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River pollution components mean annual values estimation by computer modeling
K.J. Kachiashvili1, D.G. Gordeziani2, D. I. Melikdzhanian3, D.V. Nakani4
1I. Vekua Institute of Applied Mathematics, Tbilisi State University, Tbilisi, kartlos5@yahoo.com
2I. Vekua Institute of Applied Mathematics, Tbilisi State University, Tbilisi,
gord@viam.hepi.edu.ge
3Center of Ecological Safety, The Georgian Technical University, Tbilisi,
davidmelikdzhanian@yahoo.com
4Department of Engineering Ecology and Hydrology, Georgian Agrarian University, Tbilisi
The methods that allow with application of the computer modeling to estimate values of pollution
ingredients discharged from the pollution sources during a year in the rivers are offered. With the
help of the modeling results conclusions are made about distribution, change and provenance
reasons of river pollutants values on the control sections.
Key words: modeling, pollution, river, control section, pollution sources.
Introduction
The purpose of the work is by computer modeling to estimate mean annual value of pollution
components discharged from pollution sources working on river control sections. As an example
are considered located in the western Georgia and running in The Black Sea four rivers of the river
Khobistskali basin (which is one of basic pollution source of the Black Sea), which basic pollution
sources are agricultural fields, cattle-breeding farms and small cities, located on these rivers. The
data of the rivers pollution are received with the help of monthly measurements of the appropriate
components during two years in sixteen control cross-sections of the rivers (see fig. 1, where by red
triangles are marked the monitoring cross-sections, and by red circles are marked the cities located
on the rivers). The length of the river Khobistskali that is the greatest river of the Khobistskali basin
is – 74.8 km, the medium width is 68 m, and the medium depth is 1.035 m. The distances between
six monitoring cross-sections located on it (see fig. 1) accordingly are: 23 km, 5 km, 15.5 km, 1.3
km and 30 km. The length of the river Chanistskali is 37.3 km, the medium width is 17.5 m, and
the medium depth is 0.51 m. The distance between two monitoring cross-sections located on it (see
fig. 1) is 37.3 km. The length of the river Ochkhomuri is 42.7 km, the medium width is 19 m, and
the medium depth is 0.39 m. The distances between monitoring cross-sections located on it (see fig.
1) accordingly are: 11.7 km, 12 km and 19 km. The length of the river Choga is 12 km, the medium
width is 7 m, and the medium depth is 0.18 m and the distance between monitoring cross-sections
located on it (see fig. 1) is 11 km.
The results received by computer modeling
The modeling was realized with applied programs package for IBM-compatible personal
computers for calculation of polluting substances concentration in any point of a river. It allow
calculate the pollutants concentrations in any point of the river depending on pollution conditions
from many sources. This package is developed by the authors of the given work [1, 2]. In it are
realized spatially one –, two – and three – dimensional advective diffusion models under different
initial and boundary conditions [3 – 5]. In particular: a) with a not local boundary condition on the
end of a controllable section with an allowance for the coefficient of natural self purification of
the river; b) with a boundary condition of full mixing at the end of the river controlled section; c)
without the account of vertical advection with a not local boundary condition on the end of a
controllable section with an allowance for the coefficient of natural self purification of the river;
d) without the account of vertical advection with a boundary condition of full mixing at the end of
the river controlled section; e) diffusion equation with a not local boundary condition on the end of
a controllable section with an allowance for the coefficient of natural self purification of the
river; f) diffusion equation with a boundary condition of full mixing at the end of the river
controlled section.
It is supposed, that the researched section of the river contains some of dot or extended pollution
sources. They can be, for example, ends of pipes, through which pollution sources dump in the
river wastes, the underground sources or other rivers running into the researched river on a consi -
dered section. Exactly such sources are agricultural fields, cattle-breeding farms, on the rivers
located built-up areas and comparatively small rivers, which run in the big rivers. It is supposed,
that in the beginning of the given section the concentrations of polluting substances are known, i.e.
their meanings are measured that have place in the considered case indeed.
Modeling have carried out by basic biological parameters, nitrates (NO3) and phosphates (PO4),
outgoing from agricultural fields and cattle-breeding farms. The monitoring results of 2002 and
2003 were used for modeling. The idea of modeling consists in the following. On the basis of the
monitoring results are known the mean annual concentrations of the mentioned components in each
control cross-sections of the rivers. If we admit, that on the given section of the river the pollution
sources do not work, then existing in the top section of the river the pollution level should decrease
in the bottom section at the expense of proceeding in the river of natural processes and ability of
self purification. In reality for the Khobistskali’s basin rivers this fact does not take place, as on
each section of the river the appropriate pollution sources work. Therefore, if with the help of the
developed mathematical models we calculate the polluting component concentration in the bottom
section of the river on existing concentration in the top section and after a condition, that on this
section of the river does not work any pollution source except of other river (if such runs in it on
this section), then with a difference between measured and calculated concentrations we easily
calculate polluting components values discharged in the river from pollution sources worked on
this section.
In considered concrete case for modeling was used one-dimensional mathematical model of
pollution diffusion and transfer [3 – 7]. It is caused by the following circumstances: in first, on the
geometrical sizes of the considered rivers (in a case, when length of that section of the river, which
modeling is carried out, 10 times and more surpass its width, to provide width is not meaningful
because of full mixing of water of the river on a considered section of the river; Also, if width of
the river 10 and more time surpasses its depth, for the same reason, the taking into account of depth
loses the sense [6]), and in second, because the average year data are used and the accuracy of
model more high rank, in this case, loses the sense. The modeling results received by us for the
Khobistskali’s basin rivers with the help of one, two and three dimensional models, precisely have
confirmed the mantioned reason. I.e. two and three dimensional models on all width and depth
were given identical results with one-dimensional model that completely corresponds to the above-
mentioned.
The concentrations of NO3 and PO4 on all the lengths of the rivers Choga, Ochkhomuri, Chanis-
tskali and Khobistskali are calculated through the identical steps. In case of the river Choga the
length of the step is equal to 343,75 meters, in case of the r. Ochkhomuri the length of the step is
equal to 1334,4 meters, in case of the r. Chanistskali the length of the step is equal to 1165,6
meters, and in case of the r. Khobistskali the length of the step is equal to 2337,5 meters. For the r.
Choga the time of full updating of water, i.e. that time, which is necessary for runing of water from
a source of the river up to its confluence in other river, is equal to
15 h 36 min. For the rivers
Ochkhomuri, Chanistskali and Khobistskali this time are accordingly equaled to
39 h 12 min,
20 h 25 min,
9 h 27 min. Therefore, at modeling of the river through the appropriate interval of
time it is possible taking of calculated value of concentration in any point of the river on all length,
as it corresponds to the concentration in initial section recalculated by the appropriate model in the
interesting point.
2
In the tables 1, 2, 3, 4 are given the calculation results of mean annual values of the pollutants
got from the appropriate sources in separate sections of the rivers during 2002, 2003.
The calculation of mean annual values of pollutants discharged in the given section from above
located pollution sources carried out as follows
)(365)(24(sec)60sec)(sec)/()/( 3
mod dayhourmvEmgSSyearkgS mesyear
,
where
year
S
- is mean annual value of a polluting component discharged in the given section of the
river from sources working on this section;
mes
S
- is measured mean annual value of concentration of a polluting component on the
appropriate section;
mod
S
- is mean annual value of concentration of a polluting component calculated by the model
on the appropriate section;
vE
- is the flow rate in the appropriate section of the river.
The calculated results by mathematical models are given in the tables 1, 2, 3 and 4. In the two
last column of the tables are given by the considered rivers brought mean annual volumes of pollu-
tion components in places of them confluence calculated as by directly measurement results, and by
direct summation of the calculated by model the appropriate values in separate sections of the
rivers. On the basis of these results is concluded:
- In 2002, 2003 r. Choga by parameter NO3 basically was polluted at sources, up to first cross-
section. In 2002 by parameter PO4 the river was polluted in more to bottom part, i.e. between the
first and second cross-sections. In 2003 the situation has changed also in parameter PO4 the river
was polluted more up to the first cross-section. The pollution of the river by both considered
parameters in 2003 is significant decrease after comparison with 2002: by parameter NO 3 from
566,4 ton/years till 276,4 ton/years (
2 times), and by parameter PO4 from 4,18 kg/years till 3,17
kg/years (
1,32 times). A difference between measured and calculated values defined mean
annual volumes of the polluting components brought by the river Choga in the r. Ochkhomuri, on
our sight, specifies high quality of modeling, if take into account that circumstance, that the
modeling was carried out on the basis of the defective initial data (because of absence of the better).
For example, expenses of the river (as well as for other rivers of the Khobistskali’s basin)
completly was measured only in 2003, in 2002 only three times were measured the water expenses;
exactly are not known the coefficients of diffusion and non conservativity etc. Despite of told the
modeling and measurement results with acceptable accuracy coincide with each other, that specifies
accuracy of the used technique.
- The pollution of the river Ochkhomuri by parameter NO3 in 2002 in its all control sections
was practically equally, except of last section, where the pollution
1,9 times is surpassed of the
pollution of other sections. In 2003 the river is most of all polluted with mantioned parameter on
initial and final sections. In 2002 the third section of the river is most of all polluted by parameter
PO4, and in 2003 namely this sextion is polluted less of all. The r. Choga runs in the r. Ochkhomuri
in this section. As already have noted in 2002 the pollution of the r. Choga by parameter NO 3
2
times are surpassed the pollution of 2003, and by parameter PO4 -
1,32 times. The pollution of
the r. Ochkhomuri on the last section (where the r. Choga runs in it) in 2002
2,7 times are surpas-
sed the pollution of 2003 by parameter NO3 and
2,8 times - by parameter PO4. The mean annual
volumes, calculated by model and directly by measured meanings, brought in of pollution com-
ponents by the river Ochkhomuri in the river Khobistsksli practically are equal among themselves.
Brought by the river Ochkhomuri in the river Khobistsksli the mean annual values of pollution
components on both considered components considerably has decreased after compa rison with
2002: by parameter NO3 from 7,119 ton/years till 3,685 ton/years (
2 times), and by parameter
PO4 from 36,212 kg/years till 33,661 kg/years (
1,08 times).
- The r. Chanistskali by parameters NO3 and PO4 both in 2002, and in 2003 is more polluted in
the second section than in the first. In this section the river pollutes not only by the agricultural
fields and cattle-breeding farms, but also by waste water of the city Tsalendjikha too. The pollution
of the river by parameter NO3 in 2002 surpasses the pollution of 2003 and by parameter PO4 the
3
pollution of 2002 lags from the pollution of 2003. In particular, at 2002 the mean annual volume of
the component NO3 discharged in the river Khobistskali is equal to 18,026 ton/year, which on the
volume of 2003, 11,197 ton/year, surpass
1,6 times, and mean annual volume of the component
PO4 in 2002 is equal to 88,515 kg/year, which lags from mean annual volume of 2003, 123,018
kg/years,
1,4 times. Calculated by mathematical models and directly by measured values brought
by the river Chanistskali in the river Khobistskali volumes of pollution components coincide with
each other by very high accuracy. In our opinion, one of the reasons of such good result consists
that calculation of self purification coefficient of the river for considered components was possible
for data of the river Chanistskali, which were used for the other rivers too.
- The river Khobistskali in 2002 is most of all polluted in the first and last sections. On these sec-
tions, except of agricultural fields and cattle-breeding farms the river accordingly becomes polluted
by waste water of the cities Chkhorotsku and Khobi. On the next place by pollution there is the
fourth section of the river, where the river Chanistskali runs into it. In 2003 the river is almost
equally polluted in the first and fourth sections, i.e. the sections on which work the city Chkhoro -
tsku and the r. Chanistskali. The last section, where on the river work the city Khobi, is one of least
polluted. This fact is very much interesting, which one more time confirms the reason, that by the
considered components the basic pollution sources of the rivers are agricultural fields and cattle -
breeding farms. The pollution of the r. Khobistskali by the parameter NO3 in 2002 surpasses the
pollution of 2003 and by parameter PO4 the pollution of 2002 lags behind pollution of 2003. In
particular, by the river Khobistskali in the Black Sea introduced the mean annual volume of the
component NO3 is equal to 62,772 ton/year, which surpasses the volume of 2003 43,605 ton/years
1,4 times, and the mean annual volume of the component PO4 for 2002 is equal 562,695 kg/year,
which lag from the mean annual volume of 2003 673,473 kg/year
1,2 times. The calculated by
the mathematical model and in direct by measured values brought by the river Khobistskali in the
Black Sea volumes of pollution components coincide with each other with acceptable accu racy,
especially if we lake into account the above mentioned (in case of the river Choga).
Conclusion
With application of the mathematical models, developed by authors of this work, and appropriate
program realizations of transport in the rivers of pollution components have carried out the
calculation of pollution components values discharged for 2002 and 2003 on sections of the rivers
between the control cross-sections from appropriate pollution sources. By the help of these values:
1) have estimated a share of the pollution sources working on each of the section of the river in
total amount of the river pollution; 2) have estimated a change of pollution components values
discharged for 2002, 2003 on separate sections of the river, i.e. in the concrete the efficiency of
those measures which were carried out in these years on the mantioned pollution sources in the
appropriate region; 3) within the framework of those opportunities, which are given by division of
the rivers into the monitoring sections, from each other have divided working on the river
agricultural and others (for example, cities, located on the rivers; into them run other rivers)
pollution sources; 4) developed and tested on the real data the mathematical models of rivers
pollution are the component of ecologo-economic models of the considered agricultural region with
which help possibly to calculate ecological loading coming on the environment, in particular, on
closely laying river and agricultural fields from the single area of a farmer fild in view of its initial
condition and brought in fertilizers, and also in the existing situation to calculate quantity and
quality of expected harvest of concrete agricultural culture, on the basis of that will be appreciated
the expected economic efficiency realized agricultural projects and to the farmers will be given the
economically justified recommendations for action.
References
[1] Kachiashvili K.J., Gordeziani D.G., Melikdzhanian D.Y., Khuchua V.I., Stepanishvili V.A.
Software Packages for Automation of Environmental Monitoring and Experimental Data Proces-
4
sing // Proceedings of the third international conference advances of computer methods in
geotechnical and geoenvironmental engineering, Moscow, 1 – 4 February, 2000. p.p. 273-278.
[2] Kachiashvili K.J., Gordeziani D. G., Melikdzhanian D. I., Stepanishvili V.A. Packages of the
applied programs for the solution of problems of ecology and processing of the experimental data //
Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 17,
# 3, 2002. p.p. 97 – 100.
[3] Kachiashvili K.J., Gordeziani D.G., Melikdzhanian D.I. Mathematical models of Pollutants
Transport with Allowance for Many Affecting Pollution Sources // Urban Drainage Modeling
Symposium, May 20-24, 2001, Orlando, Florida. P. 10.
[4] Kachiashvili K.J., Melikdzhanian D. I. Analytical description of the coastal line of the river for
simplification and improvement of process of calculation of polluting substances concentration //
Reports of Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics, Vol. 17,
# 3, 2002. p.p. 101 – 109.
[5] KachiashviIi K.J., Gordeziani D. G., Melikdzhanian D. I. Mathematical modeling quantity and
quality river water in urban areas // “Managing Water Resource Extremes: Are We for Floods and
Droughts of the 21-th Century?”, Water Resources Planning and management Council Environ -
mental and Water Resources Institute of ASCE, Roanoke, Virginia, May 19-22, 2002.
[6] Karaushev A. V. River Hydraulic. – Leningrad: Hydrometeorological Establishments, 1969.-
416 p.
[7] Primak A.V., Kafarov V.V., KachiashviIi K.I. System analysis of air and water quality control.-
Kiev: Naukova Dumka, 1991.-360 p.- (Science and technical progress)
The table 1. The calculation results of pollutants mean annual meanings got from the
appropriate sources in separate sites of the r. Choga during 2002, 2003.
R. Choga
Year The pollu-
tant ingre-
dient
Until the
first
section
Between
the control
section
Flow into the
r. Ochkhomuri
(by measuring)
Flow into the r.
Ochkhomuri
(by modeling)
2002 NO3
kg/year
381,2 185,2 503,6 566,4
PO4
kg/year
1,68 2,5 3,8 4,18
2003 NO3
kg/year
252,8 23,6 234,73 276,4
PO4
kg/year
2,2 0,972 2,814 3,172
The table 2. The calculation results of pollutants mean annual meanings got from the
appropriate sources in separate sites of the r. Ochkhomuri during 2002, 2003.
R. Ochkhomuri
Year The
pollutant
ingredient
Until the
first
section
In the
first site
In the
second
site
In the
third site
Flow into
the r. Kho-
bistskali
(by mea-
suring)
Flow into
the r. Kho-
bistskali
(by
mode-
ling)
2002 NO3
ton/year
1,494 1,392 1,45
9
2,774 7,390 7,119
PO49,170 8,316 15,663 3,063 36,375 36,212
5
kg/year
2003 NO3
ton/year
1,125 0,8844 0,537 1,140 3,894 3,685
PO4
kg/year
8,292 7,477 5,523 12,36
9
40,800 33,661
The table 3. The calculation results of pollutants mean annual meanings got from the
appropriate sources in separate sites of the r. Chanistskali during 2002, 2003.
R. Chanistskali
Year The pollu-
tant ingre-
dient
Until the
first
section
Between
the control
section
Flow into the r.
Khobistskali
(by measuring)
Flow into the r.
Khobistskali
(by modeling)
2002 NO3
ton/year
1,326 16,7 18,03 18,026
PO4
kg/year
9,5 79,012 88,683 88,515
2003 NO3
ton/year
1,5 9,7 11,198 11,197
PO4
kg/year
20,749 102,269 122,872 123,018
The table 4. The calculation results of pollutants mean annual meanings got from the
appropriate sources in separate sites of the r. Khobistskali during 2002, 2003.
R. Khobistskali
Year The
pollutant
ingredie
nt
Until the
first
section
In the
first site
In the
second
section
In the
third
section
In the
fourth
section
In the
fifth
section
Flow into
the black
sea (by
measuring)
Flow into the
black sea by
sections
(by modeling)
200
2
NO3
ton/year
11,75
4
16,3
37
4,94
9
2,31 14,66
9
12,7
53
52,710 62,772
PO4
kg/year
121,
027
106,8
5
32,9
49
61,5
27
79,38
6
160,
956
457,278 562,695
200
3
NO3
ton/year
8,48
8
11,3
8
6,55
3
0,879 12,68 3,62
5
36,809 43,605
PO4
kg/year
128,
274
200,9
46
25,7
84
81,38
4
198,1
89
39,49
6
560,809 673,473
6
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Black Sea
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Khobi District
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5 0 5 10 15 20 Km
Fig. 1. The river Khobistskali’s basin with control sections.
