Inclusion of Increased Air Turbulence Caused by Coke Production into Atmospheric Propagation Modelling
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Abstract
Gaussian plume models are still used in cases where shortdistance, routine calculations have to be done. They use universal parameters to parameterise the atmosphericand earth–surface impact on the dispersion of air pollutants that can produce satisfactory results in overall conditions. This is not the case in the placespecific applications, when standard models do not reflect all of the mechanisms involved in local dispersion phenomena. This limitation applies in particular to atypical objects which are characterised by high thermal and mechanical turbulence being introduced into the air. Such places form locally distinctive air turbulence reflected by specific vertical wind speed profiles. Based on the knowledge of their shape, the turbulence and diffusion intensity information may be transferred to the propagation model. The analysis of the wind profiles measured in the vicinity of the big coking plant is presented in this paper. The wind profiles’ exponent values which had been obtained on this basis were compared with the values used with standard models. Also, measured marker–gas concentrations have been related to values calculated with the use of the model equipped with modified exponents as well as to the values obtained from the traditional model.
Keywords
Coke production Gaussian plume models Pollution dispersion modelling Air turbulence Wind profile exponentsIntroduction
Gaussian plume models of the socalled old (or first) generation use parameters which characterise the influence of the atmosphere and the earth–surface on the intensity of pollutant dispersion, using universal values of empirical origin. In such models, the ability to generate mechanical turbulence by terrain surface is described by the surface roughness coefficient z0, while the powerlaw (or meteorological) exponent p constitutes a measure of both thermal and mechanical turbulences (ElHarbawi 2013; Saha 2008; Zanetti 1990). Parameterisation of the atmosphere due to thermal turbulence consists in determining atmospheric stability and introducing the right value of the exponent p into a model. The p value is chosen from the set comprising values specific for subsequent atmosphere stability classes (mainly conforming to Pasquill–Gifford stability categories). In this way, the exponent p becomes a parameter formally describing the thermal turbulence. In many models, this exponent also contains a component of mechanical turbulence, which is usually taken into account using different sets of exponential values for different types of land (typically, urban and rural) (Turner 1994; EPA 1995).
In specific applications, the standard values of the meteorological exponent do not reflect, in a fully representative way, the mechanisms of atmospheric dispersion. This is confirmed by the observation that anthropogenic factors that excel the normal parameter levels which determine the atmospheric stability might overcome the natural dispersion mechanisms. This observation is true for industrial objects (José et al. 2004). This applies in particular to nontypical objects, such as a coke oven battery, which is a lowstack emission source (about 10 m high) with heat emission of up to about 3 kW/m^{2} (own estimations). This is significantly more than the yearly averaged heat emission from the earth surface, which creates thermal turbulence in the atmosphere (in the Central Europe zone, this emission reaches 100–130 W/m^{2}) (National Research Council 1977; Madany 1996). Despite the generally small area of industrial objects that emit heat, the large unitary emission and the mechanical impact on the flow forced by industrial buildings and installations (Zaïdi et al. 2014) may result in increased or aboveaverage turbulence in their immediate vicinity. This has been confirmed both in measurement (Huq and Franzese 2012) and numerical (Lateb et al. 2010; Mirzaei and Carmeliet 2013; Xie et al. 2013) experiments.
The impact of heat emission on atmospheric dispersion has been a subject of research for years, focusing primarily on the phenomenon of the ‘heat island’. It is commonly observed in larger cities—irrespective of the climate zone in which they are located—and consists of local modifications of the atmosphere characteristics caused by the shape and properties of the earth’s surface and the significant emission of heat, moisture and air pollution. The work on the phenomenon of heat islands was initiated in the 1970s (Garstang et al. 1975) and intensively conducted in the subsequent years (Oke 1981; Landsberg 1981). As a result, the main types of heat islands have been defined, and their basic structures of varying ranges and character have been recognised and categorised into the urban canopy and the urban boundary layer. Furthermore, essential features of the heat island area have been identified. Among them, the following can be distinguished: the maintenance of slightly stable or even neutral atmospheric stability directly above the city area in night conditions up to several hundred metres (typical height is about 100–300 m) (Tapper 1990); the occurrence of significantly elevated air temperature in the area (Oke 1995); the formation of an ‘urban plume’ of warm air on the leeward side of the city (starting from the outskirts of the urban areas) (Landsberg 1981; Oke 1995); the tendency to change the vertical air temperature profile towards the shape characteristic for neutral stratification, combined with local turbulence creation (Glazier et al. 1976; Godowitch et al. 1985); the frequent formation of elevated inversion over the heat island (Uno et al. 1992); the formation of HIC (Heat Island Circulation) system under weak winds (Ado 1992); and the disappearance of the heat island with an increase of the vertical mixing intensity, at the same time, under winds of higher speed (Draxler 1986; Hildebrand and Ackerman 1984).
The extent of the heat island, defined by the difference between the temperature of the air inside and outside the island (in relation to nonurban areas), can be estimated to be several dozen kilometres from the city outskirts on its leeward side. For example, in the wellknown St. Louis experiment, a 40 km long heat island was recorded on the leeward side of the city, formed by an air layer in which the temperature was elevated by 1.5 °C, extending from the earth surface up to the height of about 1 kilometre (Auer 1981).
Another phenomenon recorded in urban and industrial areas that influences dispersion in the atmosphere is the mechanical interaction of objects of considerable dimensions and air flows. Each object encircled by the moving mass of air leaves a ‘trace’ in the form of an increased turbulence path generated mechanically—and, if it emits heat, also thermally (Carpentieri 2012). From the time when atmospheric turbulence measurements were initiated, the turbulence dependence of the nature and character of the areas over which the air masses moved before reaching the measurement point was observed (Panofsky et al. 1977). Observations of this type were made in hilly or mountainous areas as well as over large water reservoirs. This effect is especially visible near lakes and other inland water bodies. Due to the low surface roughness, high heatstorage capacity and thermal inertia of water, the height of the inner boundary layer above the water surface is limited and characterised by small turbulence (Madany 1996). This turbulence of limited energy is conveyed inland along the mean velocity vectors of the wind (Panofsky et al. 1982). Similar studies were conducted in marshy areas (Walter et al. 2011). Analogical measurements at city boundaries and on flat areas with no significant terrain obstacles are described in Högström et al. (1982). In this work, results, analysis and comparisons of the wind speed measurements made in the city’s centre and beyond at two different altitudes are presented.
In all of the abovementioned papers, the authors indicated that the spectra of horizontal variations of wind components were strongly dependent on the geomorphological conditions of the terrain and on the windward side of the points at which the measurements were made. Moreover, it was found that the described tendency, manifested in the existence of ‘memory’, collecting effects of components influencing the flow in the form of proper turbulence level, is clearly evident in the lowfrequency spectra of turbulence. In the highfrequency range, this tendency is weak—the spectra of component velocity variances show a short time in which they adjust their values to the nature of the surface over which the flow takes place in the moment. The described behaviour is referred to by the term ‘spectral lag’ (Högström et al. 1982). Lowfrequency turbulence, deviating from values characteristic for local geomorphological conditions due to the influence of distant sources of turbulence lying on the windward side of the measuring point, was also described in other works. Terrain shape (Andreas 1987; Smeets et al. 1998), disturbances associated with conditions which are formed at the border of convective boundary layer (McNaughton and Laubacg 2000), or both (Li et al. 2007), are indicated as sources of turbulence.
In the case of industrial objects, the factors mentioned above result in increased dynamics of pollutant dispersion in the atmosphere, which in turn are reflected in reduced concentrations. Another effect is the extended accuracy of concentrations estimated using simple box models, working under the assumption of evenly distributed vertical concentrations of pollutants (Hanna and Baja 2009).
In addition, the distance over which the modified turbulence remains is also important. In the US EPA guidelines for air quality modelling (EPA 2000), this distance, which extends from the source of the disturbance to a place where the increased turbulent atmospheric characteristics can still be observed, is defined as 3 kilometres. The AERMET meteorological preprocessor also defines 3 kilometres as the distance over which to evaluate the effects that earth–surface parameters, such as albedo, Bowen number and surface roughness, have on turbulence. Estimates of this type are designed to incorporate modified dispersion conditions into dispersion calculations, particularly for urban and industrial areas. Other studies (EPA 2000, 2004; Paine and Egan 1987) also point to the spatial variations in air turbulence that develop in the boundary layer along the wind direction, forced by changes in earth–surface characteristics and heat emissions. For areas with high roughness accompanied by significant heat emissions leading to the reduction of atmospheric stability (which is characteristic for coking plants), it is indicated that the creation length of characteristic flow turbulence may be considerably shorter than 3 kilometres (SmedmanHögström and Högström 1978).
Differences in the formation of air turbulence and the mixing height under the influence of varying thermal and mechanical surface effects are evident in empirical observations (Tapper 1990) in atmospheric boundary layer investigations (Gryning and Batchvarova 2007) and in numerical simulations (Lateb et al. 2010). These differences are reflected in the ‘urban’ and ‘rural’ meteorological exponent values of traditional Gaussian models, the first of which contains the information about additional turbulence associated primarily with differences in the shortwave solar heat accumulated in the urban area and beyond. These differences are, for example, clearly visible in almost identical exponent values (~ 0.15) expressing moderately unstable atmosphere (B) in urban conditions and neutral stability (D) in nonurban conditions (Turner 1994; EPA 1995). Experimental studies show that modified dispersion parameters have to be taken into account both in Gaussian (Huq and Franzese 2012) and more complex models (Batchvarova and Gryning 2005; Carpentieri et al. 2012). While talking about increased air turbulence, other relevant phenomena can also be pointed out (Wang et al. 2017a, b).
In the present paper, the estimations of meteorological exponent values were done on the basis of vertical wind profiles, the shape of which in the planetary boundary layer—as well as the respective p values—relates to atmospheric turbulence (Saha 2008) and is influenced thermally and mechanically by large industrial objects. The analysis of these wind profiles allows for the assessment of locally occurring atmospheric turbulence in the vicinity of such subjects (EPA 2000). Valuations of this kind were conducted for one of the Polish coking plants.
Methods and Site Description
 wind direction measurement range

0/360°,
 wind direction measurement resolution

1°,
 wind speed measurement range

0/60 m/s,
 wind speed measurement resolution

0.1 m/s,
 wind speed measurement threshold

0.4 m/s.
 temperature measurement range

− 40/+ 60 °C,
 temperature measurement accuracy

± 0.1 °C
The SM076 logger, also placed on the mast, performed three basic functions: processing of measurement signals, transmission of the data in a given time regime via., a connected GSM transmission link and data collection and archiving. With a sampling frequency of 1 second, the SM076 measured mid and lowfrequency components of wind direction and speed.
In addition, the AsterMet tower has been equipped with a protection system from atmospheric discharges and electrical interference, both from the power supply and transmission.
More than 52,000 wind profiles were taken into account when estimating the value of the p parameter, of which about 32,200 profiles were analysed after discarding erroneous or high uncertainty values. We have obtained approximately 430 profiles for the extremely unstable class (A), 2800 profiles for the moderately unstable class (B), 3160 profiles for the slightly unstable class (C), 16,450 profiles for the class of neutral stability (D), 4620 for the slightly stable class (E) and 3700 profiles for the moderately stable class (F).
Individual values of the exponent p were assigned to the stability classes appearing in the time of profile measurements. Stability evaluations were made using the Solar Radiation DeltaT (EPA 1994) method, on the basis of wind speed measured at a height of 10 m, along with the vertical temperature gradient and the solar radiation. Both were recorded at the nearby regular meteorological station between October 2012 and 2013. In this way 6 sets of p values corresponding to the standardised stabilities of the atmosphere were obtained.
Next, a directional analysis of turbulence was performed. For this goal, each set of p values was divided into two subsets due to the direction of the wind. The first contains observations made while the wind direction was in the range of 330°–60°, comprising airflow from above the coke oven batteries [these winds were marked as north (N)]. The black dashed line in Fig. 1 indicates the secant of this angle traversing the point of the meteorological tower location. The approximate location of the coke oven batteries is indicated by an ellipse on the same figure. The second subset of p values includes measurements related to the remaining directions of airflow (winds marked as WSE with corresponding secant azimuths: 105°; 195°; 285°). In total, 12 medians of p calculated from the vertical wind profiles for each of 6 standardized stability classes and 2 wind directions (N and WSE) were taken as the final values of the p exponents. The selection of a median, instead of mean, as a function which should serve to calculate the expected value of the exponent p was made to decrease the influence of the values laying beyond the borders of adjacent stability classes.
Results
Basic parameters of descriptive statistics
Atmosphere stability classification  Ab  Mean ± SD  Me  Range 

Wind direction inside the angle 330°–60° (wind N)  
A  37  0.156 ± 0.073  0.163  0.000–0.317 
B  272  0.214 ± 0.181  0.179  0.000–1.544 
C  540  0.183 ± 0.065  0.172  0.025–0.461 
D  3479  0.198 ± 0.101  0.179  0.000–1.639 
E  759  0.245 ± 0.124  0.222  0.034–1.365 
F  983  0.308 ± 0.216  0.252  0.000–1.639 
Wind direction outside the angle 330°–60° (wind WSE)  
A  388  0.187 ± 0.104  0.179  0.000–0.468 
B  2505  0.256 ± 0.175  0.216  0.000–1.489 
C  2623  0.231 ± 0.106  0.218  0.000–1.238 
D  12970  0.269 ± 0.186  0.225  0.000–2.622 
E  3862  0.374 ± 0.281  0.298  0.000–1.639 
F  2746  0.518 ± 0.363  0.431  0.000–1.683 
Values of W statistics and calculated level of significance P for the Shapiro–Wilk test of the p exponents for the analysed wind directions and the subsequent classes of atmospheric stability, assuming α = 0.05
Atmosphere stability class  W  P  

Wind N  Wind WSE  Wind N  Wind WSE  
A  0.937  0.983  0.039  0.001 
B  0.648  0.814  ~ 0.000  ~ 0.000 
C  0.963  0.948  ~ 0.000  ~ 0.000 
D  0.721  0.948  ~ 0.000  ~ 0.000 
E  0.681  0.807  ~ 0.000  ~ 0.000 
F  0.776  0.896  ~ 0.000  ~ 0.000 
Values of obtained p medians and results of the Mann–Whitney test for the analysed wind directions in subsequent atmospheric stability classes, assuming α = 0.05
Wind direction  Median (Me)  

A  B  C  D  E  F  
Wind N  0.163  0.179  0.172  0.179  0.222  0.252 
Wind WSE  0.179  0.216  0.218  0.225  0.298  0.431 
P  0.1238  0.0002  ~ 0.0000  ~ 0.0000  ~ 0.0000  ~ 0.0000 
Differences are valid  No  Yes  Yes  Yes  Yes  Yes 
All statistical analyses were performed using the Statistica EN v. 12 software package.
Also, the NMSE was calculated for the model with modified exponents and adjusted emission height (Żeliński et al. 2016). The NMSE value of 8.83 has been found.
Discussion
The present work has confirmed the influence of large industrial objects on the flow of air masses. It was demonstrated, using statistical methods, that for a coking plant this effect is reflected by the value of the exponent p calculated from wind profiles. It has been observed on the basis of measurement analyses that, for low atmospheric stability classes (especially A, but also B) corresponding to high atmospheric turbulence caused by intensive solar heat, the values of measured exponents for opposed wind directions (N and WSE) are similar (Table 3). This indicates a slight effect of technological heat on atmospheric turbulence, or its lack. For stability class A this lack of influence is confirmed by the Mann–Whitney test of exponent equality, revealing a level of significance greater than the assumed value of α = 0.05. On the contrary, for the stable stability classes of the atmosphere (E and F), due to the limited inflow of solar heat, the impact of the technological heat becomes significantly higher. This is revealed by big differences in the exponent values for the N and WSE winds as well as in the nearzero values of the calculated significance level. For stabilities B–D this trend is preserved, with smaller differences.
Values of the exponent p for each stability class
Exponent p  Stability class  

A  B  C  D  E  F  
Polish standard  0.08  0.143  0.196  0.27  0.363  0.44 
Urban  0.15  0.15  0.20  0.25  0.30  0.30 
The relatively narrow gap and smaller interquartile range between the 10th and 90th percentile for the N winds indicate the more regular character of the flow from this direction, which is the result of turbulence from locally interacting technological sources (Batchvarova and Gryning 2005; Gousseau et al. 2011). Their influence consists in overlapping meteorological parameters of a stochastic nature by local effects constant in time, affecting air flow in the lower atmosphere (Landsberg 1981; Blocken et al. 2008), which limits the element of stochasticity formed by thermally and morphologically differentiated areas surrounding the coking plant. The impact of the plant is also reflected in the box and whisker graph (Fig. 6), particularly for the stability classes E and F. It is revealed by significant differences in the upper percentiles and upper quartiles calculated for the N and WSE wind directions. These parameters correspond to the lowair turbulence in each stability class. As a consequence, there is also a smaller gap between the 10th and 90th percentile and a smaller interquartile range for the N direction in comparison to WSE winds. On the contrary, the differences between the lowest percentiles and the lowest quartiles noted for the N and WSE directions, which correspond to highair turbulence in each stability class, are significantly smaller in all stability classes. This reflects the overall lower share of coking plants in turbulence when the natural turbulence level is raised.
The meteorological exponents obtained in the measurements were compared with their two counterparts. The first of them is used in the standard, universal Polish dispersion model, the second one in Gaussian models employed for computations in urban conditions (EPA 1995; Moussiopoulos 1997). In the first, standard exponent values for B and C stability classes are similar to the values obtained in measurements with the N winds. In other cases, significant differences in the values of the corresponding exponents are noted, as for stability class A, the standard exponent is lower, whilst for neutral and stable stability (classes D–F) it is higher for both N and WSE winds.
In turn, the exponents obtained for WSE winds are similar in trend and value to urban exponents, except for classes B and F (which may be due to the duplication of city exponent values from A to B and also from E to F; see Table 4).
It is also worth pointing out the frequency of particular stability class occurrences in the investigated time interval. The class represented by the greatest number of occurrences in this period was neutral stability (D), whilst the smallest one was class A. Classes E and F, which cause the greatest impact of coking processes on the environment, are characterised by the second and third largest number of occurrences. This implies the need of using measured—and thus more accurate—exponent values particularly in these two classes, to increase the overall reliability of impact analysis that utilises longperiod calculations in which values of p are used.
The analysis of concentrations observed and calculated with the use of traditional and modified exponents reveals the far better behaviour of models incorporating latter ones. It is visible in each of the 24 comparisons between concentrations measured and calculated with—and without modified exponents. All refer to different meteorological conditions but each of them shows more accurate (to a greater or smaller extent) result of calculations while using modified exponents. This is also visible both for the best matching concentrations distributions (Fig. 3) and for distributions shown in Fig. 4 referring to the worst result obtained. The analysis of concentrations reveals also a specific character of modelling errors—the common overestimation of modelled values over observed—however, clearly smaller in a case of the model using modified exponents.
NMSE values calculated for four popular models
Model  Experiment  

Prairie Grass  EPRI Kincaid  EPRI Indianapolis  
ADMS  1117^{b}  Not completed  Not completed 
AERMOD  1144  0400  0368 
HPDM  6676*  0298^{b}  0341^{b} 
ISC3  4581*  1652*  0479 
As it was mentioned, NMSE calculated for the standard Polish dispersion model adjusted to the conditions of the investigated coking plant yields 8.83. It is quite close to the level presented by other popular models (at least for the Prairie Grass data), although apparently two of them (ADMS, AERMOD) belonging to the class of the “next” generation plume models, are consistently better. This result is certainly influenced by the fact that vital meteorological measurements, as twicedaily NWS upperair observations, were not incorporated into modelling with the adjusted model, which makes a characterization of the meteorological conditions for the tracer dispersion site less precise and means the deterioration of the overall model performance. The measurement had also been made outside the centerline of the plume which certainly influenced the final NMSE value while compare to presented data. Taking into consideration that without presented adjustments the same model makes calculations for the same object with NMSE value yielding 56.65, one can say that changes made in meteorological exponents have vastly improved model performance. It is worth to emphasise that the model with presented adjustments is suitable to be used only for the object, for which it was created or similar.
Conclusions

The presented measurements and observations reveal significant differences in the value of the exponent p established for winds N and for other wind directions, which reflects the thermal and mechanical impact from the coke oven battery and other technological sources, on the overall air turbulence.

Clearly, the lower values of meteorological exponents obtained from our measurements in comparison to the ones commonly used for stable stability—at which pollution concentration maxima for low industrial sources appear—lead to the conclusion that maximum concentrations calculated for such sources with traditional Gaussian dispersion models tend to be overestimated. This is confirmed by the results of SF_{6} measurements.

Highfrequency occurrences of neutral stability, characterised by lower exponent values than are commonly in use, should lead in calculations to a reduction in the calculated annual averages of concentration and dust deposition, below the level obtained with traditional models.

The values of the Polish standard exponents, used for a case of industrial object characterised by the high emission of heat, are not only too high for the stable and neutral stability classes, but are also too low for the extremely unstable classes.
Notes
Acknowledgements
The paper has been prepared within the framework of the project no. POIG.01.01.02–24–017/08 ‘Smart Coke Plant Meeting the Requirements of Best Available Techniques’ cofinanced by the European Regional Development Fund (ERDF). The results presented in this paper were obtained during the research project entitled „Monitorowanie uregulowań prawnych i wspólnotowych oraz działania wspierające samorządy oraz przemysł w zakresie ochrony środowiska” (IChPW No 11.18.008), financed by the Polish Ministry of Science and Higher Education.
Compliance with ethical standards
Conflict of interest statement
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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