CC BY
35
УДК 504.51(28):661.715.6
Jamil A. K. M. Rahman1, L. I. Kantor2, E. V. Druzhinskaya1, E. A. Kantor1
ANALYSIS OF THE UFA RIVER CONDITION BASED ON BENZO(A)PYRENE CONCENTRATION AT DIFFERENT
WATER SOURCE SECTIONS
I Ufa State Petroleum Technological University I, Kosmonavtov Str., 450062, Ufa, Russia; ph. (347) 2420718, e-mail: evgkantor@mail.ru 2Ufavodokanal Municipal Unitary Enterprise I57/2, Rossiskaya Str, 450098, Ufa, Russia
Джамиль А. К. М. Рахман (асп.)1, Л. И. Кантор (к.т.н.)2, Е. В. Дружинская (ст. преп.)1, Е. А. Кантор (д.х.н., проф.,зав.каф)1
АНАЛИЗ СОДЕРЖАНИЯ БЕНЗ(А)ПИРЕНА В РАЗЛИЧНЫХ СТВОРАХ Р. УФЫ
1 Уфимский государственный нефтяной технический университет, кафедра физики 450062, г. Уфа, ул. Космонавтов, I; тел. (347) 24207I8, e-mail: evgkantor@mail.ru 2Муниципальное унитарное предприятие «Уфаводоканал» 450098, г. Уфа, ул. Российская, I57/2
Проведен анализ результатов определения содержания бенз(а)пирена в воде в трех створах реки Уфы в 1995—2012 гг. с применением сезонной декомпозиции временного ряда. Использованы аддитивная и мультипликативная модели, для выделения сезонной составляющей применены методы скользящих средних, среднемно-голетних и среднегодовых значений. Вычислены сезонные индексы. Для моделирования предложено использовать линейную зависимость количества бенз(а)пирена в различных створах источника воды. Показано, что коэффициент корреляции превышает 0.97.
Ключевые слова: бенз(а)пирен; временной ряд; корреляционный анализ; полициклические ароматические углеводороды; сезонный индекс.
This purpose of this article is to examine the analysis of the results that determine the concentration of benzo(a)pyrene in water at three different cross-sections situated along the Ufa River using seasonal decomposition of the time series according to the measurement data gathered between years 1995 and 2012. Additive and multiplicative models were used; values of the moving average, the multi-year average and annual average methods were used to isolate the seasonal component. Seasonal indices were calculated. For modeling purposes, it is convenient to use linear dependence of the amount of benzo(a)pyrene measured at the various cross-sections of a water source. By using the moving average method it was found that correlation coefficient exceeds 0.97.
Key words: benzo(a)pyrene; correlation analysis; moving average; seasonal indices; time series analysis.
Previously, we analyzed the solution state in Ufa River at the three sections, which were located before the industrial area and the city downtown (section 1), beyond the industrial area yet before downtown (section 2), and beyond city limits (section 3) The study is based on the results of quantitative chemical analysis of benzo(a)pyrene (B(a)P) concentration in Ufa River, as provided by the Center of Analytical Control, Municipal Unitary Enterprise «Ufavodokanal» for the years 1995— 2003 3 and 2004-2012.
Дата поступления 02.05.14
It is assumed that the extension of the period of observation provides a more accurate mathematical description yielding higher level of predictability around a described parameter.
The analysis of generalized time series of B(a)P concentration in River Ufa sections 1-3 was completed, based on the observations made over the course of 18 years between 1995 and 2012. Resulting tendencies and significant deviations have been discussed in detail previously 3, for two specific periods (19952003 and 2004-2012).
Е1дыгв 1. Тгте series of Ьвпг(а)ругепв сопсеп&гаИоп8 аЬ Ькгее cross-sections of и/а Кювг гн 1995—2012
Time series component values in benzo(a)pyrene concentration in the water of cross sections 1-3 of Ufa River in 1995-2012, %
Smoothing methods Moving average Annual average Multi-year average
Models Add Mult Add Mult Add Mult
Section 1
Deterministic 19 18 21 20 21 23
Irregular 81 82 79 80 79 77
Section 2
Deterministic 11 11 12 11 12 15
Irregular 89 89 88 89 88 85
Section 3
Deterministic 18 19 20 19 20 13
Irregular 82 81 80 81 80 87
In general, during the study period of 1995—2012, decrease of B(a)P presence is observed in all three sections. This can be confirmed with the following data evaluation since 2001 B(a)P concentration in water of more than 1.0 ng/dm3 was recorded twice in section 1 (October 2003 and May 2009) and four times in section 3 (April 2001, December 2002, January 2009, April 2009 December 2012), 1.21 ng/dm3 maximum B(a)P concentration in section 2 was recorded in May 2001 (Fig. 1).
Implementation of the time series analysis to describe B(a)P concentration in sections 1—3 includes the construction of both additive (Add) and multiplicative (Mult) models with different smoothing options moving averages (MA), annual (AA) and multiyear averages (MulA) (table 1) 4-10.
Based on the provided table results, it must be mentioned that in all sections changes of the time series component are practically independent from both the model type and the smoothing method. So, in section 1 random component is in the range of 77—82 %, in section 2 - 85-89 %, in section 3 - 80-87 %. Furthermore, in all sections seasonal factor value is not greater than 8%, and in most cases lie in the range of 4-6 % (table 1).
It is expected that multi-year average values for the period 1995-2012 will have intermediate values compared with this indicator for the periods 1995-2003 and 2004-2012, and as both the observation period include nine years, figures for annual average for the period 19952012 are almost average value (table 2).
Table 2
Multiyear average values in sections 1-3 at various time periods
Sections 3 Multiyear averages, ng/dm
1995-2003 2004-2012 1995-2012
Section 1 0.64 0.26 0.45
Section 2 0.72 0.26 0.49
Section 3 0.76 0.33 0.54
Table 3
Correlation coefficient between the parameters of the time series of B(a)P concentration in water sections 1-3 in the period 1995-2003/2004-2012
Period/Period AA MA MA* Conc.
Section 1
1995-2003/ 2004-2012 -0.14 0.05 -0.95 -0.16
Section 2
1995-2003/ 2004-2012 0.20 0.14 -0.97 -0.14
Section 3
1995-2003/ 2004-2012 -0.21 -0.07 -0.91 -0.08
Interesting results are obtained during the search for correlations among water quality indicators in different sections for different periods of observations (table 3, 4). It is only in the case with moving averages* (carried out averaging of moving averages (MA*) obtained for the period 1995-2003, by calculating the average values corresponding to each month of the annual cycle) values that the derived correlation coefficient is high between the periods 1995-2003/2004-2012.
Moreover, the negative values for this indicator suggest multidirectional changes of compared quantities.
Correlation coefficient values between the annual averages (AA), Moving averages (MA), Moving averages* (MA*) and B(a)P concentrations in sections 1-3 of Ufa River during the different periods
Sections AA MA MA* Conc.
1995-2003
Section 1/ Section 2 0.79 0.63 0.95 0.21
Section 1/ Section 3 0.97 0.92 0.94 0.49
Section 2/ Section 3 0.70 0.45 0.99 0.26
2004-2012
Section 1/ Section 2 0.94 0.90 0.90 0.64
Section 1/ Section 3 0.85 0.95 0.74 0.44
Section 2/ Section 3 0.89 0.93 0.88 0.53
1995-2012
Section 1/ Section 2 0.85 0.78 0.95 0.29
Section 1/ Section 3 0.97 0.95 0.97 0.55
Section 2/ Section 3 0.78 0.67 0.99 0.32
Table 5
Seasonal indices of the time series of B(a)P concentration in sections 1-3 of Ufa River using different models and smoothing methods during the period 1995-2012
Smoothing < < < < < < < < <
methods 2 < iE 2 < iE 2 < iE
Additive model
Months Section 1 Section 2 Section 3
January 0.09 0.17 0.17 -0.12 0.06 0.06 0.16 0.40 0.40
February -0.07 -0.05 -0.05 -0.12 -0.07 -0.07 -0.11 -0.05 -0.05
March -0.05 -0.11 -0.11 -0.17 -0.19 -0.19 0.00 -0.10 -0.10
April 0.07 0.05 0.05 0.03 0.07 0.07 0.08 0.07 0.07
May 0.00 0.20 0.20 -0.03 -0.05 -0.05 0.06 0.06 0.06
June 0.03 0.03 0.03 -0.10 -0.16 -0.16 -0.13 -0.17 -0.17
July -0.16 -0.18 -0.18 -0.11 -0.12 -0.12 -0.06 -0.09 -0.09
August -0.06 -0.09 -0.09 -0.16 -0.17 -0.17 -0.12 -0.15 -0.15
September -0.05 -0.08 -0.08 0.43 0.38 0.38 -0.17 -0.20 -0.20
October 0.06 0.02 0.02 0.03 0.00 0.00 0.20 0.18 0.18
November 0.10 0.05 0.05 -0.01 -0.04 -0.04 0.04 0.00 0.00
December 0.06 0.00 0.00 0.33 0.28 0.28 0.04 0.06 0.06
Multiplicative model
Months Section 1 Section 2 Section 3
January 1.15 1.23 1.37 0.88 1.11 1.13 1.23 1.35 1.73
February 0.92 0.99 0.90 0.81 0.96 0.85 0.85 0.94 0.90
March 0.90 0.92 0.76 0.76 0.78 0.62 1.00 0.96 0.82
April 1.26 1.25 1.12 1.29 1.27 1.14 1.21 1.19 1.14
May 0.99 1.11 1.43 1.22 1.18 0.90 1.06 1.02 1.11
June 0.91 0.90 1.06 0.87 0.82 0.67 0.75 0.72 0.68
July 0.66 0.64 0.60 0.84 0.80 0.77 0.76 0.70 0.84
August 0.69 0.66 0.80 0.73 0.68 0.65 0.79 0.75 0.72
September 0.87 0.81 0.82 1.22 1.14 1.78 0.66 0.68 0.64
October 1.29 1.21 1.04 1.06 0.97 1.01 1.19 1.09 1.32
November 1.12 1.05 1.11 1.01 0.96 0.92 1.27 1.22 0.99
December 1.24 1.24 1.01 1.32 1.33 1.57 1.25 1.37 1.10
The correlation coefficients between the values of the seasonal indices derived with the use of different models and smoothing methods in the time series analysis of B(a)P content during the period 1995-2012 within sections 1-3
Models and smoothing methods Additive Multiplicative
MA AA MulA MA AA MulA
Section 1
Section 1 Additive MA. 1.00 0.75 0.75 0.87 0.83 0.75
AA 0.75 1.00 1.00 0.61 0.73 1.00
MulA 0.75 1.00 1.00 0.61 0.73 1.00
Multiplicative MA. 0.87 0.61 0.61 1.00 0.96 0.63
AA 0.83 0.73 0.73 0.96 1.00 0.75
MulA 0.75 1.00 1.00 0.63 0.75 1.00
Section 2
Section 2 Additive MA. 1.00 0.94 0.94 0.79 0.67 0.94
AA 0.94 1.00 1.00 0.76 0.78 1.00
MulA 0.94 1.00 1.00 0.76 0.78 1.00
Multiplicative MA. 0.79 0.76 0.76 1.00 0.90 0.76
AA 0.67 0.78 0.78 0.90 1.00 0.78
MulA 0.94 1.00 1.00 0.76 0.78 1.00
Section 3
Section 3 Additive MA. 1.00 0.89 0.89 0.88 0.79 0.89
AA 0.89 1.00 1.00 0.78 0.80 1.00
MulA 0.89 1.00 1.00 0.78 0.80 1.00
Multiplicative MA. 0.88 0.78 0.78 1.00 0.96 0.77
AA 0.79 0.80 0.80 0.96 1.00 0.80
MulA 0.89 1.00 1.00 0.77 0.80 1.00
The conducted search of the correlations between the parameters characterizing the time series of B(a)P presence in sections 1—3 and during the different periods of time indicate that the relationship between the concentrations of B(a)P is evaluated as mild, moderate and noticeable 11, with the largest correlation coefficient being less or equal to 0.64 (table 4). Smoothing of the B(a)P concentration time series significantly increases the correlation coefficient. Tightness of the bond becomes strong and quite strong, with an exception of two reported values that suggest largely moderate correlation (table 4).
The values of seasonal indices (an additive model) for all sections and various methods of smoothing vary within —0.19—0.38 ng/dm3. Implementation of a multiplicative model results in the respective range of the same parameter within 0.60-1.78 ng/dm3 (table 5).
The relatively low correlation coefficient of 0.63 describes the relationship between the values of seasonal indices obtained through the multiplicative modeling and by using the moving averages and the multi-year average; in all other cases, the correlation coefficient is
greater than 0.7 (table 6). This, combined with the fact that the contributions of the components to the value of B(a)P concentration in water (table 1), allows us to conclude that additive and multiplicative models are in sufficient compliance, thus confirming the possibility of using any smoothing method available for time series processing.
Comparison of seasonal indices, determined at different sections (table 7) shows that the correlation coefficient values are in the range from 0 to 0.88.
Low correlation coefficients are attributed to the additive models when compared to both the additive and multiplicative models. Strongest interactions are definitive of the multiplicative models which use the smoothed annual average of B(a)P concentration. In this case the correlation coefficients obtained are 0.75 (sectionl— section 2), 0.88 (sectionl — section 3) and 0.63 (section 2— section 3). Therefore, in order to calculate the concentration of B(a)P in water at other sections based on experimentally obtained data for one of the sections, it is appropriate to implement the
Table 8
The results of correlation analysis - establishing the relationship between the values of the seasonal indices derived with the use of various models and smoothing methods during
the period 1995-2012 within a single section
The correlation coefficients between the values of the seasonal indices derived with the use of different models and smoothing methods in the time series analysis of B(a)P content during the period 1995-2012 between the sections1-3
Models and smoothing methods Additive Multiplicative
MA AA MulA MA AA MulA
Section 1
MA. 0.19 -0.01 -0.01 0.32 0.21 -0.01
см Additive AA 0.28 0.13 0.13 0.42 0.35 0.13
с о MulA 0.28 0.13 0.13 0.42 0.35 0.13
+j о ф MA. 0.45 0.41 0.41 0.62 0.58 0.41
Ю Multiplicative AA 0.52 0.55 0.55 0.70 0.75 0.56
MulA 0.27 0.12 0.12 0.42 0.35 0.13
Section 1
MA. 0.65 0.59 0.59 0.78 0.79 0.59
СО Additive AA 0.62 0.68 0.68 0.70 0.77 0.68
с о MulA 0.62 0.68 0.68 0.70 0.77 0.68
+j о ф Ю MA. 0.80 0.60 0.60 0.86 0.86 0.61
Multiplicative AA 0.78 0.61 0.61 0.85 0.88 0.62
MulA 0.61 0.68 0.68 0.69 0.77 0.68
Section 2
MA. -0.07 0.07 0.07 0.31 0.41 0.08
СО Additive AA -0.10 0.16 0.16 0.20 0.47 0.16
с о MulA -0.10 0.16 0.16 0.20 0.47 0.16
+-< о ф Ю MA. 0.04 0.16 0.16 0.41 0.53 0.16
Multiplicative AA 0.12 0.29 0.29 0.41 0.63 0.29
MulA -0.09 0.16 0.16 0.21 0.47 0.17
Smoothing methods Models Sections K b R2
MA Add/.Mult 1/1 2.321 0.996 0.757
2/2 0.885 1.000 0.616
3/3 1.696 1.003 0.775
AA Add/. Mult 1/1 1.442 0.999 0.537
2/2 0.913 1.000 0.609
3/3 1.188 0.998 0.646
MulA Add/.Mult 1/1 2.185 0.999 0.999
2/2 2.040 1.002 0.999
3/3 1.825 0.997 0.999
multiplicative model with the B(a)P concentration annual average values.
Comparison of correlation coefficients obtained while establishing the relationship among the values of the seasonal indices suggests that interdependence of sections 1 and 2 as well as sections 2 and 3 are less pronounced than in the case with sections 1 and 3, the bond between which is assessed as strong (table 7). Thus calculation of seasonal indices is possible during the transition from one type of modeling to another accompanied by the use of available smoothing methods within a single section (table 6, 8).
The transition from one section to another to estimate the seasonal indices of time series of B(a)P concentration does not yield results with sufficient convergence (table 7, 9 ).
On the other hand, the data summarized in table 5 indicates the possibility of forecasting the B(a)P concentration levels based on the experimental determination of a concentration value in one of the sections with subsequent implementation of mathematical models to calculate the other. Among the possible choices (table 10), calculation of moving averages is one of greatest interest as it is the most versatile - in all cases the value of the correlation coefficient
Parameters of linear equations of the relationship between the values of the seasonal indices derived with the use of various models and smoothing methods during the period 1995-2012 within different sections
Smoothing methods and models Sections K b R2
MA Additive section 2/ sect on 1 0.448 -0.000 0.035
section 3/ sect on 1 0.962 -0.002 0.420
section 3/ sect on 2 -0.052 -0.000 0.007
Multiplicative section 2/ sect on 1 0.622 0.378 0.506
section 3/ sect on 1 1.213 0.012 0.901
section 3/ sect on 2 0.645 0.193 0.445
3 Additive section 2/ sect on 1 0.203 -0.001 0.016
section 3/ sect on 1 1.032 -0.000 0.460
section 3/ sect on 2 0.152 0.001 0.025
Multiplicative section 2/ sect on 1 0.705 0.293 0.557
section 3/ sect on 1 1.009 -0.011 0.781
section 3/ sect on 2 0.762 0.236 0.398
MulA Additive section 2/ sect on 1 0.203 -0.001 0.016
section 3/ sect on 1 1.032 -0.000 0.460
section 3/ sect on 2 0.152 0.001 0.025
Multiplicative section 2/ sect on 1 0.194 0.805 0.017
section 3/ sect on 1 0.865 0.132 0.463
section 3/ sect on 2 0.144 0.854 0.028
Table 10
Parameters of linear equations between the B(a)P concentration and the parameters of the time series (annual averages, moving averages, and moving averages*) comparing the different sections during the period 1995-2012
Smoothing methods Sections K b R2
Concentration section 2/ section 1 0.461 0.280 0.081
section 3/ section 1 0.663 0.243 0.299
section 3/ section 2 0.240 0.427 0.102
Moving average section 2/ section 1 1.026 0.036 0.602
section 3/ section 1 1.213 -0.012 0.901
section 3/ section 2 0.645 0.193 0.445
Moving average* section 2/ section 1 0.656 0.190 0.903
section 3/ section 1 0.910 0.113 0.939
section 3/ section 2 1.348 -0.132 0.981
Annual average section 2/ section 1 0.926 0.069 0.725
section 3/ section 1 1.171 0.012 0.938
section 3/ section 2 0.869 0.118 0.611
relationship between this parameter of time series are identified as quite strong (table 5, 10)
[B(a)P2] = 0.66-[B(a)P1] + 0.190; [B(a)P3] = 0.91-[B(a)P1] + 0.113; [B(a)P3] = 1.35-[B(a)P2] - 0.132; R2=0.903; R2=0.939; R2=0.981; r=0.95; r=0.97; r=0.99
where [B(a)P1], [B(a)P2], [B(a)P3] — averaged value of moving averages of B(a)P content in sections 1-3 respectively;
R2 — coefficient of determination; r — coefficient correlation.
Overall, the results of time series analysis of B(a)P content in three successive sections of Ufa River during 1995—2012 allows us to formulate the following:
— A major contribution to the content of B(a)P is introduced by a random component, whose share lies within 77—89 %;
— Within one section modeling of B(a)P levels is possible using both multiplicative and additive model along with any smoothing method (moving averages, annual and multi-year averages);
— Possibility is provided to estimate B(a)P concentration at other sections based on the known experimental value for at least one section.
Литература
1. Кантор Л. И., Шемагонова Е. В.// Водные ресурсы.- 2002.- №6.- P.686.
2. Шемагонова Е. А., Кантор Л. И., Кантор Е. А. // Безопасность жизнедеятельности.- 2004.-№5.- С. 40.
3. Джамиль А. К. М. Рахман, Кантор Л. И., Дру-жинская Е. В., Кантор Е. А. // Баш. хим. ж.-2013.- Т.20, №4.- С.113.
4. Тюрин Ю. Н., Макаров А. А. Анализ данных на компьютере /Под ред. В. Э. Фигурнова. — М.: ИНФРА-М, 2002.— 528 с.
5. Daniel Реса. The Autocorrelation Function Of Seasonal ARMA Models // Journal of Time Series Analysis.- 1984.- V.5, №4.- P.269.
6. Cartwright P. A. // Journal of Time Series Analysis. 1985.- V.6, №4.- P.203.
7. Billah B., Hyndman R. J. and Koehler A. B. // Journal of Statistical Computation and Simulation. 2005.- V.75, №10.- P.831.
8. Gould P. G., Koehler A. B., Ord J. K., Snyder R. D., Hyndman R. J., Vahid-Araghi F. // European Journal of Operational Research.- 2008.- V.191, №1.- P.207.
9. Pеter Elek, Lаszlу МаАш // Journal of Time Series Analysis.- 2008.- V.29, №1.- P.14.
10. Paul L. Anderson, Mark M. Meerschaert, Kai Zhang. // Journal of Time Series Analysis.-2013.- V.34, №2.- P.187.
11. Якушев А. А., Горбатков С. А., Габрахманова Н. Т. Многомерные статистические и нейросете-вые модели в экономическом анализе.- Уфа: Издательский центр «Башкирский территориальный институт профессиональных бухгалтеров», 2001.- 280 с.
References
1. Kantor L. I., Shemagonova E. V. Water Resources. 2002. No.6. P.686.
2. Shemagonova E. V., Kantor L. I., Kantor E. A. Bezopasnost' zhiznedejatel'nosti. 2004. No.5. P.40.
3. Jamil A. K. M. Rahman, Kantor L. I., Dru-zhinskaja E. V., Kantor E. A. Bash. khim. zh. 2013. V.20, no.4. P.113.
4. Tyurin Yu. N., Makarov A. A. Analiz dannykh na komp'yutere / Pod red. V. E. Figurnova [Analysis of the data on the computer. Ed. of V. E. Figurnov]. Moscow: INFRA-M Publ., 2002. 528 p.
5. Daniel Peca. The Autocorrelation Function Of Seasonal ARMA Models. Journal of Time Series Analysis. 1984. V.5, no.4. P.269.
6. Cartwright P. A. Journal of Time Series Analysis. 1985. V.6, no.4. P.203.
7. Billah B., Hyndman R. J., Koehler A. B. Journal of Statistical Computation and Simulation. 2005. V.75, no.10. P.831.
8. Gould P. G., Koehler A. B., Ord J. K., Snyder R. D., Hyndman R. J., Vahid-Araghi F. European Journal of Operational Research. 2008. V.191, no.1. P.207.
9. Peter Elek, Laszly Marku. Journal of Time Series Analysis. 2008. V.29, no.1. P.14.
10. Paul L. Anderson, Mark M. Meerschaert, Kai Zhang. Journal of Time Series Analysis. 2013. V.34, no.2. P.187.
11. Yakushev A. A., Gorbatkov S. A., Gabdrakh-manova N. T. Mnogomernye statisticheskie metody i neirosetevye modeli v ekonomicheskom analize [Multivariate statistical and neural network models in the economic analysis]. Ufa: «Bashkirskii territorialnyi institut professionalnykh buhgalterov» Publ., 2001. 280 p.
