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Revista ingeniería de construcción

versión On-line ISSN 0718-5073

Rev. ing. constr. vol.26 no.2 Santiago ago. 2011 

Revista Ingeniería de Construcción Vol. 26 N°2, Agosto de 2011 PAG. 187 - 207


Gravity methods as a tool to calculate greenhouse gas emissions from road traffic in urban planning

Los métodos gravitacionales como herramienta para el cálculo de las emisiones de gases de efecto invernadero derivadas del tráfico rodado en la planificación urbana


Sergio Zubelzu Mínguez*1, Alfonso López Díaz*, Miguel Ángel Gutiérrez García*, Fernando Blanco Silva**

* Universidad Católica de Ávila. ESPAÑA.
** Universidad de Santiago de Compostela. ESPAÑA.

Dirección para Correspondencia


This paper proposes a methodology for estimating greenhouse gas emissions from road traffic. The method uses information about the cities and their growth estimates in order to model traffic by using a gravity model. These kind of mathematical models allow study the number of trips "originated in" or "destined for" a particular area and distribute them to calculate the greenhouse gases emissions from these trips. In this way the information regarding these emissions can be used in urban planning phase and preventive and compensatory measures can be included in these processes.

Keywords: Greenhouse gas, gravity model, urban design, urban planning, road traffic.


1. Introduction

Kyoto Protocol adoption (1997) imposed the need to compensating emissions of greenhouse gases (GHGs) generated in some sectors of activity commonly known as regulated sectors.

But beyond these sectors, there is growing interest in knowing and even in compensating the greenhouse gases generated in other areas, different than those ruled by Kyoto Protocol.

Some of these other areas is traffic, which can be considered as one of the most significant ones because of its horizontal character, its particular relationship with the entire economy and the aggregate magnitude of movements of which depends the daily functioning of the cities .

This importance of road traffic is justified for many reasons among which may be included those related to urban design. Nowadays dynamics of urban planning is oriented toward single-family building types, intensive in terms of the amount of land needed and, therefore, mostly dependent on private road traffic transport (Correa, 2010).

In this context, it would be useful to have a mechanism to know and to compensate GHG emissions due to road traffic in cities: The requirements for such mechanism and the objectives of this study are:

1. Propose a method to help identify the responsible for greenhouse gases emission so that the cost resulting from any compensation can be imputed to such part.
2. The method should be integrated at an early stage in which compensation of emissions is possible, at least theoretically, through urban design instruments.
3. The method should provide a useful mechanism in order to quantify the source of GHGs generation due to traffic.
4. Finally, it must provide comparable results with the actual data generation that can be measure once implemented urban developments.

In this paper we will propose a methodology for determining GHG emissions based on techniques of spatial distribution of traffic and provide solutions to the above limitations. To expose practical application of the proposed model it will be analyzed Villaluenga de La Sagra sample, a town of 3,000 inhabitants located in Toledo province (Spain), largely residential, strategically located in an environment of industrial cities and between two large cities that exert a strong effect attractor of movements generated in Villaluenga: Madrid (65 km) and Toledo (25 km).

2. Discusion and development

Problem Statement

Of the four goals outlined in the previous section, the first two have to do with the type of method and how to integrate it into the urban planning process.

Linking the model, the urban design process allows its alignment to the ex ante calculation (Intergovernmental Panel on Climate Change, 2003), resulting estimated GHG emissions.

Actual calculation of emissions must be made as ex post (Intergovernmental Panel on Climate Change, 2003) based on technical capacity and actual traffic measurements that allow the identification of the origin and destination of movements and contrast the veracity of the hypothesis calculation considered in the model.

The ex ante estimation allows the inclusion of correction mechanisms in the urban planning process by providing additional information that may also be included in the models of decision-making about urban design (Transportation Research Board, National Academy of Science, 2000): plot definition of roads, type and location of connection infrastructure, demand for public transportation systems, including concentration or spatial distribution of density or buildable areas, distribution of uses of land ...

The use of a mechanism ex ante guaranteeing regulation of the process by allowing possible inclusion of simple solutions to compensate emissions within urban design, for example, reservation of additional zones for green areas (potential sinks of GHGs) as a compensatory measure of the generated emissions.

Obviously, compensation of emissions could also be made purchasing certain types of emission allowances available on the market. For practical purposes, the difference between the acquisition of emision rights or the inclusion of additional areas for parks, should be compared in monetary terms based on the cost of acquiring such additional land to be incorporated as a filler to urban developments which compensation GHG is desired. However, the inclusion of additional areas as parks creates additional benefits (some of which are externalities of housing development) and it is easier to implement if seen as a burden to urbanization process and not as municipal taxation (or equivalent concept for rights adquisiton in any form).

Having well justified the advisability of an ex ante approach incorporated to the urban planning process, the third objective alluded to the method and its expected results in terms of the subsequent estimation of GHG emissions. A method must be used in order to quantify the traffic generation responsible for the referred gas emissions.

This method should also characterize the traffic generated by distributing it on each existing route within the municipality that is being studied. It should not be forgotten that in many cases movements generated in municipalities have a much larger level of influence than the local one, and that is why the method should be based on the assumption that traffic generated is drawn according to supra municipal variables.

Thus, for the definition of a method capable of meeting the above needs spatial distribution of traffic models are used. These models are a tool for studying generation and distribution of traffic, especially the road one, in the cities.

Within spatial distribution models, mathematical simple techniques allow to estimate from a theoretical point of view the way in which is distributed the amount of road traffic generated by a certain activity.

The last step is the transformation of simulation results of gravitational methods in terms of quantity of GHGs, a process which uses the generation rates considered for each type of transport.

3. Methodology

Focusing the study on gravitational method, this model assumes that the flow of movement between two zones i, j, called Nij,is directly proportional to traffic generation in the area of origin i and to the attraction of the destination zone j, and inversely with the cost of travel between the two areas (Willumsen, 1985):


Where gi represents the generation in area i, aj represents the attraction of the area j, and F(Cij) is called friction function, which introduces in the model the variable related to cost.

Maximum simplification of the previous model would be as follows:


In the above function variables are specified generically defined at a first moment as:

• Destination's appeal, since pjrepresents population in each of the possible target points, limiting thus the concept aj .

• Traffic generation gi depends on the activities that produce and must be specific for each of them.

• Role of friction in which represents the distance from origin to destination j, which takes a potential way in order to weight the distance factor. Potential a is called friction factor.

For practical purposes and operational issues the model usually is expressed by grouping variables that depend on destination rj making them independent from their dependent source gi:


Where rj often called partition coefficient.

The simplified version of the previous model has the advantage of simplicity, becoming easy to obtaining information regarding each variables involved: number of inhabitants of the different towns in the area of influence and distances to these populations.

However, this supposed advantage is translated into an evident loss of information that can make questionable the accuracy of results.

The first simplified variable which content may be extended is called partition coefficient. This factor includes the set of variables of which may depend the movements between the generating point and the different attraction areas (Ortúzar y Román, 2003).

Maximum simplification considers that the movements that are generated at the point being studied and directed toward other possible points of attraction are directly proportional to population of destination and inversely proportional to the distance between both points. In this paper the existence of movements between two points is assume as arising from one of the following three reasons:

• Personal reasons: the population variable is chosen as a measure of probability that the origin city dwellers have family relationships or affinity with population of destination.

• For work: the probability that a destination city dweller should move to another town to work will depend on the number of companies established at the destination town. For this reason we choose the number of companies that statistical sources consider established in each of the potential destination places.

• Commercial or recreational reasons: They are grouped into a category such movements because today many rural communities depend for their shopping and entertainment from superstores in supermarkets and hypermarkets that coexist with leisure facilities. To measure this justification of movements the number of commercial establishments located in each of the municipalities of destination are used.

Having defined the variables involved, it must be discussed how they combine in order to get the desired results. To define this aspect, it is assumed that labor based movements account 50% of the total while the personal and leisure ones represent respectively 25%.

Particular treatment method involves obtaining a weighted sum of many one of each of the variables:


Where Pj representa population of each one of possible destination populations, ej refers to total companies of each one of possible destination points and Cj aludes to total commercial places.

With respect to the counterweight to slow these reasons, it is maintain the dependence of distance between two points as the main variable that works against previous movements.

The above expression for the distribution coefficient rj provides information about attractiveness capacity of municipalities and surrounding areas of influence, so that to know flow (Nij) remains to know the number of movements generated in the origin zone i (gj). To define this generation each of origin urban municipality uses are taken into consideration, generating source coefficients. Under normal conditions these generation rates are based on empirical studies; for this work have been used frequently generation rates used in traffic studies of Madrid Community:

• Residential use: 0,46 motor vehicle trips per resident (assuming an average occupancy of 3 persons per household).
• Productive uses:
• Commercial: 0,04 trips/builded m2 (15% heavy vehicles);
• Industrial: 0,014 trips/builded m2 (80% heavy vehicles);
• Equipment: 0,016 trips/land m2 .

In areas already inhabited it is considered a movements generation rate of 2.4 trips per capita per day (typical value of the surrounding villages), 35% of which are made with heavy vehicles.

Once the generation is known for the correct quantification of GHGs should be considered modal distribution between transport alternatives. In this paper the distribution of movements is considered only between the alternatives of private vehicles and public buses, as there is no railway station nearby and, in this case, to access the train station one should get out the term by private vehicle.

Once known the number of movements generated and possible destinations of them it must be divided among the planned road network. This assumes that each homogeneous area of use provided by urban planning generates all its traffic from a centroid which is the starting point for defining each of the routes to be followed in order to access the destination points.

In normal conditions, this process is done by identifying supra-municipal roads through which one gets to each destination and distributing the rest in the interior roads until accessing those pathways according to the minimum travel distance to reach them.

In the present work it is extended the amount of information incorporated into the model and the process of distribution of traffic generated. So this issue is addressed in the following phases:

• Identification of all pathways that enable to reach each destination and delivery point based on the following percentages: highway, 70%; national highway, 20%; toll, 10%; others 10% (in case of not having available all the alternatives upon reaching a locality, traffic is divided between the existing ones maintaining proportional distributions above mentioned).

• For the determination of domestic routes followed until each one of the above ways, the minimum distance criteria is complemented with the least number of intersections, so it is assumed that part of movements choose the route with the minimum distance while the rest prefer to choose a tour that is expected to have less congestion even if it has a greater length.

There is an additional variable to consider in the model and is represented by domestic traffic. In municipalities as the one considered here the interior movements have much less importance than the exterior ones, and that is why the outer movements can be considered of an estimated of 5% of the traffic for each of the sections of the road network.

4. Results

The municipality of La Sagra Villaluenga is in Spain, north of the province of Toledo, in the region of La Sagra, a distance of 21 km to the province capital and 65 km from Madrid, the country capital .

It has a central urban residential core and 2.776 inhabitants and urbanization isolated to the south (called La Jerecita) which has 693 registered inhabitants.

Figure1. Localization of Villaluenga de la Sagra

Figure 2. Existing core population of Villaluenga de la Sagra

The process involves quantification of movements generated in the first place in existing urban areas by applying the rates set forth in the above methodology:

Table 1. Traffic generation in the current urban core

One should also estimate the amount of traffic generated in expected planned growth areas. The following image shows the plan of classification of future land considered by the municipality:

Figura 3. Growth expected for urban planning

The number of movements that will generate the growth expected are obtaines from proposed application rate traffic generation and urban parameters displayed on each of the sectors of land for development (see Table A.1 Anex 1).

Once you know the number of trips to be generated, the next step is to identify those points that can be target of such movements. To do this, select the most important cities and towns of the environment and which are located at such a distance that it allows the influence. Calculate the distribution of coefficients from the data of population and number of commercial companies and total (see Table A.2 Anex 1).

The friction factor used was 1.5 (typical value for medium-distance routes).

Once you know prior data you should performe distribution of flows between each of the possible roads. The first of the tasks is to identify the connection points with the different supra municipal ways that enable to reach the destinations places mentioned. They are:

• Highway A-42 Madrid-Toledo that allows connections to the urban core with north and south populations.
• National Highway N-401, ancient highway Madrid-Toledo, that allows connections only toward south.
• Highway CM-9050, connects the towns of the West from North Villaluenga de la Sagra.
• Highway TO-4511 connects with towns located at the East.
• Toll Highway AP-41 connects only with Madrid or Toledo.

These road infrastructure are seen in the picture below:

Figure 4. Present infrastructures in Villaluenga de la Sagra

In addition to the above infrastructure, the plan foresees a new internal road network to order the generated traffic. It is:

Figure 5. Internal road network and connections among municipalities

Once identified supra pathways, their possible connections, the next step is to allocate to each infrastructure the movements that from every sector of origin are directed toward each destination points, based on the percentages of use expected for each type of infrastructure referred to in methodology chapter (see Table A.3 in Annex 1).

For example, to reach Madrid from Villaluenga de La Sagra, 88% of movements will be made through A-42 and the remaining 12% done through AP-41, whereas in the case of Toledo, 89% will be done through A-42, 5.5% through N-401 and the remaining 5.5% by AP-41.

Then it must be distributed the distribution coefficient (rj) of each possible destinations based on the above percentages (the total ratio of these percentages are included in Table A.3 of Annex 1). The result of this distribution is included in Table A.4 in Annex 1.

For example, the distribution coefficient of Madrid is 37.52% (representing movements generated in one sector and aimed toward Madrid) is shared between A-42 (33.01% represents 88% of 37.52% and represents the portion of what will go to Madrid generated through A-42) and AP-41 (4.01% which happens to be 12% of 37.52% refered to the generated movements that will go to Madrid through AP-41).

In the case of Toledo the distribution coefficient turns out to be 6.11% which is distributed among A-42 (89% of 6.11%, representing a 5.44%), N-401 (5, 5% of 6.11% representing a 0.34%) and AP-41 (5.5% of 6.11% which is also 0.34%).

Once known the distribution coefficients specific for each of the possible access to each of the possible destination points, the next step is to determine the internal routes from each of the areas of generation until reaching each possible access.

To perform this step it is assumed that all the traffic generated by each of the zones is concentrated in its centroid. For example, from the industrial sector SO6 which traffic is generated at the centroid 1, must go through the sections 5 and 6 in order to access highway A-42, or sections 1, 2, 5 and 7 (or 1, 2, 3 and 4) to go to the Western municipalities through the highway CM-9050.

Figure 6. Example of traffic distribution sector SO6

The amount of traffic contributed by the sector to these two sections will be the amount of traffic generated by it (68.40 273.60 heavy and light vehicles) the proportional part that must access A-42 to reach each destination with possible access through this road (0.06% of movements - 68.40 and 273.60 - which will go toward Ajofrín, 0.11% to be directed towards Argés and so on for every possible destination):

This exercise should be performed for each urban growth area in order to obtain the total movement in each section of the road network. In the case study, the results are as follows:

Table 2. Total traffic network by number of road

Having defined the total movements for each one of the sections that form the different routes, it is calculated the GHG emissions attributable to road traffic (measured as tonnes of CO2 equivalent) of the total municipal area.

This should include use of emission factors that allow to translate units used by vehicles into tonnes of CO2 equivalent. The prime source of these emission factors are found in the publications of the IPCC (IPCC, 2006) including emission factors for different economic activities. In general, these emission factors are referenced to specific characteristics of fuels used and which result of complex practical implementation (calorific value of fuel used). This has motivated the development of documents which transform these factors indexed features best suitable to its practical use (length traveled by a vehicle). Among these initiatives is the work done by the Department for Environment, Food and Rural Affairs (DEFRA), United Kingdom, which factors have been used in this work and are included in the following table (DEFRA, 2009)

Table 3. GHG generation coefficients

It is assumed an average occupancy of buses of 12 people, an average load of heavy vehicles of 1.5 t and a 10% of tourism movements that are absorbed by existing bus lines that run a distance inside the distance term of 4 km.

The results of this calculation are seen in the following Table:

Table 4. GHG emissions by sections of road network

5. Conclusions

Under this perspective and with the methodology proposed, one can obtain data of the amount of GHGs attributable to road traffic within a municipality due to urban planning decisions. In the case of the municipality of Villaluenga de la Sagra, with the hypotheses considered, the planned road network and public transport alternatives provided, the total amount of GHGs attributable to road traffic would be of 16.8 tCO2 eq / day. This requires a development and a complete occupation of the planning schedule and a total of 16,000 inhabitants upon planning.

The proposed method requires the assumption of certain simplifying assumptions regarding several variables (especially the traffic generation rates for each use and the friction coefficient) to be focused in a single way depending on the location of the method.

But the main advantage of the proposed method lies in its ex ante and ease of integration into the urban planning process so that compensatory measures can be taken via incorporation of CO2 sinks, such as through the reserve in the planning of land for urban forest use thus avoiding the potential user to assume the expenditure required to compensate emissions.

The method also provides specific information on the roads network specifying the expected emissions for each way. This information can be included in the decisions planning models by adopting solutions that reduce emissions from conflicting sections and contribute to efficient and sustainable urban design.

6. Annex

Table A.1. Generation of traffic in planned urban development

Table A.2. Distribution coefficient of the surrounding municipalities

Tabla A.3. Infrastructure sharing between movements

Tabla A.4. Specializing distribution coefficients

7. References

Correa G. (2010), Transporte y Ciudad [versión electrónica]. Eure, 36 (107), 133-137.

DEFRA (2009), 2009 Guidelines to Defra/DECC's GHG Conversion Factors for Company Reporting. 30 de septiembre de 2009. Department of Energy and Climate Change (DECC), Department for Environment, Food and Rural Affairs (DEFRA).

Intergovernmental Panel on Climate Change (IPCC) (2003), Buendía L, Gytarsky M, Hiraishi T, Krug T, Kruger D, Penman J, Pipatti R, Miwa K, Ngara T, Tanabe K, Wagner F. Good Practice Guidance for Land Use, Land-Use Change and Forestry. Institute for Global Environmental Strategies

Intergovernmental Panel on Climate Change (IPCC) (2006), Buendía L., Eggelston S., Miwa K, Ngara T, Tanabe K. IPCC 2006, 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Institute for Global Environmental Strategies

Ortúzar J. y Román C. (2003), El problema de modelación de demanda desde una perspectiva desagregada: el caso del transporte [versión electrónica]. Eure, XXIX (88), 149-171.

Transportation Research Board, National Academy of Science (2000), Highway Capacity Manual

Willumsen L. (1985), Modelos simplificados de transporte urbano [versión electrónica]. Eure, XII (33), 49-64 World Resources Institute (2008), GHG Protocol tool for mobile combustión. Versión 2.0


Fecha de recepción: 01/ 02/ 2011, Fecha de aceptación: 20/ 06/ 2011.

Correa G. (2010), Transporte y Ciudad [versión electrónica]. Eure, 36 (107), 133-137.        [ Links ]

DEFRA (2009), 2009 Guidelines to Defra/DECC's GHG Conversion Factors for Company Reporting. 30 de septiembre de 2009. Department of Energy and Climate Change (DECC), Department for Environment, Food and Rural Affairs (DEFRA).         [ Links ]

Intergovernmental Panel on Climate Change (IPCC) (2003), Buendía L, Gytarsky M, Hiraishi T, Krug T, Kruger D, Penman J, Pipatti R, Miwa K, Ngara T, Tanabe K, Wagner F. Good Practice Guidance for Land Use, Land-Use Change and Forestry. Institute for Global Environmental Strategies        [ Links ]

Intergovernmental Panel on Climate Change (IPCC) (2006), Buendía L., Eggelston S., Miwa K, Ngara T, Tanabe K. IPCC 2006, 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Institute for Global Environmental Strategies         [ Links ]

Ortúzar J. y Román C. (2003), El problema de modelación de demanda desde una perspectiva desagregada: el caso del transporte [versión electrónica]. Eure, XXIX (88), 149-171.         [ Links ]

Transportation Research Board, National Academy of Science (2000), Highway Capacity Manual        [ Links ]

Willumsen L. (1985), Modelos simplificados de transporte urbano [versión electrónica]. Eure, XII (33), 49-64         [ Links ]

World Resources Institute (2008), GHG Protocol tool for mobile combustión. Versión 2.0        [ Links ]

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