Journal of Geographic Information and Decision Analysis, vol.1, no.1, pp. 25-43.

A New Approach to Multi-criteria Decision Making in Water Resources

Robert J. Tkach
Department of Civil and Geological Engineering and Natural Resources Institute, The University of Manitoba, Winnipeg, MB R3T 2N2, Canada
rob@fids.ce.umanitoba.ca
http://www.ce.umanitoba.ca/~rob/
 

Slobodan P. Simonovic
Department of Civil and Geological Engineering and Natural Resources Institute, The University of Manitoba, Winnipeg, MB R3T 2N2, Canada
simon@ce.umanitoba.ca
http://www.ce.umanitoba.ca/~simon/



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

Contents


1. Introduction
Selecting the best strategy from a number of potential alternatives in water resources planning 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 decision making (MCDM) techniques. They can be used to facilitate the decision-making process by 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 the past (Simonovic 1989; Shafike et al. 1992; and Greshan et al. 1982).
        The evaluation and ranking of alternatives by MCDM techniques is based on criteria values associated with each of the alternatives, and the objectives and preferences of the various decision makers. The criteria used in the evaluation of water resources alternatives, which may be quantitative and/or qualitative, often exhibit spatial variability. For example, implementation of a particular alternative could produce favorable impacts at one location while resulting in negative consequences at another. Conventional MCDM techniques are not able to address uneven spatial distribution of the criteria values in the evaluation and ranking of alternatives.
        The main objective of the research described in this paper is to develop a MCDM technique capable of capturing the spatial distribution of the criteria values associated with the various alternatives. The new MCDM technique developed in this research, named Spatial Compromise Programming (SCP) combines the Compromise Programming (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 main objective of the case study is to generate, evaluate, and rank a set of potential flood protection 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 the region is determined using SCP. Comparison of the results produced through the application 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, and evaluation of the Spatial Compromise Programming technique. The next section begins with an overview of the use of GIS in decision making. A brief description of the Compromise Programming technique follows. With the help of a very simple example, the shortcomings of this technique for spatial decision making are identified. The following section of the paper describes the Spatial Compromise Programming technique. Using the same simple example, the mechanics of SCP are illustrated. The final section of this paper describes the case study. The paper concludes with a discussion and comparison of the evaluation of the flood control alternatives using Compromise Programming and Spatial Compromise Programming.

2. GIS and decision-making

2.1. Introduction

Geographic Information Systems are a rapidly evolving technology that can be used for the efficient storage, analysis, and management of spatial information. Environmental or natural resources management decisions almost always require the analysis of spatial information. GIS technologies have been used to facilitate decision making in the field of water resources and many other fields of study. Carver (1991) presents an example application of the integration of multi-criteria evaluation techniques with GIS in searching 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 the decision-making process in water resources management. Given existing and projected water supplies and demands combination of the two technologies determines potential water deficits and surpluses. Pereira and Duckstein (1993) apply the Compromise Programming technique within a GIS in order to evaluate potential habitats for the endangered 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 analytical capabilities with spatial information. In addition to this, many of them are equipped with a graphical user interface, which increases the decision-maker's comprehension of the spatial information that is involved in the problem being addressed. Based on these two potential additions to the decision making process, a GIS is often included as a major component in the development of Decision Support Systems (DSS). Because of the spatial component that a GIS adds to conventional DSS, this combination of technologies has been referred to as Spatial Decision Support Systems (SDSS). Recent papers by Walsh (1993), Fürst et al. (1993), Simonovic (1993), Leipnik et 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 where the number of alternatives is large. Multi-attribute utility techniques rely on linear additive 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 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 solutions that 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 and constitute the compromise set. The ideal solution is one which provides the extreme value for each of the criteria considered in the analysis. The distance from the ideal solution for each 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 values themselves, the relative importance of the various criteria to the decision makers, and the importance of the maximal deviation from the ideal solution (Simonovic 1989). Shown in Equation (1) is the operational expression used to compute the family of distance metrics (Lj) for a set of n criteria and m alternatives.

                                            (1)

where:
Lj is the distance metric;
f*i is the optimal value of the ith criteria;
fi,w is the worst value of the ith criteria;
fi,j is the value of the ith criteria for alternative j;
wi are weights indicating decision maker preferences;
p is a parameter (1£ p £ ¥);
i is indicates the number of criteria i = 1,,n; and
j is indicates the number of alternatives j = 1,,m.

        Introduction of wi allows the expression of the decision makers' preferences concerning the relative importance of various criteria. The parameter p reflects the importance of the maximal deviation from the ideal point. Thus a double-weighting scheme exists: for p = 1 all deviations are weighted equally; for p = 2 each deviation is weighted in proportion to its magnitude. The larger the deviation the larger the weight. For the value of p = ¥, the min-max criterion is achieved (Simonovic 1989).
        In using CP and many other MCDM techniques to evaluate a set of potential alternatives 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 still within 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 CP technique by solving Equation (1) for different values of the weight p. As the range of the weight 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 of p = 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 in identifying the best compromise solutions using CP, only the region as a whole is considered, and local impacts associated with different alternatives are ignored.

2.3. Importance of Spatial Variation in Criteria Values

The 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 locations within the floodplain. The distribution of the flood impacts is a function of the implemented flood protection measures. Implementation of a particular measure may reduce 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 MCDM techniques typically use average or total impacts incurred across the entire region being considered. The following is a very simple example that demonstrates the existence of spatial 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, this example 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 spatial variability in the criteria values. To alleviate the flood damage in this region, three potential mitigation alternatives (dyking strategies) are proposed. In each alternative, one of 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 velocity for each alternative and land use type are shown in Figures 2 and 3, respectively.


Figure 2  Flood Water Depth


Figure 3: Flood Water Velocity

        Selection of the best alternative for this example is based on minimizing the flood water depth and velocity. Using one of the MCDM techniques, (not necessary due to the problem's simplicity) such as the CP technique, the criteria values for each alternative would first be averaged across the region of interest. The average flood water depth for alternatives 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 units respectively. Without any additional computations it is obvious that alternative three, having the least average flood water depth and velocity, would be considered the best flood 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 the flood water impacts, resulting from implementation of each of the three alternatives, are not evenly distributed across the region of interest. Thus, the selection of alternative three does not necessarily provide all areas in the region with the same level of protection. In fact, implementation of this alternative, as shown by the criteria values, provides only appropriate protection to the farmland.

2.4. Spatial Compromise Programming

        Geographic information system technologies can be used to include spatial considerations in MCDM. Past applications of GIS in MCDM have predominantly involved the determination of the best spatial location for an alternative according to a predetermined set of criteria (Carver 1991; Pereira and Duckstein 1993). The research presented here expands the previous idea to one of determining the best alternative for each 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 by embedding the Compromise Programming technique within a GIS framework. All aspects 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 required calculations (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 the application of CP, the family of distance metrics is the basis on which the alternatives are evaluated. However, with the SCP technique, rather than determining a single value per alternative, a distance metric is calculated for each location (represented by an individual raster cell) in the region of interest for each alternative. The region of interest encompasses all geographic locations that are impacted by the combined group of alternatives and is represented by a raster feature image of the study area.
        Criteria values associated with each of the alternatives are contained within sets of criteria images, which are geo-referenced with the feature image. Alternatives have their own 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 a criteria image contains the criteria value associated with a particular alternative. If the criteria value is spatially variable then each affected cell, or location, within the image contains a different value.
        Using the criteria images, and the decision-maker's preferences, a distance metric image is produced for each alternative. Contained in the distance metric images are distance metric values for each raster cell calculated using Equation (1). The algorithmic procedure for producing a distance metric image is shown in Figure 4. All computations are performed using GIS commands.

Figure 4: Calculation of Distance Metric Values in GIS Framework
Figure 4  Calculation of Distance Metric Values in GIS Framework

       Using the values stored in the distance metric images, the best alternative is determined 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 a number corresponding to the best alternative.
        Research similar to that presented in this paper can be found in Pereira and Duckstein (1993). In the work done by Pereira and Duckstein the CP technique was applied 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 the region 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 distance metric image was produced for the region, for each tested value of the parameter p in Equation (1). Each distance metric image was then discretized into ten habitat quality classes at ordinal levels by comparing the distance metric values in each cell across each individual image.
        The research presented in this paper is an extension of the work by Pereira and Duckstein (1993). The two main contributions of our work are: (a) replacement of a single distance metric image for the whole region with a distance metric image for each potential flood protection alternative; and (b) comparison of distance metric values for each 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 potential alternatives. Required as input for this technique are raster images describing the topography of the case study area, as well as the extent of the potential impacts of each alternative. Figure 1, which shows the land use types in a grid like fashion, represents the raster feature image describing the region of interest. The three sets of flood water depth and velocity values shown in Figures 2 and 3, represent the criteria images for each of the alternatives. Figure 5 is the final best alternative image generated by evaluating the three flood protection measures using the SCP technique.


Figure 5  Best Alternative Image

        The numbers corresponding to the best alternative are contained in each cell of the image. Thus, the implementation of SCP shows that alternative three, determined to be the best alternative by Compromise Programming, is not the best solution for each location in the region of interest.
        Using GIS technology the spatial variability of the criteria values is taken into consideration. The best alternative for each location in the region of interest is determined by the application of the SCP technique. The complex decision making process in the field of water resources can benefit from the additional information provided by this new technique.

3. Floodplain analysis of the Read River Valley

3.1. Background

A 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-central portion of the province of Manitoba, Canada. It consists of low-lying flat prairies predominantly used for agricultural purposes. The valley is very prone to flooding and has historically (in 1826, 1950, 1979, and 1996) incurred extensive damages to both urban and agricultural areas from floods. The major floods are typically seasonal in nature, and are the result of combined spring snowmelt and rainfall runoff along both the Red and Assiniboine Rivers (Krenz and Leitch 1993). The 1950 flooding event in Winnipeg 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 Geological Survey 1952). However, the true cost of the flood may have exceeded 100 million dollars. During this flood communities located upstream of the City of Winnipeg were completely submerged and significant portions of the City of Winnipeg were extensively flooded. 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
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 of structural and non-structural flood mitigation measures have been implemented over time (Figure 7). These include: (a) a dyking system along both the Red and Assiniboine Rivers; (b) flood pumping stations within the City of Winnipeg; (c) Shellmouth Reservoir; (d) the Portage Diversion; and (e) the Red River Floodway.

Figure 7: Flood Protection System for the City of Winnipeg and Surrounding Area
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 event corresponds to a predicted return period of approximately 165 years (Rannie 1980). Though this level of flood protection is quite high, the overall flood mitigation strategy for this area requires improvement. Because the protection measures have been developed separately over time, at present they are operated somewhat independently. The level of coordination that does exist requires updating. The optimal efficiency of the existing 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. 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 the closest community upstream from the Red River Floodway inlet and gate structure.
        The Red River Floodway, Manitoba's largest flood protection project, was completed in 1968. The floodway is a 30 mile long channel, with a flow capacity of 60 000 cfs, which diverts floodwaters around the east side of the City of Winnipeg and then reconnects with the Red River near the town of Lockport. The entrance to the floodway is on the south side of the City, near the community of St. Adolphe. The flow of water within the Red River is unaffected by the floodway until the discharge reaches 30,000 cfs. At this flow the water surface reaches sufficient elevation to permit flow into the floodway. The flow of water into the floodway channel is controlled by a gate structure located downstream of the floodway entrance. The gates, which are normally flush with the bottom of the river, can be raised to produce a backwater effect that forces water into the 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 state of emergency, in order to save the downstream City of Winnipeg, flooding of the upstream communities is required (Manitoba Department of Natural Resources 1984). This decision is typically based on the economic value of potential flood damage and is a source 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 for Winnipeg 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 best flood 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 a set of potential flood protection alternatives for the St. Adolphe region, (b) estimate the flood impact, and (c) evaluate and rank the potential alternatives. Potential protection alternatives are ranked on the basis of minimizing flood impacts in the St. Adolphe region. Both, the SCP and the CP techniques are applied in the evaluation process.

3.4. Floodplain Analysis Model

The floodplain analysis model is used to simulate floods for the purpose of generating flood protection alternatives, as well as to evaluate and rank the potential alternatives. The floodplain analysis model is comprised of a GIS and a conventional mathematical model.
        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 a raster-based GIS software which delivers a strong analytical functionality at an affordable cost (Meyer et al. 1993).
        The HEC-2 (United States Army Corps of Engineers 1982) package is selected to perform the necessary hydraulic modeling of the floodplain analysis. This model can be used 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 and weirs are accounted for in the estimation of the water surface elevation using HEC-2.
        The floodplain analysis model requires a description of the characteristics of the Red River Valley. The GIS and HEC-2 databases are used to store all the necessary input information.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 by converting and interpolating data collected by (a) processing three-dimensional aerial photographs (1:20,000 scale), (b) conventional land surveying, and (c) digitizing topographic maps. The feature images identify the two-dimensional locations of both natural and man-made features in the Red River Valley with respect to the UTM-14N coordinate system. Each raster cell in the feature images contains a numerical identifier corresponding to the specific feature located in the coordinate boundaries of that cell. Fourteen different classes of features are distinguished in the feature images. An example feature image for the St. Adolphe region is shown in Figure 8.

Figure 8: An Example Feature Image of St. Adolphe Region
Figure 8  An Example Feature Image of St. Adolphe Region

        DEMs are raster images describing the elevation of the ground surface corresponding to the same locations and reference system as the feature images. Thus, for every feature image in the data set there is a corresponding DEM. Each raster cell in the DEMs contains a number equal to the ground surface elevation corresponding to the location of that cell.
        The HEC-2 model database is comprised of a specially formatted input file. This file contains a description of the hydraulic characteristics of the case study area. A previously prepared 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 ground surface elevations describing each cross-section within the HEC-2 input file are a subset of 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 protection alternatives for the case study area. Using the HEC-2 model the Red River water surface elevation is estimated. Using GIS commands and external programs, the water surface elevation is transformed into a raster image identifying the maximum water surface elevation for each location in the region. The GIS component of the floodplain analysis model 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. Adolphe region.

4.1. Flood Protection Alternatives

The original GIS and HEC-2 databases contain a description of the existing topographic features and flood protection measures of the Red River Valley. Thus simulating a given flood 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 flood protection alternatives for St. Adolphe, the region's characteristics within the floodplain analysis model databases need to be modified. These changes should reflect the potential implementation of new structural or non-structural flood mitigation measures, or the alteration of existing ones.
        A wide variety of flood protection alternatives could be generated with the floodplain analysis model. Four flood protection alternatives are generated for the town of St. Adolphe and surrounding area by combining the following flood protection measures: (a) construction of small ring dykes around specific areas; (b) alteration of operation policy for the Red River Floodway; (c) flood proofing of features having high risk of flood damage; and (d) flood warning for the community of St. Adolphe and surrounding areas. A description of the different combinations of previously introduced measures 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 flood protection for the town of St. Adolphe and surrounding area. As this community experiences flooding frequently, knowledge of an impending flood can be used to significantly reduce the damage produced by flood waters. For this base alternative, flood warning is provided to the community and surrounding areas. In order to protect the City of Winnipeg, the Red River Floodway operates under the existing operating rule.

Alternative 2 - Protection of Upstream Communities. For better protection of the upstream communities the second alternative includes the lowering of the floodway gates. This results in a water surface elevation decrease of 0.3 m at the floodway entrance. Also, in this alternative all buildings in the study region are flood-proofed to a height of 1 m above the natural ground elevation. Finally, no flood warning is provided to the upstream communities.

Alternative 3 - Protection of the City of Winnipeg. In this alternative the floodway operation is altered to provide better protection for the City of Winnipeg. The height of the floodway gates is changed to increase the water surface elevation at the floodway entrance by 0.3 m. In providing a better level of protection for the city this alternative results 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 further reduce the impacts caused by flood water, the communities are provided with flood warning.

Alternative 4 - Protection of St. Adolphe. For this alternative the entire town is surrounded 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 study region are provided with flood warning.

4.2. Evaluation Criteria

The floodplain analysis model is used to simulate the effects of the four proposed protection 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 flooded feature images, which identify the locations and features, which are affected by the flood, given implementation of each alternative. The flooded feature images were used to determine the flood water impacts that are incurred by the region given hypothetical implementation of each new flood protection alternative. These flood water impacts are used as a basis to evaluate and rank the potential alternatives.
        Three different types of flood water impacts were used as criteria to evaluate the proposed 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 with each cell containing the magnitude of the impact.
Criteria 1 - Flood Water Depth. The flood water depth image is prepared using a combination of the flooded feature image, the water surface elevation as contained in the reach 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 image containing 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 the alternatives is the dollar value of damage to flooded structures within the region of interest. Three different classes of buildings (industrial, municipal, and residential) are identified in the feature image for each region. Damage to each of the buildings is calculated 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 buildings located in the Red River Valley were developed in 1983 by ECOS Engineering Services Ltd. The damages indicated by the developed curves represent average values for all general 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 its total worth (i.e., structure and contents). However, the flood depth used to develop the curves includes both flooding to the basement level of the structure, if one existed, and the depth of water above the ground surface.As the prepared flood water depth images only contain information on the level of water above the ground surface, modification to the ECOS stage-damage curves is necessary. The ECOS curves are modified in such a manner 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
Figure 9  Modified Stage Damage Curve

Using the modified stage-damage curve, an image representing damage to flooded buildings 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 the evaluation of the alternatives is a measure of the benefit from flooding the upstream communities. In the case study region, upstream communities, such as St. Adolphe, often experience increased flooding due to the floodway operation aimed at reducing damages to the City of Winnipeg. Thus, from an economic standpoint it is suggested that there is a benefit associated with flooding the upstream areas. The more water that is stored further away from Winnipeg, by flooding the upstream areas, the greater the benefit, or reduction in 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 water stored upstream resulting from the implementation of each alternative is shown in the flood 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 volume of water in each location is known. The distance of each raster cell from the City of Winnipeg can be determined using GIS commands. The magnitude of the benefit associated with flooding upstream areas is calculated by multiplying the flood water depth 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 would produce 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 three criteria discussed above. Both, the CP and the SCP techniques are used to evaluate the alternatives. The CP technique is used to identify the best flood protection alternative for the region as a whole. Using the SCP technique the best alternative is determined for each location in the St. Adolphe region. The latter approach allows consideration of local impacts produced by flooding. By identifying the best alternative for each geographic location, 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 input for both CP and SCP techniques. The importance of the deviation of solution from the ideal value is reflected by the value of p in Equation (1). In this study, a single value of p = 2 (a straight line, shortest distance metric) is used following the recommendations from the 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) to address the potential different preferences of the various interest groups.

Table 1  Decision Makers' Preferences
Criteria
Decision Makers' Preferences (wi)
Weight Set #1
Weight Set #2
Weight Set #3
1
0.25
0.20
0.30
2
0.50
0.50
0.50
3
0.25
0.30
0.20

        In all three sets of weights, the highest priority is given to the criteria measuring damage to submerged structures. Usually in multi-criteria analyses, one option indicating equal importance of all criteria is considered. However, due to the importance of the building 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 capture the 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 the whole region. As CP does not account for spatial variation of the criteria values, the values contained within the criteria images had to be converted into a format, which could be used with this technique. A single number representing the impacts produced by each flood protection alternative is calculated for each of the three criteria. The flood water depth and flooding benefit are averaged across the region, while the damage to all classes of buildings in the region is totaled. The results are shown in Table 2.

Table 2  Spatially Invariable Criteria Values
Alternative
Criteria Values
Flood Water Depth (m)
Building Damage ($)
Flooding Benefit 
(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 protection strategy 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
3
3
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

SPA is capable of addressing the spatial variation in criteria values. Using the criteria images and the weights from Table 1, each of the four potential flood protection alternatives is evaluated with the SCP technique. The first evaluation step involves the development of a distance metric image for each alternative. The resulting images contain a distance metric value in each raster cell that corresponds to the relative impact produced by each alternative. The best alternative for each location is identified by comparing the distance metric values corresponding to the four potential alternatives. An image identifying the most acceptable alternative for each location in the region is produced 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 significant effect of the decision-makers' preferences on the outcome of the evaluation. A number of general observations regarding the effectiveness of the potential flood protection alternatives for various locations in the region of interest can be made. In each of the three 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. Since alternative four provides a complete protection of St. Adolphe, it is the most acceptable flood 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 of the town of St. Adolphe, consist predominantly of uninhabited areas or farmland. The most appropriate protection alternative for these areas changes frequently with the decision-makers' preferences. For weight set #1 the predominant choice is alternative 2 (Figure 10).

Figure 10: Best Alternative Image for Weight Set #1
Figure 10  Best Alternative Image for Weight Set #1

        The second set of weights represents the interests of the downstream region. The evaluation of the potential flood protection strategies would favor alternatives that store a larger volume of water upstream of the Red River Floodway. The effect of this set of decision-makers' preferences is shown in Figure 11. Alternatives one and four are selected 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 four correspond to a slightly greater overall depth of flood waters in the St. Adolphe region.
 

Figure 11: Best Alternative Image for Weight Set #2
Figure 11 Best 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 to the benefits associated with flooding the region of interest. This set of weights represents the decision-makers' preferences in protecting upstream communities. In this case the alternatives selected as the most appropriate for the study region are those that minimize the overall upstream volume, or depth, of flood water. For almost all locations within the town of St. Adolphe, as shown in Figure 12, alternative four is selected as the most appropriate. This is expected since the ring dyke used in this alternative is constructed to eliminate flooding in the community. For uninhabited areas outside St. Adolphe, because alternative two offers the lowest overall flood water depth, it is predominantly selected as the most appropriate.

Figure 12: Best Alternative Image for Weight Set #3
Figure 12  Best Alternative Image for Weight Set #3

5. Conclusions

Water resources analyses require use of spatially distributed information. GIS technologies are an effective tool for storing, processing, managing, and analyzing spatial information. Two practical applications of a GIS in the field of water resources are illustrated in this paper: (a) the use of a GIS for floodplain analysis; and (b) the use of a GIS in water resources multi-criteria decision-making.
        The main contribution of the work presented in this paper is the introduction of an original MCDM technique named Spatial Compromise Programming, developed by embedding the conventional Compromise Programming technique within a GIS framework.
        Both CP and SCP are used to evaluate the potential flood protection alternatives for a portion of the Red River Valley, Manitoba, Canada. The use of conventional CP results in 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 be the best for all locations in the study region. By maintaining the spatial variability of the criteria values, localized impacts associated with each alternative are taken in consideration with the application of the SCP technique. The technique is used to determine the best flood protection for each distinct location in the St. Adolphe region. It is shown that alternative four, selected as the best by CP, is not necessarily the best alternative for all areas in the region. It is also demonstrated that the choice of the best alternative for many locations is very sensitive to the decision-makers' preferences.
        Local impacts produced by different alternatives are addressed through the use of the SCP technique. This is accomplished by maintaining the spatial variability of the criteria values in the evaluation of the alternatives. Application of the SCP technique provides decision-makers with additional information important in water resources decision making. We hope that this will lead to better and more efficient decision making in the field of water resources.

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