Measuring the Accessibility of Public Transport: A Critical Comparison Between Methods in Helsinki
Appl. Spatial Analysis
Measuring the Accessibility of Public Transport: A Critical Comparison Between Methods in Helsinki
X. Albacete 0 1 2
D. Olaru 0 1 2
V. Paül 0 1 2
S. Biermann 0 1 2
0 Business School , Management and Organisations , University of Western Australia , P.O. Box M261, 6009 Perth, WA , Australia
1 Department of Environmental Sciences, Research Group of Environmental Informatics, University of Eastern Finland , P.O. Box 1627, FI-70211 Kuopio , Finland
2 School of Earth and Environment, Planning and Transport Research Centre (PATREC), University of Western Australia , P.O. Box M004, 6009 Perth, WA , Australia
This research compares two location-based methods of evaluating public transport accessibility and applies them in Helsinki. After discussing a series of methodological aspects, the authors calculate the Structural Accessibility Layer (SAL) public transport indicator and the Public Transport and Walking Accessibility Index (PTWAI) for a grid with 8,325 zones, comparable in size to the smallest census unit. Both methods are operational for urban planners and policy makers interested in a relatively straightforward way of quantifying the accessibility of sustainable transport modes such as public transport. The results display similar accessibility patterns when moving from larger to smaller isochrones (60 to 38 min). However, the findings are inconclusive between SAL and PTWAI: SAL (38 min) displays good accessibility by public transport (more than 94 % of the population living within two-thirds of the metropolitan area has very high and high access to public transport), but PTWAI indicates that 35 % of the population, primarily households with children (43 %), experience low and very low access. The contrasting results are mainly due to the derivation of the two indicators and have considerable implications for policy making. The findings of this research imply that PTWAI is preferable to planning assessments regarding public transport, given its relatively richer content. However, for multi-mode-based accessibility categorization, SAL appears more appropriate. It is the analyst's role to understand the objective and contents of each index and choose the tool fit for their purpose. Then, a judgement should be made on the trade-off between the
detail of the measures and results and the computational burden. Given the
sensitivity of the models to various input parameters and assumptions,
crossvalidation and replication are key for ascertaining the credibility and usefulness
of the models.
Promoting sustainable transport modes in urban areas (namely, walking, cycling
and public transport) has become a primary objective in urban policy making.
Projects such URBAN-LEDS
reflect global attention to this issue.
As a consequence of such interest, recent years have witnessed an explosion in the
number of methods developed for measuring accessibility, especially by
sustainable transport modes
(Bhat et al. 2002; Kwan et al. 2003; Murray and Wu 2003;
Halden et al. 2005; Páez et al. 2012)
. Measuring accessibility, in turn provides a
benchmark for the evaluation of future scenarios for urban populations
Wegener and Fürst 1999)
. For example,
Handy and Niemeier (1997)
methods for measuring accessibility, Geurs and Ritsema van Eck (2001) list 23
Halden et al. (2005)
present 19. However,
Mavoa et al. (2012)
there is no effective comparison among these methods. Similarly,
Curl et al.
point out the lack of performance-based assessments indicating the actual
usability of these various methods. Previous research includes limited examples of
comparisons between methods (e.g., qualitative reviews,
(Lei and Church 2010)
differences between normative and positive implementations of accessibility
indicators, (Páez et al. 2012); the effect of geographical context and scale,
1998; Kim and Kwan 2003)
, but to our knowledge, no research investigated
specific quantitative comparisons of different methods and measurements.
This article compares the Structural Accessibility Layer
(SAL – Silva 2008)
and the Public Transit and Walking Accessibility Index
(PTWAI - Mavoa et al.
methods for measuring accessibility. This is done by using a case study of
the Helsinki metropolitan area, chosen because of data availability and personal
knowledge of the area. This article is of interest for scholars, as it will help clarify
the impact of methodologies on evaluating public transport accessibility, assisting
policy makers gain a better understanding of the strengths and weaknesses of each
method in terms of their empirical use for urban planning and management.
Finally, this research compares methods in Helsinki, where no previous
comparison has been undertaken.
The remainder of this article is organized as follows: First, it reviews the
accessibility measures and their components (Section 2). Second, it examines
the two location-based methods of interest (Section 3) and their adaptation to
the context of Helsinki (Section 4). Finally, it discusses the suitability of the
methods for urban planners and policy makers to quantify accessibility of
sustainable transport modes (Section 5), as well as the contributions of the
case study results to the scientific debate involving use of accessibility methods
Reviewing Accessibility Measures
Researchers have defined accessibility variously as Bthe potential of opportunities for
(Hansen 1959, p.2)
, Bthe inherent characteristic (or advantage) of a place
with respect to overcoming some form of spatially operating source of friction (for
example, time and/or distance)^
(Ingram 1971, p.101)
and Bthe extent to which
landuse and transport systems enable (groups of) individuals to reach activities or
destinations by means of a (combination of) transport mode (s)^
(Geurs and van Wee 2004,
. The common element in these definitions is the ability Bto reach^, which
indicates that, basically, accessibility means people’s ability to get to or arrive at
destinations, services or opportunities by means of a movement or transport.
All accessibility measurements assess the connections between land-use and
transport in some form. Thus, accessibility measurement has been useful for evaluating how
this interrelation affects usage of travel modes, including sustainable transport such as
public transit, cycling, and walking
. Scholarly reviews classify
accessibility measurements and their components in several ways
(van Wee et al. 2001;
Halden et al. 2000, 2005)
Kwan et al. (2003)
indicate that the geographical access Bcan be conceived as an
attribute of either location (place accessibility) or individuals (personal accessibility)^
(p. 130), and can be evaluated at a global and local scale, embedding time or otherwise.
Geurs and van Wee (2004) summarise four types of accessibility measures. First,
infrastructure-based accessibility or proximity measures focus on times, congestion and
operating speed in the transport (road or rail) network (i.e., generalised cost to reach
activities). Second, utility-based accessibility indicators are measured at the individual
level, assuming that the users aim to maximize the benefit of their travel after accounting
for the cost
(Ben-Akiva and Lerman 1985)
. Therefore, they account for both user and
transport modal characteristics. Third, person-based measures focus on the availability of
the activities for a person within a given time, focusing on the individual freedom to
participate in activities under given conditions of time and transport
(see time-space prisms,
Hägerstrand 1970; Kim and Kwan 2003, or activity/action spaces, Axhausen 2007)
Finally, location-based (also known as zonal-level) accessibility measures account for the
spatial distribution of opportunities and the demand for them.
Páez et al. (2012)
provide an alternative view of the accessibility measures, particularly
how they are implemented, to address positive and normative analysis needs. They refer to
normative (prescriptive) measures reflecting how far it is reasonable to travel or how Bit
ought to be^, and to positive (descriptive) measures, based on experienced traveling
conditions. Regardless of the perspective, there are numerous ways to measure
accessibility, however all combine two components of accessibility: cost of reaching destinations and
the quality and quantity of opportunities available at those locations.
Curl et al. (2011)
, location-based accessibility measures are the most
commonly used, because they are easier to assess and communicate and are less data
hungry; thus, researchers typically deem them appropriate for informing and monitoring
the achievement of transport planning goals. Moreover, the other measures have some
limitations that are absent in location-based measures: infrastructure-based measures are
not sufficient for analysing the spatial distribution of opportunities, and utility-based and
person-based accessibility measures are costly in terms of data requirements and difficult
Location-based accessibility measures can be further divided into five types of
(Geurs and Ritsema van Eck 2001; Tillema et al. 2003; Geurs and van
: (1) distance approaches based on direct distance measurement
Bertolini et al. 2005; Curtis and Scheurer 2010; Ingram 1971)
; (2) contour
measures (Breheny 1978) based on opportunities that can be accessed within a
certain travel time, distance or cost
(e.g., O'Sullivan et al. 2000)
; (3) potential
, scaled by a deterrence function
Gutierrez and Gomez 1999
Kawabata and Shen 2006
); (4) measures
based on balancing factors of spatial interaction models (
Williams and Fotheringham 1984
Fotheringham and O'Kelly 1989
; and (5)
measures derived from time-space geograp
hy based on Hägerstrand’s (1970
(classified as person-based measure in Geurs and van Wee
(e.g.,; Miller 1991; Lovett et al. 2002)
In the current research, we follow Geurs and van Wee’s (2004) classification,
because they clearly break down the various components of accessibility (Table 1)
and use them to classify various methods of determining accessibility.
The transport component is based on the supply of infrastructure, demand for
passenger and freight transport, and characteristics of the resulting infrastructure
use; it is measured in terms of time, cost, effort and distance decay functions. The
land-use component is based on the spatial distribution of the supplied
destinations/opportunities and of the demand of activities and their characteristics.
The interaction between the supplied destinations and the demand forms the basis
of the competition measurements.
The scale of the area considered in the competition measures may have a strong
effect on the final results
(Goudie 2002; Páez and Scott 2005)
. The most commonly
recommended action is to have as much disaggregated spatial data as possible so that
the results are as detailed as possible
(Handy and Niemeier 1997)
The temporal component pertains to the Breachability^ of activities at different
times of day, weeks, seasons or years, and the times at which people participate in
Finally, the individual component is based on the needs, abilities and opportunities of
the citizens of interest
(Vlek and Steg 1996)
. In general, the individual component of
accessibility is incorporated into accessibility measures by stratifying the population
according to a selection of relevant characteristics. The more characteristics are
incorporated in the measure, the more precise the outcome of actual accessibility; however, more
characteristics require more data, and interpretation is more difficult. In addition, not all
components are directly considered in all types of activity-based measures (see Table 1).
For evaluation purposes, researchers have discussed the accessibility measurements
from two perspectives: objective and subjective. On the one hand, Geurs and van Wee
(2004) propose an objective evaluation, based on changes in the service level of the
transport modes, to assess demand and competition between opportunities and
adaptability to the individual needs, abilities and opportunities. The authors’ objective
evaluation follows the trend proposed by
et al. (2009)
Curl et al. (2011)
Aditjandra et al. (2013)
, who are not in favour of the
use of Boutcome indicators^ reflecting the behaviour of the population (e.g., current
travel times) because they are based on the population’s learning/adaptability to the
current network conditions.
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On the other hand,
Handy and Niemeier (1997)
Bertolini et al. (2005)
consider the subjective perception as a key element for the evaluation of
accessibility. They argue for the need to incorporate Bhow residents perceive and evaluate
(Handy and Niemeier 1997, p. 1176)
and Bthe uses and
perceptions of the residents, workers and visitors of an area^
(Bertolini et al. 2005, p.
. Páez et al. (2012) show that both positive and normative approaches have
their place and are useful to address specific needs: Bby helping to understand in a
positivistic way the current situation (e.g., identification of issues of possible
policy interest), or to design, given a desired (i.e., normative) outcome, policy
and planning interventions^ (p. 142).
The focus of the current paper is on location-based measures. They are the most
frequently used, because they can be calculated with data regularly collected by
urban and transport planning departments/organisations. The review is
highlighting a diversity of measures and approaches in measuring accessibility. Here we
compare two contour methods previously used in accessibility assessment for
public transport at the city level.
For the current analysis, two methods were selected for measuring accessibility:
SAL and PTWAI. The selection was based on four criteria: (1) both methods are
classified as location-based measures and presented using areas of similar access,
which means their outputs are comparable; (2) the methods have been applied to
evaluate the public transport accessibility in urban areas; (3) data required for
analysis could be acquired from different sources available for Helsinki (in
particular, HSL 2010; Jaakola et al.1 (2015); LIPAS 2013); and (4) the methods
have been developed sequentially (PTWAI takes the SAL as a reference). A third
method, LUPTAI, proposed by
Yigitcanlar et al. (2007)
was originally considered
to be additionally integrated in the current study since it is a multi-contour
measure and is aimed for measuring accessibility by public transport; however,
due to data limitations it was not included in this paper.
Sections 3.1 and 3.2 are describing the methods as originally developed, and
Section 3.3 how they were applied for Helsinki.
The Structural Accessibility Layer (SAL)
The SAL, proposed by
, Bassesses how urban structure constrains travel
(Silva and Pinho 2010, p. 2737)
. It includes the land-use and transport
components, but not the temporal and individual components. It includes two
accessibility measures, the diversity of activity index (DivAct) and a comparative accessibility
measure (accessibility cluster) for categorization. It is expected the duplet to offer a
better understanding of the land-use and transport conditions provided for mobility.
DivAct, based on the dissimilarity index proposed by
Cervero and Kockelman
, measures the number of activity types reachable within a given threshold time.
1 For calculation of travel time between cells, see Jaakola et al. (2015).
DivAct is calculated as the fraction of different services available in the area reached
within a certain threshold time (relation 1):.
X iActi* f i
X i f i
where i is the type of activity (out of a set of 18), Acti is a binary variable indicating
whether the activity i is accessible within the threshold time or otherwise, and fi their
potential frequency of use.
Its range from zero (no accessible activities within the set boundaries) to one (all
activities accessible within the threshold) shows how close residences are to a variety of
activities considering a certain travel mode or combination of modes.
The results of the DivAct are consequently used to derive a comparative
accessibility measure by travel mode. Three DivAct indices (for car C, public transport PT, and
non-motorised NM modes) are plotted on a benchmarking cube, where each axis is
divided into three categories, creating 27 classes, then amassed into nine accessibility
clusters. These clusters define the availability of transport modes for reaching desired
activities and their use simplifies the analysis by aggregating Bconditions favouring the
use of the same transport mode (or modes)^
(Silva and Pinho 2010, p. 2738)
Given the purpose of this study, we use here only DivAct for public transport,
therefore, it is expected that SAL’s capacity to categorize accessibility in 27 classes and
nine clusters is strongly under-used.
The comparative accessibility measure divides the DivAct index into three
categories, A, B, and C: the benchmark (class A of high access) is the cumulative value of the
potential use of opportunities/activity types not necessarily within walking distance
(e.g., universities, non-food shopping, most leisure activities); class B ranges from the
threshold values settled for class A in the upper limit to the value 0.50 in the lower
limit; finally class C ranges from 0.50 to 0. The accessibility classes are not mode
specific, but rather reflect the Bperception of the importance of activities in everyday
travel and of the use frequency of these activities^
(Silva and Pinho 2010, p. 2741)
thresholds are context specific, thus researchers may adopt other values better fitting
their case study. Figure 1 provides the workflow for the SAL and PTWAI calculations
undertaken in this study.
The Public Transport Walking Access Index (PTWAI)
The PTWAI is a measure used by
Mavoa et al. (2012)
to calculate accessibility for
public transport and walking in New Zealand (the other indicator being a transit
frequency index). The authors aimed to develop a tool for understanding public transit
accessibility (access to destinations via public transit and walking modes), which is
particularly important for encouraging mode shifts towards non-car travel. The PTWAI
includes land-use, transport and partially temporal components (using actual timetables
and an assumed waiting time). However, the individual component is not considered
(for comparison of accessibility components between the two methods, see Table 2).
In contrast with SAL, PTWAI is destination based. Each land cell is scored on
different services, based on how accessible they are. The range is 0 to 4, where 4
SAL (DivAct for PT only)
Service allocated within the furthest threshold 1, otherwise 0
Service allocated within the closest threshold 4
Service allocated within the second closest threshold 3
Service allocated within the third closest threshold 2
Service allocated within the furthest threshold 1
Service outside threshold 0
Average scores of the five domains
Weighted average of all services within the threshold
Average scores of services belonging to the same domain
Classification in five categories (very low to very high access)
represents the most proximal category (<10 min) where the services are located. For
example, if the closest primary school is accessible by public transport within 15 min
from an origin, the land cell receives a score of 3. If the closest tertiary institution is
reachable in 50 min by public transport, the score is 1 (Table 3). Then, PTWAI clusters
services and its final score is calculated in two steps: 1) average of scores between
services belonging to the same domain; and 2) sum of the scores between domains, as
shown in Fig. 1. This means that for each land cell PTWAI receives a value between 0
and 20, where 0 indicates a completely inaccessible parcel and 20 means highly
accessible (within an average travel time below 10 min). The results of PTWAI are
presented in five categories (very low to very high), each covering four points over the
0–20 range. In this sense, PTWAI could be indirectly considered a
potentialaccessibility measure, since the scoring of the services, based on the category of
isochrones, is similar to an indirect decay function.
Adjustment for Making the Methods Comparable
Original data for the study included a grid of 8,325 cells of 250×250 m covering the
metropolitan region of Helsinki. The size of the cells depended on the area having a
minimum of 10 residents per cell
(Statistics Finland 2012)
, and the presence of
(LIPAS 2013; Service Map online)
. The cell size is comparable to
Silva and Pinho’s (2010)
level of analysis, with an average census tract area of 6.25 ha,
but smaller than the mesh-block applied by Mavoa et al. 2012 (an average of 51 ha).
To make the methods comparable, some adaptations were required. For example, the
DivAct index for PT only was used in applying SAL, excluding car or non-motorised
transport. This was needed to ensure consistency of SAL with PTWAI, which considers
only access by the public transport system
(for a more detailed explanation, see Salonen
and Toivonen 2013)
. In this case study, both methods considered network-based access/
egress times to and from public transport, as well as timetable-based waiting and
transfer times. This is similar to Mavoa et al.’s (2012) approach to PTWAI, but distinct
, who simplified waiting at the stops to a generic 5-min interval and
the transfer to an equivalent to 100 m at maximum. Taking into account commuting
times occurring on the network (and the actual schedule of transit services) increases
the robustness of the methodology applied here and the results. As Lei and Church
(2010, p. 289) suggest, Btransit times can vary considerably over a network depending
upon schedules, transfer times, etc.; so using network distance as a proxy for time may
introduce considerable error^. Thus, we expect these measurements to yield sounder
In addition, both methods used a common set of 28 opportunities (everyday
destinations), combined into five domains: work/education, health, non-educational
social services, shopping, and recreational purposes. The education domain contains six
opportunities: universities and separated centres for preschool education, adult
education, vocational education, basic education and secondary education. The health
domain contains hospitals and health centres. The non-educational social services domain
contains eight opportunities: centres for youth hobby, substance abuse, children’s day
care, social assistance, disabled care, elderly services, child and family welfare and
employment care.2 The shopping domain contains only food shopping centres. Finally,
the recreational domain contains 11 opportunities: theatres, restaurants, parks, religious
buildings, museums, libraries, cultural facilities, morning and afternoon activities, sport
centres and children’s playgrounds
(Service Map of Helsinki & Espoo, 2014)
2 The non-educational social services substituted the financial domain
Mavoa et al. (2012)
proposed, because data for those services were not available.
Finally, two maximum threshold travel times were used in both models to compare
the methods (Table 3). The threshold time for SAL (38 min) was obtained from
previous travel surveys
(Salonen et al. 2014)
and represents the average trip time.
Salonen et al. (2013)
showed that at least 10 % of the population could reach
local urban facilities, such as libraries, by public transport within 6 min (including
walking, waiting and in-vehicle time). This may be explained by the short headways
and high-density urban facilities in certain areas of Helsinki.
Because PTWAI is reported in five levels of access, the final SAL accessibility level
was further refined and rescaled using five quantitative segments (index normalised to
value one): BVery High^ (index≥0.85); BHigh^ (0.65≤ index<0.85), BMedium^ (0.45≤
index<0.65), BLow^ (0.25 ≤ index<0.45) and BVery Low^ (index<0.25). As output of
the measurement, four maps were created: a. SAL (60 min); b. PTWAI (60 min); c.
SAL (38 min); and d. PTWAI (38 min), along with the differences between them.
PTWAI score is based on the averages of aggregate accessibility scores by domains.
Thusly, opportunities contained in domains with fewer opportunities are weighted more
in the final score than the opportunities within domains with more facilities..
Although adaptations were made, there is a fundamental difference between the two
methods: whereas SAL offers a binary score (0 or 1) for each transport mode (the
activity type is accessible within the threshold or not), PTWAI offers a more refined
score (from 0 to 4). Figure 2 displays graphically how DivAct and PTWAI accessibility
scores are derived. This difference should be acknowledged when comparing the
results from both methods, since SAL is a single contour measure, while PTWAI is a
Section 4 describes the empirical setting for the comparison of the two methods.
Data from multiple secondary sources was used for analysis: geo-referenced land-use
and transport data, census, and household travel survey indicators
2012; LIPAS 2013; HSL 2013)
The Helsinki Capital Region (HCR) is formed by the cities of Helsinki, Espoo,
Vantaa and Kauniainen; in practical terms, the cities are meant to be a functional region
with Helsinki as the main city. These four cities occupy 964 Km2 and are home to one
million residents (representing approximately 20 % of the Finnish population).
The transport network for commuting within the HCR is diverse. The region follows
a radial structure on train and tram infrastructure (Fig. 3), whose centre is at Helsinki
Central Station. However, the bus network follows a more transversal distribution, due
to the three ring roads (in yellow in Fig. 3) surrounding the HCR.
Public transport represents a key modal alternative in the Helsinki region, with a
share of 43 % of the total amount of trips. The number of trips by PT has increased to
355.5 million in 2013, and 80 % of the population owns a Travel Card or other public
3 One of the reviewers pointed out this aspect and generously offered an earlier version of Figure 2, which we
adapted and extended for this publication.
The 2013 distribution of public transport passengers indicates the dominance of bus
ridership (50.6 %), followed by heavy and light rail (17.8 % by metro; 15.9 % by tram;
15.1 % by commuter train) and 0.5 % by ferry.
To varying degrees, Helsinki’s residents use walking, cycling, car, PT and other
transport modes, depending on the purpose of travel and the modes available
between origins and destinations
(see HSL 2010)
. During working days, six
activities (home, work, school, shopping, leisure and work related) prevail. Table 4
shows that two-thirds of the trips are made from home for commuting, shopping and
The analysis includes three parts:
mapping of SAL and PTWAI accessibility measures and direct comparison (for
two different accessibility thresholds, 60 and 38 min);
analysis of the relationship between accessibility and socio-economic
summary/descriptive statistics of accessibility measures.
Comparing SAL and PTWAI
We obtained accessibility classes by aggregating the average scores of the domains in
the case of PTWAI (Table 3) and by normalizing the diversity of activities (DivAct)
level proportionally to the thresholds of the categories described in PTWAI. Although
similar input values were used and the application of the two methods had similar
objectives, different results were obtained, mainly due to the difference between
singlecontour and multi-contour characteristics of SAL and PTWAI.
The resulting accessibility classes were differently distributed between methods: the
SAL output resulted in more cells classified as very high accessibility levels than the
PTWAI analysis (see Figs 4 and 5). Most Helsinki areas have very high accessibility to
Adapted from HSL (2010, Fig. 27)
the five classes of destinations by public transport using SAL measures. Yet, only a
small part of Helsinki (the city centre) appears to have high access according to the
Moreover, the spatial distribution of the classes differed between the resulting maps.
In SAL (Fig. 4), the Bvery high^ accessibility class seems to be mainly located within
the ring roads, whereas when using PTWAI (Fig. 5), the same accessibility class
appears only in the CBD of Helsinki and in small areas surrounding the underground
stations located in Vantaa (east of Helsinki). The map is consistent with the population
density (see Fig. 6).
Figure 7 presents the map of differences between the SAL and PTWAI accessibility
values for easier interpretation.
The most populated areas have the highest PTWAI access, reflecting equitable,
wellthought-out planning decisions. There is also good access for the highest income zones
in the west but not in the east.
With very few exceptions (northwest suburbs, at the end of the train lines and the
southwest harbour), PTWAI accessibility is lower than SAL. The largest differences are for
the southwest area close to Espoo, an area of low density and socio-economic status.
When repeating the analysis using the proposed threshold time for SAL (38 min),
the accessibility categories for both methods dropped (Figs. 8 and 9), as expected.
The same spatial pattern of the accessibility categories remains as previously observed
for 60 min in Figs. 4 and 5, with a more pronounced border effect around the ring road
(Fig. 8) and train and underground stops (Fig. 9). A difference map (Fig. 10) is
provided for clearer visualisation of the areas under or overestimated
accessibility by the two methods.
Notably, whereas Fig. 7 shows that both methods produce the same results for the
central area of Helsinki, Fig. 10 suggests relative convergence of the two methods for
the suburban areas.
SAL, PTWAI, and Socio-Demographic Characteristics
A specific objective of this study has been to find how the metrics/methods
perform in identifying population groups that are less well catered by public
Table 5 profiles the five levels of accessibility zones based on socio-demographic
characteristics. The SAL indicator offers a more optimistic view of the accessibility
than the PTWAI indicator for both 60- and 38-min accessibility levels.
In terms of general accessibility, the results in Helsinki are comparable with Mavoa
et al.’s (2012) findings for the Auckland region: more than 80 % of the population and
more than 90 % of the families with children live in areas with medium-high public
transport. However, the urban population living in areas with lower accessibility is
younger (29–32 years), which suggests that some measures for inclusion are needed
(see Fig. 11).
PTWAI measures are more refined and the results appear more conservative,
with the 38-min isochrones indicating low and very low access for 35 % of the
population, primarily households with children (43 %). The SAL measures
indicate very high accessibility for > 77 % of the population and 72 % of the
households with children, whereas PTWAI display that most of the population
resides in medium to high access. The profiling of the areas also shows that
people living in areas of very high PTWAI access are older than in areas
identified as highly and very highly accessible by SAL. In addition, the
distribution of pensioners is distinct between the two sets of maps: whereas most
pensioners live in very high access areas, as identified by SAL, only a small
fraction of them are included in the residential areas of very high access with
PTWAI. This spatial distribution also contributes to the contrasting results for the
median income of the residents. Surprisingly, the highest median income seems to
appear for the residents living in medium and high SAL access areas, but
lowmedium PTWAI areas. The finding, along with the positive association between
average household age and income, may be indicative of the life-cycle stage of the
population group living in a certain area; with couples with children and senior
couples seeking higher access than young individuals and couples.
The dissimilar results between SAL and PTWAI 38 have considerable implications
for the usage of these methods for analysing the level of accessibility by public
transport. As it can be observed from Figs. 6 to 9, the resulting indexes from SAL
are overestimating the accessibility compared with the result index obtained from
PTWAI. In addition, the areas where both methods bring similar results correspond
only to the zones where there is a high density of services.
As Fig. 2 suggests, the single contour nature of SAL cannot be expected to
produce the same level of variation in the output as PTWAI. In order to minimise
the effects on the methodology, it is of special interest to compare the results
from PTWAI using 60 min as threshold time with SAL using 38 min as
threshold time. In this way, the binary effect of SAL is reduced when selecting
the minimum threshold time and the diversity in the results from PTWAI is
minimised by using the maximum threshold time (60 min). When looking at the
results presented in Table 5, the difference in the percentage of population and of
households with children remains substantial. SAL presents 77.92 % of the
population residing in very high accessibility index whereas in PTWAI is only
12.41 % of the population. A similar result is observed for the percentage of
households with children, while SAL presents 72.08 % of the households as
living in areas with very high accessibility index, in PTWAI it is on 6.91 % of
them living in areas of the same category. Overall, PTWAI (60 min) suggests
that the prevailing accessibility level is medium.
6 6 3 5 1
.83 .44 .90 .48 .91 .92 .46 .92 .22 .29
0 6 4 4 6 8 3 4 1 1
3 4 8
LA ou ith .90 .91 .15 .44 .18 .57 .02 .19 .0 2
S % H w 0 0 0 1 9 0 2 5 2 7
L d o
S % P
L re e
A v g
S A A
y L p
it A o
il S % P
e L a
d A re
y S % A
1 9 1
9 3 15 .72 .98 .45 .10 .05 .
.0 .1 . 2 4
0 0 0 0 9 0 1 2 1 8
0 9 6 4 0 9 0 9 0 8
2 7 1 7 4 2 3 8 4 2
2 0 1 4 3 4
.74 .53 .83 .58 .42 .41 .82 .64 .87 .88
0 4 3 4 1 6 2 4 1 2
SAL and PTWAI Distributions
To further compare the accessibility outcomes, we used the same categories for the
resulting accessibility index and plotted their frequencies (Fig. 12). As expected,
both methods show sensible changes in the outcome accessibility index when
modifying the threshold times. However, because of its derivation, SAL measure
displays a high negative skewness, with highest frequency of cells being in the
highest accessibility class. Alternatively, for the PTWAI, the distribution of
frequencies follows a more normal distribution, with a larger amount of cells with
low accessibility index. When reducing the threshold from 60 to 38 min, both
PTWAI and SAL distributions are less skewed and kurtotic, although SAL
remains negatively skewed.
The distributions presented in Fig. 12 support the discussion on how both methods
are calculated and applied. The multi-contour nature of PTWAI allows a finer level of
disaggregation of the measures prior to calculating the final index and the output
appears to follow a normal distribution of the final accessibility indexes. Conversely,
the single-contour nature of DivAct in SAL increases the dependency of the method on
the type of services included for the final index calculation and its distribution of the
final accessibility index tends to be shifted towards extreme values.
The aim of this study is to adapt, test and evaluate the policy implications of alternate
location-based accessibility measures for public transport for the case study of Helsinki
metro area. The current article compared two operational methods, SAL
(Mavoa et al. 2012)
, to assess their advantages and limitations and clarify
The methods were adapted to ensure direct comparability and improved by
considering traffic conditions instead of timetabled times. The analysis started with visualising
and quantifying the accessibility provided by the PT system and land-use in the
Helsinki metropolitan area (separate for SAL and PTWAI), then it compared the results
of the two methods.
The common spatial resolution, the set of opportunities and travel times of the two
methods allowed us to discard potential effects of those variables on the final results.
Our results suggest that accessibility calculated following PTWAI method show a more
normal distribution due to the multi-contour measure of the method, with maps clearly
showing areas with potential easy access to the public transport network; the results of
SAL method are more aggregated due to a single-contour measure of the method, and
as such the resulting maps are more homogeneous. When both methods used the same
threshold values (60 and 38 min), set of opportunities and combination of access to
different opportunities, the access measures, scoring components separately, offered
more detailed accessibility maps. As Geurs and van Wee (2004), p. 137 suggest, Bthe
interpretation can be much improved by estimating the separate influence of the
different components of accessibility^. This relevant difference explains the final
performance of the methods. PTWAI offers moderate estimations, whereas SAL
presents a more positive perspective of the city accessibility.
These results clearly reflect the original intention and derivation of the SAL and
PTWAI indicators, but the novice may ponder that either method should lead to the
same conclusions. The distinct insights challenge the user, question the robustness of
the findings and call for cross-validation. The differences in spatial distribution and
socio-demographics between the two methods suggest that these methodologies are
sensitive to inputs, space and time and they should be further explored. Given the
relevance and utility of accessibility measures to guide policy making in urban areas, to
promote more sustainable transport solutions, identify areas potentially disadvantaged/
excluded4 and observe the effects of future transport systems and land-use changes in
accessibility, it is key to develop, test and validate methodologies that can be easily
implemented in planning practices. Replication and cross-validation are indispensable
parts of a modelling toolkit that can lend support to the credibility of the approaches.
In terms of practical use, the findings can inform planning. Mode substitution
towards PT is likely to be more feasible in locations with high PTWAI. Attempts to
encourage mode substitution in locations with low PTWAI (in orange and red in Fig. 5,
the southeast and north areas of the HCR) are unlikely to be successful. Thus, the
PTWAI and SAL maps provide insights into locations where public transport
improvements could be prioritised to increase the overall accessibility of Helsinki’s population.
Limitations and Further Directions
This research adapted, applied, and compared two accessibility measures of public
transport accessibility in Helsinki. The findings of this research imply that PTWAI is
more suitable to planning assessments than the DivAct of SAL, given its relatively
richer content. However, it is worth mentioning that the original goal of SAL is not to
measure the accessibility by public transport, but to categorize accessibility by using
three types of transport modes. If more travel modes were included in the study, SAL
would work better than PTWAI. Additionally, in terms of computation, SAL requires
lighter proceeding work since the DivAct index for each transport mode depends only
4 Although the focus of the current research is sustainability, we acknowledge that a significant importance of
PT accessibility relates to equity issues.
on a single threshold; while in the case of PTWAI the calculation is not so
A major limitation of the analysis is that the transport component is applied
considering only the opportunities within the isochrones (threshold times) and giving
all of them the same relevance. Although
pointed out this shortcoming decades ago, the relatively simple
derivation of accessibility remains a major appeal for many jurisdictions. The PTWAI
method provides evidence that scoring the different time values allows a degree of
qualitative discrimination between destination cells. Nevertheless, the PTWAI method
does not completely overcome other important limitations in contour measures
regarding the allocation of the threshold levels for the isochrones categories, as well as the
need to assess the actual attraction of the opportunities in the area. This method may
lead to an overestimation of accessibility. Ideally, accessibility could be calculated at
the individual/household level.
The same principle applies to the land-use component. Whereas in SAL the
existence of a single opportunity within the threshold time increases the final DivAct index,
in PTWAI such diversity is indirectly scaled according to the score values given to the
different isochrones. Nevertheless, it is also true that PTWAI does not account for the
variation in access level provided by the same type of opportunities, because only the
highest valued isochrones that encompass the destination cell are considered in the final
accessibility score. Therefore, because both methods rely to a great extent on land-use
mix, in the cases where certain opportunities were spatially clustered and benefitted
from good public transport and walking connections, the final result from both methods
is expected to be similar.
Additionally, the additive nature of PTWAI conceals circumstances. When an area
presents high access to for example shopping, social, and recreational facilities; and
average access to education, health and financial services; the area scores equally to
another area where the situation is vice versa. Obviously, the combinations of services
meet distinct needs. The former location may be appealing for young couples, whereas
the latter may be highly sought by households with children. However, our PTWAI and
SAL results represent indices for a generic average individual/household with the same
needs, preferences and constraints.
This highlights the need for accessibility measures to account for the individual/
personal component, as recommended by
Kwan and Weber (2003)
and Curl et al.
(2011). Individual perception of accessibility
(Curl et al. 2011; Stanley and
, heterogeneity in individual circumstances
(Kwan and Weber 2003)
and soft barriers
(Hine and Mitchell 2001; Lucas 2006)
have been shown to have a
relevant role in accessibility.
Regarding the temporal component, we calculated the commuting time between
origins and opportunities for regular weekdays, at nonpeak hours, without including
congestion effects. This assumption that public transport services are available at the
same frequency as in the peak period and unaffected by car travel, is another limitation
of the study. However, data availability prevented further exploration of this aspect.
To effectively map the accessibility in a given transport and land-use system, policy
makers and urban planners should not limit themselves to single time values; rather,
they should test for potential access to destinations by public transport and walking
using a range of times/costs required to reach those opportunities, in this sense, the
multi-contour nature of PTWAI allowed certain disaggregation of the results. For urban
planners, the possibility of automation in building PTWAI maps would allow what-if
scenarios by modifying the land-use component within the existing transport system.
However, none of the methods should be used as an expression of actual accessibility
for citizens, because they do not consider relevant temporal and individual components.
Although this research indicates that PTWAI appears more detailed and sensitive to
landuse and transport changes when measuring accessibility with a single transport mode, further
progress is required to account for individual and temporal constraints for effective evaluation
of opportunities, to obtain a more fine-grained analysis of a population’s mobility needs.
To include the individual component (moving down in Table 1), urban planners and
policy makers could use individual surveys to evaluate whether the availability of the
travel mode alone is enough to persuade travellers to choose PT considering their
personal circumstances. Likewise, the methods compared in this paper did not take into
account trip-based measures, neglecting multi-purpose trips and trip chaining. Future
research comparing them may highlight substantial differences in the accessibility results.
Another limitation of our research is the spatial resolution we used. As
suggest, we disaggregated the data as much as possible; however,
perhaps an optimal resolution level would go further, considering the actual origins and
destinations of travellers. In any case, analysts must assess the optimal level of
disaggregation on a case-by-case basis, using the specific geographical setting and data
availability. Given that accessibility level within a cell does not vary, we argue that the
smaller the area the better; however, the topography and population/employment
density may indicate otherwise. If possible, a sensitivity analysis of the role of applying
various spatial data resolution levels (e.g., aggregating cells in larger geographical
units, using administrative boundaries) needs to be investigated.
Finally, more research is needed to compare contour-based accessibility methods to
assess those elements to be considered for further improvement of the methods. To this
end, potential research could be conducted on the comparison of the present methods
with the Land Use and Public Transport Accessibility Indexing Model
et al. 2007)
. In terms of application, it is the analyst’s role to choose the tool
fit-forpurpose. A judgement should be made on the trade-off between the detail of the
measures and results and the computational burden, for a given objective.
Acknowledgments This work was supported by the Rakennetun Ympäristön Tohtoriohjelma (RYM-TO)
[T20500/913615/RYM-TO]; Kunnallisalan Kehittämissäätiö (kaks.fi) and the Helsinki Metropolitan Region
Urban Research Program (KatuMetro). The authors thank the reviewers and the editor for their detailed
feedback and valuable insights, which have helped them to improve the manuscript and also to Mr. Andrew
Lo for the invaluable support.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International
License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and
reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were made.
Aditjandra , P. T. , Mulley , C. , & Nelson , J. D. ( 2013 ). The influence of neighbourhood design on travel behaviour: empirical evidence from north east England . Transport Policy , 26 , 54 - 65 .
Axhausen , K. W. ( 2007 ). Activity spaces, biographies, social networks and their welfare gains and externalities: some hypotheses and empirical results . Mobilities , 2 ( 1 ), 15 - 36 .
Badland , H. M. , Schofield , G. M. , Witten , K. , Schluter , P. J. , Mavoa , S. , Kearns , R. A. , Hinckson , E. A. , Oliver , M. , Kaiwai , H. , Jensen , V. G. , Ergler , C. , McGrath , L. , & McPhee , J. ( 2009 ). Understanding the relationship between activity and neighbourhoods (URBAN) study: research design and methodology . BMC Public Health , 9 , 224 .
Ben-Akiva , M. , & Lerman , S. R. ( 1979 ). Disaggregate travel and mobility choice models and measures of accessibility . In D. A. Hensher & P. R. Sopher (Eds.), Behavioural travel modelling (pp. 654 - 679 ). Andover: Croom Helm.
Ben-Akiva , M. , & Lerman , S. R. ( 1985 ). Discrete choice analyses: theory and application to travel demand . Cambridge: MIT Press.
Bertolini , L. , Clercq , F. , & Kapoen , L. ( 2005 ). Sustainable accessibility: a conceptual framework to integrate transport and land use plan-making Two test-applications in the Netherlands and a reflection on the way forward . Transport Policy , 12 , 207 - 220 .
Bhat , C. , Handy , S. , Kockelman , K. , Mahmassani , H. , Gopal , A. , Srour , I. , & Weston , L. 2002 , BDevelopment of an Urban Accessibility Index: Formulations, Aggregation, and Application^, Report 4938-4 University of Texas at Austin, http://www-dtp.cc.utexas.edu/research/ctr/pdf_reports/4938_4.pdf.
Breheny , M. J. ( 1978 ). The measurement of spatial opportunity in strategic planning . Regional Studies , 12 ( 4 ), 463 - 479 .
Cervero , R. , & Kockelman , K. ( 1997 ). Travel demand and the 3Ds: density diversity and design . Transportation Research Part D: Transport and Environment , 2 , 199 - 219 .
Curl , A. , Nelson , J. D. , & Anable , J. ( 2011 ). Does accessibility planning address what matters? a review of current practice and practitioner perspectives . Research in Transportation Business & Management, 2 , 3 - 11 .
Curtis , C. , & Scheurer , J. ( 2010 ). Planning for sustainable accessibility: developing tools to aid discussion and decision making . Progress in Planning , 74 , 31 - 41 .
Fotheringham , A. S. , & O'Kelly , M. E. ( 1989 ). Spatial interaction models: formulation and applications . Dordrecht: Kluwer Academic Press.
Geurs , K. T. , & van Wee , B. ( 2004 ). Accessibility evaluation of land-use and transport strategies: review and research directions . Journal of Transport Geography , 12 , 127 - 140 .
Geurs , K.T. & Ritsema van Eck , J.R. , ( 2001 ). BAccessibility measures: review and applications. Evaluation of accessibility impacts of land-use transportation scenarios, and related social and economic impact^ , RIVM Report 408505 006 edn, National Institute of Public Health and the Environment , Bilthoven, Netherlands.
Goudie , D. ( 2002 ). Zonal method for urban travel surveys: sustainability and sample distance from the CBD . Journal of Transport Geography , 10 , 287 - 301 .
Gutierrez , J. , & Gomez , G. ( 1999 ). The impact of orbit motorways on intra-metropolitan accessibility: the case of Madrid's M-40 . Journal of Transport Geography , 7 , 1 - 15 .
Hägerstrand , T. ( 1970 ). What about people in regional science? Papers in Regional Science , 4 ( 1 ), 6 - 21 .
Halden , D. , McGuigan , D. , Nisbet , A. & McKinnon , A. , ( 2000 ) BAccessibility: review of measuring techniques and their application^ , Scottish Executive
Halden , D. , Jones , P. , & Wixey , S. ( 2005 ). Accessibility analysis literature review . London: University of Westminster.
Handy , S. ( 2002 ). Travel behaviour-land use interactions: an overview and assessment of the research . In H. S. Mahmassani (Ed.), Perpetual motion (pp. 223 - 236 ). Oxford: Pergamon Press.
Handy , S. L. , & Niemeier , D. A. ( 1997 ). Measuring accessibility: an exploration of issues and alternatives . Environment and Planning A , 29 , 1175 - 1194 .
Hansen , W. G. ( 1959 ). How accessibility shapes land use . Journal of the American Institute of Planners , 25 ( 2 ), 73 - 76 .
Hine , J. , & Mitchell, F. ( 2001 ). Better for everyone? travel experiences and transport exclusion . Urban Studies , 38 ( 2 ), 319 - 332 .
HSL. ( 2010 ). Liikkumistottumukset Helsingin seudun työssäkäyntialueella vuonna 2008 . Helsinki: Edita Prima Oy.
HSL. ( 2013 ). Liikkumistottumukset Helsingin seudun työssäkäyntialueella vuonna 2013 . Helsinki: Edita Prima Oy.
ICLEI , U. , ( 2014 ) BUrban-LEDS^ , Available: http://urbanleds.iclei.org/ [ 2014 , 11 /16].
Ingram , D. R. ( 1971 ). The concept of accessibility: a search for an operational form . Regional Studies , 5 , 101 - 107 .
Jaakkola , T. , Tenkanen , H. , Toivonen , T. , ( 2015 ). BMetropAccess-Digiroad^, in MetropAccess: Helsingin metropolialueen moniulotteista saavutettavuutta tutkimassa , Toivonen et al., eds., Helsingin yliopiston Geotieteiden ja maantieteen laitoksen julkaisuja C8 .
Kawabata , M. , & Shen , Q. ( 2006 ). Job accessibility as an indicator of auto-oriented urban structure: a comparison of Boston and Los Angeles with Tokyo. Environment and Planning B: Planning and Design , 33 ( 1 ), 115 - 130 .
Kim , H.-M. , & Kwan , M.-P. ( 2003 ). Space-time accessibility measures: a geocomputational algorithm with a focus on the feasible opportunity set and possible activity duration . Journal of Geographical Systems , 5 , 71 - 91 .
Koenig , J. G. ( 1980 ). Indicators of urban accessibility: theory and application . Transportation , 9 ( 2 ), 145 - 172 .
Kwan , M. P. ( 1998 ). Space-time and integral measures of individual accessibility: a comparative analysis using a point-based framework . Geographical Analysis , 30 , 191 - 216 .
Kwan , M. , & Weber , J. ( 2003 ). Individual accessibility revisited: Implications for geographical analysis in the twenty-first century . Geographical Analysis , 34 ( 4 ), 341 - 353 .
Kwan , M.-P. , Murray , A. T. , O'Kelly , M. E. , & Tiefelsdorf , M. ( 2003 ). Recent advances in accessibility research: representation methodology and applications . Journal of Geographical Systems , 5 , 129 - 138 .
Lei , T. L. , & Church , R. L. ( 2010 ). Mapping transit-based access: integrating GIS, routes and schedules . International Journal of Geographical Information Science , 24 ( 2 ), 283 - 304 .
LIPAS. , ( 2013 ). Liikuntapaikat.fi [Homepage from the University of Jyväskylä], Available: http://lipas.cc. jyu. fi/lipas [ 2014 , 04 /07].
Lovett , A. , Haynes , R. , Sunnenberg , G. , & Gale , S. ( 2002 ). Car travel time and accessibility by bus to general practitioner services: a study using patient registers and GIS . Social Science & Medicine, 55 , 97 - 111 .
Lucas , K. ( 2006 ). Providing transport for social inclusion within a framework for environmental justice in the UK . Transportation Research Part A: Policy and Practice , 40 ( 10 ), 801 - 809 .
Mavoa , S. , Witten , K. , McCreanor , T. , & O'Sullivan , D. ( 2012 ). GIS based destination accessibility via public transit and walking in Auckland, New Zealand . Journal of Transport Geography , 20 ( 1 ), 15 - 22 .
Miller , H. J. ( 1991 ). Modelling accessibility using space-time prism concepts within geographical information systems . International Journal of Geographical Information Systems , 5 ( 3 ), 287 - 301 .
Murray , A. T. , & Wu , X. ( 2003 ). Accessibility tradeoffs in public transi planning . Journal of Geographical Information Systems , 5 ( 1 ), 93 - 107 .
O'Sullivan , D. , Morrison , A. , & Shearer , J. ( 2000 ). Using desktop GIS for the investigation of accessibility by public transport: an isochrone approach . International Journal of Geographical Information Science , 14 , 85 - 104 .
Páez , A. , & Scott , D. ( 2005 ). Spatial statistics for urban analysis: a review of techniques with examples . GeoJournal , 61 ( 1 ), 53 - 67 .
Páez , A. , Scott , D. M. , & Morency , C. ( 2012 ). Measuring accessibility: positive and normative implementations of various accessibility indicators . Journal of Transport Geography , 25 , 141 - 153 .
Salonen , M. , & Toivonen , T. ( 2013 ). Modelling travel time in urban networks: comparable measures for private car and public transport . Journal of Transport Geography , 31 , 143 - 153 .
Salonen , M. , Broberg , A. , Kyttä , M. , & Toivonen , T. ( 2014 ). Do suburban residents prefer time-wise optimal or sustainable travel modes? combining public participation GIS and multimodal travel time analysis for daily mobility research . Applied Geography , 53 , 438 - 448 .
Service Map of Helsinki, Espoo, ( 2014 ). Vantaa and Kaunainen, Homepage of Helsinki City, Available: http:// www.hel.fi/palvelukartta (03/12).
Silva , C. ( 2008 ). BComparative accessibility for mobility management . The structural accessibility layer^ , working paper, University of Oporto
Silva , C. , & Pinho , P. ( 2010 ). The Structural Accessibility Layer (SAL): revealing how urban structure constrains travel choice . Environment and Planning A , 42 ( 11 ), 2735 - 2752 .
Stanley , J. , & Vella-Brodrick , D. ( 2009 ). The usefulness of social exclusion to inform social policy in transport . Transport Policy , 16 ( 3 ), 90 - 96 .
Statistics Finland . ( 2012 ). BPopulation in 250 meter grid squares^, in Ruutuaineistot yhdyskuntarakenteen seurantaj'rjestelm'ss'(YKR) data set .
Tillema , T. , Van Wee , B. & Tom De , J. ( 2003 ). BRoad pricing from a geographical perspective: A literature review and implications for research into accessibility^ , European Regional Science Association, 43rd ERSA Congress, August 27 -30.
Van Wee , B. , Hagoort , M. , & Annema , J. A. ( 2001 ). Accessibility measures with competition . Journal of Transport Geography , 9 ( 3 ), 199 - 208 .
Vickerman , R. W. ( 1974 ). Accessibility attraction, and potential: a review of some concepts and their for determining mobility . Environment and Planning A , 6 , 675 - 691 .
Vlek , C. & Steg , L. ( 1996 ). BSocietal reasons, conditions and policy strategies for reducing the use of motor vehicles^, in Towards sustainable transportation , Vancouver, Canada, March 24 -27.
Wachs , M. ( 1978 ). Accessibility, Mobility and Travel Need , Croom Helm, London.
Wegener , M. & Fürst , F. ( 1999 ). Land-Use Transport Interaction: State of the Art, Institut für Raumplanung , Dortmund.
Williams , P.A. & Fotheringham , A. S. ( 1984 ). The calibration of spatial interaction models by maximum likelihood estimation with program SIMODEL, Geographic Monograph Series , vol. 7 , Department of Geography, Indiana University
Wilson , A. G. ( 1967 ). A statistical theory of spatial distribution models . Transportation Research , 1 , 253 - 269 .
Wilson , A. G. ( 1971 ). A family of spatial interaction models and associated developments . Environment and Planning , 1 , 1 - 32 .
Yigitcanlar , T. , Sipe , N. G. , Evans , R. , & Pitot , M. ( 2007 ). A GIS-based land use and public transport accessibility indexing model . Australian Planner , 44 ( 3 ), 30 - 37 .