Prioritization of sub-catchments of a river basin using DEM and Fuzzy VIKOR

Fuzzy VIKOR, a decision making technique, is applied to prioritize 224 sub-catchments of Mahanadi Basin, India. Seven geomorphology based criteria viz., drainage density, bifurcation ratio, stream frequency, texture ratio, form factor, elongation ratio and circulatory ratio are estimated from ﬁ ve digital elevation models (DEMs). Triangular membership functions were formulated for each criterion for each sub-catchment which are based on individual values obtained from individual DEM ’ s. Entropy method is employed for estimation of weights of criteria and a similar mechanism is followed while formulating triangular membership function for weights. Eight groups are formulated with a number of sub-catchments in each group as 5, 26, 69, 65, 29, 11, 12, 7 for taking up conservation measures. Effect of varying strategy weight, ( ν ) on the ranking pattern is also studied and found that ν value effects ranking pattern signi ﬁ cantly.


INTRODUCTION
Water is the most precious natural resource available on Earth. It is unequivocally one of the most important factors for the life to thrive and prosper. The steady rise of human and livestock population, urbanization, demands from other sectors and erratic rainfall have put pressure on this scarce resource and this pressure is likely to grow in the near future. It becomes imperative to form a strategy for effective, efficient and sustainable improving/development of catchments which are basis for water resources and land management. Alarmingly, problem of erosion is becoming more complex due to increasing human activities, deforestation, inadequate and poor farming practices and effects both quantity and quality of soil, accelerates sediment deposition in reservoirs, floodplains, and even impacts agriculture significantly. All these factors are eventually leading to deterioration of the quality of catchments in developing countries. Keeping this in view, catchments are expected to be improved such that expectations from them can be met. However, due to financial and other limitations, improvement, maintenance and management strategies cannot be implemented simultaneously for all the catchments necessitating prioritization. Accordingly, catchments which require earlier soil and water conservation treatment can be first improved and other catchments can follow as per their priority for improvements. Another lacuna for improvement is inadequate data availability of the catchments.
Water resources planners in the absence of adequate/precise/gauged data are employing geomorphological parameters (Rai et al. 2001;Kumar et al. 2017) i.e., linear parameters (Bifurcation Ratio, Drainage Density, Stream Flow Frequency and Texture Ratio) and shape parameters (Circulatory Ratio, Form Factor and Elongation Ratio) for characterizing the catchment and can be used as the basis for prioritizing the catchments. Kumar et al. (2017) mentioned that linear and shape parameters have a direct and inverse relationship with erodibility respectively. A higher value of linear parameters and low value of shape parameters represents higher erodibility (Raju & Nagesh Kumar 2013). Here prioritization or ranking is the process of arranging the catchments in the order of their importance, employing decision making algorithms facilitating the process of prioritization (Lee et al. 2015). Incorporating effective improvement strategies will not only lead to improvement of catchments over time, but will also enable to improve the socio-economic aspect of the area through the sustained generation of employment for the local population.
Complimentarily, digital elevation models' (DEMs) capability to yield more precise terrain information with much ease, accelerated the application of DEM based geomorphic models (Wolock & Price 1994;Williams et al. 2000). Noman et al. (2001) extensively reviewed delineation of flood plain from digital terrain models with various perspectives. Manfreda et al. (2011) highlighted the role of DEMs in detecting flood prone areas. They employed DEMs such as the ASTER global, Shuttle Radar Topography Mission (SRTM), and national elevation data to assess their sensitiveness to the chosen problem. They found that SRTM DEM is suitable for delineation of flood-prone areas. Yan et al. (2014) highlighted the role of DEMs as a main data source in the field of geomorphology. Papaioannou et al. (2015) analyzed the role of DEM derived geomorphological and hydrological attributes for identification of flood prone areas.
On the geomorphology aspects, Thakkar & Dhiman (2007) performed morphometric analysis and prioritization of eight watersheds of Mohr watershed, Gujarat, India. They also compared various morphological parameters. Rudraiah et al. (2008) studied part of Kagna river basin, Karnataka, India using remote sensing and geographical information systems (GIS). Javed et al. (2009) applied morphometric analysis for prioritization of sub-watersheds for Kanera watershed, Madhya Pradesh, India. Out of the seven sub-watersheds (SW1 to SW7), SW1 and SW6 qualified for high priority, whereas SW7 was categorized as medium priority. Deshmukh et al. (2011) analyzed eight watersheds (W1 to W8) adjacent to Narmada and Sher rivers for analysis of erodibility. It was found that the watersheds W5 and W6 were high and least degraded respectively. Javed et al. (2011) prioritized fourteen sub-watersheds (SW1 to SW14) of Jaggar watershed, Eastern Rajasthan based on morphometric analysis and land use/land cover categories. It was observed that only SW7 and SW10 fall under very high priority. Kanth & Hassan (2012) prioritized nineteen watersheds of Wular Catchment, India and a compound value was calculated for identifying highest, medium and low priority zones. Yasmin et al. (2013) performed morphometric analysis for Milli watershed, Karnataka, India using GIS. They found that GIS was useful for similar situations. Uniyal & Gupta (2013) prioritized twenty micro-watersheds (MW1 to MW20) of Bhilangana watershed of Uttarakhand, India and classified into high, medium and low priority for conservation and management. Raju & Nagesh Kumar (2013) applied TOPSIS for prioritizing twenty two micro-watersheds of Kherthal catchment, Rajasthan, India using seven geomorphological parameters. Entropy method was used to compute weights of geomorphological parameters. It was observed that the methodology adopted was found to be effective. Aher et al. (2014) identified critical and priority sub-watersheds in water scarce region of India and applied weighted sum analysis approach for ranking each hydrological unit. They found that 51.66% of sub-watersheds were in the moderately to highly susceptible zones. Iqbal & Sajjad (2014) prioritized five watersheds, D1A, D1B, D1C, D2A, D2B of Dudhganga catchment. It was found that D1C and D1A fall under high and medium priority respectively. Jaiswal et al. (2014) prioritized thirty six sub-watersheds of Benisagar dam catchment of Bundelkhand region, Madhya Pradesh, India and applied Saaty's analytical hierarchy process with nine erosion hazards for identification of environmentally stressed sub-watersheds. Similar studies were also reported by Jaiswal et al. (2015) using fuzzy Analytic Hierarchy Process. Patel et al. (2015) identified suitable sites for thirteen mini-watersheds of Hathmati for identifying water harvesting structures and found that watershed number 2 was of maximum priority. Makwana & Tiwari (2016) prioritized nineteen sub-watersheds in the semi-arid middle region of Gujarat, India using the compound parameter. They used remote SRTM data for the analysis. They opined that prioritization helps to implement soil conservation measures. Chandniha & Kansal (2017) performed prioritization of nine sub-watersheds of Piperiya watershed, Hasdeo river basin and classified them into high, medium and low priorities. Singh & Singh (2017) made an effort to prioritize sub-watersheds of Dangri River watershed, Haryana, India based on Snyder's synthetic unit hydrograph and grouped them as high, medium and low soil-erosive. They compared the outcome with land use/ land cover and morphometric analysis. Patel et al. (2012), Zhang et al. (2015), Khanday & Javed (2016) and Kumar et al. (2017) performed similar studies.
It is observed that (a) most of the studies used geomorphological parameters for ranking of the watersheds without assigning any weightage to them (b) no study was reported in fuzzy environment for ranking of the watersheds in geomorphological perspective. In other words, no study was reported in Indian conditions where DEM data from five sources were used for computing geomorphological parameters and on the basis of which ranking of sub-catchments were performed in fuzzy environment.
Keeping the above observations from the literature review and practical aspects into consideration, the objectives of the present study are formulated as follows: • To estimate geomorphological parameters, namely, Drainage Density, Bifurcation Ratio, Stream Frequency, Texture Ratio, Form Factor, Elongation Ratio and Circulatory Ratio for all the 224 sub-catchments of Mahanadi Basin, India using five different DEM sources, namely, GMTED2010 7.5 arc-sec, SRTM (30 m & 90 m), ASTER and CARTOSAT-1.
• To explore the applicability of (a) Entropy method for obtaining weights for the parameters (b) Fuzzy VIKOR (Vise Kriterijumska Optimizacija I Kompromisno Resenje), a decision making technique, to prioritize 224 sub-catchments of Mahanadi Basin in India. Present paper covers introduction, case study, description of methods, results and discussion followed by conclusions.

CASE STUDY
Mahanadi basin lies between East longitudes 80°30 0 and 86°50 0 , and North latitudes 19°15 0 and 23°35 0 . The basin is broadly divided into three sub-basins; Upper, Middle and Lower consisting of 91, 88, 48 sub-catchments (totalling to 227) (Figure 1). The climate in the basin is predominantly sub-tropical. The annual rainfall trend based on 34 years of India Meteorological Department (IMD) grid data shows a trend towards an increase of about 100 mm of rainfall since 1971. The annual variability of rainfall in the basin indicates that the year 1994 had the highest annual rainfall of ∼1,780 mm whereas 1979 had the least rainfall in the past 34 years (∼900 mm). The climate is predominantly sub-tropical. April and May are the hottest months. Maximum temperature hovers upto 40°C ( Jalali 2015).

METHODS EMPLOYED AND METHODOLOGY GIS analysis
GIS analysis was performed on all the DEM datasets for delineating sub-catchments which include Georeferencing, shape file creation, joining of DEM tiles and terrain pre-processing (repeated for 224 sub-catchments and for all DEM datasets).

Counting of streams
The number of streams present in each sub-catchment were counted for the estimation of geomorphological parameters (Refer Table 1). A program was developed for auto-counting of streams present in each sub-catchment. The output of the model gives information about each stream segment present in a catchment along with its stream order. This information was utilized to count number of streams present in each stream order. The point at which streams join another stream is called a node. In modern days, GIS programs can efficiently assign a unique number to each node present in stream network. 'From node number' is the point from which stream segment has originated. 'To node number' is the point at which a stream segment is terminating.

Entropy method
Entropy method is employed to obtain weights of the geomorphological criteria (Raju & Nagesh Kumar 2014).
Steps of the methodology are as follows: 1. Formulation of payoff matrix (Array of sub-catchments and geomorphological criteria) and computation of normalized payoff matrix (p ij ); i and j respectively represent sub-catchments (1,2,…m) and criteria (1,2,…n) 2. Entropy value for each geomorphological criteria j, 3. Computation of degree of diversification of criteria

No units
Circulatory ratio (R c ) 12:57 A P 2

Fuzzy VIKOR
The first priority sub-catchment is obtained through Fuzzy VIKOR. Brief methodology of fuzzy VIKOR is as follows: ('f' was added before the variable to represent it as fuzzy variable) (Wu et al. 2016): 1. Input the fuzzy payoff matrix, fx ij in triangular membership function form (l ij , m ij , u ij ) consisting of sub-catchments and criteria. 2. Identify fuzzy best value ff Ã j and worst value ff ÃÃ j for each criterion; for example in case of maximization, such as benefit perspective, In case of minimization, such as cost perspective, 4. Computation of index values fS i (S l i , S m i , S u i ) and fR i (R l i , R m i , R u i ) representing the separation measures for sub-catchment A i from the best and worst values (Lee et al. 2015).
5. Computation of values of summation operator fQ i , using the Equation (8) function. ν varies from 0 to 1. Defuzzification of fQ i yields which provides crisp value. Lower Q i value based sub-catchment is preferred for analysis and can be given priority for taking up soil and conservation improvements.
The flowchart of the approach developed is presented in Figure 2.

Estimation of geomorphological parameters and weights
Total number of pixels present in DEM raster was estimated using GIS software and procedure mentioned above is used for finding the area, perimeter and length of each sub-catchment. MatLab (www. mathworks.com) based program was developed for computation of the seven geomorphological parameters for all 224 sub-catchments based on the information in Table 1 differences are (0.054, 11, 0.049, 0.222, 0.052, 0.06, 78.05). Significant variation is observed for some geomorphological parameters across all DEM sets. The present study aims at handling the variation in fuzzy environment for better modeling of the case study and suggests a methodology where variation is observed in similar situations elsewhere. Weights of criteria related to each DEM are computed using entropy method (Equations (1)-(3)). Table 2 presents weights of the various parameters for the 5 DEM sources. It is observed that texture ratio, bifurcation ratio and stream frequency contribute around 85% of total weightage whereas remaining four criteria contribute around 15% while ranking sub-catchments. In all the DEM sources, Texture ratio, bifurcation ratio and stream frequency are occupying first three positions.

Membership function formulation
Triangular membership functions are proposed to handle the deviation of geomorphological parameters obtained from the 5 DEMs. For example, bifurcation ratios obtained for DEMs 1 to 5 for sub-catchment 2 are 3.1667, 3.1667, 3.2407, 3.119, 3.4643 and these values are arranged in the ascending order 3.119, 3.1667, 3.1667, 3.2407, 3.4643. While formulating in triangular membership form, first, third and last values are chosen as the elements representing lower, middle and upper (l, m, u) i.e., (3.119, 3.1667, 3.4643). Similar process is repeated for all the seven parameters for all the 224 sub-catchments respectively. Similar procedure is adopted for weights of criteria for formulation of triangular membership. These are presented as part of Table 2.

Ranking/grouping of the sub-catchments
MatLab based Fuzzy VIKOR code is developed for ranking the 224 sub-catchments based on the formulated payoff matrix in a fuzzy environment. Various steps employed in ranking/grouping the subcatchments are as follows: Main aim of normalized fuzzy difference matrix is to make the data dimensionless. This is required when different features are simultaneously considered. High values of first four criteria, Drainage Density , Bifurcation Ratio, Stream Frequency, Texture Ratio are preferred whereas low values of Form Factor, Elongation Ratio and Circulatory Ratio are preferred (Kumar et al. 2017). Accordingly, normalized fuzzy difference matrix values are computed (Equations (4) and (5)).
Bifurcation Ratio values for sub-catchment 1 are (2.556, 2.6111, 2.6111). Ideal (f Ã j ) and anti-ideal (f ÃÃ j ) values for each Bifurcation Ratio are found to be (11,12,13) and (2, 2, 2) and accordingly u Ã j and l ÃÃ j values are chosen as 13 and 2. Based on Equation (4), normalized fuzzy difference value is:   (13) were applied for 224 sub-catchments using the described methodology for computing fS i , fR i , fQ i . Lower Q i is preferred and ranking is performed accordingly. Table 3 presents ranking pattern/grouping of the sub-catchments.
It is observed that Q i values for most of the catchments are almost same with minute differences. Keeping this in view, grouping of the catchments is performed instead of ranking based on the range of Q i values. A total of eight groups are formulated with number of catchments in each group as 5,26,69,65,29,11,12,7 respectively. Highest number of catchments are falling in group 3 and 4 with a Q value range of 0.16-0.20 & 0.21-0.25. It is observed that group 1 can be explored for improvement on a priority basis and accordingly other groups can be improved as noted in Table 3.
Ranking method proposed here facilitates prioritization of sub-catchments. These sub-catchments based on their priority can be provided suitable conservation measures which ultimately are expected to provide sustainable water management practices in the Mahanadi river basin. Some of the conservation measures that can be explored are check dams, initiation of woody plants, masonry stone bunds construction, gullies reforestation, ponds and embankments. However, precise information on the magnitude and rates of erosion and sedimentation and socioeconomic and environmental effects are key to success in implementing sustainable soil conservation programs.

CONCLUSIONS
In this study, data from five DEM sources i.e., GMTED2010 7.5 arc-sec, SRTM90, SRTM30, ASTER and CARTOSAT-1 were used to calculate the 7 geomorphological parameters for 224 sub-catchments of Mahanadi basin. Fuzzy VIKOR, was utilized for prioritizing the sub-catchments. Eight groups of sub-catchments were formulated for possible implementation of conservation measures for the chosen strategy weight of 0.5. However, careful selection of strategy weight is essential for meaningful inferences from the present study. Present study is preliminary work initiated to evaluate the study area in terms of sub-catchments prioritization. This will be followed by field validation which is targeted as further study.