MATHEMATICAL MODELLING OF THE HIGHWAY INFLUENCE TO AIR POLLUTION MATHEMATICAL MODELLING OF THE HIGHWAY INFLUENCE TO AIR POLLUTION

Negatívny vplyv dopravy na znečistenie ovzdušia je všeobecne známy. Doprava v mestách prispieva k znečisteniu ovzdušia viac ako 50 %, v centrálnych častiach miest viac ako 70 % [5]. Riešenie problému rastúcej hustoty dopravy si vyžaduje výstavbu nových ciest, hlavne diaľnic. Je potrebné si zodpovedať na otázku, či diaľnice riešia tiež problém negatívneho vplyvu dopravy na znečistenie ovzdušia. Výstavba diaľnice neznižuje počet áut prechádzajúcich daným miestom. Skôr tento počet zvyšuje, pretože diaľnice priťahujú veľký počet vodičov motorových vozidiel, ktorí by ináč použili inú dopravnú komunikáciu. Diaľnice zvyšujú priemernú rýchlosť dopravného prúdu. Preto spotreba paliva narastá, čo spôsobuje nárast emisie hlavných znečisťujúcich látok, ktoré produkuje doprava: NOx – suma oxidov dusíka, CO – oxid uhoľnatý, VOC – prchavé organické zlúčeniny.


Introduction
The negative effect of traffic to air pollution is generally well known. The traffic in cities contributes to more than 50 percent of air pollution and in the central part of cities more than 70 percent [5]. The solution of the increasing traffic density problem demands construction of new roads, mainly highways. It is also necessary to answer the question if highways solve the problem of negative influence of traffic to air pollution. Building highways does not bring down the number of cars that pass through a given place. It sooner raises this number because highways attract more drivers that would otherwise use another route. Highways increase the average speed of the traffic stream. Therefore, fuel consumption increases and results is increasing emission of the main harmful substances produced by traffic: NO x -the sum of nitrogen oxides; CO -carbon monoxide and VOC -volatile organic compounds.
By the projecting of highways it is necessary to take into consideration that the negative influence of highways affects the smallest number of people. Construction of highways out of city living parts is not possible. It is important that the highway could run in such a way, that in the zone, where the concentrations of NO x and CO exceed the short-term imission standards, the number of the permanent living inhabitants was minimalized. The emission of carbon monoxide by highway traffic is approximately fourtimes higher than the emission of nitrogen oxides but the imission standard is 50 times higher, e.g. CO is 50 times less toxic then NO x . Therefore, it is comprehensible that the negative influence of the highway should be judged according to the NO x concentration, and the width of the protective zone round the highway should be determined by the isoline 200 g.m Ϫ3 NO x concentration. The distribution of NO x , CO and VOC concentration is calculated on Prezentácia metodiky výpočtu automobilového znečistenia ovzdušia a jej modifikácie pre výpočet distribúcie koncentrácie hlavných zložiek spaľovania paliva okolo diaľnice je jeden z cieľov tohto članku.
One of the purposes of this paper is to present air pollution calculation methodology from car traffic and its modification for calculation of concentration distribution of the fuel combustion main products around the highways.

Methodology of air pollution calculation from car traffic
In the first approximation a street may be taken as a line source of pollutants. The dispersion of pollutants from a line source is described by the stationary, two-dimensional equation of turbulent diffusion: Street may be imagined as a canyon enclosed from either one or both sides by the buildings. For this type of street the limiting conditions will be where C -is the pollutant concentration in mg.m Ϫ3 , K x , K z -components of diffusion coefficient in the corresponding direction in m 2 .s Ϫ1 , U -the wind speed in m.s Ϫ1 , h -the height of the built-up area in m, H -the altitude of the mixed layer in m, S -the width of the street canyon in m, Q -the specific emission of the road in mg.m Ϫ2 .s Ϫ1 , -the coefficient of the pollutant passage through the walls of the built-up area in m.s Ϫ1 .
The first limiting condition simulates the reflection and passage of pollutants through the walls of built-up area. We can express the coefficient by the relation where ⌬ x is the width of the footway on the both sides of the road. PR ϭ 1 for continual built-up area PR ϭ 0 for the road out from built-up area.
The second and third limiting condition express the pollutant production over the road as well as the perfect reflection of the pollutant on the ground surface and on the upper level of the mixed layer.
Ďalší vývoj dopravy je neoddeliteľne spojený s otázkami hodnôt životného štýlu, spôsobu života a hospodárstva. Treba si uvedomiť, že doprava ovplyvňuje životné prostredie kladným aj záporným spôsobom: G pozitívne tým, že účelným premiestňovaním osôb a tovaru zabezpečuje potreby spoločnosti a výkon niektorých služieb i výrazne prispieva k rastu turizmu, The limiting problem (1), (1a) was solved numerically by the method of finite differences. This is an implicit method and thus unconditionally stable. It consists of fact that instead of functions of continuous arguments, the functions of discrete arguments are considered, and their values are given in the grid points. The calculation domain is constructed so, that the whole canyon is divided in horizontal direction into the three columns of the boxes. The calculated pollutant concentration in a grid point presents the mean pollutant concentration in this box, in the centre of which the grid point is situated.
The mean pollutant concentration in a given box will depend on the dimension of the box. The width of the highway is not always possible to calculate from the number of the lanes. For that reason the width of the calculated section of highway is given interactively through the screen.
The distance of a chosen isoline of pollutant concentration from the highway depends on the wind direction. This distance is maximal when the wind direction is perpendicular to the axis of the highway. For this reason the distance from the highway is calculated, in which NOx concentration achieves the value of 200 g.m Ϫ3 (short-term imission standard for NO x ). The whole amount of pollutants NO x , CO and VOC emitted by the existing road traffic during some time interval, usually during one year, is also calculated.
The relation calculates specific emission of the road Q from the number of the passenger cars and duty vehicles (POS and PNAK), which passed the highway in the averaging time of the pollutant concentration T (0.5 h, 24 h) Specific emissions EOS and ENAK depend on the technical level of the cars. In present time the specific emission given in the Table 2 are used in calculations.

Transport
The transport sector is one of the main energy and environmental problems, because it is part of the biggest consumption of petrified energy sources and is responsible for essential affect to environment. This opinion results from the "Transport in quickly changing variable Europe" report, processing by "Transport 2000 plus" of European community [1].
Future evolution of traffic is inseparably connected with environment values questions, manner of life (modus vivendi) and economy. It is necessary to sense that the traffic is influencing the environment positively and negatively, too: G Positive effect of traffic is providing for society needs and performance of some services by effective transportation of persons, goods, and traffic also goes towards the rise of tourism.
Posudzované sú množstvá nasledujúcich znečisťujúcich látok: G CO oxid uhoľnatý, G NO x oxidy dusíka, G VOC uhľovodíky. G Negative effect of traffic has long-term impact of nonrevivable natural source consumption part, by the instrumentally of short -term impact to surroundings and humans.
The most significant effects of car traffic to environment with the impact to the population's health are noise and imissions. Therefore, they take a substantial place in Environmental Impact Assessment methodology -EIA.
Air pollution, one of the immediate impacts of traffic on its surroundings, is mainly a result of moving cars, motors operation, but also by whirling of sedimentary dust elements on the road and in its surroundings, and by individual car part abrasions, for example, brake lining, tires, etc. Therefore, the imission study should be part of road design documentation up to the mark of variant decision by the appropriate location choice. In order to fulfil its aim, it ought to include the modelling of gaseous emissions production from car traffic in such a proportion that it will be possible to compare different variants of the route.

Imission study
In imission study there should be imission creation arbitration from: G actual traffic on the existing network of roads in regarding area, G forecast traffic on the existing network of roads in regarding area, provided that the redesigned road will not be realised, called zero variant, G forecast traffic on the redesigned road in regarding area, G residual traffic on the existing network of roads in regarding area, provided that redesigned road will be realised, G suggestion of arrangements for air pollution reduction, G suggestion of air monitoring.
Imission study drafted in this way can be the foundation for the environmental impact assessment process according to the Law NR SR č. 127/94 Z. z. [2].
With the exploitation of described computing program, which deliberates all determining factors influencing the gaseous emissions production, it is possible to simulate air pollution of the road surroundings.
Input information for modelling: G emission factors for actual and future vehicle stock, G traffic volume and its composition by the type of vehicles, G longitudinal gradient of road, G urban and eventually suburban treatment of traffic, G speed of vehicle drive, G atmospheric conditions. Following pollutants are appreciated: G CO carbon oxide, G NO x nitrogen oxides, G VOC volatile organic compounds.

Outputs:
G diffusion in open atmosphere -CO, NO x , VOC concentrations, -total year production, -max. concentration in atmosphere from highest traffic, G frontier of the limit excess 200 g.m Ϫ3 NO x distance from the road axis.

Principles of the air pollution evaluating
Nitrogen oxides -NO x -belong to deleterious substances, which is representative one of the most momentous element of exhaust gas by contemporary petrol structure. Because they reach the highest harmful pollutant concentrations, they are identifiable by monitoring or calculation and have the strictest limits. Hence, they use a similar indicator of air pollution by exhaust gas.
In imission studies air pollution is appreciated according to the total production emissions quantity from the car traffic in t.year Ϫ1 , moreover the max. NO x concentration in air in breathing zone (1,5 m over the pavement surface) is pursuing from 1/2 hour peak value of the traffic and the input is the quantum of inhabitants stricken by air pollution over the allowable imission standard.

Specific emission of the cars in Slovakia
Tab. 2 Total amount production of deleterious substances is influenced mainly by intensity and structure of the traffic flow (rate of heavy vehicles), length of the route and the longitudinal gradient and intensity of the road. Thus, by longer distance of the road, more deleterious substances are produced in the air.
Maximal deleterious substances concentration in the air depends on the traffic flow intensity and structure, oblong gradient

Modelling of air pollution from planned highway construction
G Figure 2 presents a rise of traffic between years 2005 and 2035, when by the constructing of highways it can come to considerable decline of the rest of traffic at the same time. G Table 3 presents the total summary value of emissions production in air from the summary of traffic on all streets for zero variant and the comparison for contact of highway D1 and residual traffic on actual roads.
The difference is noticeable since year 2015, where the variants V1a and V7 appear most favourable.
From tables 4 and 5 it is evident that the growing up of traffic to double is predicted, but by constructing highways, total production of emissions in year 2035 will rise only about 5 percent. That is induced by the fact that the model solution takes the cutting edge out from the enforcement of Slovak edict 248/91, which is the  Pri porovnávaní stavu pre rok 2035 najnižšie hodnoty akumulovanej koncentrácie sa predpokladajú pre variant V1a, ktoré by boli na ceste I/61 nižšie ako pri nultom variante.

Záver
Účinky emisií vznikajúcich od dopravy sú v konkrétnych územiach veľmi závažné a podiel dopravných prostriedkov ako ich pôvodcov je na územie nerovnomerne rozptýlený. Riešenie tohto problému môže mať efekt len vtedy, ak bude mať celosvetový charakter. Medzinárodné dohody, rozsiahla a cieľavedomá spolupráca continuation of EHK statutes and from this fact results the assumption of vehicle stock modification and the reduction of exhausters value at automobiles past year 2010 approximately to 40 percent by NO x , to 50 percent by CO, VOC and to 75 percent by solid elements in comparison with year 1995. G Figure 4 presents expected layers of short-term NO x concentration of peak half-hour traffic by value 6 percent regarding total traffic intensity.
Change of drive by itself from discontinuous city mode to smooth highway mode induces the decline of NO x concentration. Variant V1a predicts minimal values, and variant V2 maximal values. G Maximal short-term concentrations are accumulated in places where the route of highway converge to the route of existing communication at 220 m distance, because the area of interference with the hygienic limit is overrun, specified for short-term NO x concentration in the air -200 g/m 3 . The indications are present in figures 4 and 5.
By the comparison of status considering year 2035, the lowest accumulated concentration values are predicted for variant V1a, which could have been lower on the road I/61 than by zero variant.
From the results documented in this way according to emission production model from traffic in several items by regarding total emission production as well as by regarding accumulated values (sum D1 and residual traffic on actual roads) of short-term NO x concentration, variant V1 appears more favourable.

Conclusions
Impacts of traffic emissions in given areas are very momentous and the ratio of vehicles and their generators is unevenly dispersed. The solution of this problem can be effective only when its character will be worldwide. International conventions, extensive and systematic co-operation and realisation of agreements give the Už teraz sú jasné predstavy riešenia zaťaženia životného prostredia osobnými automobilmi. Postupné celosvetové zavedenie automobilov so zdvihovým objemom motora 3000 cm 3 (počíta sa s obnovou vozidlového parku v rokoch 2000 až 2005) sa prejaví nielen v relatívnej úspore pohonných látok, ale aj v relatívnom poklese produkcie emisií.
The conceptions of solution an environmental loading with vehicles are evident already. Consecutive worldwide applications of the so-called three-litre automobile (make allowance for assumption of vehicle stock -between years 2000 and 2005) will be registered not only in relative saving of fuel, but also in relative decline of emission production.
The basic factor influencing the amount and structure of produced emissions is composition of fuel, type and conditions of motor work and style of drive.
From the information presented in the study result that location of the route and an especially sensitive vertical line directly influence the produced emission capacity. By increasing drivespeed the emission production and concentration rises, but when comparing the production of emmisions by discontinuous driving in the city and by continuous driving out of the city comes to important difference. Therefore, total emission production is influenced by density level intersections, and the dispersion of pollution is affected by height and density of built-up area. Obr. 6