Research Journal of Recent Sciences _________________________________________________ ISSN 2277-2502 Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 93 A Comparative Evolutionary Analysis and Prediction of Carbon Dioxide Emission in Different Countries Basak Pijush and Nandi Sumit2*Department of Mathematics, Narula Institute of Technology, Agarpara, Kolkata-700109, West Bengal, INDIA Department of Chemistry, Narula Institute of Technology, Agarpara, Kolkata-700109, West Bengal, INDIAAvailable online at: www.isca.in, www.isca.me Received 24th November 2014, revised 20th January 2015, accepted 3rd February 2015 AbstractClimatic change in recent times is one of the serious issues throughout the world which is mainly due to the cause of global warming. Global warming is much alarming to the human beings and also to the existence of life on earth. The main cause for global warming is uncontrolled anthropogenic emission of green house gases like carbon dioxide, methane, chlorofluorocarbons etc. Among the green house gases, carbon-dioxide contributes a major share in this aspect. The rate of carbon-dioxide emission varies in different countries like India, USA, China, Japan and also in European countries depending on several conditions mainly industrialization, population explosion and economic growth. In this paper, an attempt has been made for the quantification of carbon dioxide emission in different countries using historical data of hundred years around the globe. Here, we formulate an evolutionary gas emission model using non-linear least square method and regression analysis has been done based on the above data for quantification of the emission. Finally, we predict the long term evolutionary trend of gas emission using instantaneous rate of change (IROC) in the subjected countries along with a comparative study of the carbon dioxide emission in different countries. Keywords: Global warming, least square, regression analysis, carbon dioxide, IROC. Introduction Change of climate is one of the most serious concerns today all around the world. One of the important issues of climate change is global warming which attracts considerable attention to scientists, researchers and academicians throughout the world. Different green house gases like carbon dioxide (CO), nitrous oxide (NO), methane (CH), ozone (O) etc. are responsible for this unwanted situation but the uncontrolled emission of COfrom different sources is the most important one and the amount of emission of CO for the last fifty years from fossil fuels is tremendous. The concentration of CO2 in earth’s atmosphere was about 280±10 parts per million by volume (ppmv) in 1750. By 1999, it was 367 ppmv and rising by about 1.5 ppmv per year. If emission continues, the concentration will reach 500 ppmv at the end of twenty first century which is very much alarming for the existence for life on earth. The uncontrolled emission of CO from different sources is increasing in different parts of the continent. Some countries or parts of country are severely affected due to mainly deforestation, growing of industry, population explosion and increasing use of automobiles. However, the pattern of growth is time and area dependent. This pattern changes from less industrial and less populated area to rapidly industry oriented and densely populated part of the country. It is therefore essential to have study of emission of CO in different parts over the globe. Main sources for the emission of CO are solid fuels, liquid fuels and gaseous fuels. Source wise, India is significantly different from global averages. The major global sources of CO are liquid fuels whereas solid fuels come second in importance. Emission of CO in different countries is much fear-provoking. Several studies have been done by different researchers for the emission of CO in India5-7. Country wise, India leads as far as mean CO emission between 1980 and 2000. It is closely followed by China. USA, Japan and European countries also contribute a major share for the increasing amount of CO in the atmosphere from different sources. General trends in all these countries are high proportion of emissions from coal and automobiles. Emission of CO by mathematical modeling has been done region wise by several researchers all over the world. Mathematical understanding of CO emission for different countries like Japan9,10 China8,11 and USA12,13 have been done by some researchers also. Tokos et al.13 made a study on the modeling of CO emission with a system of differential equations for six attribute variables for the continental United States from 1950 to 2005. But in Indian context, very few studies are undertaken. Authors studied total CO emission in Indian perspective as well as based on attributes14,15. Parikh et al.16 described CO emission structure of Indian economy based on fuel type, sector wise, final demand and expenditure classes. In the present study, we developed mathematical models using non linear least square regression for the emission of CO2 in different countries of the world. The countries considered here are India, China, Japan, USA and European countries for about Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 94 hundred years (1890-1985). Emission data are collected from different literatures2,17. Using real historical data, analytical form of the equations are developed. Instantaneous Rate of Change (IROC) of emissionhas been derived from the developed equation which is utilized for the estimation of COemission for different countries for short and long range of time. Methodology In order to generate mathematical model of carbon dioxide emission, we visualize the works of Tokos et al.13, Jin. et al.18and Basak and Nandi15. The authors suggest a third degree polynomial model for emission of the gas namely, Y = a + b.x + c.x + d.x (1)where Y is the emission of CO and x represents time in years. Least Square method: Given data (x,y), (x,y),…,(x,y) , an error associated may be presented as (2) The equation (2) above is the N times variance of the data set (error) {y – (a + bx1 + cx2 + dx)},…., {y – (a + bxN + cx2 + dx )} and is a function of four variables a, b, c and d. The goal is to estimate a, b, c and d with a view to minimize the error. Equating to zero, the partial derivatives with respect to a, b, c, d can be written as The corresponding normal equations are (3) For given set of points ( ); (i=1,2,…,N), the equation (3) can be solved for a, b, c, d; whereas equation (3) is the third degree polynomial best fit. It has been observed that in all the cases, the values of the 2nd order derivatives viz. , , etc. come out to be positive at the points a, b, c. d indicating minimization of E. Thus, the third degree fitted polynomial of CO emissionis estimated as Y= , + x + .x2 + .x (4) Instantaneous Rate of Change of emission (IROC): In order to compute the rate of change of emission of the CO, the derivative of equation (4) is computed in the form dY/dx= + .x+ .x (5) The equation (5) at a particular time is utilized for prediction of the emission of the concerned gas.Results and Discussions Emission of COin Asian countries like India, China and Japan: For the analysis of emission of CO in Asian countries like India, China and Japan, the dynamic models utilizing the data set of about hundred years are expressed in the following way IND = 23713.918-3.88413596.x-0.0155114625.x+ 5.78179652E-006.x (6a) CHN =37716.7383-7.90331459.x-0.0253356863.x+ 1.00364778E-5.x (6b) JPN =25853.957-4.52507401 .x-0.017040059 .x+ 6.45304863E-6 .x3 (6c) where x represents time in years. A graphical display of the actual data and the solution of the above models by least square method are compared in figure 1a, 1b and 1c for India, China and Japan respectively. These shows CO emissions have a power series growing trend. Figure-1a CO Emission in India 051015202520406080100120140160180200 CO2 Emission (Tg)Time (1 unit = 5 years) Observed results Estimated results Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 95 Figure-1b CO Emission in China Figure-1c CO Emission in Japan It has been observed from the graphical display that emission of CO2 in China is much higher than India and Japan for the last hundred years. In recent years, the rapid growth leads to rapid consumption of fuels in automobiles and industry in these three countries. The goodness of the analytical model can be measured by utilizing the statistical criteria R2 (R2 adjusted). The calculated values of R2 (R2 adjusted) for three Asian countries are presented in table-1. Table 1 Statistical Evaluation Criteria for CO Emission Country R 2 R 2 adjusted India 0.8534 0.8276 China 0.9574 0.9499 Japan 0.9307 0.9185 The value of R2 (R2 adjusted) reflect the fact that good models have been identified for the emission of CO in India, China and Japan. IROC of CO emission in India, China and Japan: IROC is an important parameter which is useful for the prediction of future emission of gas. Here, IROC of CO emission in India, China and Japan as a function of time are given analytically by dY/dx (India) = -3.88413596 – 0.031022925.x +0.00001734538.x (7a) dY/dx (China) = -7.90331459 – 0.05066713726 .x +3.01094334364778E-5. x (7b) dY/dx (Japan) = -4.52507401 – 0.034080118 . x + 19.35914589E-6 .x (7c) A graphical display of expression 7a, 7b and 7c are given by figure 2a, 2b and 2c for India, China and Japan respectively. Figure-2a IROC of India Figure-2b IROC of China 05101520253035-1 IROCYear (1 unit = 4 years) 05101520253035101214 IROCTime (1 unit = 4 years) 0510152025200400600800 CO2 emissionTgTime (1 unit = 5 years) Observed results Estimated results 051015202550100150200250 CO2 Emission (Tg)Time (1 unit = 5 years) Observed results Estimated results Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 96 Figure-2c IROC of Japan One can utilize equation 7a, 7b or 7c or the graph to estimate the rate of change of CO emission in India, China and Japan respectively for short and long term of time. For India, it is negative before 1905 and the decreasing trend in India was gradually slower before 1905. After 1905, CO emission instantaneous variation is positive and emission grows rapidly. For all the countries especially in China, rapid increasing trend of IROC value signifies that uncontrolled emission of CO into atmosphere from different sources occurs for the last hundred years which is very much alarming. The vertical lines in figure 2a, 2b and 2c indicate completion of hundred years of estimated IROC values for the emitted gas. Now, if we go beyond the vertical lines, we can easily predict the future IROC for the gas from where the future emission of CO can be done for short and long range of time in the three countries. Increasing trend of IROC in future indicates continuous uninhibited emission of CO from different sources which must be controlled for the sake of mankind. Table-2 Details of residual analysis for CO emission Year India China Japan Empirical IROC DF IROC Residual Empirical IROC DF IROC Residual Empirical IROC DF IROC Residual 1890 0.7547 2.0825 -1.3278 0.4454 0.5485 -0.1031 0.1482 -1.6363 1.7845 1895 0.6989 0.4277 0.2712 0.1430 0.3819 -0.2389 0.2325 4.1713 -3.9387 1900 0.5063 0.1236 0.3827 1.1511 0.2967 0.8545 0.2030 1.1201 -0.0171 1905 0.4832 -0.0461 0.5293 0.2717 0.2444 0.0273 0.2063 0.6757 -0.4694 1910 0.2946 -0.2137 0.5083 0.0396 0.2091 -0.1695 0.1676 0.4921 -0.3245 1915 0.1707 -0.4827 0.6534 0.1283 0.1834 -0.0550 0.1858 0.3895 -0.2037 1920 0.2019 -1.3425 1.5444 0.0840 0.1639 -0.0799 0.0899 0.3234 -0.2335 1925 0.1431 5.1258 -4.9827 0.0433 0.1485 -0.1052 0.0665 0.2773 -0.2108 1930 -0.0571 1.0337 -1.0908 0.0186 0.0186 -0.1174 0.1532 0.2429 -0.0896 1935 0.3636 0.6058 -0.2421 0.0460 0.1257 -0.0797 0.2000 0.2163 -0.0163 1940 -0.1555 0.4382 -0.5937 0.1431 0.1170 0.0261 -0.2479 0.1950 -0.4429 1945 0.4386 0.3473 0.0913 0.0957 0.1095 -0.0138 0.2195 0.1776 0.0418 1950 0.5069 0.2895 0.2174 0.3517 0.1030 0.2486 0.7617 0.1632 0.5984 1955 0.3485 0.2493 0.0993 0.3429 0.0973 0.2455 0.2727 0.1510 0.1217 1960 0.4440 0.2194 0.22461 -0.2378 0.0923 -0.3301 0.3415 0.1405 0.2010 1965 0.4550 0.1963 0.2586 0.2048 0.0878 0.1170 05094 0.1314 0.3779 1970 0.3382 0.1779 0.1603 0.2371 0.0838 0.1532 -0.0071 0.1234 -0.1305 1975 0.4884 0.1628 0.3256 0.0325 0.0802 -0.0477 0.0804 0.1164 -0.0359 1980 0.2863 0.1501 0.1362 0.0320 0.0769 -0.0449 -0.0009 0.1101 -0.1110 1985 0.4398 0.1394 0.3004 0.1979 0.0738 0.1240 0.1651 0.1045 0.0606 Mean of Residual 0.1207 0.0196 -0.1875 Standard deviation of Residual 1.2625 0.2397 1.0016 Standard error of Residual 0.2823 0.0535 0.2239 05101520253035 IROCTime (1 unit = 4 years) Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 97 The goodness of the Instantaneous rate of changes is presented in table-2. In the table, the empirical or instantaneous rate of change for the emission of CO2 in India, China and Japan, the corresponding instantaneous rate of change using the developed differential equation, DF IROC along with the residual being the difference of the two have been presented. It has been observed from the table that mean residual for India, China and Japan are 0.1207, 0.0196 and -0.1875 respectively which very are small and so the standard error. This certainly indicates that we have identified good models for emission of CO for these three Asian countries. Now, we can predict instantaneous variation of CO2 emissions in future from the IROC graphical display for these three countries. Table-3 shows prediction of empirical IROC and future emission of CO in India, China and Japan. We can see that in the year 2040, total CO emission from all sources in India, China and Japan will be 323.28, 1363.30 and 493.11 Tg respectively if proper care to curb the emission is not be taken. Emission of COin USA and Europe: For the analysis of emission of CO in USA and Europe, the dynamic models utilizing the data set of about hundred years are expressed in the following way USA =101644.961-17.6519642.x-0.06658917484.x+2.51649053E-5.x (8a) EUR =57773.9727-11.2152081 .x-0.0379425883 .x+1.46929851E-5 .x (8b) where x represents time in years. A graphical display of the actual data and the solution of the equation 8a and 8b are given in figure 3a and 3b for USA and Europe respectively. Table-3 IROC and prediction of CO2 in future Year 2020 2025 2030 2035 2040 IROC in future India 4.2256 4.4213 4.6179 4.8153 5.0137 China 12.5990 12.9546 13.3118 13.6703 14.0305 Japan 5.6261 5.8473 6.0693 6.2924 6.5165 Emission Prediction (Tg) India 230.9174 252.5343 275.1341 298.7168 323.2881 China 1097.0525 1160.9355 1226.6041 1294.0583 1363.3085 Japan 371.7101 400.3929 430.1863 461.0902 493.1113 Figure 3a CO Emission in USA Figure 3b CO Emission in Europe 051015202520040060080010001200 CO2 Emission (Tg)Time (1 unit = 5 years) Observed results Estimated results 05101520252003004005006007008009001000 CO2 Emission (Tg)Time (1 unit = 5 years) Observed results Estimated results Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 98 Figure 3a and 3b show the comparative study of the emission of CO in USA and Europe and displayed that pattern of emissions dropped near the 1940 in both the cases. This may be due to the Second World War when a huge devastation occurred. The rapid growth of emission for the last fifty years may be due to rapid increase in the use of automobiles and enhancement of industrialization and urbanization in USA and European countries. For understanding the quality of the proposed analytical model, the statistical criteria such as R2 (R2 adjusted) are evaluated. The calculated values of R2 (R2 adjusted) are presented in table 4. Table 4 Statistical Evaluation Criteria for CO Emission Country R 2 R 2 adjusted USA 0.9212 0.9073 Europe 0.8747 0.8525 The value of R2 (R2 adjusted) attest the fact that good models for both the cases have been identified. IROC of CO emission in USA and Europe: IROC of COemission in USA and Europe as a function of time are given analytically by dY/dx (USA) = -17.6519642 – 0.1331634968 .x + 7.54947159E-5 .x (9a) dY/dx (Europe) = -11.2152081 – 0.0758851776 . x + 4.40789553E-5 .x (9b) A graphical display of expression 9a and 9b are given in figure 4a and 4b as follows Figure-4a IROC of USA The rate of change of CO emission in USA and Europe for short and long term of time can be obtained from the above displayed figure 4a and 4b respectively. Again future prediction for IROC and emission can be done from the above graphical display. Furthermore, residual analysis is performed on the proposed differentials and is presented in table-5. As seen from the table, the residuals and standard error are extremely small leading to identification of a good model. Figure-4b IROC of EuropeTable-6 shows the future IROC and emission prediction for USA and European countries in the next twenty five years. It has been observed from the table that emission prediction of CO2 are 2189.94 and 1731.57 Tg for USA and European countries respectively in the year 2040 if emission continues in the present rate.Conclusion In the present study, we have developed equations using non linear least square method that characterize the behavior of emission pattern of CO for five major parts of the globe like India, China, Japan, USA and Europe utilizing the data set of about 100 years from 1890 to 1985. Sources of emission of COconsidered here are different attributes namely, fossil fuels, cement industry and gas flaring. In addition to the given analytical expression for emission in each case, we have utilized three different statistical procedures, namely R adjusted and residual analysis to evaluate the quality of the proposed analytical methods. In all the cases, the statistical procedures attest the good quality of the proposed evolutionary systems. Finally, we have used these models to predict CO emissions by deriving IROC for the next twenty five years in the respective countries /part of continent. This study may be the theoretical basis for the future researchers of CO emission in different regions of globe and our model may be utilized for functional and efficient planning and strategic applications for the declining of appalling global warming in near future. 0510152025303510152025 IROCTime (1 unit = 4 years) 051015202530351012141618 IROCTime (1 unit = 4 years) Research Journal of Recent Sciences ______________________________________________________________ ISSN 2277-2502Vol. 4(ISC-2014), 93-100 (2015) Res. J. Recent. Sci. International Science Congress Association 99 Table 5 Details of residual analysis for CO emission Year USA Europe Empirical IROC DF IROC Residual Empirical IROC DF IROC Residual 1890 0.0913 0.0106 0.0806 0.1482 0.0637 0.0105 1895 0.1134 0.0216 0.0919 0.2201 0.0688 0.1512 1900 -0.0064 0.0321 -0.0384 0.7661 0.0729 0.0037 1905 0.0799 0.0417 0.0382 0.1523 0.0758 0.0765 1910 -0.0509 0.0502 -0.1012 0.0333 0.0779 -0.1112 1915 0.1452 0.0577 0.0875 0.0047 0.0791 -0.0839 1920 -0.1327 0.0638 -0.1965 0.1179 0.0797 0.0382 1925 0.0531 0.0688 -0.0157 0.0723 0.0798 -0.0074 1930 -0.1538 0.0726 -0.2264 - 0.0597 0.0794 -0.1392 1935 0.1452 0.0755 0.0697 0.0861 0.0787 0.0073 1940 0.2388 0.0774 0.1614 -0.4513 0.0766 -0.5291 1945 0.1025 0.0786 0.0239 0.8055 0.0776 0.7288 1950 -0.0190 0.0792 -0.0981 0.2678 0.0754 0.1924 1955 0.0936 0.0792 0.0144 0.1151 0.0740 0.0411 1960 0.1841 0.0788 0.1053 0.2181 0.0725 01455 1965 0.3420 0.0782 0.2638 0.1644 0.0711 0.0934 1970 -0.0134 0.0772 -0.0906 0.0133 0.0696 -0.0562 1975 0.0135 0.0761 0.0596 0.0813 0.0685 0..0132 1980 -0.0269 0.0748 -0.1018 -0.0794 0.0665 -0.1460 1985 0.1067 0.0735 0.0332 0.0204 0.0651 -0.0447 Mean of Residual 0.0076 0.0183 Standard deviation of Residual 0.1162 0.2200 Standard error of Residual 0.0260 0.0492 Table 6 IROC and prediction of CO2 in futureYear 2020 2025 2030 2035 2040 IROC in future USA 21.4064 22.2674 23.1323 24.0009 24.8733 Europe 15.3565 15.8686 16.3828 16.8993 17.4180 Emission Prediction (Tg) USA 1727.2422 1836.4239 1949.9299 2067.7602 2189.9404 Europe 1403.8922 1481.9531 1562.5855 1645.7893 1731.5796 References 1.Battle M., Bender M.L., Tans P.P., White J.W., Ellis J.T., Conway T. and Francey R.J., Global carbon sinks and their variability inferred from atmospheric oxygen and 13C, Science, 287(5462), 2467-2470 (2000) 2.Ghoshal T., Bhattacharyya R., State level carbon dioxide emissions of India 1980-2000, Contemporary Issues and Ideas in Social Sciences, (2008) 3.Houghton J. et al., Climate Change, The Scientific basis, Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, New York, Cambridge University Press, 183-238 (2001) 4.Houghton J.T. and Ding Y., Climate Change, The Scientific basis In Prentice, I. 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