Studies of the influence of vegetation cover on the process of transfer and diffusion of harmful substances in the atmosphere

. A mathematical model is proposed to monitor and predict the concentration of harmful substances emitted from natural and anthropogenic sources of pollution; it can be used to estimate the capture of aerosol particles in the atmosphere by vegetation elements. The developed mathematical model makes it possible to more accurately predict the degree of environmental pollution and develop measures to reduce it. Using this model and the corresponding numerical algorithm for solving problems, computational experiments were conducted with real weather and climate factors obtained from online services. From the computational experiments conducted, the main parameters were determined; one of them is the influence of vegetation elements on the process of diffusion and transport of aerosol particles in the atmosphere, which plays a significant role in the process under consideration. To check the reliability of the proposed mathematical apparatus, computational experiments were performed and the results were compared with the results obtained by other researchers.


Introduction
Air pollution -from smog over cities to indoor smoke -is a serious threat to health and the climate.According to statistics [1], the combined exposure to atmospheric and household air pollution causes about 7 million premature deaths each year, mainly as a result of an increase in mortality from stroke, heart disease, chronic obstructive pulmonary disease, lung cancer, and acute respiratory infections.More than 80% of people living in urban areas, where air pollution is monitored, are exposed to air quality levels that exceed the WHO recommendation of 10 mg/m3; at that, the countries with low-and middle-income suffer the highest exposure.
The main sources of environmental pollution are motor vehicles, power generation, building heating systems, agriculture, waste incineration, and industry.In addition, more than 3 billion people worldwide use polluting technologies and fuels (including biomass, coal, and kerosene) to cook, heat, and light their homes and wash pollutants outdoors.
Modern industrial development leads to a growing influence of man's activity on the environment, especially in industrial areas.The ecological state of these territories is becoming the subject of increasing concern since unfavourable conditions can adversely affect human health and ecosystems.Models, computational algorithms, and information systems are widely used for effective monitoring and forecasting of the ecological state of industrial territories.
Modeling the ecological state of industrial areas makes it possible to scientifically predict and analyze various aspects, such as air quality, water and soil pollution, and the spread of harmful substances.Computer models take into account complex factors such as weather conditions, topography, and various sources of pollution to provide detailed forecast and assessment of the impact on the environment.
Mathematical simulation plays an important role in understanding the complex processes occurring in nature around us.One such aspect is the study of the processes of transport and diffusion of pollutants in the atmosphere.Atmospheric pollution is a serious problem faced by many cities and industrial areas around the world.Understanding how pollution spreads and dissipates in the atmosphere is essential to developing effective strategies to manage and combat this phenomenon.
The factors affecting the transport and diffusion of pollutants are aerosol particles that consist of vegetation elements.Aerosols play a significant role in the formation of the atmospheric composition, and their presence can significantly affect the transport and diffusion of pollutants.Vegetation elements in the atmosphere can enter these particles through biological processes such as biogenic emissions, plant pollen, and other biological fractions.
Vegetation cover has a strong influence on the interaction between the soil surface and the atmosphere.Since more than 30% of the earth's surface is still covered with various types of vegetation, the study of meteorological processes that occur in the vegetation cover and above it, is of interest, especially for issues related to ecology and the environment.For this reason, vegetation cover, as an underlying surface, often enters ecological models at various scales.During the last decades, many scientific works have been devoted to the study of this problem and great efforts have already been made to better describe the interaction between the vegetation cover and the environment.
Modeling the processes of transfer and diffusion of aerosol particles in the atmosphere is a complex task that requires taking into account various factors, such as changes in wind speed, temperature, humidity, the presence of vegetation elements, and others.In particular, considering the capture of particles by vegetation elements is an important aspect of modeling the processes of transport and diffusion of aerosol particles in the atmosphere.Plants can capture aerosol particles from the air on their leaves, stems, and roots.The efficiency of this process depends on the type and density of vegetation [2].
Vegetation, as the main part of forest ecosystem, performs the functions of absorbing gaseous impurities from the atmospheric air, retaining microparticles and liquid on the surface of leaves, branches, and trunks, taking liquid and nutrients from soil, converting them into biomass, and releases waste products into the atmosphere and soil (respiration, evaporation, leaf decay, pollen, seeds).
An account for the capture of particles by vegetation elements when modeling the processes of transport and diffusion of aerosol particles in the atmosphere makes it possible to more accurately describe the transport of these particles in the atmosphere.This can be useful for determining levels of air pollution and assessing the effects of aerosols on human health and ecosystems.In addition, the modeling considering the particle capture by vegetation can be useful to investigate carbon-cycling issues in natural ecosystems such as forests and soils.
In [3], the distribution and influence of harmful substances from gas stations on nearby buildings were studied, taking into account the aerodynamics of wind flows.The authors of the article rightly emphasized that the study of this process -the spread of harmful substances in natural conditions -causes certain difficulties.Based on the results of theoretical and experimental studies obtained earlier, they numerically simulated the spread of pollutants emitted from gas stations and analysed their impact on nearby buildings, taking into account the flowing air currents.The results obtained allowed the authors to assess the state of the environment at any point and at any distance from the gas station and predict the degree of influence of atmospheric air pollution on the environmental safety of residential buildings during the construction of gas stations.
The study in [4] presents a three-dimensional mathematical model of the transport and diffusion of atmospheric impurities and the results of calculations of environmental pollution from solid rocket engines in different periods of the year in a region with characteristic meteorological parameters.In numerical experiments, the grid step in spatial coordinates, the grid step in time, and some parameters of the numerical scheme varied.
The study of vegetation dynamics is critical to the management of biodiversity, water and air pollution in open ecosystems.Unlike forests or other relatively stable ecosystems, open ecosystems can have dramatically changing vegetation conditions as they are subject to natural disturbances, long-term trends and short-term events [5].Therefore, it is difficult to accurately predict the state of vegetation in this type of ecosystem.The use of deep learningbased approaches to predict vegetation dynamics in an open ecosystem is studied in this article on the example of fynbos shrubs growing in the Cape Floristic Region of South Africa, which is the world's biodiversity hotspot.
Reference [6] presents the results of experimental studies of atmospheric pollution of the snow cover with suspended solids, ionic components, and polyaromatic hydrocarbons in the winter season of 2016/17 in the vicinity of the Iskitim cement plant.Studies were conducted to determine the content of macro-microelements and polyaromatic hydrocarbons (PAHs) in snow cover samples taken in the area of the cement plant.According to the data obtained, the level of man-made burden caused by the cement plant on the adjacent territory was estimated.A comparative analysis of the measured and calculated sediment concentration and the amount of dissolved calcium and nitrates in snow samples was made.
In [7], the classes of information tasks are defined that provide operational control and retrospective analysis of the state of the atmosphere in the territories of industrial regions.Approaches to the construction of software systems as part of automated monitoring systems are determined.A description of the algorithmic support for the analysis of territorial and temporal variability of the state of territories based on similarity measures and characteristics of the statistical relationship of state parameters is given.The results of computational experiments using the proposed approaches for the analysis of the ecological state of the territories of large cities in the Republic of Azerbaijan and the Republic of Bashkortostan are presented.
The study in [8] predicts the spread of pollutants outside the sanitary protection zone of tailing enterprises (a tailing pond is a complex of special structures and equipment designed for the storage or burial of radioactive, toxic waste, and dumps of mineral processing).The authors, using mathematical models of Gauss and gradient transfer, calculated the scattering of impurities under conditions of developed turbulent exchange.On the basis of computational experiments, a forecast was made of the volume concentration of pollutants in the surface layer of atmospheric air due to deflationary processes.
In the dissertation, reference [9], an ecological assessment of the territory of the city of Voronezh was conducted on the basis of the developed complex methodology, which made it possible to identify zones with different levels of pollution of snow cover and groundwater with iron, manganese, and their compounds and to register the response of the anthropogenic impact on the stability of biota development.With the use of GIS technologies, maps of the integral assessment of the quality of the environment in the area under study were plotted.The presence of a direct relationship between the state of vegetation and the degree of atmospheric pollution was revealed.
In [10], the characteristics that affect the stability of the surface layers of the atmosphere and determine the processes of turbulent transport are considered.A method is proposed in the article for calculating the dispersion of pollutants in the surface layer of the atmosphere, based on the methods of computational fluid dynamics.The use of this technique makes it possible to take into account the influence of complex terrain and the nature of development.
As an example of calculating the spread of pollutants, the paper presents the calculation of acetone emissions from a separate source located in the immediate vicinity of the building.The presented results of calculations clearly show the complex nature of the distribution of concentration fields in the immediate vicinity of buildings, as well as in conditions of dense buildings and complex terrain.Modeling such a complex distribution is practically impossible without the use of a powerful tool of computational fluid dynamics.
There are numerous studies devoted to modeling the process of transport and diffusion of aerosol particles in the atmosphere, which consider the capture of particles by vegetation elements.One such study is given in [11], where the modeling of the atmospheric flow and particle transport in city streets was conducted, taking into account the presence of plants.The simulation results showed that vegetation could significantly reduce the concentration of airborne particles by trapping particles on vegetation elements.
Research aimed at studying the influence of trees on the dispersion of air pollutants in urban areas is given in [12].The authors used computational fluid dynamics (CFD) simulations to study the aerodynamic impact of trees on the dispersion of air pollutants.The study focused on two aspects of the aerodynamic impact of trees on the dispersion of air pollutants: 1) the influence of tree characteristics such as height and density on airflow patterns and 2) the influence of trees on the dispersion of air pollutants.The CFD model used in the study was validated through wind tunnel experiments and field measurements.
The authors of article [13] explore the potential of roadside coniferous vegetation to mitigate air pollution.During the study, the air quality was measured at four locations in Cincinnati, Ohio over the course of one year, comparing air quality at locations with and without roadside conifers.The results showed that roadside conifers had a significant impact on reducing air pollution, especially particulate matter (PM) and nitrogen dioxide (NO2).Coniferous trees have been found to reduce PM concentrations by up to 60% and NO2 concentrations by up to 30%.The authors attribute the effect of air pollution mitigation to the ability of roadside conifers to absorb pollutants through their leaves and trap particles on the needles.The authors noted that this study highlights the importance of green infrastructure, such as roadside vegetation, in reducing air pollution and improving public health.
In [14], the authors considered the behaviour of the concentration and fluxes of scalar quantities (such as heat, moisture, and pollution) in the lee of forest patches.The authors used modeling based on large eddy simulation (LES) of turbulence to investigate this phenomenon.They compared the simulation results with experimental data obtained from the German database.The article shows that in the forest zone, the wind is non-uniform, and there are areas where the concentration and fluxes of scalar quantities increase compared to their values in open space.This effect is due to the fact that the trees in the forest reduce vertical turbulence and create more stable conditions, which leads to an increase in the concentration and fluxes of scalars in the lee of forest patches.The article is important for understanding the role of forests in the global cycle of matter and energy and can be useful for developing strategies for managing forest ecosystems to reduce the impact of pollution on the environment.However, it is worth considering that the data in the article are based on simulations and additional field studies are required to confirm the results.
To analyze the evolution of carbon dioxide in the vegetation cover, a numerical method for solving a boundary value problem with boundary conditions of the 2nd and 3rd kinds is used [15].The method is based on the solution to an additional differential equation of a The mitigation of pollutant emissions by any vegetation barrier depends on local conditions such as atmospheric stability, traffic density and speed, fleet composition, turbulence induced by vehicle motion, presence of buildings, roadway configuration, and wind direction.Although the influence of all these factors was not considered in this study, several key factors were studied that are likely to influence the effectiveness of plant barriers in reducing local air pollution, including wind speed and vegetation size.In addition, the emission height of pollutants in this study was 3 m, which may not fully reflect the emissions from trucks, which are generally observed at a slightly higher height, approximately 4 m.In addition, all vegetation barriers were considered in this study near the highway (at a distance 5 m between the traffic area and the beginning of the barrier).The barrier sizes considered in this study suggested optimal growth, so there was no spacing in the barrier.The fact that the plant barrier is dense without spacing depends on the initial size of the plants, the spacing between the trees planted, the quality of soil for healthy growth, and the maintenance and pruning of the barrier after planting.Additional field evaluations of the simulation results could increase the robustness of our recommendations.
Thus, an account for the capture of particles by vegetation elements is an important aspect of modeling the processes of transport and diffusion of aerosol particles in the atmosphere, which can give a more accurate understating of these processes and their impact on the environment.
Based on these considerations, the authors of this article considered modeling the process of transfer and diffusion of aerosol particles in the atmosphere, taking into account the capture of particles by vegetation elements.This makes it possible to account for the influence of vegetation on the processes of transfer and diffusion of aerosol particles since plants can capture particles from the air.

Formulation of the problem
Let us consider a mathematical model for the spread of aerosol particles in the atmosphere, described by the complete equation of hydromechanics, taking into account the capture of pollutant particles by vegetation elements: with the following initial and boundary conditions: Here,  is the concentration of harmful substances in the atmosphere; t is time; 0  is the initial concentration of harmful substances in the atmosphere; ; E  is the concentration entered through the boundaries of the domain under consideration; , , x y z is the coordinate frame; ,, u  is the wind speed in three directions; g w is the particle settling rate;  is the coefficient of absorption of harmful substances in the atmosphere; α(z) is the coefficient characterizing the capture of particles by vegetation elements; , are the diffusion and turbulence coefficients; Q is the power of the source;  is the Dirac function; ξ is the coefficient of mass transfer through the boundaries of the calculation domain;  is the coefficient of particle interaction with the underlying surface; 0 f is the stationary source of emission of harmful substances from the underlying surface.
Since the modeling of vegetation elements, such as branches and leaves, requires large computational costs, the influence of vegetation on the airflow is averaged over space and taken into account by adding the corresponding absorption and source terms to the governing equations [16]: where  is the air density, kg/m3; Cd is the drag coefficient; L(z) is the density profile of the leaf surface of vegetation (or the index of leaf surface area per unit volume); U is the air flow rate; ui is the speed in the direction under consideration.
Leaf area density (LAD) is a parameter used to describe the structure of plant communities and characterize the number of leaves in a certain area or the volume of plant mass.Leaf area density is defined as the total leaf area per unit volume or area of plant mass.It is generally expressed in units of leaf area per unit volume or area of square meters per cubic meter (m²/m³) or square meters per square meter (m²/m²) [13,17]: Lm is the maximum leaf area density in the vegetation; z is the height, zm is the height at which Lm occurs (zm = 0.4 h); h is the height of the vegetation.

Solution method
Since the problem posed is described by a system of partial differential equations with varying coefficients, it is difficult to obtain an analytical solution.For the numerical solution to problem (1)-( 5), a numerical algorithm based on the finite-difference approximation of differential operators to difference operators was developed [18].It should be emphasized that the formulated problem (1)-( 5) was solved using the method of splitting by physical processes, that is, for the effective solution of the problem posed, it was split by physical processes -into the convection part, the diffusion part, and the part of the substance absorption in the atmosphere [19].More details about the solution of the computational algorithm can be found in our publications [19][20][21].

Experimental results
Within the framework of this study, an object-oriented software and tool complex was developed, which includes a number of related software tools developed using modern, most widely used technologies, such as the Python programming language, Django frameworks, Django-rest-framework, sets of OSM visualization libraries, OWM, Googlemaps, numpy, pandas, scipy, matplotlib, requests, folium, bs4, etc.The source was considered as an object at the site of GRAND POLIMER PLAST LLC, located in the Kagan district of the Bukhara region of the Republic of Uzbekistan (Figs. 2 -4).
A computational experiment showed that as the height of the vegetation grows its leaf area density decreases Fig. 1, a).From figures 1 b), c), d), e), it can be seen that if the height of the vegetation is the same, then the leaf area density decreases, and in both cases, it depends on parameter Lm.In a single plant, as a rule, leaf area density tends to decrease as plant height increases.This is because as a plant grows taller, it must allocate more resources to support its stem and branches, leaving fewer resources to produce leaves.However, the exact relationship between leaf area density and height can vary depending on the type of plant and the environment in which it grows.In different plants: in a forest or other natural ecosystem, the relationship between leaf area density and height can be more complex.For example, in a closed forest canopy, taller trees may have less leaf area density due to competition for light, while small trees may have greater leaf area density due to their ability to grow in shaded conditions.Similarly, in open grassland or desert, taller grasses may have greater leaf area due to their need for photosynthesis in direct sunlight, while short grasses may have lower leaf area.To conduct a comprehensive study of the process of pollutants spread in the atmosphere, computational experiments were conducted with real weather and climatic factors obtained online.
As follows from the results of the numerical calculations, the dynamics of changes in the concentration of harmful substances in the atmosphere significantly depends on the wind speed in the surface layer of the atmosphere (Fig. 2).At critical wind speeds, changes in the concentration of harmful substances in the atmosphere mainly occur due to the transfer of atmospheric air mass in the surface layer, while the height of the source of harmful substances indirectly affects the transfer distance.
The area covered by the concentration of harmful substances in the atmosphere significantly depends on the velocity direction of the air mass of the atmosphere (Fig. 3).From the dynamics of the transfer of pollutants in the atmosphere, it can be seen (Figs. 2, 3,) that, depending on the change in the wind direction and speed, the concentration of pollutants in the atmosphere and the area of their transfer change over time.
The numerical calculations performed showed that another significant factor affecting the change in the concentration of pollutants in the surface layer of the atmosphere is the vegetation cover and the coefficient of of harmful substances in the atmosphere, which depend on the time of year and day.

Conclusions
Thus, taking into account the capture of particles by vegetation elements is an important aspect of modeling the processes of transport and diffusion of aerosol particles in the atmosphere, as it can give a more accurate idea of these processes and their impact on the environment.A computational experiment has established that as vegetation grows in height, its leaf area density decreases (Fig. 1 The results of the study show that a decrease in leaf area density leads to lower particle settling and hence, to a change in particle size.The maturity of the vegetation barrier affects the critical particle size at which vegetation deposition and dispersion of pollutants predominate; thus, it is a very important parameter considering the reduction of pollutant emissions.The practical output of the study is the possibility of developing recommendations to support decision-making on maintaining the ecological balance of the environment in industrial regions, as well as protecting it from the possible negative impact of technogenic factors.
Computational experiments were conducted to check the adequacy of the developed mathematical apparatus; the results of these experiments were compared with field data.A comprehensive analysis of the processes of atmospheric pollution in a real production facility located in the Kagan district of the Bukhara region of Uzbekistan was performed.Figures 2,  3, and 4 show that the change in the concentration of aerosols in the atmosphere depends significantly on the actual change in wind speed by day, on the coefficient characterizing the capture of particles by vegetation elements, on the horizontal diffusion coefficient, and on the vertical turbulence coefficient.The concentration of pollutants in the surface layer of the atmosphere changes over time depending on the actual wind speeds.With an increase in wind speed, the accumulation of concentration of pollutants around the source does not occur, and the area of distribution of pollutants increases with time.As shown by the numerical calculations, with moderate wind and calm, the concentration of harmful substances around the source accumulates at a level of 280 to 350 m.At that, the concentration of harmful substances in the atmosphere increases with increasing power of the source.The greater the intensity of aerosol sources and horizontal components of the wind speed, the wider the area of pollutant transfer in the atmosphere.
Although research to model the transport and diffusion of aerosol particles with respect to particle capture by vegetation elements is ongoing, the results are already showing the potential of using vegetation cover to improve air quality in cities.
This study also highlights several recommendations that urban planners should consider when planting vegetation barriers to improve air quality in areas with high levels of traffic pollution.First, urban planners need to consider vegetation growth rates and maintenance requirements so that they can actively maintain vegetation barriers at the ideal height and achieve optimal pollutant reduction after planting.Factors of local climate will influence the type of vegetation chosen and how fast it will grow, so urban planners should choose vegetation types that lend themselves to pruning in terms of logistics and time, taking into account the growth rate of the plant species chosen for certain areas.Second, dense vegetation with high LAD values should be chosen as it is more effective in reducing pollutant emissions due to higher deposition and dispersion of pollutants on the leeward side of the barrier.Third, the height of the introduced vegetation barrier should be about 4-6 m to mitigate pollutant emissions.However, if this is not possible due to factors such as cost or geographic compatibility, then the selected vegetation must mature to its maximum LAD, which varies by species.For example, some tree species reach their peak at 10 to 15 years of age and at a height of 1.5 to 2 m.Using younger vegetation before it reaches its peak of the LAD is not ideal as it is still developing and, therefore, has lower LAD values and may be too low for pollutants to pass over it unhindered.Fourth, by defining an ideal barrier height between 4m and 6m, city planners can determine the planting space between trees that will provide optimal barrier growth.

Fig. 1 a
Fig. 1 a), b), c), e), f).Leaf area density profiles for all cases of dense vegetation evaluated in this study, where Lm is the maximum leaf area density that occurs at a height of z = 0.4h.