Keywords

1 Introduction

Since time immemorial, man is facing an enemy as powerful as unpredictable: the floods. In fact, floods are the most frequent natural disasters [1] and the most dangerous with their magnitude and suddenness [2]. Floods are a natural and seasonal phenomenon which corresponds to a flooding of an area usually out of the water.

The causes of these latter have evolved and their consequences are continuing to grow. Unfortunately, there are so far no means that can act upon the devastating effects of flooding and urban flooding, the only alternative is to take precautions at best by setting their knowledge at the forefront of policy priorities and intervention strategies [1].

During the last twenty-five years (1999–2014), Morocco has experienced a series of major floods, which affected more than 557,270 people by making 1192 deaths [3]. The damage caused by these floods hit three billions Dirhams [3]. The city of Casablanca, the economic capital of Morocco has not been spared. In fact, Heavy rainfall in 1996 as well as 2010 had caused extensive damage (collapse of dilapidated houses, electricity failure, paralysis of transport, school closures, and road accidents) and even losses of lives. The metropolis is characterized by the presence of the historical path of Oued Bouskoura that ran through, at the time, the city from east to west. The gradual occupation and urbanization of the major bed of Oued Bouskoura over the last decades and construction in the 80 s of the Eljadidaa road makes of this environment a vulnerable area for the population and infrastructure there.

The methodology of this study is the use of a geographic information system coupled with the hierarchical multi-criteria analysis developed by T. Saaty (Saaty 1980) for the identification and quantification of urban elements lying in the natural course of Oued Bouskoura and are at risk of flooding. The result is supplied as a synthetic cartography of the global indicator of vulnerability allowing a clear view of the risk associated with the flooding hazard. The result is an effective and useful tool for supporting decision-making for decision makers in the context of an integrated management for the areas of Casablanca subject to flooding.

1.1 Study Area

Casablanca is situated on the Moroccan Atlantic coast, west central Morocco. In geographic coordinates, the city is located about 33° 34′ 42.44″ North latitude and 7° 36′ 23.89″ West longitude. Casablanca is characterized by a semi-arid climate with normal average temperature (calculated from 1961 to 1990) ranging from 12.7 °C in winter to 21 °C in summer. The average annual rainfall is 427 mm. They may reach values lower than 200 mm or sometimes exceeding 800 mm [4].

Oued Bouskoura is undoubtedly one of the major threats to the city of Casablanca. The danger lies in the fact that the city is built on the natural bed of Oued Bouskoura. This gives particular importance to this area that covers three urban municipalities we have taken as a sample for the application of our model. This being said, nothing prevents the application of the methodology of this study to be generalized across the area of Casablanca (Fig. 1).

Fig. 1
figure 1

Study area

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1.2 Methodological Approach

The methodology of this study is the use of a geographic information system coupled with the hierarchical multi-criteria analysis developed by T. Saaty (Saaty 1980) for the identification and quantification of urban elements lying in the natural course of Oued Bouskoura and are at risk of flooding.

The elaborated assessment tool allows analyzing and evaluating local vulnerability to urban flooding in three types of issues: human issues, environmental issues and material issues. Each of these issues is the subject of an analysis and evaluation grid that enables the development of vulnerability indicators from the detailed lists of criteria. The result is supplied as a synthetic cartography of the global indicator of vulnerability allowing a clear view of the risk associated with the flooding hazard. The result is an effective and useful tool for supporting decision-making for decision makers in the context of an integrated management for the areas of Casablanca subject to flooding.

2 The Use of Multi-criteria Analysis Methods in the Vulnerability Assessment

2.1 Multicriteria Methods for Assessing the Vulnerability of a Territory

The methods of decision support or, more accurately, the multi-criteria methods for decision support are fairly recent techniques and under development [5]. Historically, these methods were used by managers of companies or project managers as decision support tools to deal with problems of choice of solution or alternative assessment. In fact, methods of decision support have been developed to facilitate the choice between a number of options available or evaluation in complex situations where several qualitative and quantitative criteria come into play [6]. More recently they have been applied repeatedly in environmental issues such as vulnerability assessment of a territory, in terms of flood risk, industrial risks or risks for transport of hazardous materials [7].

Today, there exist several decision support methods such as comparison criteria, weighted averages, the ordinal method, factor analysis or even multi-criteria approach to decision support AHP (Analytical Hierarchy Process) [6]. The latter, which is the methodological context of our study, was proposed by Thomas Saaty in the 1980s it consists in ordering solutions based on different criteria while examining the consistency and the logic of judgments about the weight of criterion considered and preferences of decision makers [8].

2.2 AHP Method: Principles and Computation

The process of the AHP method can be summarized in four steps: analyze the problem concerned, build a hierarchical decomposition by declining each objective comparison criteria, determine priorities for targets from expert judgment by checking the consistency of subjective assessments and aggregate at the end the experts’ answers to get the vulnerability functions.

One of the most creative tasks in decision making is to choose the factors that are important for the decision [9]. Using the AHP method is initially based on the decomposition of the problem by performing a qualitative and quantitative accurate census of different criteria (vulnerable targets and vulnerability factors) [6]. This initial analysis is highly dependent on judgments, needs and knowledge of the participants in the process of decision making. Note also that the fineness of this decomposition depends on the “wealth” of the databases used (land use map, urban planning, population census, transportation networks, public facilities, etc.)

The second stage of the AHP method is to build a hierarchical tree composed of objectives, criteria, sub-criteria and targets in the form of father-son pair. This hierarchy provides a structured view of the problem studied in offering the user/decision maker better concentration on specific criteria [10].

Each criterion must be identified with its definition and intensity [8]. In fact, the weight of each item is determined using the pairwise comparison method. This involves comparing the different criteria son pairwise compared to the initial target (father criteria) to assess their importance. This comparison is done primarily through the collection of expert opinions through a questionnaire in the form of “evaluation matrix” and according to a so-called specific Saaty scale [11] (Table 1).

Table 1 The AHP pairwise comparison scale [16]
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The evaluation matrices are square matrices, the order equal to the number of comparison criteria. The experts pronounce on the importance of criterion c1 of the 1st line with criteria c2, c3, …, cn appearing successively at the top of each column. This operation is subsequently performed for each criterion of each line of the matrix. The sum of the weights of all criteria son of the same father criterion is 1. This weight rule is called “interdependent relationship.”

In a decision problem, it is absolutely essential to measure the “degree” of consistency of judgments that are placed. In fact, the 3rd stage of the AHP method is to check the consistency of binary comparisons from expert judgment and included in the evaluation matrices. The consistency of the answers is estimated using a known ratio: Consistency Ratio (CR) [6]. This ratio is obtained from the eigenvalue of the comparison matrices and which should be less than 10 %. Calculating the Coherence Ratio is as follows.

Consider C = (Cij) an evaluation matrix with Cij the relative weight of the criterion Ci with respect to Cj criterion. C the matrix of order n with:

$${\text{C}}_{\text{ij}} \ne 0,\,{\text{C}}_{\text{ij}} = 1/{\text{C}}_{\text{ji}} \,{\text{e}}_{\text{t}} \,{\text{C}}_{\text{ii}} = 1.$$
(1)

The matrix is perfectly consistent if the weights Cij are transitive, that is to say, for all i, j and k has the following equation:

$${\text{C}}_{\text{ij}} = {\text{C}}_{\text{ik}} *{\text{C}}_{\text{kj}} .$$
(2)

In fact, for example, if an expert is pronounced for a greater relative weight for the target (I) relative to the target (K), and to a greater weight of the target (K) relative to (J) logically, the same expert will have to be pronounced for the greater weight of the target (I) relative to (J) [11].

In this case of judgment perfectly transitive, the matrix C can be written as the following vector form: C * V = λ * V where V is the eigenvector and λ is the eigenvalue of the matrix. In the case of a perfectly consistent matrix the λ value is equal to the order n and the rank of the matrix is equal to 1.

However, the weights established in the AHP process are based on human judgments that make it difficult to have a perfect Coherence Ratio (50). In this case, the previous equation is:

$${\text{C}}*{\text{V}} =\uplambda_{ \hbox{max} } *{\text{V}}\quad{\text{where}}\quad\uplambda_{ \hbox{max} } \, \ge {\text{n}}.$$
(3)

The difference between λmax and n indicates “the degree of inconsistency” of the judgment made [12].

3 Hierarchical Tree and Conception of a GIS Model

3.1 Development of Hierarchical Tree

The elaborated assessment tool developed within the framework of this study allows analyzing and evaluating local vulnerability to urban flooding in three types of issues: human issues, environmental issues and material issues. Each of these issues is the subject of an analysis and evaluation grid that enables the development of vulnerability indicators from the detailed lists of criteria. The suggested hierarchy is an overall view of the problem in terms of objective, criteria and alternatives.

Human vulnerable targets can be divided into three broad categories: resident population, non-resident population and population with assisted evacuation. Given the high density of population in the cities, using a small-scale measurement is paramount [13]. In our case, the following criteria were considered extremely important to be part of our evaluation criteria of human vulnerability: Total population (between 10 and 65, under 10 and over 65) population in the workplace and the reception centers (hotels, summer centers), and finally the population of hospital centers, schools and pretension centers.

The Material issues are six major types based on land use: residential buildings, industrial and commercial areas, administration and service, leisure and family gardens, transportation and public facilities. These elements are then divided into more detailed targets.

In addition to economic and social damage, floods in urban areas can also influence the environment and biodiversity of an ecosystem [14]. To assess the ecological risk of flooding, environmental vulnerability is represented by the following: potential contamination, the effect of overland flow on green landscaped and agricultural spaces, bare land, forests and zoos. Just like the material issues, these issues are subdivided and vulnerability factors can be assigned.

3.2 Data Structure According to Conceptual Model

Following the analysis and identification of needs, we identified the spatial data necessary for the completion of this study and completed the conceptual modeling (feature class, subclasses, entities, attributes, sub type of attributes). The data were later collected from different sources (cadastral data, road networks, population, water and sanitation networks, electricity network …). This model was largely inspired from the Barczack and Grivault model in work “Geographical Information System for the assessment of vulnerability to urban surface runoff” [2].

4 Result of Analytic Hierarchical Process

4.1 Sectorization of the Study Area

According to the data dictionary of our conceptual model, the targets are in different geometric shapes and vectors (area, line, and point). Thus, they need to be standardized for their combination [6]. The commonly used generalization technique is the meshing of the study area [7, 15]. The choice of the size and number of meshes used are attributes of the degree of accuracy of the data and space studied itself [6]. We opted for a meshing of about 200 m from the side of each mesh. This makes a number of 4000 mesh to cover the entire study area. Note that we can use a narrower mesh (about 50 m) in a specific sector for further analysis needs.

4.2 Quantification of Targets

Quantification of human targets was based primarily on statistics of demography by the High Commission for planning municipality. The number of inhabitants per cell (Hm) was calculated from the population of the municipality (Pc) of the total number of housing in the municipality (Nlc) and the number of dwellings in the mesh (Nlm) using the following formula:

$${\text{H}}_{\text{m}} = {\text{Nl}}_{\text{m}} *{\text{P}}_{\text{c}} /{\text{Nl}}_{\text{c}} .$$
(4)

Unfortunately, there are no data on the employment potential of each municipality. The population at the workplace (Pasm) was estimated through the total active population in the city of Casablanca (Pa), the total number of economic entities by sector (Nec), the percentage distribution of the workforce by sector (Pas) and the number of existing economic entities of the same sector in a mesh (Nasm):

$${\text{P}}_{\text{asm}} = {\text{P}}_{\text{a}}\,*\,{\text{P}}_{\text{as}} \,*\,\left( {{\text{N}}_{\text{asm}} /{\text{N}}_{\text{ec}} } \right).$$
(5)

To quantify the economic and environmental targets, we determined for each areal target corresponding quantization factor (Fqs) using the surface of the target in the mesh (Sm) and the maximum surface of the target in a mesh (Smax) of the study area.

$${\text{F}}_{\text{qs}} \, = \,{\text{S}}_{\text{m}} \,/\,{\text{S}}_{ \hbox{max} } .$$
(6)

Similarly, for linear targets, quantization factors (Fql) are derived from the length of the target in the mesh (Lm) and the maximum length of the target in a mesh.

$${\text{F}}_{\text{ql}} \, = \,{\text{L}}_{\text{m}} /{\text{L}}_{ \hbox{max} } .$$
(7)

The comparison matrices containing the expert judgments were the subject of a specific treatment to associate all assessments. Questionnaires that were retained are those with a coherence ratio less than 10 %. The calculation of the eigenvectors of each matrix was used to calculate the overall vulnerability function.

$${\text{V}}_{\text{global}} .\, = \,0. 80 6 4*{\text{V}}_{\text{humain}} \, + \, \, 0.0 3 2 2\,*{\text{V}}_{\text{materiel}} \, + \,0. 1 6 1 2\,*{\text{V}}_{\text{environnemental}} .$$
(8)

4.3 Discussion and Vulnerability Index Mapping

The analysis of the first results obtained from the evaluation matrices treated shows greater importance given to human vulnerability with 80 %, followed by environmental vulnerability of 17 % and at the end the materiel vulnerability with only 3 %. The presentation of the results with GIS data processing software leads to vulnerability maps as cited in the following example (Fig. 2).

Fig. 2
figure 2

Materiel vulnerability mapping

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5 Conclusion and Perspectives

The assessment of the vulnerability of urban land by using the AHP method is an exercise that requires a profound technical knowledge, specific resources and territorial and statistical data. Our research approach is to use a multi-criteria analysis method for the classification of the human, material and environmental stakes in the Casablanca area. The results obtained after using spatial analysis tool are represented as global vulnerability maps.

We must also consider the limitations of the proposed end approach to improve the relevance of results. Indeed, the AHP method was mainly criticized for too subjective aspect of judgments made by the experts. On the implementation side of the results obtained in a GIS, the mesh used as the unit of analysis is based on the assumption of a homogeneous distribution of the land use population within a islet. The lack of comprehensive, reliable and up to date on the Casablanca area is considered one of the major challenges we faced throughout the process.

This analysis will be enriched gradually by the integration of new matrices of judgment and the consideration of new issues that were not considered in this study. It would also be important to consider the temporal component, including the calculation of resident population and the workplace.