estimation of distance-decay parameters - gis-based indicators of recreational accessibility

8/21/2019 Estimation of distance-decay parameters - GIS-based indicators of recreational accessibility

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Estimation of distance-decay parameters - GIS-based

indicators of recreational accessibility

Hans Skov-Petersen

Danish Forest and Landscape Research InstituteDepartment of Urban and Regional Planning

Hørsholm Kongevej 11DK-2970 Hørsholm

[email protected]

Abstract. Distance-decay - as a quantitative conception of the phenomenathat things being further away are less likely to be used – has been used asone of the base assumptions when modelling human spatial behaviour,including assessment of accessibility of resources and mobility of the users.

The article presents and discusses a number of approaches to distance-decay,as basis for calculation of environmental indicators as well as to serve as parameters to numeric models. Based on a concrete case of car-bornrecreational behaviour in Denmark, it is demonstrated how distance-decay

parameters can be estimated and implemented in a GIS-context. Further on, procedures for setting digital topological networks up for calculation ofindicators of accessibility and mobility are given. Finally, a number ofresulting indicator-maps are shown.

Keywords: GIS, recreation, accessibility, mobility, distance-decay, indicators

1 Introduction

The location of the resources relative to the users, the transport-system, and the way

space and distances influences the potential usage of facilities are central issueswhen modelling accessibility and mobility. The influence of distance on potentialusage is often conceptualised through distance-decay functions (e.g. Hansen, 1959,Koenig, 1980 or Fortheringham, 1981), expressing the way increasing distance ortravel-cost has an inverse effect on the possible usage, i.e. it is less likely thatfacilities far away is used that those at closer range.

Using GIS for accessibility-modelling ahs a number of advantages, including: a) it provides an easy assessment of transportation options, as represented by a digitalroad network, b) data can be handled in a generally more flexible way, including awider range of options for integration of data from different sources, and finally c)


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GIS enables cartographic presentation of results, which again opens for visualinterpretation and error assessment.

It is the purpose of this paper to:

• Discuss the various ways models of interaction, including accessibility andmobility, have implemented distance-decay,

• to discuss the performance of different approaches to distance-decay,

• to demonstrate how distance-decay parameters can be estimated from empiricaldata for a concrete case of car-borne recreational activities in Denmark, andfinally

• to present cartographic results of models based on the concept of distance-

decay.

2 Accessibility, mobility and indicators

When addressing issues related to human spatial behaviour, including land use- and

transportation-planning, the assessment of accessibility and mobility often comesinto question. The definition of the two terms is non-trivial and has been addressed by a vast number of authors since the emergence of the early attempts of theinteraction modelling (Hansen, 1959). A comprehensive attempt to define andclassify accessibility and mobility is beyond the scope of the present text. Interestedreaders are advised to consult e.g. Koenig (1980), Heanue, et.al. (1995), Handy and

Niemeier (1997), or with special reference to access to the landscape, Skov-Petersen(forthcoming).

A first very coarse, distinction can be made between spatial/physical accessibility on

one side and social accessibility and mobility on the other. Spatial or physicalmobility is the ability to physically move in space and achieve goals or objectives at

a transport-distance or –time from the origin. For the purpose of the present paper aspatial, physical approach to accessibility and mobility is taken. Social mobility –the option for changing socio-economic status (Johnston, 2000) is not considered.Modelling spatial/physical accessibility and mobility is aiming at a quantitativeassessment of the transportation options with respect to the potential use and/or the potential need for specified locations. This way accessibility becomes a measure of

spatial opportunities (Cervero, et al., 1999) rather than actual behaviour or wishes.Both indicators of accessibility and mobility must include a notion of at least two parameters: the mode of transport, including the way the transport system influenceshuman activity and a localised quantification of the resource made available and/or potential need (e.g. Wickerman, 1974 and Geertman and V. Eck, 1995). This can be

further developed to include three components: the transport system, and adistinction between the location of the facilities and the location of the users (e.g.Handy and Niemeier, 1997 or Johnston, 2000). The concepts of the negativeinfluence at increasing distances on human behaviour – often referred to as distance-decay – is discussed overleaf in this text.


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An attempt to define mobility could be ‘the ease by which a person at a specifiedlocation can reach and make use of a certain facility’ (Kronbak, 2000). This waymobility must be seen as an attribute to the point of departure, e.g. the dwellings ofthe people under consideration (Heanue, et al., 1995). The ease or cost to reach the

facility can be assessed in time, money, distance etc. Measures of mobility can beaggregated or disaggregated . The distance or travel-time to the closest school froma dwelling is an example of a disaggregated mobility-measure. If all the availablefacilities within a specified distance or cost are considered, an aggregated measureoccurs. This way, potential resource can be used, as an indicator of aggregatedmobility, e.g. the available area of parks within 30 minutes of walk.

Fig. 1. Potential available resource – an indicator of mobility: Measured in terms ofthe available resource which persons at a specified location can potentially reach..

Accessibility, on the other hand can be defined as ‘the ease by which a facility can

be reached from one or more locations or points of departure’ (Kronbak, 2000).Hence, accessibility becomes an attribute to the facility (Heanue, et.al. 1995). Asmentioned in the context of mobility, the ease or impedance can be measure in time,

money, distances etc. Again a set of aggregated and disaggregated measures can bedescribed. Morris, et.al. (1978) uses the term relative accessibility for disaggregatedaccessibility. The same authors refer to aggregated measures as integral

accessibility. An example of disaggregated accessibility could be how well amuseum can be reached by the children from a specified school. An aggregatedaccessibility indicator could be the total number of children that can reach aspecified museum within 30 minutes drive by public transport.

Fig. 2. Potential usage – an indicator of accessibility. Measured in terms of the ease by which a facility can be reached from one or more points of departure.


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The distinction between accessibility and mobility - the potential usage and resource – is not always made. Very often the term accessibility is used for both phenomena’s. An example is given by Cervero et al. (1999) who addresses both‘housing accessibility’ and ‘job accessibility’. The first, being an attribute to the

residential areas, would according to the discussion above be seen as an indicators ormeasure of mobility. The latter is an attribute to the employment areas, and canaccordingly be seen as an indicator or measure of ‘proper’ accessibility, as it will beused for the remainder of this text.

The use and generation of Indicators are often motivated by the need for monitoring

the state of the environment on an even basis over time and different regions. In theintroduction chapter of the ‘Europe’s Environment – the Dobris Assessment’(Stanners and Bourdeau, 1991, p 6) a call is made for the generation of a set ofdescriptive indicators for the production of environmental quality profiles enablingcomparison the environmental status between regions. Further the indicators shouldhelp explaining the changes over time. To facilitate these two objectives, indicators

should catch the ‘essence’ of the state of the environment in a standardised andcommunicative way. An example relevant in the present context, is the use of localaccess to green areas within 15 minutes walk as an indicator of urban environment(Stanners and Bourdeau, 1991, p 264).

Accordingly the distinction between assessment of accessibility and mobility in

terms of indicators and quantitative models of phenomena’s based on empiricalmeasurements becomes evident. Indicators are meant to have comparability andcommunicativity as core characteristics whereas quantitative models attempt todescribe the phenomena as accurately as possible.

3 Formulation of distance-decay functions

Tobler (1970) (cited in Johnston, 2000, p. 182) formulates a ‘first law of geography:everything is related to everything else, but near things are more related thandistant things’. The attenuation of a pattern or process with distance– a phenomenawhich is of course intuitively and empirically easily recognised and broadly

accepted – is often referred to as distance-decay. Other terms used for the sameinclude Impedance Function (Koenig, 1980, Handy and Niemeier, 1993) andDistance Lapse Rate (Johnston et al. 2000).

A generalised formulation of potential accessibility or mobility, based on the ‘mass’(facilities or needs) surrounding sites including distance-decay is shown below

(formula 1).


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P M f d i j ijn

j

==

∑ * ( )1

Where:Pi is the potential accessibility or mobility of place i,

M j is the ‘mass’, e.g. population of place j,f() is the distance-decay function, anddij is the distance or cost between target i and origin j

Formula 1: Calculation of potential using a generalised distance decay function.

In the case of a sharp threshold – masses of points being further away than the giventhreshold are simply not included in the calculation – the decay function f(d ij ) can beformulated as formula 2. This special case of distance-decay is referred to by Koenig(1980), and Cervero et.al (1999) as ‘isocronic definition‘, and ‘cumulative

opportunities measure’ by Handy and Niemeier (1997).

f(dij) = 1 for dij threshold, e.g. 30 minutes

Formula 2 : Example of distance decay function as a sharp threshold.

Inspired by the Newtonian theories of gravitational attraction a classically

implementations of a distance decay are power functions (formula 3). Other writersincluding Fortheringham (1981, pp 425) broadens up the term ‘gravity model’ toinclude ‘…any aggregated spatial interaction model in which interaction volume isa function of nodal propulsiveness, nodal attractiveness and distance’ .

∑=

=n

j ij

j

id M P

1λ

Where:Pi is the potential number of e.g. people attracted to town i,M j is the ‘mass’, e.g. populations of the town j,dij is the distance between i and j, and

λ is the exponent of the potential function.

Formula 3 : Calculation of potential using a power distance-decay function.

Alternatively an exponential function can be used to represent the distance decay.


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∑=−=

n

j ijii

d M P 1

)*exp(* λ

Where

Pi is the potential number of e.g. people attracted to town i,M j is the ‘mass’ e.g. populations of the town j,dij is the distance between i and j, and

λ is the exponent of the function.

Formula 4 : Calculation of potential using a exponential distance-decay function.

The estimation of the exponent parameter λ is crucial. The higher, the more abrupt is

the ‘cut of’ of influence of populations being situated at greater distances. As stated by Fortheringham (1981, p 425) ‘ A distance-decay parameters measures the

relationship between observed interaction patterns and distance when all otherdeterminants of interaction are constant’ . The parameter is estimated as a best-fit tothe current situation, represented by an empirical data-set. Distance-decay, both in

terms of the function involved and the parameters, varies between different regions,for different activities, and different modes of transport. In his now classical studyHansen (1959) list findings of parameters-estimates of 2.0+ for school trips, 2.0 forshopping trips, 1.1 for social trips and 0.9 for work trips. This indicates that theaverage radius of activity for interaction between home and work is greater than between home and school, which corresponds well with what is intuitively expected.

Several writers including Koenig (1980), Davidson, (1997) and Dalvi and Martin(1976) regards Hansen (1959) as one of the first definitions and formulations ofaccessibility indicators. The latter even refers to an accessibility index based on a power-distance-decay function as ‘.. the Hansen type of measure…’ (p 18 and p 19).

According to Fortheringham (1981) estimates of distance-decay parameters are

functions of spatial structure as well as interaction behaviour. Hereby the modellingof spatial behaviour is not just as a consequent of the available transport-system –which again is, at least partly, a function of the local topography etc. - but alsosocial differences etc. Hence, distance decay-parameters will be different fordifferent regions. Figures given for residential exchange between American citiesshows to vary from -0,01 in the area of Chicago – indicating that people tend to

move very short - to it’s highest values of -2,3 and more in a NW/SE band across thecentral Rocky Mountain area (indicating very long exchanges of dwelling). In SEUSA parameters between -1,4 and -1,9 are found. It is not surprising that peoplemove longer in scarcely populated areas than in areas of higher population densities.

1 The reason why the parameters provided by Fortheringham (1981) are all negatives is that

the interaction measure used is multiplying the mass-variable with the distance variable

(raised to the power of decay-parameters). In the Hansen (1959) study referred above a

measure like formula 3 is used, which leads to positive distance-decay parameters.


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The issue is, that when reusing distance-decay parameters in other geographicalareas care should be taken.

Further more when comparing decay parameters arising from different sources care

should be taken that the units of the original empirical data are comparable. Eventhough the same decay-function is used, estimated parameters based on measures inmiles, minutes and in km will obviously not be the same.

When it comes to reaching better description and explanation of imperial data higherorder approaches – including power and exponential decay-function – have an

obvious advantage. The precision of the model and hereby the resulting predictionwill in many cases be better if a better fit to the in-going data is obtained. On theother hand, the results of higher order models might not be as easily communicatedas can more simple measures. Example given the number of people that can reach alocation within half an hour – being a simple, sharp threshold or isocronic measure –is readily understood whereas a population-potential including a higher order

distance-decay is much harder to comprehend by laypersons (for example of thisdiscussion see Koenig (1980), Geertman, 1996, Handy and Niemeier, 1997, orSkov-Petersen, 1998). Further care should be taken if no empirical data are availablefor estimation of parameters for higher order decay functions. The implementation

of standard values – e.g. 1.8 as the λ-value in power models – seems hard to justify

especially when considering the above discussion of distance-decay parameterssensitivity to differences in geography, activity and unit of cost. A sharp thresholdapproach must be considered because of the advantage of enabling an easierunderstanding of the background of the model and hence the results.


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Fig. 3. Potential forest resource (an indicator of mobility) within 5 min drive by car.Please note that the threshold of the legend is based on quartiles, i.e. the first class –out of ten – contains the 10 % of the number of polygons having the lowest values

etc. 2Therefore – and because the potential resource obviously are different for thedifferent time bands (5, 15, and 30 minutes) - values are not directly comparative between figures 2, 4 and 5. The same goes for the figures 11-14.

The selection of time restriction in a sharp threshold-model is obviously important.As discussed earlier the time restriction ought to reflect an empirical knowledge. Onthe other hand, there is also a scale factor including the type of phenomena and thespatial configuration of the region or area under consideration. On one side if thetime restriction becomes too big related to the extend of the geographical region –and the underlying data (forests and population) are more or less evenly distributed

over the area – the results will be just concentric rings reflecting the shape of thearea. E.g. the case of 30 minutes drive (fig.5): Roughly speaking 30 minutes drive isthe radius of the island of Zealand. As can be seen - and what is not surprising – themobility is biggest close to the centre of the island, i.e. most of the island can reachit. This way the map will reflect the underlying geography, rather than the phenomena considered. On the other side, if time restriction becomes smaller – like

in the case of 5 minutes drive (fig.3) – the map will look more and more like the

original forest map. If a time band of 0 minutes were investigated the result would be exactly like the original map. Scale, phenomena, and knowledge of behaviour

2 Alternatively the quintile thresholds could be set in a way that the first class represents the

polygons covering first 10 % of the area etc.


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must all be kept in mind when considering sharp threshold distance-decay parameters.

Fig. 4. Potential forest resource (an indicator of mobility) within 15 min drive bycar.

Fig. 5. Potential forest resource (an indicator of mobility) within 30 min drive bycar.

To conclude the above discussion, a rule of thumb could be to use sharp thresholds

when the measures of interaction are to be used as direct presentation of indicatorsof mobility or accessibility. When the measures are to be used as parameters in a


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model for explaining and prediction the utility or available resources, a higher orderdecay-functions should be considered.

4 Fitting distance-decay parameters for car-trips to the nature.

For the present case-study empirical data obtained from household interviews wasused (Jensen, 1999). The interviewed persons were asked how much time they spendand which means of transport they used last time they had recreation activity in thenature. The responses were given in pre-set intervals, 0-2 minutes, 2-5 etc. Table 1

shows the accumulated number of persons responding that they used car, stratifiedinto time-intervals. Further, the numbers are accumulated, and recalculated intorelative numbers (compared to the total number of answers). Finally theaccumulated, relative figures were inverted to vary from 1 at the shortest distancesto 0 at the longest. The estimation of power and exponential parameters was

performed by non-linear regression. Estimation of isocronic, sharp threshold was performed by fitting non-accumulated data to a gaussian distribution function.

0 2 8 8 0,01 0,99

2 5 76 84 0,08 0,92

5 10 269 353 0,32 0,68

10 15 343 696 0,63 0,37

15 30 231 927 0,84 0,16

30 60 116 1043 0,94 0,06

60 90 33 1076 0,97 0,03

90 150 33 1109 1,00 0,00

Table 1: Empirical background for estimation of distance decay-parameters. The

total number of relevant (car drivers) responses is 1109. The last columncorresponds to the measurements of fig. 6.

In fig. 6 the empirical data is plotted against a power, an exponential and a sharpthreshold distance-decay function. It appears that the exponential function gives the best fit.


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0

0,2

0,4

0,6

0,8

1

1,2

0 20 40 60 80 100 120 140 160

Measure

Potential

Exponentiel

Threshold

Fig. 6. Example of revealed behaviour in terms of time spent when going by carfrom the home to the nature (Jensen, 1999). Parameters were derived by non-linearregression techniques, using the SAS (Statistical Analysis System) procedure NLIN

(SAS, 1999): Potential (power): λ = -0,346625. Exponential: λ = -0,049281.Threshold: Mean = 13,36. It appears that the exponential function gives the best

numeric description of the empirical data.

The shape of the curve of fig. 6 representing the empirical data gives the impressionof a slight S-shape, which could lead to an expectation that a gausian function, or agausian function with an offset, could provides an even better fit. The advantage of agausian distance-decay is that it can take into account the phenomena that changesin distance might be less significant both when it comes to very close distances as

well as very far. E.g. the present case of recreational behaviour: Whether there is 5or 10 minutes transport time might not make much of a difference when selecting asite for a walk. Neither would a change from 45 to 50 minutes. But a change between 25 to 30 could turn out to be crucial. To that matter the gausian approach

can be seen as closer to the sharp threshold approach. One of the rare referencesmade to implementation to a gaussian approach to distance-decay is provided by

Vickerman (1974). For the purpose of the present text no further attempt has beenmade to implement the concept and techniques of a gausian based distance-decayfunction. This is partly due to the fact that gaussian distance-decay is not directlysupported by of the GIS-programmes considered.


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5 Method and data-background

For the purpose of the present context the vector-approach to spatial data analysiswas selected. The ARC/INFO GIS-software supported by applications created by

means of the scripting language AML was used. The transport options wasrepresented by a road network. The population data and the nature resource wererepresented by polygon coverage’s (see fig. 7, 8, and 9). For the aggregation of

forest- and population-information to the nodes of the network a generic routine wasdeveloped. The routine can be used for other purposes of the same kind. There aretwo basic operations involved in the calculation: Attachment of information to thenodes of the road-network be means of polygon-to-point a ggregation of backgrounddata (e.g. population and nature resources) and calculation of accessibility ormobility, including creation of a connectivity matrix (see fig. 10).

Population (Parish)1 - 2727 - 3434 - 4545 - 6161 - 8989 - 176176 - 515515 - 17061706 - 34650

Forest

Fig. 7. Population densities (persons per

km2) of Danish parishes (1:25.000) used

as data-background for the present study.

Fig. 8. Forests of Denmark used as data-

background for the study. Obtained from1:200.000 digital vector map.


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Network linksHighwayOther primary roadOther roadOther roadOther road

! Network nodes

Facilities (forests) and needs (population) are attached to the nodesdisplayed as squares. The travel cost –

in terms of driving time, calculatedfrom distances and speed limits – areattributed to the links (arcs) connectingthe nodes. The resulting accessibility isassigned to the nodes. For presentation(see the results below) the accessibility

information from the nodes is linked tothe Thiessen polygons representingeach node.

Fig. 9. Local example (the Lillebælt bridges between the island of Funen and Jutland) of the road-

network used for the study (1:200.000).

The polygon-to-point aggregation is performed by creation of Thiessen polygons

around the nodes of the network and subsequently overlaying them with the background polygon data – population or forest. With respect to the forests the area

intersecting the Thiessen polygons are summed. For the population the product ofthe intersecting area and the population density is added – one set for each Thiessen polygon.

The mode of aggregation is this way depending on the type of the in-going data. Ifdata are area independent – e.g. as total population per parish – they have to be

recalculated into figures relative to the area – e.g. population densities (see formula5). In the case of e.g. aggregation of the available forest area for each node thecalculation is simpler – a sheer addition of the areas of the forest falling with in the‘shed’ of each node3.

3 This type of aggregation is referred to as interpolation of extensive variables by Flowerdew

and Green (1995) where a further discussion of the issue is found.


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∑=

=1

*n j

jij x A Xi

Formula 5: Aggregation of area data,

where: Xi is the aggregated value of node i Aij is the area over the intersection of the thiessen polygon of node i and the in

going polygon j and x j is the area independent value (e.g. population density) of the in going

polygon j. x j will always be 1 in the simple case of collection of areas (e.g. in

the present case of forest resources).

In principle, a connectivity matrix represents connections - as distances or costs -along the cheapest or shortest route of all combinations of nodes in a network. In a

bi-directional network

4

where all nodes (n) can reach each other the number ofelements of the connectivity matrix will be n2 – n. In a unidirectional network the

number of combinations will be (n2 – n)/2. To reduce the resulting data-set many

systems facilitates the possibility of only making calculations for nodes within aspecified maximum cost or distances (e.g. 1000 metre). If implemented, a distancedecay function can subsidiary be applied to connectivity matrix.

4 In a bi-directional network the impedance along one link (the line between two nodes, say a

and b) differs whether going from a to b or vice versa (Hagget and Chorley, 1969)..


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Road network ForestsUrban areas

Thiessen polygons

Connetivity matrix

1 22

34

Fig. 10. Method for aggregation of polygon data to network nodes. For details, please refer tothe text below.

1. Creation of Thiessen polygons around the nodes of the road network.2. Aggregation of the background data (population data and nature areas), based on

the overlay with the Thiessen polygons. The calculated data are linked back tothe nodes of the road network.

3. Calculation of a distance or impedance matrix – e.g. the distance between allnodes that are less than 1000 meters apart.

4. Summarising the data from nodes connected by the impedance matrix. And

finally linking back the summarised data to the nodes of the road network.

In most cases – at least in the context of ARC/INFO – step 3 and 4 are an integral part of the command used (ACCESSIBILITY) and therefore not directly issued by

the operator. Both sharp thresholds, potential and exponential distance-decay

functions are supported this way. When processing in ARC/INFO, ‘sharp

threshold’ cases, the λ-parameters is simply set to 0, meaning that space has no

influence. The threshold is controlled by a maximum-impedance parameter setelsewhere. In a more rare case, like when implementing a gausian distance decayfunction the connectivity matrix has to be build explicitly, e.g. by using the

NODEDISTANCE command.


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6 Results

Fig. 11 and 12 show cartographic representations of results from modellingaccessibility in Denmark, based on the distance-decay parameters estimated in the

previous section. As was earlier stated, accessibility is an attribute to facilities, e.g.natural areas. The maps must interpreted as the number of people that can reach alocation, given the provided distance-decay. It appears that it is much easier tocommunicate results of sharp threshold calculation – ‘at this spot 24351 persons cancome within 15 minutes drive from their home’ – than is results from higher orderdecay functions, including exponential. Even though both maps are based on the

same empirical data and even though numbers are situated approximately in thesame range, they appear quite different. Fig. 11 – the sharp threshold case – displaysa much more contrast-rich picture than the exponential case. This corresponds quitewell with what is expected from looking at the graphs of fig. 7: Locations that aregenerally slightly more than 15 minutes away from areas of high publication wi ll

tend to be underestimated compare to the exponential case. On the other handaccessibility will be overestimated if the general distance to populated areas areslightly less that 15 minutes. It must be concluded that even though the exponentialcase gives a better ‘fit’ to empirical data the message comes true more easy for the‘sharp threshold map’.


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Number of people0 - 39823982 - 57855785 - 72587258 - 87878787 - 1104411044 - 1390413904 - 1757917579 - 2461124611 - 4298542985 - 230727

Fig. 11. Denmark: accessibility (sharp threshold = 15 minutes drive by car). Toenhance contrast the classes of the legend are quintile, i.e. the number of units ofeach legend class is even. Figures are comparable to fig. 12, even though thresholds between classes are not the same.


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Number of people0 - 1842818428 - 2694926949 - 3420434204 - 4173941739 - 4884348843 - 5694556945 - 6507465074 - 7672576725 - 9969699696 - 214021

fig. 12. Denmark: accessibility (exponential, λ = -0,049281). Note that the classes oflegend are quintile


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Sqr. Km. of forest < 1111 - 19

19 - 2626 - 3131 - 3737 - 4343 - 5151 - 60

60 - 75 > 75

Fig. 13. Denmark: Potential resources (km2forest) as indicator of mobility (sharp

threshold = 15 minutes drive by car). To enhance contrast the classes of the legendare quintile, i.e. the number of units of each legend class is even. Figures arecomparable to fig. 14, even though thresholds between classes are not the same.


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Sqr. Km. forest < 7474- 9595 - 113113 - 130130 - 145145 - 161161 - 178178 - 202202 - 246 > 246

Fig. 14. Denmark: Potential resource (km2

forest) as indicators of mobility

(exponential, λ = -0,049281). Note that the classes of legend are quintile.

Fig. 13 and 14 shows cartographic presentation of indicators of mobility calculatedon the basis of estimated distance-decay parameters from the previous section. The


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most apparent different between the two maps is that fig. 13 based on a sharpthreshold indicator appears much less smooth and more contrasted than the one based on the exponential decay-function (fig. 14). The maps show the potentialresource in terms of km2 forest with respect to one or the other distance-decay

function and should be read something like ‘If I am living at this location …. Iwould have this amount of forest at my facility’. Again as above it appears that asharp threshold indicators is more readily communicated and understood than theone based on exponential distance-decay function.

7 Conclusion

A set of different approaches to distance-decay has been discussed anddemonstrated. The quality or success of the model-results can be judged from twodifferent angles: a) its communicative qualities as in the case of environmental

indicators and b) as a quantitative description of phenomena, based on empiricaldata. It has been argued and demonstrated that a sharp threshold approach todistance-decay reveals more easily understood results making them more useful inthe context of e.g. decision-making involving laypersons, politicians or other nothaving sufficient technical or professional background to grasp results from models based on higher-order distance-decay functions. If the aim is as numerically accurateas possible to describe a phenomenon, based on higher-order decay-functions can be

implemented. But it requires that relevant empirical data is available. Humanactivity and hereby the functions and parameters describing them varies over time,space and between different activities. Use of higher-order decay-functions forgeneration of indicators or map of larger areas or representing non-specifiedactivities therefore makes no sense. If the objective is to generate knowledge of whatwill happen over time if conditions changes, the predictive accuracy of the model is

required, calling for more complex modelling approaches, including higher-orderdistance-decay functions.

There is a need for both indicators of accessibility and mobility. The potentialnumber of users, as an indicator of accessibility, is needed by the managers of thefacilities. E.g. it is necessary for the forest manager to obtain estimates of the

potential number of visitors. The urban planner on the other hand, needs estimates ofthe green resource for different parts of the urban area under consideration.

8 References

Cervero, R., Rood, T. and Appleyard, B. 1999. Tracking accessibility: employmentand housing opportunities in the San Francisco Bay Area. Environment andPlanning A, Vol. 31. Pp 1259-1278.

Dalvi, M.Q. and Martin, K.M. 1976. The measurement of accessibility: Some preliminary results. Transportation 5. Pp. 17-42.


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Davidson, K.B. 1977. Accessibility in transport/land-use modelling and assessment.Environment and planning A, Vol 9. Pp 1401-1416.

Fortheringham, A.S. 1981. Spatial structure and distance-decay parameters. Annalsof the Association of American Geographers. Vol. 71, No. 3. Pp. 425-436.

Geertman, S. and Van Eck, J.R.R. 1995. GIS and models of accessibility potential:

An Application in Planning. International Journal of Geographical InformationSystems. Vol. 9. No. 1. Pp. 67–80.

Hagget, P., and Chorley, R. 1969. Network analysis in Geography. Edward Arnold.

Handy, S.L. and Niemeier, D.A. 1997. Measuring accessibility: an exploration ofissues and alternatives. Environment and planning A. Vol. 29. Pp. 1175-1194.

Hansen, W.G. 1959. How accessibility shapes land use. Journal of the AmericanInstitute of Planners. Vol. 25. Pp. 73-76. Reprinted with permission by Kraus

reprint corporation (1966).

Heanue, K., Menchkhoff, G., Peyrebrune, H. and Pisarski, A. 1995. Urban

mobility: An international perspective. Routes Roads Special 1. PIARC WorldAssociation.

Jensen, F.S. 1999. Pers.Com. Frank Søndergård Jensen, Danish Forest and Landscape

Research Institute. [email protected]. General description of the project supplying thedata is provided by Jensen, F.S. 1999. Forest recreation in Denmark from 1970s tothe 1990s. The Research Series, Nr. 26. Danish Forest and Landscape ResearchInstitute. Hørsholm kongevej 11, Dk-2970 Hørsholm. Denmark.

Johnston, R. J., Gregory, D., Pratt, G. and Watts, M. (eds.) 2000. The dictionaryof human geography, 4’th edition. Blackwell Publishers Ltd.

Koenig, J.G. 1980. Indicators of urban accessibility: Theory and application.Transportation 9. Pp 145-172.

Morris, J.M., Dumble, P.L. and Wigan, M.R., 1978. Accessibility indicators fortransport planning. Transport Research A. Vol. 13A. Pp. 91–109.

SAS, 1999. SAS users manual. Statistical Analysis Systems.

Skov-Petersen, H. 1998. GIS-analysis of barrier effect of larger traffic constructions.

GIS planet 1998. Lisbon.

Skov-Petersen, H. 2001. Indicators of accessibility and Mobility, with specialreference to recreational behaviour in the landscape. Forthcoming.

Stanners, D. and Bourdeau, P. (eds). 1995. Europe’s Environment – The DOBRISAssessment. European Environment Agency.

Vickerman, R.W. 1974. Accessibility, attraction, and potential: a review of someconcepts and their use in determining mobility.

estimation of distance-decay parameters - gis-based indicators of recreational accessibility

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