=Paper=
{{Paper
|id=Vol-2254/10000131
|storemode=property
|title=High-performance
calculations for modeling of processes of transfer of pollution in an
atmospheric boundary layer from superficial sources
|pdfUrl=https://ceur-ws.org/Vol-2254/10000131.pdf
|volume=Vol-2254
|authors=Eugeny Alexeev,Sergey Rychkov,Anatoliy
Shatrov
}}
==High-performance
calculations for modeling of processes of transfer of pollution in an
atmospheric boundary layer from superficial sources==
https://ceur-ws.org/Vol-2254/10000131.pdf
High-performance calculations for modeling of
processes of transfer of pollution in an
atmospheric boundary layer from superficial
sources
Eugeny R. Alexeev Sergey L. Rychkov Anatoliy V. Shatrov
Applied Math. Dept. Fundamental Math. Dept. Math. Modelling Dept.
er alekseev@vyatsu.ru sl rychkov@vyatsu.ru shatrov@vyatsu.ru
Vyatka State University
Moskovskaya ul., 36, 610000 Kirov, Russia
Abstract
The quasi-two-dimensional model of impurity propagation from a man-
made source is devised on the basis of a three-dimensional model of
hydrothermodynamics of mesoscale processes in the lower atmosphere
with account for the thermal nonuniformity of the underlying surface in
the environs of a large industrial city. The boundary conditions and the
model coefficients are determined using the parametrization method.
The results of numerical calculations are presented. The calculations
are performed using parallel algorithms on a cluster supercomputer of
the Vyatka State University. They show that, due to the action of an in-
homogeneous horizontal temperature gradient in the lower atmosphere,
vortex flows can be formed above populated areas. The disturbed wind
flow has a considerable effect on the impurity propagation pattern in
the neighborhood of the sources. This model is used for a research of
processes of aerosol pollution transfer from solid waste landfill.
1 Introduction
The aim of this work is to consider developed mathematical models of an aerosol impurity propagation and the
computer program complexes created on their basis that are implemented into analysis by various conditions of
the atmospheric streams passed over the pollution sources which are the solid waste landfills in the territory of
the Kirov region.
About 3,5 million tons of garbage are formed in the neighborhood of a city with a million population annually.
A deposition (accumulation) is a traditional way of disposal of municipal solid waste. At this approach waste
collects out on dumps. The structure of grounds with municipal solid waste is the same in modern cities of
various countries. The main components (parts) of municipal solid waste are paper, fossils, glass, plastic, wood,
fabrics and leather. These components are combustible and capable to decomposition. Microorganisms emit
Copyright c by the paper’s authors. Copying permitted for private and academic purposes.
In: Marco Schaerf, Massimo Mecella, Drozdova Viktoria Igorevna, Kalmykov Igor Anatolievich (eds.): Proceedings of REMS 2018
– Russian Federation & Europe Multidisciplinary Symposium on Computer Science and ICT, Stavropol – Dombay, Russia, 15–20
October 2018, published at http://ceur-ws.org
methane during accumulation and decomposition of this garbage. Burying garbage of solid waste becomes a
source of formation of the harmful substances polluting ground waters, poisoning the soil and the atmosphere.
In this work the mathematical model for assessment of transfer of aerosol pollution from solid waste landfill
is considered. Deterioration in an ecological situation results in need rather precisely to predict and make
operational decisions on definition of consequences of pollution that it demands creation of special mathematical
tools, models which reflect the occurring phenomena. Models of mesoscale atmospheric processes are widely
used in studying local daily weather phenomena, convective processes, and impurity transport in the lower
atmosphere. For this purpose, models of different types have been developed [Bel83, Pen85, Alo02]. The
classical system of equations of mesoscale processes put forward by I.A. Kibel [Kib70] includes the equations of
motion, continuity, heat conduction, and moisture transfer, together with the closing equations for determining
the turbulent transfer coefficients. In modeling the atmospheric boundary layer this system is supplemented with
boundary conditions which take into account the interaction of the underlying surface and the ground layer of
the atmosphere. In studying the lower atmosphere it was found that a human-induced heat spot, named also a
heat island [Vel79, Tar91], can arise above a city or a large populated area and the importance of the action of
thermal nonuniformity of the underlying surface on mesoscale atmospheric processes was noted. In view of the
intricacy of the modeling and the calculations, when using even modern computers, it makes sense to apply such
two-dimensional models that retain the basic physical properties of the atmospheric processes under research.
In this study, the quasi-two-dimensional model proposed describes three-dimensional convective processes in a
thin rotating air layer in the presence of man-made heat and impurity sources. Its derivation is based on the
well-known approach [Ari87, Ari88] successfully used in geophysical applications [Shv00, Shv09a].
2 Math Model of the Problem
We will consider the lower-atmosphere boundary layer restricting ourselves to mesoscale processes for which
the layer height D and the horizontal scale L satisfy the relation is much less then 1. We will take the three-
dimensional equations of the hydrothermodynamics of dry atmosphere in a rotating Cartesian coordinate system
[Pen85] as the original equations
∂u ∂u ∂u ∂u ∂Φ ∂ ∂u
+u +v +w =− + lv + AM ∆u + kM (1)
∂t ∂x ∂y ∂z ∂x ∂z ∂z
∂v ∂v ∂v ∂v ∂Φ ∂ ∂v
+u +v +w =− − lu + AM ∆v + kM (2)
∂t ∂x ∂y ∂z ∂y ∂z ∂z
∂w ∂w ∂w ∂w ∂Φ ∂ ∂w
+u +v +w =− + βθ + AM ∆w + kM (3)
∂t ∂x ∂y ∂z ∂z ∂z ∂z
∂u ∂v ∂w
+ + =0 (4)
∂x ∂y ∂z
∂θ ∂θ ∂θ ∂θ ∂ ∂θ
+u +v +w = AT ∆θ + kT (5)
∂t ∂x ∂y ∂z ∂z ∂z
∂ϕ ∂ϕ ∂ϕ ∂ϕ ∂2ϕ
+u +v +w + σϕ = AS ∆ϕ + kS 2 (6)
∂t ∂x ∂y ∂z ∂z
The initial and boundary conditions are as follows:
u = −cg sin(dd), v = −cg cos(dd), θ = θS , ϕ=0 t=0 (7)
∂u ∂v ∂θ ∂ϕ
= = w = 0, = 0, =0 z=D (8)
∂z ∂z ∂z ∂z
∂θ ∂ϕ
u = v = w = 0, = γ(θ − θS ), = αϕ − fS z=0 (9)
∂z ∂z
In Eqs. (1- 9) t is time, ∆ is the Laplace operator, Ox, Oy, and Oz are the eastward, northward, and upward
coordinate axes, (u, v, w) is the air flow velocity vector, Φ = RTm p′ /p is the geopotential fluctuation, where
R is the specific gas constant and Tm is the mean air temperature in the layer, p is the atmospheric pressure,
p = pp0 , where p is the potential pressure dependent only on the altitude, l is the Coriolis parameter, β = gθ
R
is the buoyancy parameter, θ = T pp0 Cp is the potential temperature, where T is the air temperature, p0 is the
atmospheric pressure near the ground, and Cp is the specific heat at a constant pressure; ϕ is the impurity
concentration, σ is the impurity absorption coefficient in the atmosphere, θS is the air temperature at the
roughness level of the underlying surface, cg is the geostrophic wind velocity [Gil82] at the upper free boundary
of the atmospheric boundary layer, dd is the geostrophic wind azimuth, γ is the heat transfer coefficient, α is the
coefficient of impurity absorption by the underlying
Pm surface, AM ,AT , AS , kM , kT , kS are coefficients of gorizontal
and vertical turbulent diffusion and fS = i=1 fi δ(x − xi )δ(y − yi ) -intensivity of sources of impurity, xi and yi
are coordinates of sources, m - number of sources. We will consider an LL area. The geostrophic wind velocity
cg above the atmospheric boundary layer and its direction, as well as the boundary layer height D, are assumed
to be known. The horizontal wind velocity fields are calculated from the formulas [Gil82] u = cg sin(dd) and
v = cg cos(dd), where dd = 0 corresponds to the north wind and dd = π/2 to the east wind. The wind can also
be preassigned as the layer-average velocity field (mean across the layer). At the lateral boundaries it is assumed
that
∂v ∂θ ∂ϕ
= 0, = 0, =0 (10)
∂n ∂n ∂n
n is vector of external normal.
For to model mathematically the impurity transport from a ground source we will introduce a quasi-
twodimensional model based on the locally-equilibrium approach. This technique was presented in [Shv00,
Shv09a, Sch98, Shv06].
For the numerical solution of the task the explicit finite difference scheme [Sch98] is used. We will construct
a grid, having entered discrete values of arguments:
xi = ih, i = 0, 1, . . . , N ; yj = jh, j = 0, 1, . . . , N h = 1/N (11)
n initial point of time
0 0 0
ji,j = j(0, i, j); yi,j = y(0, i, j); qi,j = q(0, i, j) (12)
On the following temporary layer the equation according to the explicit scheme pays off at:
n+1 n
qi,j − qi,j n n 1 n
n n
+ {yi,j , qi,j }= ∆qi,j − q̄ qi,j − q̄i,j (13)
t P es s
n+1 n m
ji,j − ji,j 1
f¯k d(xi − xk )d(yj − yk )
X
n n n n
+ {yi,j , ji,j } = ∆j − s̄ji,j + A (14)
t P es i,j
k=1
For boundary conditions:
n+1 n+1 n+1 n+1 n+1 n+1 n+1 n+1
j0,j = j1,j ; jN,j = jN −1,j ; ji,0 = ji,1 ; ji,N = ji,N −1 (15)
n+1 n+1 n+1 n+1 n+1 n+1 n+1 n+1
q0,j = q1,j ; qN,j = qN −1,j ; qi,0 = qi,1 ; qi,N = qi,N −1 (16)
3 Creation of Algorithm for Solution of Problem
Calculations are carried out in three stages, in three various programs:
1 stage: classification of a land relief:
1) In the MapInfo program the territory within 20 km from solid waste landfill in the item Perekop (southern
suburb of the city Kirovo-Chepetsk) is allocated. For this purpose the square with sizes of 20*20 km is under
construction and the ground is located in the center of the set area (Fig. 1). Further the given card layer (with
the allocated area) is transferred to the SIP program (Fig. 2);
2) For classification of a land relief raster images of May 25th, 2017 with an accuracy of 20 m at 1 pixel are
used. These rasters are entered in the SIP program, the card layer from the MapInfo program is enclosed and
further classification of the area by means of a method of classification ISODATA is made. The program classifies
the area by the following types: field; wood, bush; road, settlement; reservoir. This classification remains in the
form of a vector layer for a possibility of the subsequent use in the MapInfo program.
2 stage: creation of a grid of squares.
1) In the MapInfo program by means of the utility of GRIDVIEW the chosen area (20 km in the neighborhood
of the ground of the item Perekop) breaks into squares the sizes of 20*20 m.
2) For each of the received square is under construction centrodes where data are entered;
3) SQL inquiry which defines is created to what type of the area each of squares belongs. This definition
happens to the help of SQL of inquiry which essence in the following: if centrodes of a square gets to a certain
area, then and for all square the value of this area is appropriated. Further all results are entered in the table
where a certain type of the area is appropriated to each square.
3 stage: calculation by itself.
1) Range of cages to which the pollution source gets is determined by a grid of squares;
2) Settlement data are entered in files of initial data, values of coefficients are entered;
3) The program built in Fortran is started.
4 Results of Modelling
The parallel computational algorithm was realized in the Intel Fortran 12 in Packet Intel Cluster Studio for Linux
Open MP, installed on the Vyatka State University HPC Enigma X000 cluster supercomputer. The calculations
were carried out on the basis of the system of equations (11- 16) with the initial and boundary conditions. The
explicit difference scheme [Nau09] was used on a 1000 × 1000 grid. In accordance with the theory of Monin
and Obukhov [Pen85, Alo02, Mon88], the coefficients of vertical and horizontal turbulent viscosity, thermal
conductivity, and diffusion for mesoscale turbulent processes in the lower atmosphere were assumed the same,
namely, kM , T, S = lD2 , where D = 400m and AM , T, S = 400m2 /s.
In the reference frame chosen the westward wind was blowing from left to right. The wind velocity cg
was varied from 1 to 10 m/s. In most of calculations the velocity was 2 m/s; in this case, the temperature
inhomogeneity effect on the wind flow in the vicinity of a heat source is most clearly expressed. The interaction
between aerosol impurity and the underlying surface was taken into account on the basis of the information
on the nonuniformities of the temperature and absorption coefficient distributions taken from the map of land
utilization of the computation domain. The air temperature θS varied from 18◦ C outside populated areas to
23◦ C in the city of Kirov and Kirovo-Chepetsk. A minimum temperature was observable at the north boundary
of the area. The coefficient of impurity absorption by the underlying surface was taken to be α = 0.0139m−1
outside populated areas and α = 0.00139m−1 on their territories. A point impurity source was located on the
underlying surface, at the center of the region under consideration (within the city territory). In the calculations
it was also taken that l = 1.2410−4s−1 , σ = 5.6710−8s−1 , γ = 0.2510−3m−1 , fS = 0.999610−7kg/m4 , and
ϕMP C = 0.510−7kg/m3 .
In the calculations the layer-average fields of the impurity concentration, the air temperature, the stream
function, and the stream function disturbances were obtained. It is shown that in the case of a relatively weak
westward wind (with a velocity of 2 m/s) the horizontal temperature nonuniformity changes the wind flow
direction (Fig. 3 ). The layer-average air temperature varies from 18.5◦ to 21.5◦ C. Under the action of a heat
island a weak vortex motion arises over large populated areas (Fig. 4). This, in turn, changes the impurity
propagation direction (Fig. 4).
5 Summary
Modeling of mesoscale atmospheric processes is developed in connection with the solution of problems of mete-
orology and monitoring of the environment now. On classification of Belov and another [Kut91] three classes of
mesoscale processes are allocated: α- mesoscale (order of 200-2000 km), β- mesoscale (order of 20-200 km), γ-
mesoscale (2-20 km).
The α synoptic, describes processes of formation of atmospheric fronts, cyclones. The β- scale describes
orographical indignations, evolution of atmospheric processes over the industrial centers. The γ- scale describes
processes of transfer of aerosols from local sources. In work [Kut91] by means of three-dimensional model in
number investigates influence of thermal heterogeneity of the spreading surface on distribution of meteorological
characteristics in a boundary atmospheric layer. Application of the two-dimensional models received by averaging
across an interface is described in works [Ali80, Mat94]. In these works the mechanism of formation and devel-
opment of synoptic whirlwinds in a barocline to the atmosphere under the influence of horizontal inhomogeneity
of a stream without diffusion is investigated.
One of the most important problems of ecology is modeling of transfer and diffusion of impurity in the
atmosphere. Systematic researches of atmospheric diffusion in relation to questions of air pollution have begun
relatively recently. At school of sciences of G.I. Marchuk [Pen85, Alo02] three-dimensional models are developed
for a research of conditions of formation of processes of air pollution of local, regional and global scales under
the influence of natural and anthropogenic factors. The detailed review of works on this subject is provided in
work [Shv15a].
The model of transfer, average across layer, and diffusion of aerosols is used rather seldom. The complexity of
carrying out and interpretation of numerical experiments with three-dimensional models of hydrothermodynamics
induces to creation of simpler models which keep the most characteristic features of real processes in mesolarge-
scale atmospheric currents. One of such methods is use of quasi two-dimensional models [Ari87, Ari88, Shv00,
Shv09a], [Sch98, Shv06, Ryc09, Shv09b, Nau09], [Shv15a, Sha11, Shv12, Shv15b]. Earlier this method was used
by us for calculation of transfer of impurity from the dot and distributed sources of pollution in the neighborhood
of the large industrial center. In the presented work this technique is applied to assessment of impact of aerosol
emissions from solid waste landfills (the burning dumps). The studies in this formalization are very actual,
relevant and analogous problems weren’t earlier considered.
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Figure 1: The 20-km zone around polygon in Perekop in MapInfo program
Figure 2: The 20-km zone around polygon in Perekop in SIP program
Figure 3: Distribution of contaminations by the wind from west
Figure 4: Distribution of contaminations by the wind from north-east