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PROKAS

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## Introduction

The mathematical model PROKAS is designed to calculate the immission of an investigation point. It considers the influence of the surrounding road grid on the point of investigation up to a distance of several kilometers. It consists of the basis module PROKAS_V (Gaussian plume model). Besides this emission model the integrated building module PROKAS_B is used for calculating the immissions of densely developed roads.

## Calculation of immissions with PROKAS_V

In the draft of the guideline VDI 3782, Sheet 8 “Ausbreitungsrechnung für Kfz-Emissionen”, PROKAS_V is designated as a dispersion model to analyze the concentration distribution both for calculating the pollution load in areas with or without loose development, and for calculating the background pollution concentration of densely developed areas.

The Gaussian approach within PROKAS_V corresponds to the “Ausbreitungsmodell für Luftreinhaltepläne” guideline VDI 3782 Sheet 1. The air pollutants of the exhaust plumes are moving with a typical transport velocity ut, which results from a weighted averaging of the vertical wind profile over the concentration distribution in the exhaust plume. Because the vertical concentration profile changes with the distance to the source, ut also becomes a function of the distance to the source. This assures that the continuity equation for the pollutants is valid for any distance from the road to be analyzed.

For calculations, the total road grid is divided into short line sources and the emission of each line source is distributed to several point sources. The distance between the point sources belonging to one line source is at most 1/10 of the distance of the point source to the investigation point. All together, the road grid is approximated by several 10.000 point sources depending on its density. Sensitivity investigations have proven that the calculation results are not affected by a further shortening of the distances between the point sources. For example, the division into single sources can also incorporate the case that emissions vary along a road, for instance if some parts are subject to speed limits. In this case, the point sources in the limited part will emit with a different intensity than those without limitation.

Thanks to the procedure mentioned above it is assured that each road segment can emit simultaneously, i.e. that the whole road grid always emits. This also allows for a realistic simulation of the conditions close to intersections, where emission points exist, which are polluted simultaneously by several roads at certain wind directions. In these cases, it is not correct to determine the 98-percentile value (concentrations which are not exceeded in 98 % of the time) by calculating the influence of each individual road and combining everything at a later stage.

Also the influence of a sound protection measures of a defined length can be considered in this way. This influence inferred in papers by Romberg et al. (1986) for the Bundesanstalt für Straßenwesen. The influence of the sound protection wall is interpreted as an initial dilution, where a value s_{zo} is added as an additive term to the vertical dispersion parameter s_{z}. The dispersion model is able to consider an individual value of s_{zo} for each line source. The dispersion parameters s_{y}, and s_{z} of the guideline VDI 3782 Sheet 1 correspond to those of TA air (1986).

To correctly determine the 98-percentile value, it is important, to consider the traffic density dependent on the time of day. It also depends on the correct determination of the traffic and emission peaks. The model therefore allows the input of 5 different emission levels and their occurrence frequency.

With respect to the meteorology, PROKAS can calculate with 36 different wind direction classes, 9 different wind speed classes, and 6 different dispersion classes. The dispersion classes take into account that the dilution of exhaust gases for a given wind direction and a given wind speed also depends on the stability of the atmosphere. For instance, the dilution is lower for an “inversion” situation than for sunny, “normal” weather conditions. Altogether 36 x 9 x 6 = 1.944 weather conditions with the corresponding frequencies are considered.

Therefore for each investigation point, the calculated result consists of 1.944 weather conditions x 5 emission levels = 9.720 different concentration values along with the corresponding frequencies. This data shows how often the 9.720 concentration values occur per year. A frequency distribution is retrieved from this data. This distribution allows for the 98-percentile value to be determined. This is the 98-percentile value of the additional pollution concentration which we were looking for.

The immission parameters for the total pollution concentration are determined from the parameters of the background pollution concentration and the additional pollution concentration (due to the traffic emissions on the particular roads) according to the procedure given in the TA Luft (1986) Annex D.

The geometry of the road grid and the investigation points are digitalized or taken over from traffic pattern models, sound calculation programs, or databases. To control the correct input, the software produces a scaled graph with the road grid and the position of the investigation points, as well as a list with the distances (as calculated by the software) of the points to the line sources, and, in addition, the source strengths, the number of point sources and the length of each line source.

The results of the immission calculations (average yearly values and 98-percentile values of NO_{2}, and the average yearly values of two inert pollutants, e.g. benzene, soot, or PM10) are saved in a file for each investigation point in the form of a table. They can be graphically displayed either in the form of numerical values at the corresponding investigation points, or by colored symbols, with the color set according to the concentration.

## Calculation of immisions in densely developed roads with PROKAS_B

Immissions cannot be calculated by PROKAS_V in the case of partially or completely closed developments (for instance a street canyons). The supplementary building module PROKAS_B is used instead. It is based on model calculations with the microscale dispersion model MISKAM of all typical types of development. The nondimensional exhaust gas concentration c* was determined for 20 different types of development and 36 flow directions in 1.5 m height and 1 m distance to the next building, respectively.

The different development types are street canyons with one- or two-sided development with a varying relation of the building height to the street canyon width and a varying percentage of gaps in the development. Gap density refers to the percentage of non-developed areas along the road with (one- or both-sided) developments. The width of the street canyons is defined as the double of the distance from the middle of the road to the development closest to the road. Tab. 3.1 describes the classification of the various types of developments. Road crossings are not considered due to insights from measurements (Kutzner et al., 1995) and model simulations. According to these studies, 10 % to 30 % lesser concentrations can be observed at crossings than at the neighboring street canyons.

The exhaust gas concentrations c are calculated via the nondimensional concentrations

whereby:

c = exhaust-gas concentration [µg/m³]

c* = nondimensional exhaust-gas concentration [-]

Q = emitted pollution source strength [µg/(m s)]

B = width of street canyons [m] alternatively the double distance from the middle of the road to the development

u' = wind speed in respect to traffic induced turbulences [m/s]

The contribution to the concentrations of PROKAS_V for the background pollution concentration and of PROKAS_B are combined for all individual situations, i.e. correlated by time.

Tab. 3.1: Types of road developments considered by PROKAS_B

Type |
Development |
Building height/ |
Percentage of gaps [%] |

0* |
loose |
- |
61 - 100 |

101 |
one-sided |
1:3 |
0 - 20 |

102 |
" |
1:3 |
21 - 60 |

103 |
" |
1:2 |
0 - 20 |

104 |
" |
1:2 |
21 - 60 |

105 |
" |
1:1.5 |
0 - 20 |

106 |
" |
1:1.5 |
21 - 60 |

107 |
" |
1:1 |
0 - 20 |

108 |
" |
1:1 |
21 - 60 |

109 |
" |
1.5:1 |
0 - 20 |

110 |
" |
1.5:1 |
21 - 60 |

201 |
both-sided |
1:3 |
0 - 20 |

202 |
" |
1:3 |
21 - 60 |

203 |
" |
1:2 |
0 - 20 |

204 |
" |
1:2 |
21 - 60 |

205 |
" |
1:1.5 |
0 - 20 |

206 |
" |
1:1.5 |
21 - 60 |

207 |
" |
1:1 |
0 - 20 |

208 |
" |
1:1 |
21 - 60 |

209 |
" |
1.5:1 |
0 - 20 |

210 |
" |
1.5:1 |
21 - 60 |

The types 101 and higher are only available, if the building module **PROKAS_B** is installed. If the development-module is not available, 0 has to be set as “development type”.

Types 101 till 210 describe a central source position like in **Fig. 3.1**.

**Fig. 3.1:** Central source position for the example case of type 201. Buildings are depicted in violet; the street source is depicted in green.

## Nitrogen oxide conversion

Vehicles mainly produce NO as nitrogen oxides and only a small portion of NO_{2}

NO is converted to NO_{2} on its dispersion path. The conversion rate is concentration dependent. With an increasing distance to the road, proportionally more and more NO is converted to NO_{2}.

The nitrogen oxide conversion is dealt with accord to the draft of the guideline VDI 3782 Sheet 8. This procedure is briefly explained in the following passage.

The conversion rate is parameterized through a ratio of NO_{2}/NO_{x} by a high number of measurements of the nitrogen oxides NO and NO_{2} at measurement stations in Germany (Romberg et al., 1996, see Fig. 1). NO_{x} is the sum of NO and NO_{2}, identified as NO_{2}, which means each mol (also of NO) is calculated with a mass of 46 g. Among the measurement stations, some heavily influenced by traffic, as for instance Frankfurt City or Cologne-Neumarkt, some are in remote areas, as for instance Villingen-Schwenningen in the Black Forest. The measurement values are published by the Umweltbundesamt in Berlin (UBA, 1991), the Statistische Landesamt Baden-Württemberg in Stuttgart (Statistische Berichte BW, 1985 until 1991), the Landesanstalt für Immissionsschutz, Nordrhein-Westfalen (LIS, 1985 until 1991), and the Bundesanstalt für Straßenwesen (Esser, 1992 and 1993). All are yearly values for the years 1985 through 1989, or 1990.

With the help of this parameterization, the average yearly immission of NO_{2} and the 98-percentile value for NO_{2} immission is known for each NO_{x} immission. The NO_{x} immission is obtained at the investigation points according to the previously described method. The correlation between NO_{2} and the NO_{x} total pollution concentration is obtained via a regression curve of the conversion rate NO_{2}/NO_{x}. (Fig. 1). The most likely value of the NO_{2} total pollution concentration is obtained via this regression curve.

## Comparison of the model results with measurements (validation)

To compare the calculation values with measurement values the following datasets were used:

- Measurements of the Bundesanstalt für Straßenwesen (BASt) at the A 4 at Bergisch Gladbach (Esser, 1995)
- Measurements of the UMEG, Karlsruhe, in the context of the permanent measuring stations of the Land Baden-Württemberg in Karlsruhe and Stuttgart (UMEG, 1995a and 1995b)
- Sample measurements of the Landesamt für Umwelt und Geologie Sachsen, of the UMEG, and of the Amt für Umweltschutz der Stadt Dresden in Dresden (1994/95).

The measuring stations were situated in loosely developed as well as in densely developed areas. The total pollution of loosely developed areas was calculated with PROKAS_V, the background pollution concentration from the surrounding road grid in densely developed areas using PROKAS_V with additional pollution calculations coming from PROKAS_B.

The comparison is displayed in Fig. 2 and Fig. 3. In total, a satisfying conformity is observable between measurements and calculations. The comparison of the datasets indicates the expected deviations in Tab 5.1.

Tab. 5.1: Relative deviation of the calculated results with PROKAS_V (in street canyons with background pollution with PROKAS_V and additional pollution with PROKAS_B) in comparison to measured values at the investigation points in Karlsruhe, Stuttgart, and Dresden, and at the A 4. See also Fig. 2 and Fig. 3.

Statistical parameter |
Relative deviation |

NO2-yearly average |
- 20 % to + 20 % |

NO2-98-percentile value |
- 20 % to + 50 % |

Benzene yearly average |
- 20 % to + 20 % |

Soot yearly average |
- 40 % to + 10 % |

The deviations between the measured and calculated values do not only result from the modeling of the pollution dispersion, but also from uncertainties in the used input data, which are not based on ideal but on real natural conditions. That means, that parameters such as exact traffic numbers, weekly vehicles loads, meteorology, and so on, are mostly not exactly known. In addition it has to be questioned in which time span and with which frequency the single measurements were combined to yield statistical parameters.

For instance, the measured NO_{2} 98-percentile values in Dresden are generally higher than the calculated ones (Fig. 2). One reason is surely the sample character of this measurement, which results in more uncertainties in this dataset than in other datasets. Without these sample measurements, the deviations for the NO_{2} 98-percentile value is closer to __+__ 20 % for the investigated cases.

Higher relative deviations are also noticeable for soot. The reason for this is on one hand, that the comparison measurement vs. calculation was performed only in 4 cases. On the other hand, there are uncertainties in the soot emission determination as well as in the soot immission measurement. Because benzene and soot both disperse equally as inert, non-sedimenting air pollutants (soot particle diameter < 10 µm), the dispersion calculation of benzene and soot are of the same quality. Differences in the calculation results are therefore not based on the dispersion calculation, but are due to uncertainties in the emission determination, in the immission measurement technology, and in the determination of the background pollution concentrations due to explicitly not considered sources.

## Literature

Esser, J. (1992): Ausbreitung und Zusammensetzung von Stickoxiden des Kraftfahrzeugverkehrs, Bundesanstalt für Straßenwesen, Bergisch Gladbach.

Esser, J. (1993 und 1995): personal information.

Kutzner, K., Diekmann, H. und Reichenbächer, W. (1995): Luftverschmutzung in Straßenschluchten - erste Messergebnisse nach der 23. BImSchV in Berlin. VDI-Bericht 1228, VDI-Verlag, Düsseldorf.

LIS (1985 bis 1991): TEMES-Monats- und Jahresberichte. Essen: Landesanstalt für Immissionsschutz, Nordrhein-Westfalen.

Romberg, E., Bösinger, R., Lohmeyer, A., Ruhnke, R., Röth, E. (1996): NO-NO2-Umwandlung für die Anwendung bei Immissionsprognosen für Kfz-Abgase. Gefahrstoffe-Reinhaltung der Luft, Band 56, Heft 6, S. 215-218.

Statistische Berichte BW (1985-1991): Immissions-Konzentrationsmessungen. Hrsg.: Statistisches Landesamt Baden-Württemberg, Stuttgart.

TA Luft (1986): 1. Allg. Verwaltungsvorschrift zum Bundes-Immissionsschutzgesetz (Technische Anleitung zur Reinhaltung der Luft). GMBl., 37. J., Nr. 7, 28.02.1986, S. 95 - 143.

UBA (1991): Verkehrsbedingte Luft- und Lärmbelastungen - Emissionen, Immissionen, Wirkungen - (UBA Texte 40/91). Berlin: Umweltbundesamt.

UMEG (1995a): Daten der Station Karlsruhe-Straße. UMEG Gesellschaft für Umweltmessungen und Umwelterhebungen mbH Karlsruhe, persönliche Mitteilung, 20. April 1995.

UMEG (1995b): Ergebnisse von Russmessungen in Baden-Württemberg 1993-1995. Bericht Nr. 31-5/95.

Richtlinie VDI 3782 Blatt 1 (1992): Ausbreitung von Luftverunreinigungen in der Atmosphäre. Gaußsches Ausbreitungsmodell für Luftreinhaltepläne.