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Estimation for the Variation of the Concentration of Greenhouse Gases with Modified Shannon Entropy

변형된 샤논 엔트로피식을 이용한 온실가스 농도변화량 예측

  • Received : 2013.07.15
  • Accepted : 2013.10.15
  • Published : 2013.11.29

Abstract

Entropy is a measure of disorder or uncertainty. This terminology is qualitatively used in the understanding of its correlation to pollution in the environmental area. In this research, three different entropies were defined and characterized in order to quantify the qualitative entropy previously used in the environmental science. We are dealing with newly defined distinct entropies $E_1$, $E_2$, and $E_3$ originated from Shannon entropy in the information theory, reflecting concentration of three major green house gases $CO_2$, $N_2O$ and $CH_4$ represented as the probability variables. First, $E_1$ is to evaluate the total amount of entropy from concentration difference of each green house gas with respect to three periods, due to industrial revolution, post-industrial revolution, and information revolution, respectively. Next, $E_2$ is to evaluate the entropy reflecting the increasing of the logarithm base along with the accumulated time unit. Lastly, $E_3$ is to evaluate the entropy with a fixed logarithm base by 2 depending on the time. Analytical results are as follows. $E_1$ shows the degree of prediction reliability with respect to variation of green house gases. As $E_1$ increased, the concentration variation becomes stabilized, so that it follows from linear correlation. $E_2$ is a valid indicator for the mutual comparison of those green house gases. Although $E_3$ locally varies within specific periods, it eventually follows a logarithmic curve like a similar pattern observed in thermodynamic entropy.

Keywords

Shannon entropy;Greenhouse gases;Uncertainty;Degree of freedom

References

  1. Elrod, M., 1999, Greenhouse Warming Potential Model, J. Chem. Educ., 76, 1702-1705. https://doi.org/10.1021/ed076p1702
  2. Feynman, R. P., Leighton, R., Sands, M., 2007, The Feynman lecture on Physics I, Pearson Addison Wesley, 44-13-16.
  3. IPCC, 1990, IPCC First Assessment Report, IPCC.
  4. IPCC, 2001, IPCC Third Assessment Report, IPCC.
  5. Rifkin, J., 2009, Entropy, Se-Jong, Korea, 239-325.
  6. Shannon, C. E., 1948, A Mathematical Theory of Communication, Bell Syst. Tech. J., 27, 379-423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  7. Shannon, C. E., 1953, General Treatment of the problem of coding, IEEE Transactions on Information Theory, 102-104.
  8. Williams, J. M., 2008, Entropy shows that global warming should cause increased variability in the weather, http://arxiv.org/pdf/physics/0008228.pdf.

Acknowledgement

Supported by : 광운대학교