 Open Access
 Total Downloads : 559
 Authors : Dr. Sumit Nandi, Dr. Pijush Basak
 Paper ID : IJERTV3IS071194
 Volume & Issue : Volume 03, Issue 07 (July 2014)
 Published (First Online): 26072014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A Statistical Analysis of Carbon Dioxide Emission from Different Attributes in West Bengal, India
Dr. Sumit Nandi, HOD,
Department of Chemistry, Narula Institute of Technology, Kolkata, India
Dr. Pijush Basak, HOD
Department of Mathematics, Narula Institute of Technology, Kolkata, India.
Abstract Global warming is one of the most important environmental tribulations ever to confront human society and most important responsible green house gas for global warming is carbon dioxide. Increased emission of carbon dioxide from different sources to the environment is much alarming amongst which solid fuels and liquid fuels are the most important one but gaseous fuels and cement industry also add fuel to the flame. In this frightening situation, a mathematical model has been developed for the emissions of carbon dioxide based on above four attributes for the state West Bengal, India. A statistical approach, namely least square method is applied to study the behavior of the said attributes in the developed model utilizing the data set of twenty one years in West Bengal. The solutions of the environmental model match well with the real historical data from where future prediction for the emission of carbon dioxide can be made.
KeywordsCarbon dioxide emission; global warming; least square method; fuel.

INTRODUCTION
One of the major serious issues nowadays is global warming which has emerged most important environmental tribulations ever to confront humanity. This burning problem is inextricably linked to the process of development and economic growth. The main green house gases which cause global warming are carbon dioxide (CO2), methane (CH4), water vapor (H2O), nitrous oxide (N2O) and ozone (O3). Global warming has serious implications for all aspects of human life, including infectious diseases [1]. Among the green house gases, CO2 is the most important that is being affected by human activities. The concentration of CO2 in the earths atmosphere was about 280Â±10 parts per million by volume (ppmv) in 1750 [2]. By 1999 it was 367 ppmv and rising by about 1.5 ppmv per year. If emission continues in this rate, the concentration will reach 500 ppmv by the end of twenty first century which is very much alarming for the existence of living system [3].
Emission of CO2 from different sources in India is also frightening. Nandi and Basak [4] in earlier works studied the emission of carbon dioxide from different attributes in Indian perspective through search method. India is the fourth largest emitter of CO2 in the world (Source: Oak Ridge National Laboratory (ORNL), USA). Different states in India
are responsible for this undesirable emission of CO2. A state wise analytical study for total carbon dioxide emission has also been made by Basak and Nandi [5] using search method. West Bengal is one of the major contributors among identified states. Undesirable emission of CO2 from different sources varies from state to state. Main sources for this emission are solid fuels, liquid fuels and gaseous fuels and cement industry. Cement manufacturing industry releases CO2 as it uses essentially 100% calcium oxide which is obtained by burning calcium carbonate during calcinations.
Several studies have been done by different researchers on the emissions of green house gases in India. Some scientists deal with emissions in the regional level in the country also. Earlier Parikh and Gokarn [6] attempted for the estimation of emission levels in various sectors of the economy for the year 198384. The trends of CO2, SO2 and NOx between the periods 197374, 1983/84, 199192 and 199697 have been analyzed [7]. On the other hand, a time series estimate of indirect carbon emissions per unit of power consumption was provided by [8]. Ghoshal and Bhattacharyya [9] made a detailed survey regarding state level CO2 emissions of India during the year 19802000. Estimated emission of CO2 by mathematical modeling has been attempted by many researchers. Basak and Nandi [10] formulated mathematical models of total CO2 emission in some eastern and northern states of India and also predicted future emission in that states. Rust [11] demonstrated the connections between fossil fuel emissions, atmospheric CO2 concentrations and global temperatures by coupled mathematical models for their measured time series. Tokos et al [12] developed differential equations for the emission of CO2 based on six attributable/ variables. Jin et al [13] made a dynamic evolutionary model of carbon emissions in Yangtze Delta, China and they showed that due to excessive dependency of fossil fuels, carbon emission has risen dramatically after year 2000. In 1990, Goreau [14] briefly mentioned that the rate of change of CO2 emissions in the atmosphere could be studied using differential equations.
In the present study, we developed a mathematical model for the emissions of carbon dioxide in the state West Bengal, India based on four attributes. Here, data set of twenty one years has been utilized to study the behavior of the said attributes in the developed model by a statistical approach. From the analytical solution, the CO2 emissions by various
sources is to be estimated for short and long range of time so that remedial measures can be taken to reduce the emissions as far as practicable without compromising economic growth.

METHODOLOGY
To generate mathematical models of CO2 emissions in West Bengal, we consider the different sources of CO2 emissions like solid fuels (S), liquid fuels (L), gaseous fuels
(G) and cement (C) industry. In our model, for each of the attributes, the third degree polynomial model is formulated through least square method. The third degree polynomial fitted to CO2 emission [13] may be written as
y = a + b.x + c.x2 + d.x3 (1)
where y represents total CO2 emission and x represents year. Given data (x1,y1), (x2,y2),,(xn,yn) , we may define an error associated with can be presented as
Equating to zero, the partial derivatives with respect to a, b, c, d can be written as
The corresponding normal equations are
(2)
For given set of points (xi, yi); (i=1,2,,n), the equation (2) can be solved for a, b, c, d. Equation (1) is the third degree polynomial best fit. It has been found that in all the cases, the values of the 2nd order derivatives come out to be +ve at the points a, b, c. d. These provide minimization of E. Thus, the third degree fitted polynomial of carbon dioxide emission is estimated as
y = a + b. x + c.x2 + d.x3.
For evaluating model performance, we use two statistical criteria, R2 (adjusted R2) and residual analysis. The coefficient of determination R2 is defined as the proportion of the total response variation that is explained by the model. It provides an overall measure of how well the model fits. In general, R2 may be represented by the following term
where
and
SS tot = Total sum of squares (proportional to the sample variance)
SS reg = The regression sum of squares.. SS err = The sum of squares of residuals. and SS tot = SS reg + SS err
= The mean of the observed data and may be represented by
where i is the number of observations.
The adjusted R2 is defined as
where p is the total number of repressors in the linear model (not counting the constant term), and n is the sample size. R2 adjusted will adjust for degrees of freedom of the model.
For the formulation and analysis of our model, the following CO2 emission data (Table 1) is used. The data reflects the contribution of different fuels for CO2 emission in West Bengl. For our analysis, we consider twenty one years data from 1980 to 2000.
Table 1: Real data of CO2 emission from different attributes in West Bengal ('000 MT of carbon)
Year
Solid
(S)
Liquid
(L)
Gas
(G)
Cement
(C)
1980
8365.76
2720.74
82.79
292.08
1981
8991.07
2961.60
96.26
346.29
1982
9134.05
2997.07
140.28
359.64
1983
8880.37
2797.58
150.22
367.67
1984
8242.40
2744.25
162.11
379.05
1985
9043.93
3025.77
188.87
432.98
1986
8997.42
2933.30
251.02
440.88
1987
9479.26
2962.35
276.80
441.82
1988
10170.10
3062.24
303.67
481.08
1989
10067.69
3144.72
341.01
502.24
1990
10666.79
3312.79
427.94
546.31
1991
12656.39
3880.91
530.11
625.02
1992
11974.91
3974.44
498.73
553.77
1993
13001.71
4104.64
516.30
612.19
1994
14343.95
4544.94
776.56
674.38
1995
14871.95
4925.16
833.72
728.70
1996
14175.31
4923.06
951.34
782.73
1997
13291.36
4440.06
774.36
747.37
1998
11926.62
4266.10
798.89
706.57
1999
16072.77
5381.04
985.19
952.35
2000
15784.52
5588.59
969.59
953.23
1990
10666.79
11425.16
758.36
1991
12656.39
11808.36
848.02
1992
11974.91
12192.14
217.22
1993
13001.71
12576.45
425.26
1994
14343.95
12961.29
1382.66
1995
14871.95
13346.70
1525.25
1996
14175.31
13732.64
442.66
1997
13291.36
14119.15
827.78
1998
11926.62
14506.20
2579.57
1999
16072.77
14893.77
1178.99
2000
15784.52
15281.92
502.59
Mean of residuals
0.018
Standard error of residuals (SE)
31.90

RESULTS AND DISCUSSION
Now we formulate and analyze model for four attributes one by one. The general mathematical model for the solid fuel in West Bengal is given by y (S) = a + b.x + c.x2 + d.x3 where x represents year in the equation. The particular solution of the equation is given by
y (S) = 146879.156 + 14.7859 x 0.0873 x2 + 6.025 X 105 x
3
The graphical representation of the real data and the solution of the equation for the emission of carbon dioxide from solid fuel is given by figure 1.
Figure 1: Comparative emission of CO2 due to solid fuels (Real data vs model data)
Here, the rate of change of CO2 emission is compared with the model data and it is evident from Figure1 that our CO2 emission model matches well with the actual status of CO2 emission from solid fuels. Therefore, from the figure, it is possible to predict the CO2 emission from the solid fuel for short and medium terms of time. The calculated values for the solid fuel model of R2 and R2 adjusted are given by Table 2 below.
Table 2: R2 and R2 adjusted values for emission from solid fuel
R2
R2 adjusted
0.8443
0.8168
It is observed that the values of R2 and R2 adjusted are sufficiently high. Thus it may be concluded that the observed data matches reasonably well with the model. Furthermore, the residual analysis on the proposed differential equation of solid fuels is given in Table 3 below.
Year
Real data
Model data
Residual
1980
8365.76
7622.87
742.89
1981
8991.07
8000.66
990.40
1982
9134.05
8378.96
755.08
1983
8880.37
8757.86
122.50
1984
8242.40
9137.26
894.86
1985
9043.93
9517.23
473.30
1986
8997.42
9897.74
900.31
1987
9479.26
10278.77
799.50
1988
10170.10
10660.34
490.24
1989
10067.69
11042.48
974.79
Table 3: Residual analysis for emission of CO2 from solid fuels in West Bengal ('000 MT of carbon)
It is evident from the above table that the residuals are small compared to the data and so is the standard error. These results support the good quality of the proposed model for solid fuels. Here our predicted value of emission of CO2 from solid fuels for West Bengal in 2015 and 2020 are 20810.45 and 22978.12 ('000 MT of carbon) respectively.
Now, the general mathematical model for the liquid fuel of West Bengal is given by
y (L) = a + b.x + c.x2 + d.x3 where x represents year in the equation. The particular solution of the above equation is given by
y (L) = 47781.3359 + 7.1765 x 0.0383 x2 + 2.398 X 105 x3
The graphical representation of the real data and the solution of the model equation for the emission of carbon dioxide from liquid fuels are given by figure 2.
Figure 2: Comparative emission of CO2 due to liquid fuels (Real data vs model data)
From the figure, it is seen that the rate of change of emission of model data and real data are quite closer. So by comparing the model data and actual data from the above figure, one can estimate the CO2 emission from the liquid fuel for short and medium terms of time.
The calcuated values for the liquid fuel model of R2 and R2 adjusted are given by Table 4 below.
Table 4: R2 and R2 adjusted values for emission from liquid fuel
R2
R2 adjusted
0.8590
0.8342
From the value of R2 and adjusted R2, it can be concluded that we have developed a good model for the emission of carbon dioxide. Furthermore, the residual analysis on the
proposed differential equation of liquid fuels is given in Table 5 below.
Table 5: Residual analysis for emission of CO2 from liquid fuels in West Bengal ('000 MT of carbon)
Year
Real data
Model data
Residual
1980
2720.74
2368.11
362.62
1981
2961.60
2495.70
465.90
1982
2997.07
2633.48
363.58
1983
2797.58
2771.49
26.08
1984
2744.25
2909.70
165.34
1985
3025.77
3048.13
22.35
1986
2933.30
3186.76
253.45
1987
2962.35
3325.59
363.24
1988
3062.24
3464.64
402.39
1989
3144.72
3603.90
459.17
1990
3312.79
3743.36
430.57
1991
3880.91
3883.03
2.12
1992
3974.44
4022.92
48.48
1993
4104.64
4163.02
58.38
1994
4544.94
4303.32
241.61
1995
4925.16
4443.84
481.32
1996
4923.06
4584.56
338.49
1997
4440.06
4725.51
285.45
1998
4266.10
4866.66
600.55
1999
5381.04
5008.01
373.03
2000
5588.59
5149.58
439.00
Mean of residuals
0.0063
Standard error of residuals (SE)
18.70
It is clear from the table that the residuals are small compared to the data and standard error is negligibly small. These results prove good quality of the proposed model for liquid fuels. Here our predicted value of emission of CO2 from liquid fuels for West Bengal in 2015 and 2020 are 7354.11 and 8099.57 ('000 MT of carbon) respectively.
The general mathematical model for the gaseous fuel of West Bengal is given by
y (G) = a + b.x + c.x2 + d.x3 where x represents year in the equation. The particular solution of the above equation is given by
y(G)= 19394.8613 +2.1649 x 0.0118 x2 + 7.9237 X 106
x3.
The graphical representation of the actual data and the solution of the differential equation for the emission of carbon dioxide from gaseous fuels are given by figure 3.
Figure 3: Comparative emission of CO2 due to gaseous fuels (Real data vs model data)
Here, again the rate of change of CO2 emission can be compared with the model data and it is seen that the actual curve and empirical curve matches well. So from the figure that one can estimate the CO2 emission from the gaseous fuel for short and medium terms of time. For maintaining the quality of the proposed analytical model, here, we use two statistical criteria, R2, adjusted R2 and residual analysis.
The calculated values for the gaseous fuel model of R2 and R2 adjusted are given by Table 6 below.
Table 6: R2 and R2 adjusted values for emission from gaseous fuel
R2
R2 adjusted
0.9087
0.8926
It is shown from the above values that an excellent correlation of R2 and adjusted R2 is obtained. Furthermore, the residual analysis we performed on the proposed differential equation of gaseous fuels is given in Table 7 below.
Table 7: Residual analysis for emission of CO2 from gaseous fuels in West Bengal ('000 MT of carbon)
Year
Real data
Model data
Residual
1980
82.79
30.25
52.54
1981
96.26
37.74
58.51
1982
140.28
86.32
53.96
1983
150.22
134.98
15.24
1984
162.11
183.70
21.58
1985
188.87
232.50
43.63
1986
251.02
281.37
30.34
1987
276.80
330.30
53.50
1988
303.67
379.31
75.64
1989
341.01
428.39
87.38
1990
427.94
477.54
49.60
1991
530.11
526.76
3.34
1992
498.73
576.06
77.32
1993
516.30
625.42
109.11
1994
776.56
674.85
101.70
1995
833.72
724.36
109.35
1996
951.34
773.93
277.40
1997
774.36
823.58
149.22
1998
798.89
873.30
74.41
1999
985.19
923.09
62.09
2000
969.59
972.96
3.36
Mean of residuals
0.0027
Standard error of residuals (SE)
9.82
From the above table, it can be said that small residuals suggest good quality of the proposed model for gaseous fuels. Here our predicted value of emission of CO2 from gaseous fuels for West Bengal in 2015 and 2020 are 1707.06 and 1947.88 ('000 MT of carbon) respectively.
The general mathematical model for the cement industry in West Bengal is given by
y (C) = a + b.x + c.x2 + d.x3 where x represents year in the equation. The solution of the above equation is given by
y (C) = 12629.6377 + 2.3358 x 0.0075 x2 + 4.862 X 106
x3 The graphical representation of the real data and the solution of the differential equation for the emission of carbon dioxide from cement industry are given by figure 4.
Figure 4: Comparative emission of CO2 from cement industry (Real data vs model data)
Here, again the rate of changeof CO2 emission can be compared with the model data and it can be explained from the figure that one can estimate the CO2 emission from cement manufacturing industry for short and medium terms of time. For maintaining the quality of the proposed analytical model, here, we use two statistical criteria, R2 (adjusted R2 and residual analysis. The calculated values for the cement industry R2 and R2 adjusted are given by Table 8 below.
Table 8: R2 and R2 adjusted values for emission from cement industry
0.9348
0.9233
R2 R2 adjusted
It is shown from the above values that we have identified good models. Furthermore, the residual analysis we performed on the proposed differential equation of cement industry is given in Table 9 below.
Year
Real data
Model data
Residual
1980
292.08
267.08
24.99
1981
346.29
296.85
49.43
1982
359.64
326.67
32.97
1983
367.67
356.53
3.01
1984
379.05
386.43
7.37
1985
432.98
416.38
16.6
1986
440.88
446.36
5.48
1987
441.82
476.39
34.57
1988
481.08
506.47
25.42
1989
502.24
536.58
34.34
1990
546.31
566.74
20.43
1991
625.02
596.94
28.08
1992
553.77
627.19
73.42
1993
612.19
657.48
45.29
1994
674.38
687.81
13.42
1995
728.70
718.18
10.51
1996
782.73
748.60
34.13
1997
747.37
779.06
31.69
1998
706.57
809.57
102.99
1999
952.35
840.12
112.23
2000
953.23
870.71
82.52
Mean of residuals
0.0028
Standard error of residuals (SE)
7.02
Table 9: Residual analysis for emission of CO2 from cement industry in West Bengal ('000 MT of carbon)
As seen from the table, the residuals are small compared to the data and so is the standard error. These results attest to the good quality of the proposed model for cement industry. Here our predicted value of emission of CO2 from cement industry for West Bengal in 2015 and 2020 are 1311.08 and 1469.33 ('000 MT of carbon) respectively.

CONCLUSION
We have developed mathematical models based on the emission of carbon dioxide for each of the four main attributable variables in West Bengal using actual data from 1980 to 2000. The main sources of emission are gaseous fuels, liquid fuels, solid fuels and cement. Here we adopted least square method for the formulation of our model. We have used two different statistical procedures, namely R2 (R2 adjusted) and residual analysis to evaluate the quality of the proposed models. Analyzing the model by using regression analysis method, it illustrates that the model matches well with the actual status of carbon emission from four main attributable variables. All these statistical procedures advocate to the quality of the proposed models. Finally, we predict the short and medium term total carbon dioxide emissions trend in West Bengal by using our model. Proper framing of emission strategies and policies are immediately necessary to restrain the rapid increasing of emission. Our models provide a theoretical basis for the further study in future on the undesirable situation of carbon emissions and it may be useful for intended planning and formulating policies to reduce emission of global warming gases.
REFERENCES

A. A. Khasnis and M. D. Nettleman, Global warming and infectious disease, Archives of Medical Research, 36(6), 89696, 2005.

J. Houghton et al., Climate Change 2001: The Scientific basis, Contribution of Working Group I to the Third Assesment Report of the Intergovernmental Panel on Climate Change, New York, Cambrige University Press, 183238, 2001.

J. T. Houghton and Y. Ding, Climate Change 2001: The Scientific Basis In Prentice, I. C. et. al.(Ed.)The Carbon cycle and atmospheric carbon dioxide (pp. 185), Cambridge University Press, 2001.

S. Nandi and P. Basak, Emission of carbon dioxide from different attributes in India: A mathematical study IOSR Journal of Applied Chemistry, Vol. 1, 610, 2014.

P. Basak and S. Nandi, An analytical study of emission dynamics of carbon dioxide in India,. IOSR Journal of Applied Chemistry, Vol.1, 1621, 2014.

J. Parikh and S. Gokarn, Climate change and Indias energy policy options, Global Environmental Change, 3 (3), 1993.

K. Mukhopadhyay and O. Forsell, An empirical investigation of air pollution from fossil fuel combustion and its impact on health in India
during 197374 to 199697, Paper presented at the 14th international
conference on inputoutput technique held at University of Quebec, Montreal, Canada, 2002.

B. Nag and J. Parikh, Carbon emission coefficient of power consumption
in India: Baseline determination from the demand side, Energy Policy,
33 (6), 77786, 2005.

T. Ghoshal and R. Bhattacharyya, State level carbon dioxide emissions
of India 19802000, Contemporary Issues and Ideas in Social Sciences,
4 (1), 2008.

P. Basak and S. Nandi, A statistical analysis and prediction of carbon
dioxide emission in some eastern and northern states of India International Journal of Environmental Sciences, 4 (5), 956967,
2014.

B. W. Rust, Carbon dioxide, global warming and Michael Crichtons State of Fear, Computing Science and Statistics, 37, 2006.

C. P. Tokos and Y. Xu Y., Modeling carbon dioxide emissions with a
system of differential equations, Non linear Analysis: Theory,
Methods
and Applications, 71 (12), 11821197, 2009.

R. Jin, L. Tian, J. Qian and Y. Liu, The Dynamic evolutionary analysis
on carbon emissions in Yangtze delta International Journal of Nonlinear Science, 10(3), 259263. 2010.

J. T. Goreau, Balancing atmospheric carbon dioxide, Ambio, 19 (5),
230236, 1900.