Modeling dispersion dust Aerosol particles monitoring and

evaluation in desert south sahara

MOHAMMEDI FERHAT , HADDAD HANANE, LAGGOUN CHOUKI

Laboratory L.A.R.H.Y.S.S

Laboratory LMSM

University of Biskra, B.P 145 RP 07000, Biskra, ALGERIA

Abstract: This present study is desired to calculate the concentration in horizontal direction of

flow of pollutant. As any mathematical models of natural systems, a climate model is a

simplification. The degree of accepted simplification determines the complexity of the model

and restricts the applicability of the model to certain questions. Hence, the complexity of a

chosen model sets the limitations to its application. The quality of a climate model is not judged

by the mere number of processes considered, but rather by the quality of how chosen processes

and their couplings are reproduced.

Keywords: pollutants, models, advection, simulation

Received: June 12, 2022. Revised: July 15, 2023. Accepted: August 25, 2023. Published: September 18, 2023.

1. Introduction

Much progress has been made in the

monitoring, modeling and prediction of

African desert dust storms. Of particular

importance is the development of integrated

dust-storm monitoring and modeling

systems on the basis of numerical models,

satellite remote sensing, synoptic

observations and GIS (Geographic

InformationSystem) data. This paper has

three main goals:

- To introduce the physical basis and the

mathematical description of the different

components of the climate system and the

derivation of differential equations which

describe the most important climatic

processes?

- To introduce in the numerical solutions of

ordinary partial differential equations using

examples from climate modeling;

- To use and apply Matlab as a

mathematical-numerical tool. In this work

the predictability of atmospheric flow

depends on the current state of the

atmosphere. Predictability can be

determined by integrating an ensemble of

initial conditions that are within certain

predefined bounds. We employ the software

package Matlab for the numerical

simulations in this paper. The feasibility and

effectiveness of the proposed method is

demonstrated by computer simulation.

Some wildlife species require large stretches

of land in order to meet all of their needs for

food, habitat, and other resources. These

animals are called area sensitive. When the

environment is fragmented, the large patches

of habitat no longer exist. It becomes more

difficult for the wildlife to get the resources

they to survive, possibly becoming threatened

or endangered. While environmental

degradation is most commonly associated

with the activities of humans, the fact is that

environments are also constantly changing

over time. With or without the impact of

human activities, some ecosystems degrade

over time to the point where they cannot

support the life that is "meant" to live there.

The modeling of the scattering of the

pollutants in the atmosphere is based on the

resolution of an equation to the partial

derivatives that binds the temporal evolution

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

37

Volume 2, 2023

of the concentration in one point to the

phenomena of diffusion and transportation

in the atmosphere, the concentration of air

pollutants in the atmosphere is directly

linked to air quality. High ground level air

pollution concentration can affect both the

public’s health and the environment. There

are regulations in many countries that

require the applicant to do an air dispersion

modeling in order to obtain an approval

certificate for building a new facility.

Dispersion models can be used to predict the

cumulative effect of existing and planned

facilities. In order to predict Ground Level

Concentration (GLC) from various sources,

atmospheric dispersion models are essential.

In the setting of the modeling of the

scattering of the pollutants in the atmosphere

it remains to try to solve the equation

diffusion-transportation bound to the

concentrations of pollutants only. To solve

this equation various possibilities offer

themselves based: - on an algebraic

approach, and a numeric approach

In a first time we have, as makes usually

for reasons of calculation capacity,

privileged the algebraic method. This

method consists in replacing the equation to

the partial derivatives that conditions the

distribution of the concentrations by an

algebraic equation in which one takes into

account the phenomena physics of diffusion

and transportation through the intermediary

of coefficients bound downwind to the

distance, the stability and to the conditions

of broadcasts to the air atmosphere. The

method Gaussian is based on the hypothesis

of the stationeries. To introduce in the

numerical solutions of ordinary partial

differential equations using examples from

climate modeling; and, to use and apply

Matlab as a mathematical-numerical tool.

2. Approaches Mathematical

Physical

Atmospheric dispersion modeling refers to

the mathematical description of contaminant

transport in the atmosphere, physical and

chemical processes have to be described by

mathematical terms in the beginning of the

development of a continental air pollution

model [1, 5]. These processes are: horizontal

transport (advection), horizontal diffusion,

chemical transformations in the atmosphere

combined with emissions from different

sources, deposition of pollutants to the

surface, and vertical exchange (containing

both vertical transport and vertical

diffusion). The dispersion models are used

to estimate or to predict the downwind

concentration of air pollutants or toxins

emitted from sources such as industrial

plants, vehicular traffic or accidental

chemical releases. The partial differential

equation to be solved is the classical

advection dispersion equation extended with

source sink terms to account for the sorption

and degradation processes; the advection-

diffusion equation reduces to

(1)

The height difference between the virtual

source and the real source is called the

plume height. Due to the transient

conditions in which the particles is liberated

to the atmosphere, and being the dispersion

a three-dimensional phenomena, transient

results of concentration are generated for a

fixed height plane of interest (z).

The elevation phenomenon occurs as a

function of wind velocity. Consider the

numerical solution of the advection -

dispersion equation assuming that D=0. In

this case there is only advection without any

physical dispersion/diffusion

. .( )u C K c Q R

C

t



      



International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

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Volume 2, 2023

CC

V

tz







(2)

Explicit finite difference approximation

for

, 1 , , 1,i n i n i n i n

C C C C

V

tz









(3)

Where sub index i refers to node and sub

index n to time (n+1 unknown value and n

known).

The unknown concentration at time level

n+1 can be solved from

, 1 , 1,

(1 ( )

i n i n i n

tt

C v C v C

zz





  



(4)

Otherwise R is a nonlinear function of the

solute concentration C.

Equations (1-3), and (3-4) are solved

numerically using the finite difference

method.

3. Approaches Numerical

The main objective of this work is to

calculate the condition of dispersion and

diffusion of pollutants en atmosphere for

case in south Algeria. We consider again the

climate model given by equation (2.1) but

we examine its time dependence. It is clear

that an analytical solution is only possible

for few cases. For this reason, it has to be

solved using a numerical algorithm. Several

types of analytical solutions exist for the

transport/sorption/degradation problem but

they are limited to some special cases.

However, analytical solutions are very

useful tools to verify the accuracy of the

numerical solution methods and test the

correctness of a computer program. Elliptic

PDE’s are equations with second derivatives

in space and no time derivative [2,3]. The

most important examples are Laplace’s

equation, the formulations assume an

equidistant discretization; adjustments are

necessary if the grid’s resolution is spatially

dependent, Is the numerical solution (5-11)

consistent with the analytical solution;

Either to solve the hyperbolic system:

( , ) ( , ) ( , )

ii

i ij j i

j

uu

K x t m x t u f x t

tx



  





(5)

we didn't suppose here the conservation of

the sign of the characteristic ki(x,t) speed

( , )

i

dx k x t

dt 

(6)

Either ((x, t) a point of grid we write the

equations to the differentials that correspond

to him

So ki (x, t)<0 ; one writes, the numerical

solution converges towards the analytical

one.

Therefore we apply a transformation of

variables,

( , ) ( , )

( , )

( , ) ( , ) ( , )

ii

i

ij j i

j

u x t u x t

u x h t u x t

k x t h

m x t u x t f x t



 





(7)

If ki (x, t) > 0

Using central difference in space, and

forward difference in time we get

( , ) ( , )

( , )

( , ) ( , ) ( , )

ii

i

ij j i

j

u x t u x t

u x t u x h t

k x t h

m x t u x t f x t



 







(8)

Ui (x,t) the exact solution of the equations

to the partial derivatives that of the

derivatives first and seconds according to

the formula of Taylor

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

39

Volume 2, 2023

2

( , )

( , ) ( , )

2

( , ) ( , , )

i

ii

u x t

u x t u x t t

u x t n u x t

t

u x t xt

t





   



   













(9)

(0 1, )

iconst



  

,

Hence, it has been shown that the

numerical solution converges towards the

analytical solution

for arbitrarily small Δt

2

( , )

( , ) ( , ) ( , , )

()

i

i i i

i

u x t

u x h t u x t h x t h

x

const





   





(10)

This is a distinctive feature of the equation

to be solved. Central differences may also

cause general problems in the case, for

example, that periodic solutions with

unluckily chosen time steps should be

calculated.

Fig.1soil map geographic and biodiversity

south- Algeria[8]

4. Simulation

This Simulation was conducted in

MATLAB environment and the results are

presented for the case of three sources

configuration, in work of [4-9] we’ve

considered a single source in a constant

wind. To solve the 2-D governing Euler

equations a code was developed in this

work, with the software MATLAB

7.8.version using the Jameson’s scheme

(Jameson, 1981), which is a finite volume

spatial discretization method with artificial

dissipative term. We still need to include:

Multiple sources (still with constant

emission rate), Time-dependent wind

velocity, not aligned with x-axis, multiple

contaminants. Ultimately, solve the inverse

problem.

The Matlab code used to produce Fig. [2-4]

is given below. The Matlab code used to

solve Eq. (3-6) and Eq. (7-10) analytically

and numerically and plot Figs. 3 and 4 is

given below. The chemical reaction

equations were solved simultaneously with

the governing equations of transport reaction

diffusion in horizontal dispersion. We used

the Scharfetter-Gummel and Galerkin

methods in figure (5-6) for comparison.

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

40

Volume 2, 2023

5

10

15

5

10

15

20

0

20

40

60

80

100

120

x (km)

pollutans concentration as a Function of Distance

y (km)

vertical concentration

10

20

30

40

50

60

70

80

90

100

110

Figure.2.The solution of 3D transport in the

space (x) – time (t) diagram, visualized

-2

-1

0

1

2

-2

-1

0

1

2

-0.5

0

0.5

x

diffusion the different components in 3D

y

altitude

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-5

0

50

5

10

0

0.2

0.4

0.6

0.8

1

transmittance

diffusion pollutans particles transport

diffusion

Figure.3. the transport equation with

degradation and dimensionless space

variable

-6 -4 -2 0 2 4 6

-6

-4

-2

0

2

4

6

x

y

particle dispersion according to the wind speed

-10 -8 -6 -4 -2 0246810

-10

-8

-6

-4

-2

0

2

4

6

8

10

x

y

dispersion with low wind

Figure. 4. Transport with wind-Decay and

Degradation 2D.

.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

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DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Distribution verticale d’une concentration en fonction de la distance

Galerkin

Scharfetter-Gummel

décentréeUP-upwind

:

Fig.5 Profiles for fluid phase concentration

in case of transport

0.001

0.01

0.02

0.05

0.1

x (m)

y (m)

concentration (mg/m3), max = 0.18

0200 400 600 800 1000 1200 1400 1600 1800 2000

-100

-50

0

50

100

150

200

250

300

350

400

Figure: 6 concentration and dispersion as a

function of distance-contour lines

The effects of land pollution can be found

everywhere. Pollutants in the land not only

contaminate the land itself, but also have

far-reaching consequences [6, 9]. There are

a number of reasons that ecosystems [fig.5-

6], degrade over time. While it may not

always be the fault of humans, humans still

need to recognize the extent to which they

rely on the resources that the natural world

provides. In this sense, environmental

responsibility and stewardship are very

much a matter of self-preservation, and are

an integral part of healthy resource

management practices.

5. Conclusion:

When land pollution is bad enough, it

damages the soil. This means that plants

may fail to grow there, robbing the eco-

system of a food source for animals. Eco-

systems may also be upset by pollution

when the soil fails to sustain native plants,

but can still support other vegetation.

Invasive weeds that choke off the remaining

sources of native vegetation can spring up in

areas that have been weakened by pollution.

This Simulation was conducted in

MATLAB environment and the results are

presented for the case of three sources

configuration, in work of references [1-4]

we’ve considered a single source in a

constant wind. We still need to include:

Multiple sources (still with constant

emission rate), Time-dependent wind

velocity, not aligned with x-axis, multiple

contaminants. Ultimately, solve the inverse

problem. The suggested numerical solution

method for combined advection,

dispersion/diffusion and Biodegradation

gives very accurate results when compared

to analytical solutions. Many of the long-

lasting effects of land pollution, such as the

leaching of chemicals into the soil cannot be

easily reversed. The best way to deal with

land pollution is to keep it from happening

in the first place. A further important

motivation for the development and

application of climate models remains the

aim to assess future climate change.

References:

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Dispersion Modeling of Jaipur Fire, India

Research Journal of Chemical Sciences

ISSN 2231-606X, Vol. 2(2), 1-9, Feb.

(2012)

[2] Zlatev Z., Christensen J. and Eliassen A.,

Studying high ozone concentrations by

using the Danish Eulerian Model,

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(1993.

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

42

Volume 2, 2023

[3] Dixon, K. R. 1977. “Thermal Plumes

and Mercury Dynamics in Zooplankton.” In

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[8] https://www.google.dz/ cartography

south Algeria desert

[9] By Jared Skye BA Environmental

Science, Causes of Environmental

Degradation,

http://greenliving.lovetoknow.com/Causes_o

f_Environmental_Degradation

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

The authors equally contributed in the present

research, at all stages from the formulation of the

problem to the final findings and solution.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

Conflict of Interest

The authors have no conflicts of interest to declare

that are relevant to the content of this article.

Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2023.2.5

Mohammedi Ferhat,

Haddad Hanane, Laggoun Chouki

E-ISSN: 2945-0519

43

Volume 2, 2023