a new approach to multi criteria decision-making

8/8/2019 A New Approach to Multi Criteria Decision-Making

1/20

Journal of Geographic Information and Decision Analysis, vol.1, no.1, pp. 25-44, 1997

A New Approach to Multi-criteria Decision Making inWater Resources

Robert J. TkachDepartment of Civil and Geological Engineering and Natural Resources Institute, The University of

Manitoba, Winnipeg, MB R3T 2N2, [email protected]://www.ce.umanitoba.ca/~rob/

Slobodan P. SimonovicDepartment of Civil and Geological Engineering and Natural Resources Institute, The University ofManitoba, Winnipeg, MB R3T 2N2, [email protected]://www.ce.umanitoba.ca/~simon/

ABSTRACT

Spatial comparison of floodplain management alternatives in a rasterGIS environment is conceptualized as a multi criteria decision making problem. Aspatial MCDM technique is developed by combining the conventional CompromiseProgramming technique with GIS technology. This new technique is referred toherein as Spatial Compromise Programming (SCP). The main contribution of theproposed technique is its ability to address uneven spatial distribution of criteriavalues in the evaluation and ranking of alternatives. SCP is used to determine thebest alternative for each geographic location within the region of interest. Theanalysis of floodplain management strategies for the Red River Valley region ischosen as a case study to illustrate application of the Spatial CompromiseProgramming technique.KEYWORDS:GIS, multi-criteria decision making, flood control

Contents

1. Introduction2. GIS and decision-making

2.1. Introduction2.2. Compromise Programming 2.3. Importance of Spatial Variation in Criteria Value 2.4. Spatial Compromise Programming


2/20

26

3. Floodplain analysis of the Read River Valley3.1. Background3.2. Existing Flood Protection

3.3. Case Study Description3.4. Floodplain Analysis Model

4. Results of the floodplain analysis of the Red River Valley4.1. Flood Protection Alternatives4.2. Evaluation Criteria 4.3. Evaluation of Flood Control Alternatives 4.4. Compromise Programming Analysis 4.5. Spatial Compromise Programming Analysis

5. ConclusionsReferences

1. Introduction

Selecting the best strategy from a number of potential alternatives in water resourcesplanning and management is a complex decision making process (Bose and Bose 1995).It may include conflicting quantitative and qualitative criteria and multiple decision-

makers. The decision-making process can benefit from the use of multi-criteria decisionmaking (MCDM) techniques. They can be used to facilitate the decision-making processby making the process more explicit, rational, and efficient (Hobbs et al. 1992).Conventional MCDM techniques have been used in the field of water resources in thepast (Simonovic 1989; Shafike et al. 1992; and Greshan et al. 1982).

The evaluation and ranking of alternatives by MCDM techniques is based oncriteria values associated with each of the alternatives, and the objectives and preferencesof the various decision makers. The criteria used in the evaluation of water resourcesalternatives, which may be quantitative and/or qualitative, often exhibit spatialvariability. For example, implementation of a particular alternative could producefavorable impacts at one location while resulting in negative consequences at another.Conventional MCDM techniques are not able to address uneven spatial distribution of thecriteria values in the evaluation and ranking of alternatives.

The main objective of the research described in this paper is to develop a MCDMtechnique capable of capturing the spatial distribution of the criteria values associatedwith the various alternatives. The new MCDM technique developed in this research,named Spatial Compromise Programming (SCP) combines the CompromiseProgramming (CP) (Zeleny 1973) with Geographic Information System (GIS)

technology.The analysis of potential floodplain management strategies for the Red River Valley

is used as a case study to demonstrate the potential of the SCP technique. The mainobjective of the case study is to generate, evaluate, and rank a set of potential floodprotection alternatives. The flood water impacts occurring under the implementation of

different protection alternatives are used to evaluate and rank the alternatives using both,CP and SCP techniques. Through the application of the CP technique the best alternative

is determined for the entire region. The best alternative for each location within theregion is determined using SCP. Comparison of the results produced through theapplication of the two techniques is used to identify the merits of the new approach

(SCP).The remainder of the paper contains a description of the development, application,


3/20

27

and evaluation of the Spatial Compromise Programming technique. The next sectionbegins with an overview of the use of GIS in decision making. A brief description of theCompromise Programming technique follows. With the help of a very simple example,

the shortcomings of this technique for spatial decision making are identified. Thefollowing section of the paper describes the Spatial Compromise Programmingtechnique. Using the same simple example, the mechanics of SCP are illustrated. Thefinal section of this paper describes the case study. The paper concludes with a discussionand comparison of the evaluation of the flood control alternatives using CompromiseProgramming and Spatial Compromise Programming.

2. GIS and decision-making2.1. Introduction

Geographic Information Systems are a rapidly evolving technology that can be used forthe efficient storage, analysis, and management of spatial information. Environmental or

natural resources management decisions almost always require the analysis of spatialinformation. GIS technologies have been used to facilitate decision making in the field ofwater resources and many other fields of study. Carver (1991) presents an example

application of the integration of multi-criteria evaluation techniques with GIS insearching for suitable sites for the disposal of radioactive waste in the UK. McKinney

and Maidment (1993) combine a GIS with Expert System technology to enhance thedecision-making process in water resources management. Given existing and projectedwater supplies and demands combination of the two technologies determines potential

water deficits and surpluses. Pereira and Duckstein (1993) apply the CompromiseProgramming technique within a GIS in order to evaluate potential habitats for theendangered Mount Graham red squirrel. Applications in other areas include Banai

(1993), Tim (1997), and Wolfe (1997).GIS technologies facilitate the decision making process based on their analyticalcapabilities with spatial information. In addition to this, many of them are equipped witha graphical user interface, which increases the decision-maker's comprehension of thespatial information that is involved in the problem being addressed. Based on these twopotential additions to the decision making process, a GIS is often included as a majorcomponent in the development of Decision Support Systems (DSS). Because of thespatial component that a GIS adds to conventional DSS, this combination of technologieshas been referred to as Spatial Decision Support Systems (SDSS). Recent papers byWalsh (1993), Frst et al. (1993), Simonovic (1993), Leipniket al. (1993), Watkins et al.(1996), and Fedra (1997) discuss the potential applications of SDSS in environmental and

natural resources decision making.2.2. Compromise Programming MCDM is characterized by great methodological diversity with three main groups of

techniques: (a) outranking techniques ; (b) multi-attribute utility techniques; and (c)mathematical programming techniques (Goicoechea at al. 1982). Outranking techniques

require pairwise or global comparisons among alternatives, which are not practical wherethe number of alternatives is large. Multi-attribute utility techniques rely on linearadditive or simple multiplicative models for aggregating single criterion evaluations.

They are not appropriate for the analysis of complex environmental systems.Compromise Programming (CP) is a mathematical programming technique for use in a


4/20

28

continuous context (Zeleny 1973). It has also been modified for water resources multi-criteria discrete problems (Duckstein and Opricovic 1980). It is used to identify solutionsthat are closest to the ideal solution as determined by some measure of distance. The

solutions identified to be closest to the ideal solution are called compromise solutions andconstitute the compromise set. The ideal solution is one which provides the extreme valuefor each of the criteria considered in the analysis. The distance from the ideal solution foreach alternative is measured by what is referred to as the distance metric. This value,which is calculated for each alternative solution, is a function of the criteria valuesthemselves, the relative importance of the various criteria to the decision makers, and theimportance of the maximal deviation from the ideal solution (Simonovic 1989). Shown inEquation (1) is the operational expression used to compute the family of distance metrics(Lj) for a set ofn criteria and m alternatives.

(1)where:Lj is the distance metric;f

*i is the optimal value of the i

th criteria;fi,w is the worst value of the i

th criteria;fi,j is the value of the i

th criteria for alternativej;wi are weights indicating decision maker preferences;

p is a parameter (1p );i is indicates the number of criteria i = 1,? ,n; andj is indicates the number of alternativesj = 1,? ,m.

Introduction of wi allows the expression of the decision makers' preferencesconcerning the relative importance of various criteria. The parameter p reflects theimportance of the maximal deviation from the ideal point. Thus a double-weightingscheme exists: for p = 1 all deviations are weighted equally; for p = 2 each deviation isweighted in proportion to its magnitude. The larger the deviation the larger the weight.For the value ofp = , the min-max criterion is achieved (Simonovic 1989).

In using CP and many other MCDM techniques to evaluate a set of potentialalternatives a single optimal solution that equally satisfies all criteria is often infeasible.Instead of seeking a single optimal solution, a subset of noninferior (nondominated)solutions is sought. For each solution, which is outside the nondominated subset but stillwithin the feasible region, there is a nondominated solution for which all criteria are

unchanged or improved and at least one that is strictly improved (Goicoechea et al.1982). Generation of the nondominated set of alternatives is accomplished using the CPtechnique by solving Equation (1) for different values of the weightp. As the range of theweight p is infinite, further reduction of the set is necessary for practical application.Typically, the compromise set is approximated by solving Equation (1) using values ofp

= 1, 2 and .The criteria values used in Equation (1) express impacts produced by, or

characteristics associated with each of the alternatives. It is obvious that in Equation (1)there is no consideration for potential spatial variability in the criteria values. Therefore


5/20

29

in identifying the best compromise solutions using CP, only the region as a whole isconsidered, and local impacts associated with different alternatives are ignored.

2.3. Importance of Spatial Variation in Criteria ValuesThe criteria used in water resources are often spatially variable. For example, in flood

control, the impacts produced by flooding are typically not the same for all locationswithin the floodplain. The distribution of the flood impacts is a function of the

implemented flood protection measures. Implementation of a particular measure mayreduce flood impacts at one location, while providing no protection at all for another.Straightforward application of conventional MCDM techniques are not appropriate for

problems which exhibit spatial variability in the criteria values. Conventional MCDMtechniques typically use average or total impacts incurred across the entire region being

considered. The following is a very simple example that demonstrates the existence ofspatial variability in the criteria values. The same example is then used to analyze the

implications of not considering the spatial variation in criteria values.Example To be consistent with the case study discussed in the following section, thisexample is also addresses a flood control problem. The hypothetical region of interest is

shown in Figure 1.

Figure 1 Example Region of Interest

The area consists of a mixed variety of land-use types in close proximity to a river.

The region is divided into a grid, as shown in Figure 1, to help illustrate the spatialvariability in the criteria values. To alleviate the flood damage in this region, threepotential mitigation alternatives (dyk ing strategies) are proposed. In each alternative, oneof the respective land-use types is completely surrounded by dykes. Two criteria: (a)flood water depth; and (b) flood water velocity, are used for the evaluation of three

alternatives. Given a flood of an arbitrary magnitude the flood water depth and velocityfor each alternative and land use type are shown in Figures 2 and 3, respectively.

Figure 2 Flood Water Depth


6/20

30

Figure 3: Flood Water Velocity

Selection of the best alternative for this example is based on minimizing the floodwater depth and velocity. Using one of the MCDM techniques, (not necessary due to theproblem's simplicity) such as the CP technique, the criteria values for each alternativewould first be averaged across the region of interest. The average flood water depth foralternatives one, two and three is 1.22, 1.53 and 1.16 units respectively. The average

flood water velocity for alternatives one, two and three is 0.92, 1.14 and 0.87 unitsrespectively. Without any additional computations it is obvious that alternative three,having the least average flood water depth and velocity, would be considered the bestflood mitigation strategy by the CP technique for the region of interest.

In reviewing the criteria values shown in Figures 2 and 3 it is apparent that theflood water impacts, resulting from implementation of each of the three alternatives, arenot evenly distributed across the region of interest. Thus, the selection of alternative threedoes not necessarily provide all areas in the region with the same level of protection. Infact, implementation of this alternative, as shown by the criteria values, provides onlyappropriate protection to the farmland.

2.4. Spatial Compromise ProgrammingGeographic information system technologies can be used to include spatialconsiderations in MCDM. Past applications of GIS in MCDM have predominantlyinvolved the determination of the best spatial location for an alternative according to a

predetermined set of criteria (Carver 1991; Pereira and Duckstein 1993 ). The researchpresented here expands the previous idea to one of determining the best alternative foreach spatial location based on a decision maker's preferences and a set of criteria.Utilizing the proposed approach can accommodate spatial variation in criteria values.

A new methodological framework for spatial decision making is developed byembedding the Compromise Programming technique within a GIS framework. Allaspects of the CP technique are preserved within the GIS. Preparation of input data for

implementation of the CP technique is done using GIS raster images. All requiredcalculations (Equation 1) are performed within the GIS.The Spatial Compromise Programming technique identifies the best solution from a

number of alternatives for each location within the region of interest. As in theapplication of CP, the family of distance metrics is the basis on which the alternatives areevaluated. However, with the SCP technique, rather than determining a single value peralternative, a distance metric is calculated for each location (represented by an individualraster cell) in the region of interest for each alternative. The region of interestencompasses all geographic locations that are impacted by the combined group ofalternatives and is represented by a raster feature image of the study area.


7/20

31

Criteria values associated with each of the alternatives are contained within sets ofcriteria images, which are geo-referenced with the feature image. Alternatives have theirown individual set of images, and therefore, the total number of criteria images equals the

product of the number of criteria and the number of alternatives. Each raster cell in acriteria image contains the criteria value associated with a particular alternative. If thecriteria value is spatially variable then each affected cell, or location, within the imagecontains a different value.

Using the criteria images, and the decision-maker's preferences, a distance metricimage is produced for each alternative. Contained in the distance metric images aredistance metric values for each raster cell calculated using Equation (1). The algorithmicprocedure for producing a distance metric image is shown in Figure 4. All computationsare performed using GIS commands.

Figure 4 Calculation of Distance Metric Values in GIS Framework

Using the values stored in the distance metric images, the best alternative isdetermined for each location as one with the smallest distance metric value. A new image

identifying the best alternative for each location is produced with each cell containing anumber corresponding to the best alternative.

Research similar to that presented in this paper can be found in Pereira andDuckstein (1993). In the work done by Pereira and Duckstein the CP technique wasapplied using GIS technology in order to evaluate the Graham County region as a

potential habitat for the endangered Mount Graham red squirrel. Each location in theregion was evaluated based on a set of criteria important to the survival of the red

squirrel, and was assigned a distance metric value, as calculated by the CP technique,based on the level to which each location satisfied the specified criteria. A single distancemetric image was produced for the region, for each tested value of the parameter p inEquation (1). Each distance metric image was then discretized into ten habitat qualityclasses at ordinal levels by comparing the distance metric values in each cell across eachindividual image.

The research presented in this paper is an extension of the work by Pereira andDuckstein (1993). The two main contributions of our work are: (a) replacement of asingle distance metric image for the whole region with a distance metric image for each


8/20

32

potential flood protection alternative; and (b) comparison of distance metric values foreach alternative at each geographic location.Example Using the example discussed in the previous section, the SCP technique could

be used to provide decision-makers with a more detailed evaluation of the three potentialalternatives. Required as input for this technique are raster images describing thetopography of the case study area, as well as the extent of the potential impacts of eachalternative. Figure 1, which shows the land use types in a grid like fashion, represents theraster feature image describing the region of interest. The three sets of flood water depthand velocity values shown in Figures 2 and 3, represent the criteria images for each of thealternatives. Figure 5 is the final best alternative image generated by evaluating the threeflood protection measures using the SCP technique.

Figure 5 Best Alternative Image

The numbers corresponding to the best alternative are contained in each cell of theimage. Thus, the implementation of SCP shows that alternative three, determined to bethe best alternative by Compromise Programming, is not the best solution for eachlocation in the region of interest.

Using GIS technology the spatial variability of the criteria values is taken intoconsideration. The best alternative for each location in the region of interest is determinedby the application of the SCP technique. The complex decision making process in thefield of water resources can benefit from the additional information provided by this new

technique.

3. Floodplain analysis of the Read River Valley3.1. BackgroundA floodplain analysis of the Red River Valley has been selected to illustrate the

application of the SCP technique. The Red River Valley is located in the south-centralportion of the province of Manitoba, Canada. It consists of low- lying flat prairiespredominantly used for agricultural purposes. The valley is very prone to flooding andhas historically (in 1826, 1950, 1979, and 1996) incurred extensive damages to both

urban and agricultural areas from floods. The major floods are typically seasonal innature, and are the result of combined spring snowmelt and rainfall runoff along both theRed and Assiniboine Rivers (Krenz and Leitch 1993). The 1950 flooding event inWinnipeg was one of the largest natural disasters in Canadian history (Rannie 1980).Water levels in the Red River rose 30.3 feet above datum within the City of Winnipeg(Bumsted 1993). In this flood roughly 640 square miles of cropland were submerged,approximately 10,500 homes were flooded, and 100,000 people had to be evacuated.Roughly 30 million dollars was paid out in flood damages (United States GeologicalSurvey 1952). However, the true cost of the flood may have exceeded 100 milliondollars. During this flood communities located upstream of the City of Winnipeg were


9/20

33

completely submerged and significant portions of the City of Winnipeg were extensivelyflooded. Shown in Figure 6 is the extent of the 1950 flood within the City of Winnipeg.

Figure 6 University of Manitoba during the 1950 flood, Winnipeg, Canada

3.2. Existing Flood Protection

To alleviate the damages produced by flooding in the Red River Valley a number ofstructural and non-structural flood mitigation measures have been implemented over time(Figure 7). These include: (a) a dyking system along both the Red and AssiniboineRivers; (b) flood pumping stations within the City of Winnipeg; (c) ShellmouthReservoir; (d) the Portage Diversion; and (e) the Red River Floodway.

Figure 7 Flood Protection System for the City of Winnipeg and Surrounding Area

It is estimated that the combined measures listed above can provide protection for the

City of Winnipeg from river flows up to 169,000 cfs. This magnitude of flooding eventcorresponds to a predicted return period of approximately 165 years (Rannie 1980).Though this level of flood protection is quite high, the overall flood mitigation strategyfor this area requires improvement. Because the protection measures have beendeveloped separately over time, at present they are operated somewhat independently.The level of coordination that does exist requires updating. The optimal efficiency of theexisting flood mitigation projects is not currently being attained.

3.3. Case Study Description

The focus of the Red River Valley floodplain analysis is a region (7.5 by 5 km)encompassing the community of St. Adolphe along the Red River south of Winnipeg.


10/20

34

The main flood protection for the town of St. Adolphe itself is provided by a ring dyke,which has an elevation equal to the water level of the 1950 flood. St. Adolphe is theclosest community upstream from the Red River Floodway inlet and gate structure.

The Red River Floodway, Manitoba's largest flood protection project, wascompleted in 1968. The floodway is a 30 mile long channel, with a flow capacity of 60000 cfs, which diverts floodwaters around the east side of the City of Winnipeg and thenreconnects with the Red River near the town of Lockport. The entrance to the floodway ison the south side of the City, near the community of St. Adolphe. The flow of waterwithin the Red River is unaffected by the floodway until the discharge reaches 30,000cfs. At this flow the water surface reaches sufficient elevation to permit flow into thefloodway. The flow of water into the floodway channel is controlled by a gate structurelocated downstream of the floodway entrance. The gates, which are normally flush withthe bottom of the river, can be raised to produce a backwater effect that forces water intothe floodway channel. The higher the gates are raised, the greater the backwater and thus

the more water forced into the floodway.The operations policy of the floodway is designed in such a way that under normal

conditions the backwater does not alter the upstream water levels compared to natural

water level before construction of the floodway. However, in the case of a declared stateof emergency, in order to save the downstream City of Winnipeg, flooding of theupstream communities is required (Manitoba Department of Natural Resources 1984).This decision is typically based on the economic value of potential flood damage and is asource of conflict between residents of St. Adolphe and the City of Winnipeg. Therefore,

there is a need for further re-evaluation of the current flood mitigation strategy forWinnipeg and surrounding area. The technique developed in this research can be used in

re-evaluation of the floodway operating strategy.

The main objective of the floodplain analysis in this research is to identify the bestflood mitigation strategy, from a set of potential alternatives for the case study area. A

floodplain analysis model is developed for this study. The model is used to (a) generate aset of potential flood protection alternatives for the St. Adolphe region, (b) estimate the

flood impact, and (c) evaluate and rank the potential alternatives. Potential protectionalternatives are ranked on the basis of minimizing flood impacts in the St. Adolpheregion. Both, the SCP and the CP techniques are applied in the evaluation process.

3.4. Floodplain Analysis ModelThe floodplain analysis model is used to simulate floods for the purpose of generatingflood protection alternatives, as well as to evaluate and rank the potential alternatives.

The floodplain analysis model is comprised of a GIS and a conventional mathematicalmodel.Maximum flexibility and minimum cost in selecting a GIS software led to the

selection of the IBM-PC based package IDRISI (Eastman 1992, 1995). IDRISI is araster-based GIS software which delivers a strong analytical functionality at an affordablecost (Meyer et al. 1993).

The HEC-2 (United States Army Corps of Engineers 1982) package is selected toperform the necessary hydraulic modeling of the floodplain analysis. This model can beused for estimating water surface elevations for steady or gradually varied flow in natural

or man-made channels. The effects of flow obstructions such as bridges, culverts andweirs are accounted for in the estimation of the water surface elevation using HEC-2.


11/20

35

The floodplain analysis model requires a description of the characteristics of the RedRiver Valley. The GIS and HEC-2 databases are used to store all the necessary inputinformation.The GIS database is comprised of two distinct types of raster images referred

to as feature images and Digital Elevation Models (DEMs). The images are produced byconverting and interpolating data collected by (a) processing three-dimensional aerialphotographs (1:20,000 scale), (b) conventional land surveying, and (c) digitizingtopographic maps. The feature images identify the two-dimensional locations of bothnatural and man-made features in the Red River Valley with respect to the UTM-14Ncoordinate system. Each raster cell in the feature images contains a numerical identifiercorresponding to the specific feature located in the coordinate boundaries of that cell.Fourteen different classes of features are distinguished in the feature images. An examplefeature image for the St. Adolphe region is shown in Figure 8.

Figure 8 An Example Feature Image of St. Adolphe Region

DEMs are raster images describing the elevation of the ground surface correspondingto the same locations and reference system as the feature images. Thus, for every featureimage in the data set there is a corresponding DEM. Each raster cell in the DEMscontains a number equal to the ground surface elevation corresponding to the location ofthat cell.

The HEC-2 model database is comprised of a specially formatted input file. This filecontains a description of the hydraulic characteristics of the case study area. A previouslyprepared HEC-2 input file, already calibrated using the 1979 flood event in the case study

area, was conveniently available from the Manitoba Department of Natural Resources.The majority of the data in the input file consists of two-dimensional geographic

descriptions of cross-sections of the Red River channel and overbanks. The groundsurface elevations describing each cross-section within the HEC-2 input file are a subsetof the information stored in the DEM portion of the GIS database.

4. Results of the floodplain analysis of the Red River Valley

The floodplain analysis model is first used to generate a set of flood protectionalternatives for the case study area. Using the HEC-2 model the Red River water surfaceelevation is estimated. Using GIS commands and external programs, the water surface


12/20

36

elevation is transformed into a raster image identifying the maximum water surfaceelevation for each location in the region. The GIS component of the floodplain analysismodel is then used to determine the actual spatial extent of the flood water by combining

the maximum water elevation image, the feature image, and DEM of the St. Adolpheregion.

4.1. Flood Protection Alternatives

The original GIS and HEC-2 databases contain a description of the existing topographicfeatures and flood protection measures of the Red River Valley. Thus simulating a givenflood magnitude using the original data providing an approximation of the flooding

which would actually occur in the St. Adolphe region. In order to generate new floodprotection alternatives for St. Adolphe, the region's characteristics within the floodplain

analysis model databases need to be modified. These changes should reflect the potentialimplementation of new structural or non-structural flood mitiga tion measures, or the

alteration of existing ones.A wide variety of flood protection alternatives could be generated with thefloodplain analysis model. Four flood protection alternatives are generated for the town

of St. Adolphe and surrounding area by combining the following flood protectionmeasures: (a) construction of small ring dykes around specific areas; (b) alteration ofoperation policy for the Red River Floodway; (c) flood proofing of features having highrisk of flood damage; and (d) flood warning for the community of St. Adolphe andsurrounding areas. A description of the different combinations of previously introducedmeasures used in each of the four alternatives for the case study follows.Alternative 1- Base Case. The first alternative represents the existing state of the floodprotection for the town of St. Adolphe and surrounding area. As this community

experiences flooding frequently, knowledge of an impending flood can be used tosignificantly reduce the damage produced by flood waters. For this base alternative, floodwarning is provided to the community and surrounding areas. In order to protect the Cityof Winnipeg, the Red River Floodway operates under the existing operating rule. Alternative 2 - Protection of Upstream Communities. For better protection of theupstream communities the second alternative includes the lowering of the floodwaygates. This results in a water surface elevation decrease of 0.3 m at the floodwayentrance. Also, in this alternative all buildings in the study region are flood-proofed to aheight of 1 m above the natural ground elevation. Finally, no flood warning is provided tothe upstream communities. Alternative 3 - Protection of the City of Winnipeg. In this alternative the floodwayoperation is altered to provide better protection for the City of Winnipeg. The height ofthe floodway gates is changed to increase the water surface elevation at the floodwayentrance by 0.3 m. In providing a better level of protection for the city this alternativeresults in increased upstream flooding. To combat the increased upstream water level, all

buildings in the region of interest are flood-proofed to an elevation of 1 m. To furtherreduce the impacts caused by flood water, the communities are provided with floodwarning. Alternative 4 - Protection of St. Adolphe. For this alternative the entire town issurrounded by a dyke with an elevation significantly greater than the existing topography.

For this alternative the floodway is operated normally and all areas within the studyregion are provided with flood warning.


13/20

37

4.2. Evaluation Criteria The floodplain analysis model is used to simulate the effects of the four proposedprotection alternatives. Images showing the flood water extent given implementation of

each alternative are produced. The flood water extent images are combined with the St.Adolphe feature image in order to produce a new set of images referred to as floodedfeature images, which identify the locations and features, which are affected by the flood,given implementation of each alternative. The flooded feature images were used todetermine the flood water impacts that are incurred by the region given hypotheticalimplementation of each new flood protection alternative. These flood water impacts areused as a basis to evaluate and rank the potential alternatives.

Three different types of flood water impacts were used as criteria to evaluate theproposed alternatives using the CP and the SCP techniques. Because SCP is applied using

GIS, the criteria values for each alternative must be in the form of raster images witheach cell containing the magnitude of the impact.

Criteria 1 - Flood Water Depth. The flood water depth image is prepared using acombination of the flooded feature image, the water surface elevation as contained in thereach image, and the DEM. For all flooded locations, the ground surface elevation in the

DEM is subtracted from the calculated water surface elevation resulting in an imagecontaining the water depth. Flood water depth images are produced for each flood

protection alternative.Criteria 2 - Building Damage. The second criterion used in the evaluation of thealternatives is the dollar value of damage to flooded structures within the region of

interest. Three different classes of buildings (industrial, municipal, and residential) areidentified in the feature image for each region. Damage to each of the buildings iscalculated through application of a stage-damage curve. This curve relates the damage to

a structure as a function of the flood water depth. Stage damage curves for buildingslocated in the Red River Valley were developed in 1983 by ECOS Engineering ServicesLtd. The damages indicated by the developed curves represent average values for allgeneral types of residential buildings (i.e., bungalow, two-story, etc.) located in this area.The curves relate the flooded depth of a building to damage incurred as a percent of itstotal worth (i.e., structure and contents). However, the flood depth used to develop thecurves includes both flooding to the basement level of the structure, if one existed, andthe depth of water above the ground surface.As the prepared flood water depth imagesonly contain information on the level of water above the ground surface, modification tothe ECOS stage-damage curves is necessary. The ECOS curves are modified in such amanner that the resulting stage-damage curve related above ground flood water depth to

percent damage of the building (see Figure 9).

Figure 9 Modified Stage Damage Curve


14/20

38

Using the modified stage-damage curve, an image representing damage to floodedbuildings in the study region was produced for each alternative. The estimated value for

the residential, municipal, and industrial building classes used in this study was $50,000,$100, 000, and $200,000, respectively.Criteria 3 - Benefit from Flooding Upstream Areas. The final criterion used in theevaluation of the alternatives is a measure of the benefit from flooding the upstreamcommunities. In the case study region, upstream communities, such as St. Adolp he, oftenexperience increased flooding due to the floodway operation aimed at reducing damagesto the City of Winnipeg. Thus, from an economic standpoint it is suggested that there is abenefit associated with flooding the upstream areas. The more water that is stored furtheraway from Winnipeg, by flooding the upstream areas, the greater the benefit, or reductionin downstream damages.

The magnitude of this benefit is a function of the volume of water stored upstream,

and the distance of the stored water from the City of Winnipeg. The amount of waterstored upstream resulting from the implementation of each alternative is shown in theflood water depth criteria image. Each raster cell of this image contains a value, which

corresponds to the water depth for that particular geographic location. Thus, the volumeof water in each location is known. The distance of each raster cell from the City ofWinnipeg can be determined using GIS commands. The magnitude of the benefitassociated with flooding upstream areas is calculated by multiplying the flood waterdepth in each raster cell with its proportional distance from the City of Winnipeg. In other

words, given two cells flooded to an equal elevation, the one closer to the city wouldproduce a lower benefit than one located further away. An image identifying the benefit

of flooding different locations in the study region is produced for each alternative.

4.3. Evaluation of Flood Control Alternatives The four proposed flood protection alternatives are evaluated on the basis of the threecriteria discussed above. Both, the CP and the SCP techniques are used to evaluate thealternatives. The CP technique is used to identify the best flood protection alternative forthe region as a whole. Using the SCP technique the best alternative is determined for eachlocation in the St. Adolphe region. The latter approach allows consideration of localimpacts produced by flooding. By identifying the best alternative for each geographiclocation, potential sources of conflict between upstream and downstream communities

arising from the implementation of different alternatives are made apparent.Weights indicating the relative preferences of decision makers towards the criteria

and the importance of their maximal deviation from the ideal solution are necessary inputfor both CP and SCP techniques. The importance of the deviation of solution from theideal value is reflected by the value ofp in Equation (1). In this study, a single value ofp

= 2 (a straight line, shortest distance metric) is used following the recommendations fromthe literature (Simonovic 1989). The decision makers' preferences are represented by wi

in Equation (1). In this case study three different sets of weights are selected ( Table 1) toaddress the potential different preferences of the various interest groups.


15/20

39

Table 1 Decision Makers' PreferencesCriteria Decision Makers' Preferences (wi)

Weight Set

#1

Weight Set

#2

Weight Set

#31 0.25 0.20 0.30

2 0.50 0.50 0.503 0.25 0.30 0.20

In all three sets of weights, the highest priority is given to the criteria measuringdamage to submerged structures. Usually in multi-criteria analyses, one option indicatingequal importance of all criteria is considered. However, due to the importance of thebuilding damage criteria, an option with equal weights is not included in this study.

With regards to the two remaining criteria, in the first set of weights they are

assigned an equal level of importance. The other two sets of weights attempted to capturethe differences in interests of the upstream (set #3) and downstream communities (set

#2).

4.4. Compromise Programming Analysis

The CP technique is first implemented to identify the most acceptable alternative for thewhole region. As CP does not account for spatial variation of the criteria values, thevalues contained within the criteria images had to be converted into a format, whichcould be used with this technique. A single number representing the impacts produced byeach flood protection alternative is calculated for each of the three criteria. The floodwater depth and flooding benefit are averaged across the region, while the damage to allclasses of buildings in the region is totaled. The results are shown in Table 2.

Table 2 Spatially Invariable Criteria ValuesAlternative Criteria Values

Flood WaterDepth (m)

BuildingDamage ($)

FloodingBenefit

(m4)

1 0.96 18 630 000 30.83

2 0.91 19 644 500 29.06

3 1.01 19 632 000 32.51

4 0.91 7 765 000 29.52

The final results of the evaluation using CP and input from Tables 1 and 2 are shown

in Table 3. Alternative four is determined to be the most appropriate flood protectionstrategy for the St. Adolphe region for all different weight combinations.

Table 3 Results of the Compromise Programming Analysis Alternative Weight Set #1 Weight Set #2 Weight Set #3

Lj Rank Lj Rank Lj Rank

1 0.5296 2 0.5103 2 0.5523 2

2 0.5482 3 0.5319 3 0.5676 33 0.5583 4 0.5377 4 0.5824 4

4 0.2991 1 0.2678 1 0.3336 1

4.5. Spatial Compromise Programming Analysis


16/20

40

SPA is capable of addressing the spatial variation in criteria values. Using the criteriaimages and the weights from Table 1, each of the four potential flood protectionalternatives is evaluated with the SCP technique. The first evaluation step involves the

development of a distance metric image for each alternative. The resulting imagescontain a distance metric value in each raster cell that corresponds to the relative impactproduced by each alternative. The best alternative for each location is identified bycomparing the distance metric values corresponding to the four potential alternatives. Animage identifying the most acceptable alternat ive for each location in the region isproduced for each set of decision-maker preferences (Figures 10, 11, and 12).

The difference in the images in Figures 10, 11 , and 12, indicates the significanteffect of the decision-makers' preferences on the outcome of the evaluation. A number ofgeneral observations regarding the effectiveness of the potential flood protectionalternatives for various locations in the region of interest can be made. In each of thethree sets of the decision-makers' preferences, alternative one generally proves to be the

most acceptable for building locations outside of the town of St. Adolphe. Sincealternative four provides a complete protection of St. Adolphe, it is the most acceptableflood protection strategy for locations within the town. Alternative three is generally

ineffective as a mitigation strategy. Many locations in the study region, in and outside ofthe town of St. Adolphe, consist predominantly of uninhabited areas or farmland. Themost appropriate protection alternative for these areas changes frequently with thedecision-makers' preferences. For weight set #1 the predominant choice is alternative 2(Figure 10).

Figure 10 Best Alternative Image for Weight Set #1

The second set of weights represents the interests of the downstream region. Theevaluation of the potential flood protection strategies would favor alternatives that store alarger volume of water upstream of the Red River Floodway. The effect of this set ofdecision-makers' preferences is shown in Figure 11. Alternatives one and four areselected as best for locations in which alternative two was previously selected as the most

appropriate using the first set of weights. This is logical because alternatives one and fourcorrespond to a slightly greater overall depth of flood waters in the St. Adolphe region.


17/20

41

Figure 11Best Alternative Image for Weight Set #2

The final set of weights used in the evaluation of the potential flood protection

alternatives places a greater emphasis on minimizing the flood water depth, in contrast tothe benefits associated with flooding the region of interest. This set of weights representsthe decision-makers' preferences in protecting upstream communities. In this case thealternatives selected as the most appropriate for the study region are those that minimizethe overall upstream volume, or depth, of flood water. For almost all locations within thetown of St. Adolphe, as shown in Figure 12, alternative four is selected as the mostappropriate. This is expected since the ring dyke used in this alternative is constructed toeliminate flooding in the community. For uninhabited areas outside St. Adolphe, becausealternative two offers the lowest overall flood water depth, it is predominantly selected asthe most appropriate.

Figure 12 Best Alternative Image for Weight Set #3

5. ConclusionsWater resources analyses require use of spatially distributed information. GIStechnologies are an effective tool for storing, processing, managing, and analyzing spatialinformation. Two practical applications of a GIS in the field of water resources areillustrated in this paper: (a) the use of a GIS for floodplain analysis; and (b) the use of aGIS in water resources multi-criteria decision-making.

The main contribution of the work presented in this paper is the introduction of anoriginal MCDM technique named Spatial Compromise Programming, developed byembedding the conventional Compromise Programming technique within a GISframework.


18/20

42

Both CP and SCP are used to evaluate the potential flood protection alternatives fora portion of the Red River Valley, Manitoba, Canada. The use of conventional CP resultsin alternative four being selected as the most appropriate for all sets of decision-maker

preferences. However, the SCP technique shows that this strategy may not necessarily bethe best for all locations in the study region. By maintaining the spatial variability of thecriteria values, localized impacts associated with each alternative are taken inconsideration with the application of the SCP technique. The technique is used todetermine the best flood protection for each distinct location in the St. Adolphe region. Itis shown that alternative four, selected as the best by CP, is not necessarily the bestalternative for all areas in the region. It is also demonstrated that the choice of the bestalternative for many locations is very sensitive to the decision-makers' preferences.

Local impacts produced by different alternatives are addressed through the use ofthe SCP technique. This is accomplished by maintaining the spatial variability of thecriteria values in the evaluation of the alternatives. Application of the SCP technique

provides decision-makers with additional information important in water resourcesdecision making. We hope that this will lead to better and more efficient decision makingin the field of water resources.

ReferencesBanai, R. (1993) Fuzziness in Geographical Information Systems: contributions from theanalytic hierarchy process, International Journal of Geographical Information Systems,7, 315-329.

Bose, D. and Bose, B. (1995) Evaluation of Alternatives for a Water Project Using aMultiobjective Decision Matrix, Water International, 20, 169-175.

Bumsted, J. M. (1993) The Manitoba Flood of 1950 - An Illustrated History. Canada:

Watson and Dwyer Publishers.Carver, S.J. (1991) Integrating multi-criteria evaluation with geographical information

systems,International Journal of Geographical Information Systems, 5, 321-339.Duckstein, L. and Opricovic, S. (1980) Multi-objective optimization in river basin

development, Water Resources Research, 16, 14-20.Eastman, J.R. (1992) IDRISI Geographic Information System, version 4.0. ClarkUniversity: Graduate School of Geography.Eastman, J.R. (1995)IDRISI Geographic Information System, version 1.0 for Windows.Clark University: Graduate School of Geography.

ECOS Engineering Services Ltd. (1983) Development of depth-damage curves forresidential and farm structures in southern Manitoba - Report to Environment Canada.

Regina: Inland Water Directorate.Fedra, K. (1997) Spatial Decision Support in Resources Management and EnvironmentalApplications, Proceedings of the Eleventh Annual Symposium on GeographicInformation Systems held in Vancouver, British Columbia, Canada, 302-305.Frst, J., Girstmair, G., and Nachtnebel, H.P. (1993) Application of GIS in DecisionSupport Systems for Groundwater Management. In " HydroGIS93: Application ofGeographic Information Systems in Hydrology and Water Resources " edited by K. Kovarand H.P.Nachtnebel, IAHS Publ. no. 211, pp. 13-21.


19/20


20/20

44

Wolfe, D.S. (1997) Integrated Resources Management Using Spatial Allocation: A CaseStudy, Proceedings of the Eleventh Annual Symposium on Geographic InformationSystems held in Vancouver, British Columbia, Canada, 424-427.

Zeleny, M. (1973). Compromise Programming-Multiple Criteria Decision Making,Columbia: University of South Carolina Press.

JGIDA vol.1, no.1

JGIDA Home

a new approach to multi criteria decision-making

Documents