Prediction of Stand Volume and Carbon Stock for Quercus variabilis Using Weibull Distribution Model

Weibull 분포 모형을 이용한 굴참나무 임분 재적 및 탄소저장량 추정

  • Son, Yeong Mo (Center for Forest and Climate Change, Korea Forest Research Institute) ;
  • Pyo, Jung Kee (Center for Forest and Climate Change, Korea Forest Research Institute) ;
  • Kim, So Won (Center for Forest and Climate Change, Korea Forest Research Institute) ;
  • Lee, Kyeong Hak (Center for Forest and Climate Change, Korea Forest Research Institute)
  • 손영모 (국립산림과학원 기후변화연구센터) ;
  • 표정기 (국립산림과학원 기후변화연구센터) ;
  • 김소원 (국립산림과학원 기후변화연구센터) ;
  • 이경학 (국립산림과학원 기후변화연구센터)
  • Published : 2012.12.31

Abstract

The purpose of this study is to estimate diameter distribution, volume per hectare, and carbon stock for Quercus variabilis stand. 354 Quercus variabilis stands were selected on the basis of age and structure, the data and samples for these stands are collected. For the prediction of diameter distribution, Weibull model was applied and for the estimation of the parameters, a simplified method-of-moments was applied. To verify the accuracy of estimates, models were developed using 80% of the total data and validation was done on the remaining 20%. For the verification of the model, the fitness index, the root mean square error, and Kolmogorov-Smirnov statistics were used. The fitness index of the site index, height, and volume equation estimated from verification procedure were 0.967, 0.727, and 0.988 respectively and the root mean square error were 2.763, 1.817, and 0.007 respectively. The Kolmogorov-Smirnov test applied to Weibull function resulted in 75%. From the models developed in this research, the estimated volume and above-ground carbon stock were derived as $188.69m^3/ha$, 90.30 tC/ha when site index and stem number of 50-years-old Quercus variabilis stand show 14 and 697 respectively. The results obtained from this study may provide useful information about the growth of broad-leaf species and prediction of carbon stock for Quercus variabilis stand.

본 연구의 목적은 굴참나무 임분의 직경분포와 ha당 재적 및 탄소량을 추정하는데 있다. 영급과 임분구조를 고려하여 굴참나무 임분에서 354개소를 조사하고 시료를 수집하였다. 임령에 따른 직경분포를 파악하기 위하여 Weibull 모형을 사용하였으며 모수의 추정은 단순적률법(Simplified method-of-moments)을 이용하였다. 사용된 자료 중에서 80%는 모형개발에 사용하였고, 나머지 20%는 개발된 모형의 검정에 사용하였다. 모형의 검정에는 적합도지수(Fitness Index)와 평균오차제곱(Root Mean Square Error), Kolmogorov-Smirnov 통계치가 이용되었다. 검정자료에서 추정된 지위지수, 수고, 재적식의 적합도지수는 각각 0.967, 0.727, 0.988이고 평균오차제곱은 2.763, 1.817, 0.007이며, Weibull 모형의 Kolmogorov-Smirnov 적합도는 75%를 나타내었다. 본 연구를 통해 개발된 모형에서 50년생의 굴참나무임분이 14의 지위지수와 697본의 분수를 나타내는 경우, 재적은 $188.69m^3/ha$이고 지상부 탄소량은 90.30 tC/ha으로 추정되었다. 본 연구의 결과는 활엽수 수종에 대한 생장정보의 제공이 가능하고 굴참나무 탄소량 추정에 활용이 가능하다.

Keywords

References

  1. 국립산림과학원. 2010. 산림 온실가스 인벤토리를 위한 주요 수종별 탄소배출계수. 국립산림과학원. pp. 34-37.
  2. 손영모, 이경학, 표정기. 2011. 중부지방소나무 및 굴참나무의 바이오매스 상대생장식 개발. 농업생명과학연구 45(4): 65-72.
  3. 안종만, 우종춘, 윤화영, 이동섭, 이상현, 이영진, 이우균, 임영준. 2007. 산림경영학. 향문사. pp. 38.
  4. 이경학, 손영모. 2003. 단순적률법을 이용한 소나무림에서의 Weibull 직경 분포 모수 추정. 한국산림측정학회지 6(1): 8-14.
  5. Avery, T.E. and Burkhart, H.E. 2002. Forest Measurements. 5th Edition. McGraw-Hill, Incorporation. pp. 321-347.
  6. Bailey, R.L. and Dell, T.R. 1973. Quantifying diameter distributions with the weibull function. Forest Science 19: 97-104.
  7. Borders, B.E., Souter, R.A., Bailey, R.L. and Ware, K.D. 1987. Percentile-based distributions characterize forest stand tables. Forest Science 33(2): 570-576.
  8. Buck, T.E. and Newberry, J.D. 1984. A simple algorithm for moment-based recovery of weibull distribution parameters. Forest Science 30(2): 329-332.
  9. Burkhart, H.E. 1971. Slash pine plantation yield estimates based on diameter distribution: an evaluation. Forest Science 17(4): 452-453.
  10. Cao, Q.V. and Burkhart, H.E. 1984. A segmented distribution approach for modeling diameter frequency data. Forest Science 30(1): 129-137.
  11. Cao, Q.V. 1997. A method to distribute mortality in diameter distribution models. Forest Science 43(3): 435-442.
  12. Cao, Q.V. 2004. Predicting parameters of a weibull function for modeling diameter distribution. Forest Science 50(5): 682-685.
  13. Clutter, J.L., Fortson, J.C., Pienaar, L.V., Brister, G.H. and Bailey, R.L. 1983. Timber Management : A Quantitative Approach. John Wiley and Sons, New York. pp. 333.
  14. Efron B. and Gong, G. 1983. A leisurely look at the bootstrap, the jackknife, and cross-validation. The American Statistician 37(1): 36-48.
  15. Ek, A.R., Issos, J.N. and Bailey, R.L. 1975. Solving for weibull diameter distribution parameters to obtain specified mean diameters. Forest Science 21(3): 290-292.
  16. Garcia, O. 1981. Simplified method-of-moments estimation for the weibull distribution. New Zealand Journal of Forest Science 11(3): 304-306.
  17. Gonzalez, J.C.A., Schroder, J., Soalleiro, R.R. and Gonzalez, A.D.R. 2002. Modelling the effect of thinnings on the diameter distribution of even-aged Maritime pine stands. Forest Ecology and Management 165: 57-65. https://doi.org/10.1016/S0378-1127(01)00650-8
  18. Husch, B., Beers, T.W. and Kershaw, J.A. 2003. Forest Mensuration. John Wiley and Sons, Incorporation. pp. 162-201.
  19. Intergovernmental Panel on Climate Change. 2006. 2006 Intergovernmental Panel on Climate Change Guidelines for National Greenhouse Gas Inventories. Volume 1. General Guidance and Reporting. Intergovernmental Panel on Climate Change National Greenhouse Gas Inventory Programme. Institute for Global Environmental Strategies. pp. 3.6-3.78.
  20. Korea Forest Research Institute. 2010. Survey manual for biomass and soil carbon. Korea Forest Research Institute. pp. 74.
  21. Laar, A.V. and Akca, A. 1997. Forest mensuration. Cuvillier Verlag Gottingen. pp. 132-134.
  22. Kohavi, R. 1995. A study of cross-validation and bootstrap for accuracy estimation and model selection. Appears in the International Joint Conference on Artificial Intelligence. http://robotics.stanford.edu/${\sim}$ronnyk.
  23. Little, S.N. 1982. Weibull diameter distribution for mixed stands of western conifers. Canadian Journal of Forest Research 13: 85-88.
  24. Liu, C., Zhang, L., Davis, C.J., Solomon, D.S. and Gove, J.H. 2002. A finite mixture model for characterizing the diameter distributions of mixed-species forest stands. Forest Science 48(4): 653-661.
  25. Mctague, J.P. and Bailey, R.L. 1987. Compatible basal area and diameter distribution models for thinned loblolly pine plantations in santa catarina, Brazil. Forest Science 33(1): 43-51.
  26. Murphy, P.A. and Farrar, R.M. 1988. A framework for stand structure projection of uneven-aged Loblolly-shortleaf pine stands. Forest Science 34(2): 321-332.
  27. Newton, P.F. and Amponsah, I.G. 2005. Evaluation of weibull-based parameter prediction equation systems for black spruce and jack pine stand types within the context of developing structural stand density management diagrams. Canadian Journal of Forest Research 35: 2996-3010. https://doi.org/10.1139/x05-216
  28. Reynolds, M.R. 1984. Estimating the error in model predictions. Forest Science 30(2): 454-469.
  29. Reynolds, M.R., Buck, T.E. and Huang, W. 1988. Goodness-of-fit tests and model selection procedures for diameter distribution models. Forest Science 34(2): 373-399.
  30. SAS Institute, Inc. 2004. SAS/STAT 9.1 User's Guide. SAS Institute, Incorporation. Carry. North Carolina.
  31. Schreuder, H.T., Hafley, W.L. and Bennett, F.A. 1979. Yield prediction for unthinned natural slach pine stands. Forest Science 25(1): 25-30.
  32. Shiver, B.D. 1988. Sample sizes and estimation methods for the weibull distribution for unthinned slash pine plantation diameter distributions. Forest Science 34(3): 809-814.
  33. Zhang, L., Gove, J.H., Liu, C. and Leak, W.B. 2001. A finite mixture of two weibull distributions for modeling the diameter distributions of rotated-sigmoid, uneven-aged stands. Canadian Journal of Forest Research 31: 1654-1659. https://doi.org/10.1139/x01-086