the Slave Geological Province (SGP) is the richest and most promising mining region

Applied Geography 25 (2005) 287307

www.elsevier.com/locate/apgeogE-mail address: pjdeadma@fes.uwaterloo.ca (P. Deadman).Multi-criteria evaluation and least cost path

analysis for an arctic all-weather road

David M. Atkinsona, Peter Deadmanb,*, Douglas Dudychab,Stephen Traynorc

aDepartment of Geography, Queens University, Kingston, Ont., Canada K7L 3N6bDepartment of Geography, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

cDepartment of Indian Affairs and Northern Development, Nunavut Regional Office, P.O. Box 2200, Iqaluit,

Nunavut, Canada X0A 0H0

Abstract

Increasing interest in the development of the base metal, gold, and diamond resources in the Slave

Geological Province in Nunavut has led to the proposal that a deep-water port be constructed in

Bathurst Inlet and connected to these mining regions by an all-weather road. In response to previous

concerns regarding the subjectivity of existing techniques for route determination, this paper outlines

a methodology for determining a least-cost-path for the route of an all-weather road that incorporates

multi-criteria analysis. This methodology allows for the objective comparison of alternate scenarios

for weighting the factors that determine the location of a roads route. The methodology is applied,

using three alternate scenarios for road construction that are compared so as to determine the

effectiveness and sensitivity of this approach. The strengths and limitations of this methodology are

discussed.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Multi-criteria evaluation (MCE); Pair-wise comparison; Least Cost Path; Artic; Route determination;

GIS

Introduction

Covering approximately 190,000 km2 within Nunavut and the Northwest Territories,0143-6228/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.apgeog.2005.08.001

* Corresponding author.

within Canadas north (Reynolds, 1996). Diamonds, gold, and various base metals

comprise the majority of mineral resources in the SGP. The region currently contains two

operating mines, while over 25 diamond, gold, or base metal mining projects are in various

stages of exploration or development (GNWT, 1999).

Winter roads have been used for decades throughout Northern Canada as

supply routes for temporary access to natural resources (Hayley & Valeriote, 1994).

The seasonal, weather-dependant nature of ice roads can limit the economic viability

of northern projects, especially base metal mining operations. Furthermore,

climate change scenarios indicate that the arctic will experience significant warming

(Serreze et al., 2000) this may reduce the length of the ice road season, placing

further economic pressures on mining operations in the region. In response to this

problem, proposals have been developed for the construction of a deep-water port in

Bathurst Inlet, Nunavut and an all-weather road into the mining region around

Contwoyto Lake, Nunavut (Fig. 1). An all-weather road would solve the problems

associated with the existing ice road and increase the economic feasibility of many

mining operations.

While the construction of an all-weather road through this region of the arctic could aid

in the economic development of the region, and the Canadian arctic more broadly, it also

raises a number of concerns regarding the impacts on the fragile environment of the

region. Clearly, the ability to understand and incorporate many complex factors into the

design of a route for such a road is important. Any tool capable of incorporating multiple

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307288factors into the design, selection, and evaluation of alternate routes would be useful inFig. 1. Study site.

support of the decision making process. This paper presents a geographic information

system (GIS) based methodology that combines least cost path (LCP) analysis on

a continuous surface and multi-criteria analysis (MCA) to facilitate route generation based

on multiple environmental and economic criteria. Weights for the route criteria are

generated though a pair-wise comparison of criteria based on three decision-making

scenarios (Fig. 2).

The methodology presented allows the exploration of a variety of scenarios in an

effort to strike a balance between development and the protection of the environment.

The ability to model the routing of such a road could not only reduce the costs of

construction and maintenance but also allow for sensitive environmental areas to be

avoided and protected.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 289Fig. 2. Flow diagram of the least cost path algorithm.

The study of the least-cost path problem predates the development of modern GIS.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307290Some of the earliest work came from Warntz (1957) who considered where a good must be

transported over two broad regions, each with a different cost of transportation.

There are a number of basic steps in finding a minimum cost path over a surface

partitioned into regions of different resistances to movement (Collischonn & Pilar, 2000;

Douglas, 1994) (Fig. 2):

A friction surface is created for each evaluation criterion, where each cell in the grid isassigned a value based on the relative cost of traversing that cell.

Multiple friction surfaces are weighted and combined to create a cost-of-passagesurface, representing the total cost associated with traversing each cell.

A spreading function combines two separate grids representing source points anddestination points are combined with the cost-of-passage grid to calculate an

accumulated cost surface.

The lowest cost line is traced down the accumulated-cost-surface from a departurepoint to a destination.

The resulting path is considered optimal for all criteria considered (Lee & Stucky,

1998).

The use of least-cost path analysis for real world problems has become possible with

the development with todays fast and powerful computers (Lee & Stucky, 1998). ThereCold region road construction

Many of the factors influencing the routing of an all-weather haul road in the arctic are

determined by cold region design and construction standards and techniques. Factors that

influence the performance of an arctic all-weather road include; climate, hydrology,

topography, geology, vegetation, material availability and suitability, and the soils

thermal state (Schraeder, Riddle, & Slater, 1996). The continuous permafrost is a

controlling design parameter when working in this region. The permafrost must either be

preserved (prevented from thawing) or completely removed (McFadden & Bennett, 1991).

Drainage is one of the most important considerations even though precipitation is low.

Pooled water can quickly alter the thermal regime of the underlying soils, increasing the

risk of damage to the road. The largest threat to a road embankment in cold regions is the

stability of the underlying soils. Even if the embankment itself is stable it may suffer

damage if its level of support from underlying soils changes. The richer the ice-content,

the thicker the embankment design will need to be. It is desirable to obtain gravel of the

requisite quality and quantity and keep the haul distance to a practical minimum. A good

clean gravel embankment makes a very good foundation in a very cold environment where

it is possible to contain the zero degrees Celsius isotherm within the embankment

(Schraeder et al., 1996).

Least cost path analysishave been several recent applications of least-cost path methodologies which involve:

Multi criteria evaluation

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 291When using least-cost path analysis to determine route alternatives, the perceived

importance, or weight, of each criterion will directly affect the routing outcome.

Therefore, a process to determine the relative importance of criteria is required. This

process is known as multi-criteria evaluation (MCE). The decision about which route

alternative to select would be defined as a multi-objective decision (Eastman, 1999). An

objective is understood here to imply a perspective, philosophy, or motive that guides the

construction of a specific multi-criteria decision rule. In the case of routing an arctic road,

the objective of a mining company might be economical construction, whereas the

objective of an environmental group would likely be environmental protection. The

criteria they consider, and the relative importance of these criteria, will likely be quite

different. Each party faces the challenge of assessing and clearly articulating the relative

importance of the criteria influencing the decision.

Multi-criteria evaluation requires the determination of the importance, or weight, of

each criterion to the decision making process as a whole. Within the context of multi-

spatial-criteria evaluation, Rao et al. (1991) state that a logical process for the

development of such weights is the procedure of pair-wise comparisons developed by

Saaty (1977). The procedure outlined by Saaty (1977, 1980) rates the importance of each

factor, or criterion, relative to every other factor using a 9-point reciprocal scale. Fig. 3

shows the 9-point rating scale developed by Saaty (1977).

If, for example, we were comparing factor I with factor J and were to state that factor Iselecting the fastest path with the least slope based on elevation data (Stefanakis &

Kavouras, 1995); selecting the best route for a pipeline based on land use and land cover

data (Feldman, Pelletier, Walser, Smoot, & Ahl, 1996); selecting the cheapest route to

transport commodities based on land use and topographic data (Jaga, Sundaram, &

Natarajan, 1993). Now, the computation of least-cost paths is considered the most useful

tool available for determining the optimal path from one or more origin points to one or

more destination points (Lee & Stucky, 1998). The methodology for the calculation of an

accumulated-cost surface is well documented in commercial GIS packages and in

Collischonn and Pilar (2000); Douglas (1994), and Lee and Stucky (1998). What is lacking

in many of the methodological discussions is how to appropriately weight and combine

factors to create suitable cost-surfaces and how to incorporate differing weighting

scenarios and differing points of view in the routing process.

Often activities such as the selection of an appropriate route between two points are

undertaken by an individual or a small group. In such a process, outcomes can be

influenced by personal bias toward certain objectives or the inconsistent application of the

project criteria to the route study area (Motemurro, Barnett, & Gale, 1998). Routes for

features such as roads, railways, or pipelines are often constrained by physical,

environmental, political, social, economic, and regulatory factors. A system that can

optimize relationships among these factors and identify trade-offs can produce a wide

range of alternatives (Montemurro et al., 1998).was very more important than factor J then a value of 7 would be placed in an n!n matrix

of ratings (where n is the number of factors being considered). The reciprocal of that rating

would be 1/7 meaning that J is very less important than I. The number of factor

comparisons can be determined using the following formula.

Fig. 3. Nine point reciprocal scale developed by Saaty (1977).

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307292Comparisons ZnnK1

2(1)

Let us suppose that there are three (3) criteria A, B, and C. In this case three (3)

comparisons are required to complete a 3!3 matrix Y, according to the previous formula.The three statements, and the resulting comparison matrix based on Saatys 9-point scale,

are shown in Fig. 4.

Saaty (1977) has shown that the principal eigenvector of the comparison matrix

represents a best-fit set of weights. In pair-wise comparison, consistency within

comparisons is important. Saaty (1980), states that a consistency ratio (CR) of 0.10 or

less is considered acceptable. The CR value is the probability that the weights are random.

The principal eigenvector corresponding to matrix Y is seen in vector W shown in Fig. 5

along with the consistency ratio.

In a general sense, a GIS model can be thought of as the process of combining a set of

input maps with a function to produce an output map (Bonham-Carter, 1994). For this

paper, the combination of factors represents the creation of the cost surface for least-cost

path analysis. There are a number of models for combining maps together including

Boolean operations, index overlay, and fuzzy logic. The Boolean model takes a strict

binary (true or false) approach to a problem, while the greatest disadvantage of the index

overlay is its linear additive nature. Both Eastman (1999); Bonham-Carter (1994),

suggest that a fuzzy logic approach is in many ways similar to the index overlay methodFig. 4. Criteria comparison statements, and the resulting reciprocal matrix.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 293but offers a more flexible set of combination options and improves on the linear additive

nature of the index overlay model.

In classical set theory, set membership is defined as true or false, 1 or 0. Membership in

a fuzzy set is expressed on a continuous scale from 1 (full membership) to 0 (full non-

membership). Fuzzy membership values can be applied to categorical, ordinal, or interval

variables. As long as fuzzy membership values lie within the range of 0 and 1 there are no

practical constraints on the choice of fuzzy membership values (Bonham-Carter, 1994).

Yager (1977) established that raising a fuzzy set by the power of its weighted eigenvalue,

derived from Saatys pair-wise comparison technique for developing criteria weights, was

a good method for adjusting fuzzy sets to reflect their relative importance prior to

combining fuzzy membership functions. Yager (1977); Bonham-Carter (1994), and

Zimmerman and Zysno (1980) all show that fuzzy sets provide very useful tools to

investigate multi-criteria decision problems. One reason for this is that fuzzy sets provide a

mathematical structure for manipulating and evaluating vague ideas that can become very

complex (Yager, 1977). What is important is that the idea of comparing the criteria as to

their importance incorporates an ability to account for trade-offs between criteria.

Furthermore, the power of each criterion that is included in the model corresponds to a

hierarchical structure in the sense that various experts can evaluate each fuzzy set and then

these can be combined to create a result based on all criteria.

As an example of a fuzzy membership we can examine the degree of membership in the

set defined as suitable locations for a road. Let us consider a siting of a road in relation to

a stream, where it is more desirable to be further from the stream to a maximum of 60 m;

the stream is defined as 010 m. The fuzzy values for positions start to rise above 0.0

immediately at the stream boundary (10m) and approach a value of 1.0 at the 60 m mark.

Further distance does not increase the value since the distance is far enough to not affect

the stream or the road. Such a membership function might be expressed as in Fig. 6 along

with its accompanying graphical representation of that linear function.

In this example, X is the distance in meters and x(x) is the fuzzy membership function.The ordered pairs (X, x(x)) are known as the fuzzy set (Bonham-Carter, 1994). According

Fig. 5. Eigenvector produced from the comparison matrix with consistency ratio.to Bonham-Carter (1994), the shape of fuzzy membership function need not be linear; it

can take any analytical or arbitrary shape appropriate to the problem, and can be expressed

as a continuous surface, lists, or tables of numbers. One must be aware that when

discretisizing continuous data some data may be lost in the generalization.

Previously we developed a set of weights for three criteria A, B, and C (Fig. 4). Let us

now assign a fuzzy membership value to each of those criteria. Within each criterion there

are four classes, each of which has an assigned fuzzy value (Table 1). These values are

derived from an example given in Yager (1977).

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307294Yager (1977) states that the first step is that the unit eigenvector W needs to be scaled.

The reason for this is that if all the criteria were equal then the there would be no effect on

the fuzzy values entering the decision function. Each fuzzy set is then raised by the power

Fig. 6. Fuzzy membership function and graph for stream data.of its scaled eigenvalue. The scaled values for the three criteria are shown in Table 1. This

scaling procedure means that important criteria are exponentially weighted heavy forcing

them into the decision process while small values tend to make the membership value

smaller which effectively takes them out of the process (Yager, 1977).

Zimmermann (1985) discusses a variety of fuzzy logic combinations such as the fuzzy

algebraic product, the fuzzy algebraic sum and the fuzzy gamma operator. The fuzzy

Table 1

Fuzzy values, and scaled fuzzy values, assigned to each criterias four subclasses

Fuzzy Values Criteria

Class A B C

1 0.5 0.5 0.2

2 0.7 0.4 0.1

3 0.3 0.8 0.6

4 0.6 0.4 0.9

Scaled fuzzy values Criteria

Class A0.48 B1.77 C0.75

1 0.72 0.29 0.3

2 0.84 0.2 0.03

3 0.56 0.67 0.2

4 0.78 0.2 0.92

degree of increasive or decreasiveness that is desired for a given solution. An

increasive solution includes more trade-offs creating more possible solutions, though

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 295they may not be ideal, while a decresive solution remains more rigid to the rule

structure. In the case of selecting a y value for least-cost path analysis a low value

(yZ0) can result in a path that has effectively removed the distance element to therouting and relies more on cell weights to determine the route. This could result in a

very sinuous path. Selecting a high y (yZ1) could result in a path that minimizes thedistance between two points and produce a straight path that ignores factors other than

distance.

Methods

The study area for this project is a large section of the Barren lands within the

boundaries 65678N, and 1061128W. Previously proposed routes for an all-weather roadrun from the proposed port at Bathurst inlet to the area around Contwoyto lake (Fig. 1).

The regions climate is classified as arctic tundra. The entire region is underlain with

continuous permafrost (Natural Resources Canada, 1995), with an active thaw layer of

about 0.51 m (Judge, Taylor, Burgess, & Allen, 1981).

The methodology utilizes a GIS to prepare, weight, and combine construction

factors. Actual construction costs are not included in this model as those values were

unobtainable, and the assignment of monetary costs to environmental factors is beyond

the scope of this paper. Instead a multi-criteria decision making methodology of pair-

wise comparisons is used to determine factor weights for three scenarios, an

environmentally sensitive scenario, a strict engineering scenario, and a comprehensive

scenario. These scenarios are based on subjective knowledge driven concepts. A

detailed description of the weighting methods along with any assumptions made will bealgebraic product combines fuzzy memberships through multiplication. This model is

decreasive since the output value is always less than or equal to the smallest fuzzy

membership. The fuzzy algebraic sum is complementary to the algebraic product. Unlike

the algebraic product, the algebraic sum is always greater than or equal to the largest

contributing fuzzy membership value. This creates an increasive effect although the output

is limited to a maximum value of 1.0. The final combination operator is, in essence, a

combination of the previous operators. The Gamma operation utilizes the algebraic sum

and the algebraic product in the following formula

Gamma Z Algebraic sumyAlgebraic product1Ky (2)The y is a parameter chosen in the range (0,1). When the y is 1, the combination is

the same as the algebraic sum, while when y is 0 the combination is the same as the

algebraic product (Bonham-Carter, 1994; Zimmerman & Zysno, 1980). According to

Bonham-Carter (1994), a judicious choice of y produces output values that ensure a

flexible compromise between the increasive fuzzy algebraic sum and the decreasive

effects of the fuzzy algebraic product. The selection of y is arbitrary and based onoutlined.

Construction factors

The ultimate purpose of this methodology is to combine spatial data from diverse

sources, in order to create a cost-of-passage surface that can be analyzed through least-cost

path analysis to generate route alternatives, based on a series of factor scenarios. One of

the initial steps is to identify the input factors that can be generated from the available data.

Though there are many factors that can influence the routing of a cold region road, this

methodology only examines factors for which spatial data were collected or readily

available. Cost factors for this methodology will be classified into two categories,

engineering factors, and environmental factors. Each category has what could be viewed

as a set of objectives, accompanying those objectives are spatial data inputs that would

accomplish them. Table 2 outlines both the engineering and environmental objectives and

their associated spatial data.

For a least-cost path algorithm to be applied, the vector data were converted to

raster format with a cell size of 20 m. This resolution was considered an acceptable

trade-off between processing time, with increased number of cells, and the detail for

small landscape features. Extensive pre-processing for each factor was required to

prepare it for inclusion in a least-cost path analysis. For further discussion, see

Atkinson (2003)

Table 2

Scenario criteria and associated data processing

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307296Engineering goals Spatial data Data source Pre-processing

Avoid bodies of water Lake locations NTS 1:250 K Boolean Clip 20, 40,

60 m

Minimize stream

crossing

Stream buffers NTS 1:250 K Boolean Clip 20, 40,

60 m

Maximize construction

on low ice content

surficial material

Surficial Material

Classifications

Satellite derived

classifications

(Orazietti, 2003)

Clipped to study area

Maximize proximity to

aggregate sources to

minimize haul distance

Esker and rock locations

and Haul costs

Esker databaseb

(WKSS, 1999)

Spreading function for

haul costs

Maintain low grade

(Slope)

Slope maps NTS 1:250K DEM

Avoid bodies of water Lake locations NTS 1:250K Boolean clip 20, 40,

60 m

Avoid stream crossing Stream buffers NTS 1:250K Boolean clip 20, 40,

60 m

Avoid sensitive soils Surficial material

classifications

Satellite derived

classifications

(Orazietti, 2003)

Clipped to study area

Avoid sensitive wildlife

and cultural sites

Wolf den and archaeo-

logical site buffers

Esker database

(WKSS, 1999)

Spreading funciton

2501000 m

Factor weightings

For reasons outlined previously, each factor will be defined in terms of a fuzzy

membership function. Traditionally, fuzzy membership functions are expressed on a

continuous scale from 1 (full membership) to 0 (full non-membership). Fuzzy map values

are defined according to a given spatial locations degree of membership in a set. In this

methodology the values for each factor map are assigned a fuzzy membership value based

on their degree of membership in the set suitable for a road. For example, the fuzzy set

for surficial material is based on the suitability of different materials for road construction.

Rock provides a solid base for a road so has a high degree of membership in the set

suitable for a road while deep till requires a thicker roadbed to protect the underlying

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 297permafrost so has a lower degree of membership in the suitable for a road set. For the

least cost path analysis, the polarity of the fuzzy membership function is reversed so that

values closer to 0 indicate stronger membership in the suitable for a road set. This is

necessary because the least cost path algorithm interprets the cell values as costs.

Reversing the polarity of the fuzzy membership function assigns lower cost values to cells

that are more suitable for a road.

The fuzzy values reflect the degree of membership in the suitable for a road set and

are based on information gathered through a literature review of expert knowledge.

Subjective judgment was required to translate qualitative information from the literature

into quantitative fuzzy membership values.

A detailed discussion of how the costs for each factor were developed is beyond the

scope of this paper. However, the considerations surrounding each factor are briefly

discussed below. The surficial material factor is based on the fact that lower ice content

materials, such as rock and thin till, do not require a thick road base and are less prone to

permafrost degradation. For this reason they are better materials to build a road on and thus

given a fuzzy value closer to zero. Table 3 summarizes the attribute values and

corresponding fuzzy membership values for this criterion.

The maximum slope for the road is 8%. This methodology does not account for cut and

fill construction techniques and is looking to find the route that follows the lowest natural

slope. For this reason it was decided to eliminate all areas of slope greater than 10%.

Table 3

Attribute data and fuzzy values for the surficial material factor

Surficial material

Legend Class Fuzzy

Unknown water 1 0.9

Gravel 2 0.1

Organic 3 0.7

Rock 4 0.1

T1 5 0.1

T2 6 0.3

T3 7 0.5

Unknown/cloud 8 0.4

Bridge 9 0.1

from the stream) was used to determine the decreasing fuzzy values to a maximum of 60m

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307298after which a fuzzy value of 0.1 was assigned to all distances greater than 60 m.

mx ZK0:0075x C1:05 (4)For the Archaeological and Wolf Den sites it was decided that areas within 250 m of the

site were to be eliminated from analysis to insure that no route would enter such an area.

Using a distance function and the following formula the fuzzy values were determined to

the maximum distance of 1 km after which the lowest value of 0.1 was assigned

mx ZK0:0008x C0:9 (5)Construction of a road in this region depends upon access to local aggregate sources.

Access to these sources will most likely require the further construction of access roads to

link the main road construction with the aggregate source. The designs of these access

roads also form an interesting least-cost path problem that is not within the scope of this

paper. Some understanding of haul cost is required to ensure that the main road is

constructed to minimize haul distances. The esker and rock haul distance factor was

created using a cost surface and a spreading function. Further details on the creation of this

factor can be found in Atkinson (2003).

Least cost path scenarios

To outline how this methodology allows the factors discussed above to be combined in

different ways, three decision scenarios were examined. Each scenario placed a differing

level of importance on the different factors. The scenarios result in different factor weights

and thus generate three cost-of-passage surfaces and least cost paths. The three scenarios

were developed to approximate an engineering based approach to routing a cold-region

road, an approach where more importance was given to environmental factors, and finally

an approach representing a compromise between the engineering and environmental

scenarios. Within each scenario factors deemed unnecessary to the location of a road were

given a weight of zero. The non-zero weight factors were weighted using Saatys paired

comparison technique. The comparisons were made using IDRISI 32s WEIGHT moduleContinuous fuzzy values were derived by processing the slope data with the following

linear equation where x is the percent slope.

mx Z 0:099x (3)Steep regions, with a slope between 9 and 10% were given the highest values of 0.89

and 0.99 this creates the possibility that some slopes in this range may be crossed by the

path but the higher value will limit them.

The stream distance factor acknowledges that crossing streams is necessary in road

construction but the ideal is to minimize crossings and approach them at right angles if

possible. Furthermore, if a stream is not to be crossed, the road should travel at least 60 m

away to minimize disturbances or contamination. The stream location was given a fuzzy

value of 0.9 away from that the following linear formula (where x is the distance awaywhich also output the eigenvalues for each factor along with the consistency ratio. As

Table 4

Comparison matrix with eigenvalues and scaled map weights for the (a) engineering scenario (b) environmental scenario and (c) compromise scenario cost factors

(a) Surficial Esker Dist Rock Slope Streams Eigen vector Eigen!5

Surficial 1 0.4714 2.357

Esker Dist 1/3 1 0.2303 1.1515

Rock 1/4 12 1 0.1549 0.7745

Slope 1/4 1/3 1/3 1 0.099 0.495

Streams 1/7 1/5 1/3 1/4 1 0.0444 0.222

Wolf site N/A 0

Arc site N/A 0

Consistency 0.06 Sum 1 5

(b) Surficial Esker Dist Rock Slope Streams Wolf Arch Eigen vector Eigen!7

Surficial 1 0.1491 1.04

Esker dist 1/5 1 0.0573 0.40

Rock 1/6 1/2 1 0.0436 0.31

Slope 1/3 1/2 1/2 1 0.0556 0.39

Streams 2 4 5 2 1 0.2046 1.43

Wolf site 3 5 6 3 1 1 0.2449 1.71

Arc site 3 5 6 3 1 1 1 0.2449 1.71

Consistency 0.07 Sum 1 7

(c) Surficial Esker Dist Rock Slope Streams Wolf Arch Eigen vector Eigen!7

Surficial 1 0.3119 2.1833

Esker dist 1/3 1 0.1831 1.2817

Rock 1/4 12 1 0.1376 0.9632

Slope 1/3 12 1/2 1 0.1269 0.8883

Streams 1/3 1/3 1/2 1/3 1 0.0883 0.6181

Wolf site 1/2 1/2 1/2 1/2 1/2 1 0.0761 0.5327

Arc site 1/2 1/2 1/2 1/2 1/2 1 1 0.0761 0.5327

Consistency 0.07 Sum 1 7

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previously mentioned, the eigenvalues were multiplied by the number of non-zero-weight

factors to obtain scaled eigenvalues which then were used to exponentially weight each

factors fuzzy value (Yager, 1977). The location of water bodies was included in each

scenario as a Boolean clip to the surficial material dataset. Each scenario had a hard rule

for the distance from a lake that the road could be located. The lake locations along with a

20, 60, and 40 m buffer were classed as a no-data barrier for the engineering,

environmental, and comprehensive scenarios, respectively. This Boolean operation is

analogous to a group requiring that specific land parcels be off limits to development.

For the Engineering scenario only five factors were evaluated with non-zero-weights.

These factors are surficial material, esker distance, rock distance, slope, and streams. Wolf

surfaces. A YZ0.7 is slightly increasive but generates outputs that lie slightly above the

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307300initial rage of values. This value is a good balance between the routing factors and desire to

minimize the total distance of the route. A cost surface was generated for each scenario

representing the combined frictions of the weighted factors for each cell within the study

area. These final cost surfaces were then used to generate paths.

The accumulated-cost-surface (ACS) was generated by treating the proposed port as the

destination location and then using a spreading function to sum the costs of movement

away from that destination. To generate paths from the ACS, all that was required was

Table 5

Scenario weights for each input factor

Factor Engineering weight Environmental weight Comprehensive weight

Surficial 2.357 1.04 2.1833

Esker dist 1.1515 0.40 1.2817

Rock 0.7745 0.31 0.9632

Slope 0.495 0.39 0.8883

Streams 0.222 1.43 0.6181

Wolf site 0 1.71 0.5327

Arc 0 1.71 0.5327

Sum 5 7 7den sites and Archaeological sites were given a weight of zero. Ten comparisons are made

using the 9-point scale discussed previously. The Environmental scenario evaluated seven

non-zero factors: surficial material, esker distance, rock distance, slope, streams, wolf den

sites and Archaeological sites. The final scenario, the comprehensive scenario, also

considered all seven factors as non-zero weights in the factor comparisons. Twenty-one

comparisons are made using Saatys scale. The matricies of comparison values for each

scenario are shown in Table 4.

Least cost path modeling

All spatial data analysis was undertaken using ArcGIS. The factor grids were

exponentially weighted using the weights shown in Table 5, and the fuzzy product and

fuzzy sum of the resulting weighted grids were calculated. The fuzzy product and fuzzy

sum grids were combined in a Gamma operation (YZ0.7) to produce the final cost

a starting location, in this case Lupin Mine, to then trace a least-cost line back to the

destination.

Results

Three routes were created through the least-cost path analysis, one for each weighting

scenario. Fig. 7 shows the northern sections of the study area with the three generated

routes and a fourth route that was proposed by the Government of the Northwest

Territories (GNWT) in 1999. The GNWT route, known as Route I, was determined

through an air photo analysis. The figure shows the locations and size of esker deposits,

wolf dens. Archaeological sites have been omitted from the map due to protective

legislation.

Within this route there are three areas where variation in route location occurs. These

three areas (1, 2, and 3) will be used to better compare these routes. Area 1 can be seen in

Fig. 8, area 2 in Fig. 9 and area 3 in Fig. 10.

Within area 1 the study area is rather confining for the routes. All three routes follow

very similar paths from Lupin west and then north towards the Contwoyto lake crossing

point. Aggregate sources are scarce in this area and so do not influence the path of the

route. There is a cluster of archaeological sites in the northern section. The Engineering

route bisects this cluster while the Comprehensive route travels around the cluster to

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 301Fig. 7. Least-cost paths from the proposed port on Bathurst inlet to Lupin mine.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307302the west. Route I, the GNWT route, follows a similar route to the LCP routes, though it

takes a much wider curve around the western Contwoyto bay, and, like the Engineering

Route, bisects the cluster of Archaeological sites.

Area 2 shows much more variation in route location. There are only a few

archaeological sites or wolf dens in the data for this area; they are located in the north,

and so have little effect on the LCP routes. The Engineering route is pulled further south in

this area by the aggregate deposits, then curves north again meeting up with the

comprehensive route. Route I takes northern course, coming close to some archaeological

sites, but is further from some larger aggregate deposits.

Area three has the LCP routes again following a very similar path, yet it is quite

different from route I. The LCP routes travel in a steady northeast route towards the port,

while route I travels due east quite a distance then curves north. Again this area does not

show many Archaeological sites, however there are a few Wolf dens near the port. Route I

appears to run closer to some esker deposits in the eastern portions of the area, yet they are

mostly small eskers that would not provide much aggregate.

Stream crossings

The number of stream crossings on a route can directly affect the cost of construction as

well as the environment. The engineering route crosses the most streams with 93

Fig. 8. Lupin least-cost paths in sub-area 1.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 303crossings, while the environmental route, which had streams with a larger criteria weight

from the scenario comparisons, crosses far fewer at 77. The Comprehensive route crosses

82, which is very similar to Route I, which crosses 84.

Aggregate volume

The volume of aggregate required to construct a given route is dependant upon the

underlying surficial material. The LCP routes and Route I have been examined in terms

of their underlying surficial geology. Route I values have been taken from Orazietti

(2003) who analysed all proposed routes in terms of aggregate. All routes are very

close in overall length, including Route I, approximately 300 km in length. The lengths

of road segments for each surficial geology type do vary. The largest difference is that

Route I has 23% of its route traveling over thick, ice-rich till and 7% on organic soils

which require thicker embankments to stabilize the underlying permafrost, compared to

2% and 1% respectively for the LCP routes. The majorities of LCP routes are on thin

till veneer (54%) and rock (30%), which require much less aggregate to prevent

permafrost degradation. These lengths make a significant impact on the volume of

aggregate required to construct the routes, when these least cost paths are compared to

previously proposed routes in terms of aggregate requirements there is a 20% reduction

in the required aggregate.

Fig. 9. Lupin least-cost paths in sub-area 2.

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307304Discussion

Criteria evaluation

Schraeder et al. (1996), and McFadden and Bennett (1991) all illustrate the importance

of construction factors. What is not stated is the quantified importance of each of these

factors, although certain criteria are emphasized. Personal bias toward certain objectives

and inconsistencys can often result when criteria importance is guided by an individual or

a small group (Montemurro et al., 1998).

The criteria for the methodology were selected criteria based on the engineering

literature, environmental principles, and the availability of spatial data. A mathematical

structure for manipulating, evaluating and combining, road routing criteria is provided

through the use of Saatys multi-criteria evaluation (MCE) method of pair-wise

comparisons, along with the methods of weighting and combining fuzzy sets presented

by Bonham-Carter (1994); Yager (1977). What has been illustrated is the idea that

comparing the criteria, as to their importance in selecting a route, incorporates an ability to

account for trade-offs. Second, the weight of each criterion corresponds to a hierarchical

structure, in the sense that each fuzzy set can be evaluated by various experts, and these

can then be combined to create the resulting cost surface and thus that experts least-cost

path. The criteria comparisons and thus weights that were generated through the three

Fig. 10. Lupin least-cost paths in sub-area.

scenarios, engineering, environmental, and comprehensive, were based on subjective

decisions derived from the knowledge base within the literature. Although the actual

weightings for a given scenario may be inaccurate, due to the subjective nature of the

comparisons, the use of differing scenarios, which took different views, compensates for

this. What is important is that this methodology of MCE provides a mathematical structure

to ensure that criteria are evaluated equally across the study area and not subjectively

within the study area.

Route determination: LCP versus traditional approaches

The traditional methodology that was used to produce the previously proposed routes is

that of Terrain Unit Mapping using non-digital black and white air photos and maps

(GNWT, 1999). Terrain units were evaluated by strictly using these data sources, no

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307 305fieldwork was undertaken. The GNWT routes were determined based on the criteria

outlined in Table 6.

The methodology for the previously proposed routes was subjective and qualitative.

The use of a GIS and most importantly LCP analysis provides a methodology for a less

subjective and more quantitative analysis. The power of GIS and LCP comes not only

from the ability to store geographic data, but also from the ability to analyze it more

efficiently and more conveniently than is possible with paper maps (ESRI, 2000). The LCP

analysis combines and analyzes all of the spatial criteria to produce a cost surface for the

entire study area. The LCP analysis examines a variety of data over a large area relatively

quickly and is consistent in its evaluation of criteria to find the least-cost path based on the

given data.

Strengths and limitations

A prime strength of this methodology is that it can be applied to routing applications for

a variety of study areas and differing criteria can be compared and weighted to produce

alternative routes. What is needed to apply this methodology to other locations

Table 6

Route selection criteria outlined by the GNWT

Criteria Implications

Topography Route selection should have little to no right-of-way excavation; embankment

construction should average 0.51.5 m in thickness

Bedrock surface Route location should follow glacier-smooth surfaces with micro relief of 1.0 m

Lakes Vertical and horizontal alignment considerations

River crossings Route should minimize river crossings and locate crossings that are narrows and

on suitable foundation conditions

Wet organic terrain Route locations should avoid seasonally wet or permanent organic terrain

wherever practical

Granular borrow sites Route location should consider location, volume and composition of potential

sources (i.e. esker complexes)

Permafrost Not considered a major factor in route location as entire area is a zone of

permafrost

many factors as possible; there is a gap in available data for the region. Some examples of

missing data, that may have proved useful include, snowdrift data, caribou migration data,

D.M. Atkinson et al. / Applied Geography 25 (2005) 287307306and more detailed wildlife studies. An additional factor, that was not included, that could

play a role in the routing of this all-weather road is the locations of known mineral deposits

and their potential for development. This data was not available but could create a heavily

weighted factor that could pull the road in the direction of the potential mine.

The scale of the data is another limitation. At the time of the project computer-

processing power did not permit data at a finer scale. At the resolution that these grids were

created their file size was rather large requiring several gigabytes of storage to allow for

the data management and processing. If data at a larger scale was available, the file size

may be prohibitively large, and inhibit processing.

Other challenges exist with the pair-wise comparisons and determination of fuzzy

values. The comparisons that were used in this project were based on subjective,

knowledge-based judgments, but may not represent the opinions of an expert although the

methodology permits the flexibility of using expert opinion. Another issue may be how to

compare criteria that cannot easily be compared. Physical properties of a factor are

difficult to compare to emotions or ideologies.

This project has contributed to our understanding of how pair-wise comparisons and

fuzzy data sets can be used within a GIS and LCP analysis to determine possible routings

of an arctic all-weather road. Ideally the methodology will provide a framework for further

research and provide alternatives to the previously proposed routes. With some further

refinement, the methodology could be used by developers and decision makers with

increased expert knowledge to create other routing alternatives. As better data becomes

available, along with increased digital storage and processing capabilities, improved

routes can be generated for this project and other routing applications.

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Multi-criteria evaluation and least cost path analysis for an arctic all-weather roadIntroductionCold region road constructionLeast cost path analysisMulti criteria evaluationMethodsConstruction factorsFactor weightingsLeast cost path scenariosLeast cost path modeling

ResultsStream crossingsAggregate volume

DiscussionCriteria evaluationRoute determination: LCP versus traditional approachesStrengths and limitations

References