Flood vulnerability assessment using data envelopment analysis – the case of Narmada river basin districts in central India

Flooding is a severe challenge that affects the residents, communities, planners, and policy-makers (Yang et al., 2018a, 2018b) whose own fate lies in the success or failure of ideas that they conceive and initiate for the welfare of people. The tools that help policy-makers and planners have improved significantly over the past decades as new modeling techniques and modern computational tools are finding increasing applications in assessing community vulnerabilities and resilience. However, despite new tools that support the policy-makers, and despite continuous flood-control efforts, in developing economies like India that face monsoon bursts every few years, the socio-economic damages and death toll continue to remain very high (Mohanty et al., 2020). During the monsoon season of June–September, one of the larger rivers of India – the River Narmada, often experiences flood-like conditions (Fernandes et al., 2020). Historical records indicate that large floods are relatively common hydrologic events on the Narmada river, thus making it the most intense and irregular flood regime in the seasonal tropics (Kale et al., 1994; Rajaguru et al., 1995). Additionally, according to the SDMP, M.P. (2012), the various districts of Madhya Pradesh State (M.P.) in India, the primary state out of the three states from where the river passes, are highly vulnerable to floods. As characterizing vulnerability remains the critical challenge to improving flood risk analysis and management (Balica & Wright, 2009; Chen et al., 2019; Jiménez et al., 2020), the present study focuses on the assessment of flood vulnerability in the 21 districts, lying in the Narmada river basin of the state of Madhya Pradesh, India. Moreover, the novelty of this paper is to put forth the DEA-based vulnerability assessment framework for the Narmada river basin of Madhya Pradesh and procure more sentient results related to flood management.

Vulnerability is defined as ‘The propensity or predisposition to be adversely affected. Vulnerability encompasses a variety of concepts including sensitivity or susceptibility to harm and lack of capacity to cope and adapt’ (IPCC, 2014). Thus, flood vulnerability assessment exhibits the relationship between the theoretical understandings and the practical processes (Nasiri et al., 2016). Equivalently, the identification and assessment of flood vulnerability are very significant to minimizing the damage associated with floods and is an important assessment tool for the identification of the flood-prone areas, for inducting adaptation, and for ensuring the survival of the exposed communities (Feloni et al., 2019; Sahana & Sajjad, 2019; Singh et al., 2020). Furthermore, vulnerability also quantifies the amount of loss in a disaster event, such that higher loss is indicative of the higher vulnerability to the disaster event (Huang et al., 2019).

Computation of Vulnerability implies the challenging task of combining social and geophysical components to model their interrelations to the overall flood vulnerability (Imran et al., 2019), as vulnerability remains a function of both the economic and socio-demographic factors and indicators (Deria et al., 2020). The assessment models of multidimensional flood vulnerability are simple and can be used for vulnerability analysis of natural disasters at regional or national levels (Huang et al., 2012). The analytical methods for estimating vulnerabilities are often less convincing because of the subjectivity of assigning different weights or weighting to various components. In this, a data envelopment analysis (DEA)-based model for analyzing regional vulnerability to natural disasters would be considered superior (Wei et al., 2004), primarily because the need to assign subjective weightings is done away with.

DEA is a multi-factor productivity analysis for measuring the relative efficiencies of a homogenous set of decision-making units (DMUs) that perform similar tasks by consuming multiple inputs to produce multiple outputs. It can be applied to analyze multiple outputs and multiple inputs without pre-assigned weights and without imposing any functional form on the relationships between variables. The main characteristics of DEA are:

• It can be applied to analyze multiple outputs and multiple inputs without pre-assigned weights.

• It can be used for measuring relative efficiency based on the observed data DEA model without imposing any functional form on the relationships between inputs and outputs.

• Decision makers' preferences can be incorporated into DEA models.

• It can be used as a resource allocation tool.

For the above reasons, the DEA is today regarded as one of the popular methods having advantages over traditional parametric techniques such as the regression (Zhu, 2015) and thus has been used extensively to study the efficiencies in various sectors such as in water supply systems (Kulshrestha & Vishwakarma, 2013; Vishwakarma et al., 2016; Nyathikala & Kulshrestha, 2020), solid waste management (Rogge & Jaeger, 2012; Vishwakarma et al., 2015; Giannakitsidou et al., 2020), electricity (Thakur et al., 2006), irrigation (Frija et al., 2011; Phadnis & Kulshrestha, 2012a, 2012b; Zema et al., 2018) and transport systems (Saeedi et al., 2019; Roy & Kulshrestha, 2020).

Flood risk management requires an understanding of the physical risk situation and the local socio-economic and cultural context (Klijn et al., 2021). In addition, vulnerability assessment is a part of flood risk management and is a process of identifying, quantifying, and ranking the vulnerability factors in a system (Li et al., 2011). Besides, by assessing the vulnerability of a disaster, its impact can be minimized. Consequently, as a part of flood risk management, although several studies to measure flood vulnerabilities have been conducted for a large number of river basins all across the world. However, there has been a dearth of flood vulnerability assessments for the Narmada river basin of India, considering its relatively large size. Hence this study was undertaken to determine flood vulnerability in the Narmada river basin of M.P.

There have also been only a few flood vulnerability studies reported in the literature based on DEA (Wei et al., 2004), developed a data envelopment analysis (DEA)-based model for analysis of regional vulnerability to natural disasters in China. Correspondingly, Huang et al. (2012) evaluated the flood vulnerability at the provincial level in China using the DEA technique. The dimensions considered in this study are demographic, agricultural and economic. In addition, Huang et al. (2019) proposed a coastal urban disaster vulnerability assessment method based on the confrontation, neutral and friendly, three types of data envelopment analysis (DEA) cross-efficiency models, and effectively evaluates the disaster vulnerability of 24 coastal cities in China. Similarly, Üstün & Barbarosoğlu (2014) proposed a DEA-based performance evaluation of disaster relief operations for an earthquake in Turkey and further demonstrated how to improve disaster management performance using DEA. Also, the earthquake resilience capacity of Istanbul and its districts were evaluated by data envelopment analysis (DEA) models and returns to scale analysis by Üstün (2016). Yao et al. (2020) proposed a vulnerability assessment framework of the regional water system, which integrates water quantity, contamination, water-related hazards and water use efficiency and reveals the structure of realistic water resource management to obtain more sensitive results. This study was performed on the Yangtze River of China. In the context of India, Jha et al. (2020) assessed the relative social vulnerability for floods in administratively declared flood-prone districts of Bihar for the period 2007–2016, using the super-efficiency data envelopment analysis (DEA) model.

In recent times, DEA has been finding increasing importance as a tool for evaluating and assessing vulnerabilities. In the disaster management studies by DEA models, the DMUs can eliminate their inefficiencies and thus be better prepared for future disasters (Üstün, 2016). The most advantageous aspect of the Data Envelopment Model is that it provides the user with a reference set of DMUs for each non-efficient DMU and thus, DMUs can be compared (Doyle & Green, 1994).

Equation (1) states that (V) Vulnerability is a function of (S) Sensitivity and (AC) Adaptive Capacity of the area. However, Luers et al. (2003) clarify that Vulnerability (V) can be considered as the ratio of Sensitivity (S) and state relative to a threshold, i.e., Adaptive Capacity (AC) of the area. Furthermore, upon combining the derived relations of the three parameters, Vulnerability, Sensitivity and Adaptive Capacity, from the IPCC (2014) and Luers et al. (2003), in this study in the DEA model, the Sensitivity indicators are considered as output and the Adaptive Capacity indicators as input, respectively. In all formulations, the critical parameters of vulnerability are the stress to which a system is exposed, its sensitivity, and its adaptive capacity (Adger, 2006). For example, the sensitivity in Equation (1) may comprise indicators concerning population sensitivity, economic sensitivity, and agricultural sensitivity. The adaptive capacity indicators focus on the consequences and impacts of the current and self-restoring capacity in the study area (Yang et al., 2018a, 2018b).

Through DEA, quantitative efficiencies and the weighting of any performance indicator can be assessed and compared (Diaz et al., 2004). DEA has the advantage that it constructs its functional form when given the set of inputs and outputs and does not require any underlying assumption of a functional form relating to inputs and outputs (Charles & Kumar, 2012). The various DMUs are represented by various districts whose relative vulnerabilities may be accessed using DEA. This study focuses on developing a framework that may be employed by appropriate adaptation and up-scaling to any river basin to identify areas vulnerable to floods.

The river Narmada, considered amongst the most sacred rivers in India, is the largest west flowing and fifth largest river in India (CWC, 2020). It drains a large area in Madhya Pradesh besides some areas in Maharashtra and Gujarat, as the River Narmada flows through these three states. The Narmada basin lies between east longitudes 72° 32′ to 81° 45′ and north latitudes 21° 20′ to 23° 45′, while the river drains a total area of 98,796 sq km, of which about 87% lies in the state of Madhya Pradesh (MP). The total drainage area of the Narmada river in MP is thus 85,859 sq km and forms the study area for the present work. Some studies by Choudhury (2010), Kathal (2018), Rajaguru et al.(1995), Sharma et al. (2015) etc., advocate that the Narmada river basin in central India is not only highly susceptible to floods but also is one of the most intense flood-prone regions in India.

Figure 1 shows the study area that comprises 21 districts of Madhya Pradesh, through which the Narmada river flows. The figure has the River Narmada marked in grey color and its river basin outline in black color. The districts are Alirajpur, Annupur, Balaghat, Barwani, Betul, Chhindwara, Dewas, Dhar, Dindori, Harda, Hoshangabad, Indore, Jabalpur, Katni, Khandwa, Khargone, Mandla, Narsinghpur, Raisen, Sehore, and Seoni. According to Relief & Revenue Dept (M.P.) (2019), from the year 2005 to 2019, the districts of Betul, Chhindwara, and Mandla, were affected by the floods, the highest number of times, whereas Khandwa and Khargone were affected least number of times.

NIH (2020) states that in Madhya Pradesh, the Narmada flows in a deep channel with high banks, which are not frequently over-topped. Additionally, the annual rainfall in the upper part of the Narmada catchment is more than 1,400 mm and in some areas, it exceeds 1,650 mm. However, the unaccounted rainfall in the river basin during the monsoon season (July to September) leads to excessive water flow, causing flooding (Ray & Goel, 2019). Subsequently, the River Narmada has been facing regular floods (Zainal Fikry et al., 2020). According to the Flood Memorandum (2021), in the last decade, the river faced the highest discharge in the years 2013 and 2014, respectively. The highest discharge measured at the last or most downstream hydrological observation site, at Garudeshwar (Gujrat) on the Narmada river was in the year 1970, with a value of 0.069 million cumecs. Following the NIH (2020) on the river Narmada, nearly 3,165 water resource projects are present, of which 29 are major projects, covering a total volume of 14,000 million cubic meters. Before the Hoshangabad district, three major dams are constructed on the river, Bargi, Barna and Tawa. Nevertheless, when the rainfall occurs heavily in a short period of time, the discharge at the Hoshangabad area in the river increases, leading to flooding.

According to SDMA (2020), of the total area of the Narmada river basin, 56.90% is the agricultural area, 32.88% is the forest, 6.13% is the wasteland, and nearly 3% is the built-up land (urban and rural class). As a general consequence of flooding in the study area, the districts which suffer the most, with the highest number of affected villages, roads, and areas, are Dhar, Jabalpur, Chhindwara, Balaghat, Sehore, Raisen, Hoshangabad and Harda. Besides, from the year 2013 to year 2019, around 8% of the total sown area in the study area was affected due to floods in the Narmada river. Likewise, considering the recent heavy rainfall and flood-like conditions in August and September of 2019, around 200 villages were affected or submerged due to flooding in the study region. Furthermore, in the year 2020, flooding conditions prevailed due to heavy rainfall, and around 25,000 people were rescued together by the National and State Disaster Response Force teams (NDRF/SDRF). In the year 2020 floods caused damage of around 48 million USD in the study region.

The flowchart in Figure 2 depicts the research methodology deployed to assess flood vulnerability in 21 districts that lie in the Narmada river basin of Madhya Pradesh. As shown in the flowchart in Figure 2, and corresponding to Equation (1), the indicators representing the flood-related adaptive capacity of the study area were chosen as input parameters. In contrast the indicators representing the sensitivity of the study area towards floods were chosen as the output parameters. The sources of the indicators under both the input and output parameters are mentioned in Table 2. Data envelopment analysis (DEA) is used in the study to determine the vulnerability, and the efficiency values (i.e., the ratio of output to input) obtained from the DEA model gives the Flood Vulnerability Index (FVI) values. Besides, for the same input and output parameters, the results were obtained and compared for both the CRS and VRS based DEA models. Considering the efficiencies obtained from the CRS model as the FVI values of various districts, the FVI values were further subject to cluster analysis. The values were clustered in 3 groups representing low, medium and high vulnerable districts for the study area. These FVI results were used for the spatial mapping of vulnerability in the study area.

For estimating efficient production frontiers, the DEA technique provides a promising mathematical programming alternative to the usual parametrical statistical methods used for this purpose (Banker et al., 1984). In this study, the CRS (Constant Return to Scale) technique, under the CCR formulation by Charnes et al. (1978), is used to determine the efficiency or the vulnerability of the 21 districts in the Narmada River basin. Further, the VRS (Varying Return to Scale) technique, under the BCC formulation developed by Banker et al. (1984), is also used. The CRS model assumes a Constant Returns to Scale, whereas the VRS model refers to the Variable Returns to Scale, and the returns can be increasing, decreasing, or constant depending on the orientation of the model used and the convexity constraint (Banker et al. 2004). The equations of the Envelopment models used in this paper are adopted from the methodology employed by Zhu (2015) and Charles & Kumar (2012).

In a DEA model, the Technical Efficiency is obtained as a ratio of the sum of weighted output to the sum of weighted input. Considering the Returns to Scale (RTS), in a CRS model, it is assumed that the output changes in the same proportion as input is changed, and hence the returns are constant in this case. Whereas a VRS model assumes that any change in input values will lead to a disproportionate change in the output values, such that the output can be decreasing, increasing, or constant, and hence the returns can be varying. Likewise, the orientations in a DEA model can be either input or output. Input orientation aims to minimize the inputs at a given output level, and the output orientation aims to maximize the output given at the input level (Aziz et al., 2013). In other words, the input-orientated model looks at the proportion by which inputs can be contracted to produce the same amount of outputs, while the output-orientated model looks at the proportion by which outputs can be expanded with the same amount of inputs (Nyathikala & Kulshrestha, 2020).

Assuming the districts here are the DMUs. Each DMU_j (j=1, 2,…, n) consumes a vector of inputs, to produce a vector of outputs, ⁠. The superscript T represents transpose. The DMU to be evaluated is designated as DMU₀ and its input-output vector is denoted as (w₀, y₀).

The DMU₀ (district) is target efficient only when here, i=1,2,…m and r=1,2,…s

The DMU₀ (district) is target efficient only when here, i=1,2,…m and r=1,2,…s

In Equations (2) and (3), both the and are otherwise unconstrained. represents the structural variables, when solving the models, these are the crude weights assigned to the units. Any admissible choice of provides an upper limit for the outputs and a lower limit for the inputs of DMU (Bowlin, 1998), and represent slacks. Further, in order to make an inefficient DMU reach the target frontier, slacks are required. Slack relates to the potential increase in output and reduction in the input, for the inefficient DMUs to reach the efficient benchmark targets. 0 < is a non-Archimedean infinitesimal that is defined to be smaller than any positive real number.

This restriction allows for the varying Returns to Scale.

In order to determine the closeness of observed DMU to the most productive scale, Scale Efficiency can be used. The Scale Efficiency is calculated as the ratio of the measure of Technical Efficiency of Constant Returns to Scale (CRS) model to the measure of Technical Efficiency of Variable Returns to Scale (VRS) model (Coelli, 1996; Coelli et al., 2005). So for any DMU when the VRS score equals the CRS score, the DMU is said to be operating at the most productive scale (Charles & Kumar, 2012). Thus, the Scale Efficiency provides the difference between the CRS and VRS Technical Efficiencies.

A vast number of input and output variables exist in each environment that one may regard as worthy of consideration and inclusion in the DEA model. If there are many inputs and outputs, the discriminatory power of the DEA invariably reduces as all DMUs tend to become near efficient by virtue of one variable or the other (Subramanyam, 2016). Thus, in any DEA-based study, the selection of indicators is highly crucial, and the number of input and output variables need to be strictly limited while also capturing the essence of the problem. In this study, variables were chosen based on similar studies in literature and based upon the understanding of flood disasters in the local study area.

The selection of numbers of indicators in any DEA model is very crucial. Going by the rule of thumb, three decision making units (DMUs) are needed for each input or output variable used in any DEA model in order to ensure sufficient degrees of freedom for a meaningful analysis. If less than three DMUs per input and output variable are included in the data set, there is a danger that an excessive number of the DMUs become efficient (receive a rating of one) because of an inadequate number of degrees of freedom (Bowlin, 1998). Accordingly, for the fixed number of districts in this study 21, not more than seven indicators are allowed. Consequently, in this study, three input and three output variables are chosen.

A study of relevant literature and the data availability constraints in the developing country context led to a choice of a total of 6 indicators (3 related to Adaptive Capacity while the other 3 were Sensitivity Indicators). The selected indicators on which data was available and also formed robust choices for the study were employed as input and output parameters in the DEA model and are listed in Table 1 that also shows the relevant study from the literature that employed the indicator in the context of flood vulnerability analysis of other regions. Hence, the indicators were chosen within the constraints of data availability that best represented the study region's physical, social, and economic aspects while ensuring that these indicators were employed earlier in other researchers' standard flood vulnerability literature.

The Input parameters comprised three indicators. The first of these was the forest area as a percentage of the total geographical area of the district. According to the FAO (2012), the forests as a land-usage prevent flooding by absorbing the excess runoff water. Furthermore, flood risk communication with the general public and the population at risk is increasingly important for flood risk management, especially as a precautionary measure (Hagemeier-Klose & Wagner, 2009). Thus, another set of input indicators refers to the communication network (telephone, internet, and mobile) (Batica & Gourbesville, 2016), a good proxy for which at the Indian household level is the households with televisions as this mode of media implies that the entire household, and even the community in case of most villages and small towns, gets access to early warning and therefore become more prepared and adaptive for a flood event. This is so that information reaches the maximum number of respondents, with television being the most common medium (Bradley et al., 2014). However, another indicator is the number of health centers in a district which is a proxy for the health capacity available in a district (Üstün, 2016). Therefore, the number of health centers is one of the prominent indicators of adaptive capacity.

From the perspective of the exposure of the hazard-bearing body, the exposure level of the hazard-bearing body is higher in cities with higher population density, while the exposure level of the hazard-bearing body in cities with lesser population density is lower (Huang et al., 2019). Thus, the population density is an indicator of sensitivity towards exposure. Moreover, the higher the population that lives in poverty, the higher the area's sensitivity, which eventually implies the area becomes highly vulnerable to disasters (Kusumastuti et al., 2014). For the indicator of output, the total number of villages affected in each district, the more the number of villages affected by floods in each district implies more is the sensitivity of the district for floods (Wei et al., 2004).

The greater the efficiency (which is a ratio of output to input parameters), implying more significant outputs relative to the inputs (more households below poverty line, more villages affected, and greater population densities vs. the input parameters in Table 1), entails greater flood vulnerability, or higher FVI value. Thus relative CRS efficiency is a proxy for FVI.

The results of the DEA analysis are presented in Table 2. As pointed out in the literature (example, Liu et al. (2010), Huang et al. (2019)), the higher the CRS efficiency (which in this study is represented by the flood vulnerability), the more critical the disaster for any input-output based DEA model. The FVI values (the CRS efficiency values) for various districts are plotted in Figure 3.

Of the total of 21 districts, as many as 14 districts came out to be the most vulnerable ones with the highest CRS-based DEA efficiency score of 1.00 in both the input and output-based CRS and VRS models. These districts were Alirajpur, Annupur, Balaghat, Barwani, Betul, Chhindwara, Dhar, Dindori, Harda, Indore, Jabalpur, Mandla, Raisen and Sehore, and comprise the most flood vulnerable districts. This observation of high flood vulnerability in 67% of the districts can be explained by the fact that many of them were the least developed ones in terms of infrastructure, such as the number of health centers available in these districts. Also, the districts that were bigger and had dense urbanization reported greater vulnerabilities reflecting the fact that high population densities may be responsible for making these districts disaster-prone to a greater extent. Thus, it is evident that two-thirds of the sample districts, due to their more significant vulnerabilities for floods, need greater attention requiring an integrated approach that should consider both the socio-economic and physical aspects of the districts to reduce the flood risk. Possible enhancement in the socio-economic status of residents and the reduction in population densities will greatly help in decreasing the vulnerability levels and the flood risks in these districts. The DEA results in Table 2 also show that the efficiency of only 2 districts, namely Seoni and Dewas, is less than 0.5. Hence, these two districts appear to be least vulnerable to floods. It may be noted that the values of efficiencies in both output and input oriented CRS models are the same, and this indicates that the efficiency as vulnerability is independent of the change in sensitivity (output) or adaptive capacity (input) indicators.

Table 2 also exhibits the VRS efficiencies and the Scale Efficiency scores for each district. In a DEA model, the Scale Efficiency score of one implies that the DMU in question is operating at optimal scale or the productive scale size. If the Scale Efficiency score is less than one, then the DMU is not operating at optimal scale, or there exists a difference in the VRS and CRS Technical Efficiencies. In this study, the term optimal size is interpreted as the highest vulnerability, and hence most of the districts with Scale Efficiency equal to 1 can be assumed to be highly vulnerable. In contrast, only three districts, Narsinghpur, Seoni and Dewas, with Increasing Returns to scale in each case show very low Scale Efficiency values. These districts are small-sized ones, already have low flood vulnerabilities, and the low Scale Efficiencies with increasing Returns to Scale only imply that these three districts are extremely sensitive to size change. However, if these districts grow in size, which is a usual occurrence in the developing country context and is almost a certainty given the increasing urbanization trends, these three districts will become highly flood-prone and have large FVI values. Thus, the planners and policy-makers need to ensure that urbanization trends in these three districts remain arrested. It would also greatly help if this district actually can be resized and restructured into smaller administrative units. For all other districts, the Scale Efficiency values are one or near one, indicating optimal sizes concerning FVI variations.

Districts showing decreasing Return to Scale imply that these districts give corresponding decreasing output returns when there is an increase in the input parameters. Any adverse change in inputs will bring lesser change in outputs implies that an adverse change in population densities and economic status of people is less likely to make the districts correspondingly more vulnerable to floods. Thus these districts seem to have some inherent buffering capacity for vulnerability to flood against adverse changes. On the other hand, such adverse change in population densities and economic status of people, etc., is likely to make districts with increasing returns to scale highly vulnerable to floods. Thus, the districts that return increasing returns to scale need to be extra cautious in ensuring that their population densities and economic status do not change for the worse. These districts with increasing returns of scale are more vulnerable to variations in respect to the input-output parameters, i.e., the quantity of the forest area, provisions of health care facilities, and people's socio-economic status and exposure levels. The statistics of the Vulnerability Index (efficiencies) values of the districts based on the CRS model that gives the same values for the input/output oriented models are exhibited in Table 3. The mean efficiency score of the CRS model is 0.8989, indicating a very high mean vulnerability for floods. However, the Standard Deviation of the efficiencies was 0.1929, implying that most of the districts have efficiencies close to mean, and not much of a difference in flood vulnerabilities exist amongst the vulnerable districts.

Table 4 illustrates the results of the cluster analysis and indicates 3 clusters amongst the 21 districts. On clustering, the Flood Vulnerability Index values of 21 districts, the K-Means cluster analysis resulted into the shown three grades of the districts, such that cluster 1 with cluster center as 0.99 refers to High Vulnerability, cluster 2 with cluster center as 0.73 indicates Medium Vulnerability and cluster 3 with its center as 0.4 specifies Low Vulnerability. From Figure 4, it can be seen that the districts on either end of the state have a high level of vulnerability indicated by red color. Data indicates that districts on the very East and West end of the state are underdeveloped compared to the districts in the center, and these districts are all in red. As a matter of policy, greater financial allocation needs to be made for these districts to develop better resources and infrastructures. Figure 4 also indicates the districts in the immediate center of the state, indicated in yellow, that have a medium vulnerability to floods, while the districts in green are the least vulnerable to floods. Further, the results suggest that 24% of the Narmada river catchment basin districts demonstrated low to medium flood vulnerability and may be considered relatively safer. Significantly, the low to medium vulnerable districts are also the districts with moderate and medium economic growth, suggesting that there might exist a relationship between moderate economic growth and flood vulnerabilities. However, the findings need to be corroborated from other studies as well.

A total of 76% of the study districts demonstrated high vulnerability to floods marked as red in Figure 4. These included larger districts that were most economically better developed, such as Indore, Jabalpur, Chhindwara, and the smaller and economically less developed districts like Alirajpur, Annupur, and Dindori too have high flood vulnerabilities. In the developing country context, the most economically developed districts, mostly the bigger sized, are often the ones that show the most inequities (Nijman & Wei, 2020; World Social Report, 2020), rendering the majority of the poor more vulnerable. The highly developed districts also have higher population densities leading to more overcrowded zones but better flood prevention resources. On the other hand, the underdeveloped districts have fewer population densities and lack mitigation and prevention resources, eventually becoming more vulnerable to floods (Huang et al., 2019). The poorer districts are mired in poverty and hence probably more vulnerable to flood events due to the general absence of awareness. As confirmed by the Relief & Revenue Dept (M.P.) (2019), for the recent floods of the year 2019 in the Narmada river, assistance for the provision of temporary accommodation, food, clothing, medical care of people affected and evacuated due to heavy floods, was organized for the districts of Raisen, Balaghat, Harda and Mandla. Moreover, Balaghat and Chhindwara had the highest number of people accommodated per day in the relief camp. Also, Narsinghpur, Mandla, Raisen and Seoni were the districts where the highest number of houses affected due to the floods of the year 2019. These are all districts that are economically not so developed.

The outcomes from the study confirm the findings of the primary data and the secondary evidence in the form of reports of the various government bodies.. This supports and validates the results obtained for the DEA technique employed in the present analysis. Based on the results, the highly vulnerable districts shown in red in Figure 4 would need an efficient flood disaster management plan. The healthcare facilities and communication technologies that provide awareness to local people need to be given special attention while preparing such developmental plans. As a matter of policy, the District Disaster Management Authorities constituted under the Disaster Management Act, 2005 of the government of India, may also plan and implement the option of dividing the larger sized vulnerable districts into micro-zones for better and focused management. Such micro-focusing will lead to better implementation and efficient working of the various flood disaster reduction and planning schemes and help in times of flood crises. In any case, based on each district's flood vulnerability characteristics, the individual plans for flood mitigation and prevention need to be drawn, and micro-management may be carried out effectively once the primary step of identifying vulnerabilities is undertaken as suggested in this research study.

The paper strives to develop a methodology for assessing flood vulnerability in the Narmada river basin of Madhya Pradesh while covering the region's physical, social, and economic aspects. It is expected that the present study can lead to the development of a generic framework that standardizes a methodology not just for the vulnerability assessments but also for developing resilience indices. A generalized framework would immensely help to replicate and upscale assessment of vulnerabilities for other cities and districts. Also, by prioritization of the indicators and appropriate adaptation measures, comprehensive vulnerability and resilience maps of various regions may be prepared that may be available for use during and after disaster events. Developing such customized frameworks to identify disaster vulnerable and resilient areas can help decision-makers and disaster management authorities develop short-and long-term planning and policy.

A similar framework can be designed and developed for the different areas of the country, which are prone to the various other disasters such as earthquakes, landslides, droughts, wildfires, etc. Hence extensive vulnerability and resilience mapping of any area covering the various natural disasters can be undertaken using such a technique. This can again aid in developing evidence-based strategic recommendations for decision-makers and planners. Moreover, advanced tools like this would enable evaluation of disaster vulnerability and resilience and help in evolving ways to enable stakeholders' need for education and organization during times of crisis when encountering disaster events.

This study is relevant from the viewpoint of SDG Goal -11 that aims to ‘make cities and human settlement inclusive, safe, resilient and sustainable.’ In particular, the Target 11.5 whereby by the year 2030 significant reductions in the number of deaths and people affected are envisaged to be achieved, especially from water-related disasters. Furthermore, this target aims to substantially decrease economic losses and protect the poor comprising vulnerable sections of society. Thus, assessing the flood vulnerabilities constitutes the first step in the achievement of international efforts.

In this paper, a DEA-based model was proposed for estimating the flood vulnerability, and the methodology has been applied for 21 districts in the River Narmada basin of Madhya Pradesh, India. For the development of the model, six physical and socio-economic variables were identified that act as inputs and outputs to the DEA-based model. A cluster analysis divided the flood vulnerability into three clusters, even as a majority of districts exhibited significantly high levels of flood vulnerabilities, indicative of the fact that as a matter of policy, the authorities need to adopt better management and governance practices to become resilient to flood disasters.

The limitations of this study comprise a general lack of updated data availability, especially in the developing country context. Any basis for planning and policy is always based on reliable data available for various indicators, and lack of a database would only exacerbate the vulnerabilities to flood by hindering disaster planning and management. Restrictions on data availability severely inhibit and curtail regulatory mechanisms' evolution, imposing little factual basis for planning disaster operations and preventing engineering and managerial interventions from improving vulnerabilities to flooding events. Possibly quality data available in an easily accessible public domain would ensure better disaster resilience.

As a methodology, DEA provides a powerful diagnostic tool but lacks focus on the goals of individual district disaster management practices that may vary considerably. The technique also does not spell any engineering and management strategies to improve flood vulnerabilities, and therefore micro-level studies – the district level studies – would be required to plan and strengthen community resilience.

Data cannot be made publicly available; readers should contact the corresponding author for details.