Tomaž, Podobnikar Žiga, Kokalj Krištof, Oštir · abstraction of a real world that is a selected representation of space, time, or attributes. Models are therefore the inherent

Transport Research Arena Europe 2008, Ljubljana

Modelling the spatial parameters for dynamic road pricing

Tomaž, Podobnikar dr.

Scientific Research Centre SAZU

Ljubljana, Slovenia [email protected]

Vienna University of Technology

Vienna, Austria [email protected]

Žiga, Kokalj mr.



Krištof, Oštir dr.



Abstract

Road pricing is becoming increasingly important in regulating the scale of various and multidimensional road transport impacts on the environment. In a project performed recently five possible toll-collection parameters road infrastructure, vehicle, population/community, natural and cultural heritage, and other have been identified. Each of the parameters is consisting of several variables selected and evaluated according to the criteria of sustainable development (ecological, economical and social aspects), temporal variability, vehicle classification, and measurability and reliability of results. Many variables of dynamic road pricing are distinct spatial phenomena and can therefore be efficiently modelled within geographic information systems (GIS). The paper describes a GIS modelling example of spatial variables that can be included in the computation of external costs, suitable for a calculation of the dynamic toll. A simplified case study of a highway area in Slovenia focused on analytical operations (determination and modification of class borders, overlying, geometrical operations, visibility, and neighbourhood analyses) and methods of spatial interpolation for the determination of transport impact levels on the population/community road pricing variable. The results can help evaluate the feasibility of the dynamic road pricing methodology proposed on a national scale.

1. Introduction

Road transport impacts on the environment are various and multidimensional (Lah, 2002), and road pricing is becoming increasingly important in regulating their scale (Ricci and Rainer, 1999; Santos and others, 2000). New road pricing schemes have various aims, however, they are mostly proposed (on a country- or city-wide scale) to reduce traffic congestion (e.g. Great Britain, Barcelona, Shanghai and New York), provide a source of financing for improvement of transportation infrastructure and public transport (The Netherlands and Copenhagen), reduce environmental impacts (San Francisco) and protect cultural heritage (Rome). Of course, the objectives can also be a combination of expected outcomes (Commission for Integrated Transport, 2006).

Internal transport costs are based on the principle of expenditure repayment, considering only the immediate expenses for road infrastructure. The other, wider approach, is based on a theory of


external costs, that, apart from the costs of infrastructure, takes into account also indirect costs: road accidents, congestion costs, and environmental costs, such as for example local and global air pollution, excessive noise, damage to the landscape (including devaluated visual attraction), and social costs, e.g. health costs and indirect accident costs not covered by insurances (European Commission, 1995; 2001; 2005). Our study considered the second approach to be more appropriate for implementing a dynamic road pricing principle even though its full implementation is a distant, however a long-lasting, political decision.

The set of road transport impact factors on the environment can be analysed according to their relation to impacts. In this way we can distinguish between “pollutants” or characteristics that effect emissions (e.g. fuel consumption, vehicle type, noise, light pollution, road surface characteristics, traffic density), and characteristics that determine their influences (e.g. road planning, construction, management and maintenance, landscape vulnerability, population density and its characteristics, biodiversity, protected areas and cultural heritage proximity). Environment is reflected on in a broader sense, as a strong interlace of social and natural elements (Kulauzović and others, 2006). Impact factors have been classified into five possible toll-collection parameters, i.e. road infrastructure, vehicle, population/community, natural and cultural heritage, and other, consisting of several variables each. They have been selected and evaluated according to the criteria of sustainable development (ecological, economical and social aspects), temporal variability, vehicle classification, and measurability and reliability of results. Population/community road pricing factor, analytical operations and methods of spatial interpolation for the determination of transport impact levels are presented as a case study in the following chapters.

2. Introduction to the environmental modelling

The relation between the real world as a geographical reality or a physical environment and the data set can be schematically described as a relation between real world, data model, and data/information. The data model or nominal ground is a conceptualisation and representation or abstraction of a real world that is a selected representation of space, time, or attributes. Models are therefore the inherent complexity of reality (Burrough and others, 1998). From conceptual ideas of geographical phenomena, the representation of the space and its properties could be by entities (attributes and positions) or by fields presented by continuous mathematical functions (variation of attributes). Data are described by the type of spatial objects to which spatial variables refer and by the level of measurement of these variables. The entities are presented with vector data models while continuous fields are tessellated, basically regularly with square cells (raster or matrix). Different data sets or layers, e.g. road network, hydrological data, digital elevation model (DEM) or derived slope could be recorded to various data models. The data sets of entities/continuous fields denoting information of some quantities that are adopted and included into the data model are called spatial variables. Spatial analyses and modelling are used for manipulating spatial data to create new information, produce more complex models, or assign new meanings to data.

The most common spatial analyses include topologic and cartographic modelling, modelling of networks, automated cartography, map algebra and spatial statistics. Spatial analysis that build the models could be classified as descriptive, explanatory, predictive and normative (Chou, 1997), where descriptive analysis evaluate the data and their suitability for explanatory models that are goal of this study. The other approach to spatial modelling (Anselin, 2005) starts with exploratory analysis to find interesting patterns, continue with visualisation for showing the patterns and then with spatial modelling for explaining the patterns that is also part of the study procedure. As part of the modelling procedure other type of models could be involved, e.g.


regression, Boolean, empirical. Therefore spatial modelling combine different spatial analysis regarding of decision-making process and even more, the data (variables) and models could be part of environmental decision support system (Kanevski and others, 2004) for estimation of selected environmental phenomena, e.g. erosion, light pollution, noise diffusion.

A geographic information system (GIS) represents a suitable tool for the environmental modelling. It is a system and technology designed for creating, storing, updating, analysing, displaying, and managing (manipulating) spatial data and associated attributes (ESRI, 1997). GIS applications are common in business, government, research, the internet, etc. While it has been truly operational since mid 1960s, its usage has grown significantly since the 1980s. The strength of GIS lies in its ability to visualise and analyse spatial patterns (Tomlinson, 2003), as well as to allow exploration of more complex interactions between social and natural spaces.

In this study the primarily interest is to apply the raster-based methods on continuous surfaces, and on the spatial analysis – mostly on analytical operations of continuous surfaces (classifying and reclassifying, overlaying, geometrical operations, neighbourhood operations) and on spatial interpolations (deterministic and stochastic, global and local methods, etc.). Classifying is an operation for merging attributes to selected classes. Continuous values are classified to categorical. Reclassification is an operation where more classes are reclassified to fewer. It is usually used for converting nominal or ordinal values to a Boolean binary form. Overlaying is an analytical operation that combines two or more data sets to a new one on a same area. With overlaying, the data sets are compared by logical operations (Boolean algebra: AND, OR, NOT, etc.) on binary data sets, or processed by arithmetical operators +, –, ·, /, etc. and relational operators (>, =, etc.). Analytically important processing in GIS that is related with classification and overlaying operations is map algebra (Tomlin, 1990). Geometrical operations offer calculations of distances, areas, connections, directions, etc., for example Euclidean distances and surfaces, buffer zones, cost distances, Thiessen polygons, etc. Neighbourhood operations use windows of different sizes and forms (e.g. square window 3 x 3 cells) for calculation of slope, aspect, hill shading, visibility analysis, etc. This analysis is usually on a DEM as a data set. Methods of spatial interpolations create surfaces by using field data to determine locations of unknown values to fill up the (raster) area.

3. A case study of a population/community variable

All the disturbing means of transport are unacceptable from the view of sustainability. Efficiency of people, working in a peaceful and incentive environment is higher that of people, whose sleep is diminished by loud noise and enjoyment of free time in the open limited by noise and odour of exhaust fumes. On the other hand we cannot neglect the positive effects of good transportation connectivity. Economic benefits are the most obvious; however it also encourages easier and faster social interactions and increases the accessibility of tourist centres and recreational areas. It is therefore essential to consider the impact of transport on communities already in the planning phase and also to bear in mind its inclusion in the road pricing scheme. Road pricing policy should strive for a temporarily balanced transport. Road toll can be regarded dynamic according to the time of day, week and season, depending on the impact of transport on the population living near the road infrastructure. Similar tolling differentiation is possible in relation to the duration of impacts. Influences on the human health can be divided into acute and chronic. The first originate from exposure to short term high concentrations of harmful substances, while the latter from exposure to lower concentrations but over a longer period. Because most of the impacts are space related they can be modelled by GIS. Variables that can be used for modelling can include concentrations of CO, SO2, NOx, O3, noise level, population


density, road proximity, and obstacles for spreading, such as terrain morphology or sound barriers.

The case study area analysed in the presented study is part of Dolenjska region, east of Ljubljana, Slovenia, with the area of 24 x 12 km (Figure 1). The data selected for modelling were DEM 25, highway network and buildings cadastre (© 2005, Surveying and Mapping Authority RS). All data sets were resampled to a 25 m grid for the raster data analysis. As the exact population data were not available we have considered a uniform number of people per building.

Figure 1. Study area of 24 x 12 km with highway lines (red), buildings (green).

The case study is a simplified prototype where criteria are determined according to transport impact levels on the population road pricing parameters, experiences and understanding of the problem, and availability of data.

The model P of toll-collection considering population distribution along the highways (population/community factor) was calculated with empirical formula

2P CBA +−= (Eq. 1)

where the following descriptive criteria as the influence to the population were considered according to the course of highways:

• )( ApfA = , positive for the population pA at a distance dA off the highway in interval dA > 100 m,

• )( BpfB = , negative for population pB at a distance dB off the highway in interval 0 m < dB < 100 m, and

• )( CpfC = , negative for population pC at a distance dC off the highway if exposed to a noise ∈n 0, 1 in interval 0 m < dC < 1000 m, n = 1.

For modelling of P in Eq. 1 the weights of criteria were simplified, therefore a positive criterion A has the same weight as negative B and C together. The values that present population of the criteria were normalised to the integer values in interval [0, 100] and therefore the model P contains values within the same interval.


Criterion A Criterion B Criterion C

Figure 2. Detailed presentation of the population variable (in an area of 5800 x 4800 m). Density of population is calculated for the green or yellow dots selected through criteria A, B and C. Black dots were not considered for calculation. For the C, population within the buffer that is not exposed to noise is presented with blue dots. Highways are represented with red lines.

The buffer zones as distances dA, dB, dC were calculated in a vector form with geometrical operations, as well as the areas exposed to a noise n. The area of population for criterion C was selected by logical operation dC AND n. Population density was calculated with spatial interpolation – calculating density with appropriate different kernel functions (Figure 2). The calculation of noise was substituted by visibility analysis as a neighbourhood operation. The visibility was calculated from every grid point on the highway course. We considered that the source of the noise is 3 m above the highway and that the targets (people in the buildings) are 7 m above the ground. Surface of the noise was produced by overlaying of the all binary data sets of visibility (Figure 3), and the influence was reselected to areas exposed to noise n = 1.

Figure 3. Visualisation of the criterion C (similarly as in the Figure 2). The red areas within

the selected buffer are the most exposed to noise, while greys are not exposed at all.

The continuous surface of the model P (population/community variable) presents positive and negative influences of the selected highway to population. This model presents the amount of expense that might be relocated in between the population – in a wider context; people on the red areas (bad conditions) might receive some amount from the toll budget, while people on the blue areas might not. The values from P were assigned as weights for toll calculation in the every


highway segment of 25 m length with reclassifying and overlaying operations. On the red segments the toll-collection input is higher than on the blue ones (Figure 4).

Figure 4. Detailed presentation of the model P with distribution of population, where red

patches are distinctive negative influences of highways to residence and blue distinctive positive (left). The P is assigned to highways’ segments with weights for toll-collection input (right).

4. Conclusion

The study has shown that dynamic road pricing parameters can be successfully modelled within GIS. We have tested a simple population/community variable model and have shown that the influence of traffic is spatially very heterogeneous. There are some issues that will have to be addressed in more detail in the future. First, it is critical to obtain, collect, and process appropriate spatial data. Second, suitable (basic and advanced) models have to be proposed and standardised. The main problems lie in the determination of weights. In the presented case study weights were selected empirically as most of them are missing for GIS-based modelling. The determination of weights’ suitability and their relations demand additional analyses including decision-making procedures. A thorough study of factors and parameters is therefore essential, backed by a sound toll regulation policy. Balancing the weights will be a pretentious work, especially because of demanding on-the-field measurements supported by contemporary information technology.

5. References

1. Anselin, L. (2005). Mapping and Geovisualization (ACE 592SA – Spatial Analysis), University of Illinois, Urbana – Champaign.

2. Burrough, P. and McDonnell, R. (1998). Principles of Geographical Information Systems, University Press, Oxford.

3. Commission for Integrated Transport (2006). World Review of Road Pricing. Phase 2. Case Studies.

4. European Commission (1995). Green paper – Towards fair and efficient pricing in transport. Policy options for internalising the external costs of transport in the European Union. European Commission, Brussels.


5. European Commission (2001). White paper – European transport policy for 2010. Time to decide. European Commission, Brussels.

6. European Commission (2005). Amending Directive 1999/62/EC on the charging of heavy goods vehicles for the use of certain infrastructures. Recommendations for European Parliament Second Reading.

7. Chou, Y.-H. (1997). Exploring Spatial Analysis in Geographic Information Systems, OnWord Press, Santa Fe.

8. ESRI (1997). Understanding GIS, The ARC/INFO method, John Wiley & Sons, Redlands. 9. Kanevski, M. and Maignan, M. (2004). Analysis and Modelling of Spatial Environmental

Data, EPFL Press, Lausanne.

10. Kulauzović, B., Brozovič, R., Štrukelj, D., Kolšek, V., Žnidarič A., Leban, B., Kokot, D., Lavrič, I., Ramšak, M., Oštir, K., Podobnikar T., Kokalj, Ž. 2006. Priprava izhodišč za izdelavo metodologije dinamičnega cestninjenja z upoštevanjem vidikov trajnostnega razvoja. Ministry of Transport, Ljubljana.

11. Lah, A. (ed.). (2002). Promet in okolje. Svet za varstvo okolja Republike Slovenije, Ljubljana.

12. Ricci, A., Rainer, F. (1999). Calculating transport environmental costs. Final report of the expert advisors to the High level group on infrastructure charging (Working group 2).

13. Santos, G., Rojey, L., Newbery, D. (2000). The environmental benefits from road pricing. University of Cambridge, Department of Applied Economics, Cambridge, www.econ.cam.ac.uk/dae/repec/cam/pdf/wp0020.pdf.

14. Tomlin, C.D. (1990). Geographic Information Systems and Cartographic Modelling, Prentice Hall, Englewood Cliffs, New Jersey.

15. Tomlinson, R.F. (2003). Thinking About GIS: Geographic Information System Planning for Managers, ESRI Press, Redlands.

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Tomaž, Podobnikar Žiga, Kokalj Krištof, Oštir · abstraction of a real world that is a selected representation of space, time, or attributes. Models are therefore the inherent