood hydrograph of ungauged basins was also adopted. It was then coupled with Monte Carlo method to predict the yield of the sub-basins. Finally, Kendall tau correlation coefficient test (KTCCT) and Spearman correlation coefficient test (SCCT) which are bivariate correlation tests, and receiver operating characteristics (ROC) analysis were performed with sensitivity analysis to validate the outputs of the MCDM and other adopted approaches with regard to prioritization of the sub-basins by comparing results of those methods with the results of GIUH. Ranking the sub-basins in the watershed with regard to their flash flood potential would surely help engineers and local bodies for taking necessary countermeasures.

2 Materials and methods

2.1 Study area

Akçay Basin, situated in the Western Black Sea Basin of Turkey (588,770–612,453 Y and 4,620,904–4,645,334 X coordinates based on UTM ED50 Zone 36 N), covers a 372.4-km2 drainage area and 112.4-km perimeter. The study area collects water from the elevations of 2005 m and drains into the Black Sea through Akçay Creek. The mean rainfall in the basin is about 950 mm in a year. The basin has a mountainous, steep topography with an average slope of about 45%. The area is mainly covered by forests and limited agricultural land with small, scattered villages. There is no industrial facility except a quarry in the area with Yunuslar Regulator and Hydroelectric Power Plant (HEPP) located on Akçay Creek. Hydrological soil groups in the area were determined mostly as D consisting chiefly of clay. In the basin, there is only one stream gauging station that is located at one of Akçay’s tributaries that has the largest sub-basin area. Though the station started operation in 2015, no sufficient data have yet been available for hydrological analysis to be used in this study.

2.2 Methodology

The digital elevation model of the watershed was obtained from topographic maps with 10 × 10 m resolution. Then, 11 sub-basins were delineated; the stream network was extracted by taking the threshold value of flow accumulation cells as 100 and then was ordered according to the Strahler method (Strahler 1957) as shown in Fig. 1. Various geometric parameters of sub-basins were determined, and the values of bifurcation ratio (Rb), stream frequency (Fs), drainage density (Dd), length of overland flow (L0), texture ratio (T), rho coefficient (ρ), elongation ratio (Er), form factor (Ff), shape factor (Sf), circularity ratio (Cr), compactness coefficient (Cc) and width–length ratio (WLr) chosen as flood conditioning factors regarding their flash flood potential were calculated. Table 1 shows the morphometric parameters and their values for 11 sub-basins of Akçay Basin.

Fig. 1
figure 1

Akçay basin with stream network and 11 sub-basins

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Table 1 Computed morphometric parameters of sub-basins (Baduna Kocyigit and Akay (2018)
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Figure 2 illustrates the main steps of the study, and the methodology followed in this study can be given as follows:

Fig. 2
figure 2

Main steps of the study

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  1. 1.

    Prioritization of the sub-basins was performed using traditional methods such as HD, CF and a simple SM adopted by Baduna Kocyigit and Akay (2018).

  2. 2.

    The criteria weights for AHP and ANP were determined, and prioritization of the sub-basins was performed.

  3. 3.

    The criteria weights obtained from AHP and ANP were used in TOPSIS, VIKOR and ELECTRE I, and prioritization of the sub-basins was performed.

  4. 4.

    New criteria weights were generated using former weights from AHP and ANP, and then, sub-basins were prioritized using those weights in TOPSIS, VIKOR and ELECTRE I.

  5. 5.

    Peak discharges (1/h) of the sub-basins were calculated by GIUH-Nash approach due to the lack of stream gauging data of Akçay Basin. In order to test the usability of the GIUH results, Monte Carlo analysis was performed.

  6. 6.

    SCCT and KTCCT for all methods and ROC analysis for all but excluding ELECTRE I were performed for all results including sensitivity analysis.

2.3 Prioritization of sub-basins based on traditional methods

In the study, prioritization of 11 sub-basins of Akçay Basin was first performed by three traditional approaches as (1) compound factor, (2) hazard degree and (3) a simple statistical method. According to those approaches, the selected morphometric parameters were considered in two groups regarding their flash flood potential. The parameters having a direct correlation with flash flood potential were considered in Group 1 which included Rb, Dd, Fs, T, Ff, Er and Cr, while the parameters of Group 2 consisted of Lo, ρ, Sf, Cc and WLr, which have an inverse proportion with the flood potential. In order to determine the CF value, the sub-basins were ranked regarding the flood potential of each morphometric parameter such that the most flood prone sub-basin was ranked as 11, while the sub-basin with the next higher value was ranked as 10 and so on. Then, the average of the ranked morphometric parameters for sub-basins was determined and the value of CF of each sub-basin was thus determined. The HD of each morphometric parameter ranged between one (lowest) to five (highest) and was calculated by Eqs. 1 and 2 for parameters in Group 1 and Group 2, respectively, as (Masoud et al. 2013; Basahi et al. 2016):

$$ {\text{Hazards}}\;{\text{degree }} = \frac{{4 \left( {X - X_{ \hbox{min} } } \right)}}{{\left( {X_{ \hbox{max} } - X_{ \hbox{min} } } \right)}} + 1 $$
(1)
$$ {\text{Hazards}}\;{\text{degree}} = \frac{{4 \left( {X - X_{ \hbox{max} } } \right)}}{{\left( {X_{ \hbox{min} } - X_{ \hbox{max} } } \right)}} + 1 $$
(2)

where X denotes the morphometric parameter value that HD value for each sub-basin will be calculated. Xmin and Xmax are the minimum and maximum values of the morphometric parameters, respectively. HD also shows a similar tendency with the CF value such that the more the flood potential of the sub-basin, the larger the HD. Finally, the approach for prioritization of the sub-basins adopted by Baduna Kocyigit and Akay (2018) was employed. According to this approach, as the value of the morphometric parameters of Group 1 got larger, the flood potential of the sub-basin increased. Therefore, for parameters in Group 1, the sub-basin with the highest value among all sub-basins was ranked as 1 and the next sub-basin with its value between (maximum—Δ) and (maximum—2Δ) was ranked as 2 where Δ = (maximum value-minimum value)/number of sub-basins. Hence, the rest of the sub-basins were accordingly ranked. For morphometric parameters in Group 2, the sub-basins were ranked vice versa and thus the sub-basins were prioritized. Further details about this prioritization can be found in Baduna Kocyigit and Akay (2018).

2.4 Prioritization of sub-basins using MCDM Methods

2.4.1 AHP

AHP, proposed by Saaty (1980), is a semiquantitative method considering a hierarchy that has levels of goal, criteria, possible sub-criteria and alternatives (Saaty and Vargas 1998). It is assumed that criteria do not depend on each other and do not affect alternatives which are also independent of each other. AHP does a pair-wise comparison to compute the criteria weights for usage in prioritization (Triantaphyllou and Mann 1995). In AHP method, a scale ranging from 1 to 9 known as Saaty’s scaling is used to quantitatively and qualitatively prioritize the sub-basins.

In this study, a pair-wise comparison of criteria and alternatives was made with regard to flash flood potential of the sub-basins using ranks of the parameters determined by Baduna Kocyigit and Akay (2018). Then, the differences in ranks were determined and scaled qualitatively between 1 and 9 to fit the Saaty’s scale. Thus, a pair-wise comparison matrix was created, and by averaging its row values, a normalized pair-wise vector was formed. Finally, a cluster matrix was formulated by combining these 12 pair-wise vectors. To obtain a criteria weight vector, a pair-wise comparison between the differences in the total sum of ranks of parameters was made for all sub-basins and then scaled using Saaty’s scale. Since the difference in ranks resulted in a wide range of numbers from 0 to 46, scaling was performed such that for the differences of 0, 1 and 2 the scale was set to 1, for differences 3, 4 and 5 it was set to 2 and so forth, increasing the number of difference numbers gradually from three to eight towards to the middle of scaling. From the middle to the end, the scaling was done similarly with descending order, resulting in 44, 45 and 46 for the maximum scale 9. Using the cluster matrix obtained from the comparison judgment of the ranks of the sub-basins and the corresponding criteria weight vector obtained from the comparison judgment of the total sum of the ranks of the sub-basins, priority of each sub-basin was used to give the flood potential score. The inconsistency index (I.I.) of pair-wise comparison matrix was computed by

$$ {\text{I}} . {\text{I}} .= \frac{{\lambda_{ \hbox{max} } - n}}{n - 1} $$
(3)

where λmax denotes the maximal eigenvalue, while n represents the number of alternatives.

The inconsistency ratio (I.R.) was calculated by

$$ {\text{I}} . {\text{R}} .= \frac{{{\text{I}} . {\text{I}} .}}{{{\text{R}} . {\text{I}} . {\text{I}} .}} $$
(4)

where the random index, R.I.I. value, can be approximated by 1.98(n − 2/n). Consistency of the matrix is considered to be achieved for values of I.R. smaller than 10% (Chitsaz and Banihabib 2015).

2.4.2 ANP

ANP, also developed by Saaty (2005), is the generalized form of AHP which uses networks instead of hierarchies as in AHP. In this study, four quartiles for each morphometric parameter were determined using the ranks of the sub-basins obtained by Baduna Kocyigit and Akay (2018) for that parameter. Each quartile included three priority ranks, one of which was the quartile value and the other two was determined by linear interpolation between two successive quartile ranks. Taking the ranks of the sub-basins obtained by compound factor as the ideal solution, deviation of the current priority ranks from this solution was tested by the absolute value of (1 − Rank of ideal solution/current priority rank). Thus, a matrix was formed having those percentile deviations for each parameter. Afterwards, a pair-wise comparison of percentile deviation matrix was performed row by row and the result was scaled by Saaty’s scaling such that the minimum and maximum values in the row were set to 1 and 9, respectively, and the rest of the elements in that row were scaled linearly. Thereby, a pair-wise comparison matrix was obtained. Then, this matrix was normalized and the pair-wise vector was obtained, followed by creation of super matrix using both cluster matrixes obtained in ANP and AHP. Limit super matrix was obtained so weights of the parameters, and the priorities of the sub-basins regarding flood potential were estimated. Finally, inconsistency index and inconsistency ratio were calculated as in AHP.

2.4.3 ELECTRE I

First proposed by Benayoun et al. (1966), ELECTRE I is the first of ELECTRE family models which chooses alternatives preferred by most of the criteria and which does not create intolerable discontentment on other criteria. The ELECTRE I method is simple and suitable to construct a partial prioritization and to choose a set of promising alternatives (Chen and Xu 2015). ELECTRE II method considers several concordance and discordance levels, which can be used to construct two embedded outranking relations. ELECTRE III uses the pseudo-criteria and fuzzy binary outranking relations where ELECTRE IV, the best equipped with an embedded outranking relations framework, rank the actions without using the relative criteria importance coefficients (Figueira et al. 2005). In this study, procedure presented in Chitsaz and Banihabib (2015) was adopted except that the criteria weights computed in AHP and ANP methods were used separately. Unlike TOPSIS, VIKOR, AHP and ANP methods, ELECTRE family methods are based on pair-wise comparison principle by using concordance and discordance indexes when prioritization of watersheds is finalized. In this study, ELECTRE I was selected due to its straightforward computational requirement.

2.4.4 VIKOR

VIKOR was first introduced by Opricovic (1998) and then used in solving MCDM problems by means of alternative sets of conflicting criteria (Opricovic and Tzeng 2004). According to the method, firstly positive-ideal and negative-ideal solutions are defined and sets of alternatives are ranked. Then, a multi-criteria ranking index is introduced based on the closeness to the ideal solution and a compromise solution is obtained that is closest to the ideal solution. In this study, the VIKOR method for rating options was adopted from procedure given in Chitsaz and Banihabib (2015) and Ameri et al. (2018).

2.4.5 TOPSIS

Hwang and Yoon introduced TOPSIS in 1981, and it became a very popular method for MCDM (Hwang and Yoon 1981). The method deals with real-valued data, and in time many other extensions based on the original method were proposed enabling the use of interval or fuzzy criteria or interval or fuzzy weights. According to the algorithm of TOPSIS, a decision matrix is formed and normalized. Then, closeness coefficient known as the Euclidean distance of positive-ideal and negative-ideal solutions is defined and preferred alternative is determined for higher values of that parameter (Liou and Wang 1992; Kannan 2009; Ameri et al. 2018). In this study, similar procedure as in Chitsaz and Banihabib (2015) and Ameri et al. (2018) was adopted.

2.5 Sensitivity analysis

The response of changing the priorities of the criteria was tested by sensitivity analysis given as:

$$ W_{J} = \frac{{1 - W_{i} }}{{1 - W_{i}^{0} }}W_{J}^{0} $$
(5)

where Wi and Wj are the modified and new weights of each criterion which ranged between 0 and 1 with an increment of 0.1. W 0i and W 0j denote the former weights of criteria. New criteria weights were generated using former weights of both AHP and ANP.

2.6 GIUH-Nash model

The Nash instantaneous unit hydrograph (IUH) proposed by Nash (1957) is a conceptual model that estimates the instantaneous unit hydrograph in a watershed by routing the instantaneous inflow hydrograph assuming that a cascade of n linear reservoirs having identical storage coefficients k exist. According to the method, the output values of a reservoir are taken as input values of the next reservoir, thus providing continuity between them (Hosseini et al. 2016). Nash approach is based on two-parameter gamma distribution as given in Eq. 6

$$ u\left( t \right) = \left( {\frac{t}{k}} \right)^{n - 1} \frac{{e^{ - t/k} }}{{k\Gamma }} $$
(6)

where ut is the IUH ordinate at time t (1/h) and Γ is the gamma function. Rosso (1984) proposed Eqs. 7 and 8 to determine n and k values as

$$ n = 3.29\left( {\frac{{R_{\text{b}} }}{{R_{\text{A}} }}} \right)^{0.78} R_{\text{l}}^{0.07} $$
(7)
$$ k = 0.70\left( {\frac{{R_{\text{A}} }}{{R_{\text{b}} R_{\text{l}} }}} \right)^{0.48} \frac{{L_{\varOmega } }}{v} $$
(8)

where RA and Rl denote weighted area and length ratios of the sub-basins, respectively, LΩ is the length in km of the highest order stream and v is the flood peak velocity (m/s). v can be computed by Eq. 9 as

$$ V = 0.665\alpha_{\Omega }^{0.6} \left( {i_{\text{r}} A_{\Omega } } \right)^{0.4} $$
(9)

where ir = excess rainfall intensity (cm/h), αΩ = kinematic wave parameter for the highest order channel and AΩ = watershed area (km2). For the solution of Γ function in Eq. 6, Nemes (2010) proposed Eq. 10.

$$ \varGamma = \left( {\frac{n}{e}} \right)^{n} \sqrt {\frac{2\pi }{n}} \left( {1 + \frac{1}{{12n^{2} - 0.1}}} \right)^{n} $$
(10)

where e = natural logarithm constant.

2.7 Monte Carlo analysis

In the study, Monte Carlo analysis was performed for all sub-basins due to the possible uncertainties in Rb, RA and Rl parameters which were estimated from ArcGIS facilities and used for calculation on and k values. By taking the computed n and k values for each sub-basin as the mean value and the coefficient of variance as 1% for both normal and uniform distributions, 15,000 random variables were generated. Using those random variables, the peak discharges (up) values were computed by

$$ u_{\text{p}} = \frac{{\left( {n - 1} \right)^{n - 1} }}{{k\Gamma }}e^{1 - n} . $$
(11)

Then, the upper and lower limits of 95% of confidence interval of up values were determined, and it was tested whether the up values computed by using the mean values of n and k were within these limits or not.

2.8 Validation of models

KTCCT and SCCT are nonparametric correlation tests used to determine the correlation between the predictions of traditional and MCDM approaches with the GIUH results. Both KTCCT and SCCT are dependent on the priorities of the sub-basins instead of the values of morphometric parameters. If the two compared models do not have same rank, then Eqs. 12 and 13 are used for KTCCT and SCCT, respectively.

$$ \tau = \frac{C - D}{{\frac{{n\left( {n - 1} \right)}}{2}}} $$
(12)
$$ r_{\text{s}} = 1 - \frac{{6\mathop \sum \nolimits_{i = 1}^{n} d_{i}^{2} }}{{n\left( {n^{2} - 1} \right)}} $$
(13)

where τ denotes the Kendall tau correlation coefficient, C and D are the number of concordant and discordant pairs, respectively, n is the number of alternatives, rs represents the Spearman’s rank correlation coefficient and di is the difference between priorities of models adopted and GIUH. Coefficients of τ and rs were computed using SPSS software. According to the Kendall and Spearman tables, the critical values for n = 11 are equal to 0.491 and 0.618, respectively. Although both the τ and rs express the correlation between the two compared model pairs, these two coefficients might give different results such that the value of rs can suggest an acceptable correlation while the τ might imply a poor correlation or no correlation at all. For this reason, in this study, it was assumed that there was no correlation for τ < 0.491 and rs < 0.618 and so the null hypothesis of the lack of correlation was accepted.

A receiver operating characteristic curve (ROC) is a plot that illustrates the capability of the model at all classes. When a large number of correct predictions (true positives) exist, the sensitivity is said to be high, while high (1 − specificity) values indicate a low sensitivity for a high number of false positives (Eqs. 14, 15).

$$ x = 1 - {\text{specificity}} = 1 - \left[ {\frac{\text{TN}}{{\left( {{\text{TN}} + {\text{FP}}} \right)}}} \right] $$
(14)
$$ y = {\text{sensitivity}} = \left[ {\frac{\text{TN}}{{\left( {{\text{TP}} + {\text{FN}}} \right)}}} \right] $$
(15)

where FN = false negative, FP = false positive, TN = true negative and TP = true positive (Swets 1988). Interpretation between area under curve (AUC) and prediction accuracy is given as follows: excellent (0.9–1), very good (0.8–0.9), good (0.7–0.8), moderate (0.6–0.7) and weak (0.5–0.6) (Yesilnacar and Topal 2005). In this study, model results with prediction capability having τ ≥ 0.491, rs ≥ 0.618 and AUC = 0.6 were accepted to be satisfying, especially in sensitivity analysis.

3 Results and discussion

Ranking of sub-basins for each morphometric parameter determined from traditional methods of CF, HD and SM and their scores are given in Table 2.

Table 2 Scores of sub-basins by compound factor, hazard index and simple statistic method
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In AHP and ANP, the criteria weights were determined according to an objective evaluation by preventing the subjective judgment of decision-maker in a certain framework. In AHP, ranking of each morphometric parameter for each sub-basin and sum of the rankings of each parameter for all sub-basins were taken into account to determine the criteria weights. Moreover, levels of prioritization and the effect of changes in ranking values of parameters in any level of prioritization were additionally considered in ANP. According to the two different criteria weighting methods, contribution of ranking of morphometric parameters in the assessment of flood potential of the sub-basins and the effects of those contributions on selected MCDM approaches were investigated. Table 3 shows the criteria weights determined using ANP and AHP based on this approach. According to these results, the morphometric parameters which expressed the shape and drainage characteristics of the basin were found to be equally effective on flash flood potential of the basin in ANP method, while the shape characteristics, especially the width length ratio, were found to be slightly more effective in AHP. The weight of the WLr and the ratio of the maximum to minimum criteria weights were evaluated as 0.309 and approximately 18, respectively, for AHP, whereas they were computed as 0.023 and 5 for ANP method, respectively. The outlier value of WLr parameter of a sub-basin which resulted in a criterion weight of 0.309 for AHP did not increase the flash flood potential of that sub-basin, but caused the flash flood potential of other sub-basins to be relatively higher. So, this criterion was superior to others in AHP. On the contrary, this effect was not observed to be dominant in the results of ANP since the deviations in the priority levels of the sub-basins were taken into account in this method. Furthermore, the value of I.R. for sub-basins and criteria was found to be less than 10%, so the matrix was considered to be consistent.

Table 3 Criteria weights of AHP and ANP methods
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The criteria weights obtained from AHP and ANP were then used in TOPSIS, VIKOR and ELECTRE I. According to these methods, the parameters in Group 1 were considered as the cost, while those in Group 2 were taken as benefit. Thus, the aim of the application of those methods was to prioritize the sub-basins from the least to the highest in ascending order with regard to the flash flood potential of the sub-basins. So, the sub-basins were prioritized from the one that would have the least potential for flooding with the highest benefit and the lowest cost relative to other sub-basins. Table 4 shows the number of dominant parameters, the decision indicators (Qi) and the closeness coefficients (Ccl) determined from ELECTRE I, VIKOR and TOPSIS methods for both AHP and ANP. Table 5 presents the prioritization of the sub-basins by three traditional methods and MCDM methods of AHP, ANP, TOPSIS, VIKOR and ELECTRE I.

Table 4 Results of MCDM for weights of AHP and ANP
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Table 5 Prioritization of the sub-basins by traditional and MCDM methods
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The up values computed from 15,000 random variables generated using mean values of n and k for each sub-basin and the coefficient of variance as 1% for both normal and uniform distributions that was found to be in the 95% confidence interval were compared with prioritizations of sub-basins given in Table 5. The computed τ and rs coefficients of KTCCT and SCCT with the AUC values obtained from ROC analysis are given in Table 6, whereas Fig. 3 shows the FP versus the TP rates for the adopted methods. As τ and rs values are examined, it is seen that the outputs of the methods have correlation. However, the result of TOPSIS based on criteria weights of AHP showed that there is a negative correlation. This means that the sub-basins were prioritized with regard to their groundwater recharge yield instead of their flash flood potential. Furthermore, the τ and rs values of VIKOR with criteria weights of AHP and ELECTRE I with criteria weights of ANP were found to be smaller than the upper critical value of Kendall tau and Spearman rho, so the results were found to be not satisfying. The rs value of 0.65 for the result of TOPSIS based on criteria weights of ANP showed that there was an acceptable level of correlation, whereas the value of 0.42 for τ showed that no acceptable correlation existed. Hence, the prediction capability of TOPSIS based on criteria weights of ANP was considered as unacceptable.

Table 6 rs, τ and AUC values obtained from SCCT and ROC analysis
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Fig. 3
figure 3

Results of ROC analysis for methods used in the study

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In case of ELECTRE I, the sub-basins were prioritized regarding dominant and defeated alternatives. For the sub-basins with same difference values, the sub-basin with larger drainage area was prioritized first. According to those results, higher dominant weight of the criteria from AHP positively affected the outputs. This is because the sum of the values of morphometric parameters in all sub-basins and their pair-wise comparison are the inputs for determination of the criteria weights in AHP and this tendency could be observed in the outputs of ELECTRE I.

Although the overall assessment of the methods showed that the AHP method could predict the sub-basins which had higher flood potential, the use of criteria weights obtained by AHP in TOPSIS and VIKOR caused discrepancies from ideal solution, especially in TOPSIS. On the contrary, the criteria weights obtained by ANP in TOPSIS gave better predictions than that by AHP, but it did not satisfy the evaluation criteria. On the other hand, VIKOR with ANP criteria weights gave better correlated results that were closer to the ideal solution than ANP itself. Then, sensitivity analysis was carried out for TOPSIS, VIKOR and ELECTRE I methods with modified criteria weights of AHP and ANP. The analysis was carried out for 12 criteria and 11 weights per criteria for each method. Furthermore, the KTCCT, SCCT and ROC analysis were conducted to determine τ, rs and AUC for those 132 sets. By assessing each weight set according to the τ and rs values being in the 95% confidence interval and the AUC = 0.6, where possible, the number of outputs with positive and negative associations was determined as 1 and 131 for TOPSIS–AHP, 25 and 107 for TOPSIS–ANP, 6 and 126 for VIKOR–AHP, 26 and 106 for VIKOR–ANP, 34 and 98 for ELECTRE I–AHP and finally 5 and 127 for ELECTRE I–ANP. Sensitivity analysis suggested compatible results for the outputs of TOPSIS and VIKOR as given in Table 6.

For large criteria weights of shape parameters such as Sf, Ff and Er, the TOPSIS–ANP gave better results which were close to the results presented in Table 6. The results of VIKOR–ANP were also found to be good in case of small criteria weights. Overall, distribution of the initial values of the criteria weights was found to play a key role on the outputs of sensitivity analysis and methods.

4 Conclusions

Watershed prioritization which can be a vital tool for engineers and decision-makers for watershed management can be carried out by various methods. However, many traditional methods based on morphometric analysis lack a standard classification so they may not be reliable. Especially for ungauged watersheds where there are no or scarce flow data for management, this might become more challenging for decision-makers. In such ungauged basins, yield of the basin can be estimated by reliable and robust methods that are based on statistical analysis and verified to give satisfactory predictions in many various areas. Hence, in this study, several traditional methods such as CF, HD and SM and MCDM approaches such as AHP, ANP, and ELECTRE I, VIKOR, TOPSIS in which criteria weights determined from AHP and ANP were introduced, were considered for prioritization of Akçay Basin regarding flash flood potential. When the results of traditional methods and MCDM approaches were compared, it was found that MCDM approaches gave improved results, especially in estimating the sub-basins with higher flood potential than the traditional methods which had a good correlation. Particularly, determination of the criteria weights using AHP and ANP is believed to advance the prediction capability of the MCDM approaches in this study. The results showed that the AHP method could predict the sub-basins with higher flood potential by the dominant shape features of the sub-basins. It was determined that the initial values of criteria weights were effective on the predictions and sensitivity analysis. Results of sensitivity analysis showed that the criteria weights determined from AHP increased the uncertainty in TOPSIS and VIKOR for cases with positive associations. It was concluded that the Euclidean distance which does not take into consideration the correlation of morphometric parameters in TOPSIS and aggregating functions that focus on determining compromising solution for watershed prioritization in VIKOR were more sensitive to networks and interdependences among criteria while concordance and discordance indexes of sub-basins outranked by criteria were better identified by a hierarchical structure. Different closeness coefficients and weight of the strategy of the maximum group utility could be used to improve the prediction capability of TOPSIS and VIKOR, respectively. Overall, this study showed that GIS combined with MCDM approaches for an ungauged basin can be used by decision-makers to provide an efficient management of basins regarding conservation of water resources and soil. Furthermore, the necessary countermeasures that should be taken in the basin against flooding can also be prioritized considering economic and risk analyses.