摘要

森林的永續經營講究的是工具，一些能夠提供關於地方林分，混合各種不同樹齡發展狀況的資訊的工具。要開發這一類的工具並實際應用，取得森林的資料與統計數據是不可或缺的。資料方面所參考的是貝里斯發展計劃(PfB)於2015-2016年間，對位於貝里斯北部Rio Bravo保育管理區內所進行的收割期前的存量調查報告。在本文中已附上十種的硬木類的資料。這些資料將以圖形的方式呈現，並跟據分析後對每個種類進行四分位的排序，以便於瞭解該區域內各種類的生長狀況。為了開發初步估算收割前林木總量的方法，研究上運用了一些統計方法；同時也參考一些過去關於評估樹高的研究報告，以便於理解樹高與樹寬之間的關係。

透過圖形分析的方式，研究得出這些及胸高的十種硬木中，其樹高與樹寬的生長並沒有一定的規律。不過，從四分位的角度切入，數據顯示上弦(Upper quartile)樹高為9米至14米，樹寬則為38至75公分。針對樹高總量的估算方式上，開發了一套公式，奠定收割前保守估計的良好基礎。在調整兩個樹高與樹寬的預測模型之後，得出的結論為：若要開發一個針對該地區的精確模型，必須運用混合效果的隨機方法。研究結果將有助於森林管理和監控個別樹木與林分。

Abstract
Sustainable forest management requires tools that can provide details about the development of mixed, uneven aged forest stands. For tools to be developed and implemented forest data and statistics are necessary. Data was obtained from Programme for Belize (PfB) from their 2015 - 2016 pre-harvest stock survey at the Rio Bravo Conservation and Management Area in Northern Belize. Data on ten hardwood tree species were made available for this paper. The data was visually presented and analyzed to determine the first, second and third quartiles for each species, in order to better understand growth of species in the area. Statistical techniques were used to estimate the stem-height volume. This was done in order to develop a method for preliminary estimations of standing tree volume prior to being harvested. Past studies were also reviewed to evaluate their methods of estimating tree height, in order to get a better understanding of the relationship between tree height and diameter.
Through visual analysis it was observed that the growth of stem height and diameter at breast height for the ten species did not have a pattern. However, data analysis by quartiles showed that the upper quartile for stem height ranged from 9 to 14 meters, and for diameter it ranged from 38 to 75 cm. An equation for volume estimation was developed, which provided conservative estimates of stem height volume, forming a good basis for pre-harvest estimations. Revision of two height-diameter models for height prediction led to the conclusion in order to develop an accurate model for the area a mixed-effects stochastic technique is necessary. The results of the study are presented such that they can be used as an aid in forest management and monitoring individual trees and tree stands.

References

(1) Alder, D., Synnott, T. J., Permanent Sample Plot Techniques for Mixed Tropical Forest, Oxford Forestry Institute, 1992.
(2) Barrio-Anta, M., Diéguez-Aranda, U., Castedo-Dorado, F., Álvarez- González, J. G., & Rojo-Alboreca, A., "Mimicking natural variability in tree height of pine species using a stochastic height-diameter relationship," New Zealand Journal of Forestry Science, 36(1): 21–34, 2006.
(3) Castedo-Dorado, F., Barrio, M., Parresol, B. R., & Álvarez, J. G., "A stochastic height-diameter model for martime pine ecoregions in Galicia (north-western Spain)," Annals of Forest Science, 62, 455-465, 2005.
(4) Central Intelligence Agency, Map of Belize, accessed on 16 January 2017,
<https://www.cia.gov/library/publications/resources/cia-maps-publications/map-downloads/belize_physiography.pdf>
(5) Cherrington, E. A., Cho, P., Waight, I., Santos, T. Y., Escalante, A. E., Nabet, J., & Usher, L., "Executive Summary: Forest Cover and Deforestation in Belize, 2010 - 2012," 2012, Accessed on 12 December 2016,
<http://eprints.uberibz.org/1381/1/Cherrington_et_al_2012_bz_forest_cover_deforestation_2010-2012_summary.pdf>.
(6) Cherrington, E. A., Ek, E., Cho, P., Howell, B. F., Hernandez, B. E., Anderson, E. R., Flores, A. I., Garcia, B. C., Sempris, E., & Irwin, D. E., "Forest Cover and Deforestation in Belize: 1980 - 2010," 2010, Accessed on 12 December 2016,
<https://ambergriscaye.com/art/pdfs/bz_forest_cover_1980-2010.pdf>
(7) Corral-Rivas, S., Álvarez-González, J. G., Crecente-Camp, F., & Corral-Rivas, J. J., "Local and generalized height-diameter models with random parameters for mixed, uneven-aged forests in Northwestern Durango, Mexico," Forest Ecosystems, 1:6, 2014.
(8) Crecente-Campo, F., Tomé, M., Soares, P., & Diéguez-Aranda, U., "A generalized non-linear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain," Forest Ecology and Management, 259: 943-952, 2010.
(9) Dawkins, H.C., The management of natural tropical high forest with special references to Uganda, Imperial Forestry Institute, University of Oxford, 1958.
(10) Diéguez-Aranda, U., Barrio, M., Castedo, F., & Álvarez, J. G., "Relación altura-diámetro generalizada para masas de Pinus sylvestris L. procedentes de repoblación en el noroeste de España," Investigación Agraria. Sistemas y Recursos Forestales, 14, 229–241, 2005.
(11) Fotheringham, A. S., Brunsdon, C., & Charlton, M., Geographically Weighted Regression: The analysis of spatially varying relationships, Wiley, Chichester, 2002.
(12) Larsen, D. R., Allometric Equations, Advanced Forest Biometrics, N.D., Accessed 20 January 2017, <http://oak.snr.missouri.edu/advforbio/pdf/unit7.pdf>.
(13) Li, Y-q, Deng, X-w, Huang, Z-h, Xiang, W-h, Yan, W-d, Lei, P-f, Zhou, X-l, & Peng, C-h, "Development and evaluation of models for the relationship between tree height and diameter at breast height for Chinese-Fir plantations in subtropical China," PLOS ONE, 10 (4): e0125118, 2015.
(14) Leslie, R., (Editor), A History of Belize: A nation in the making, Cubola Productions, 1997.
(15) Meerman, J. C., "Protected Areas System Assessment and Analysis: Protected Area Categories," 2005, Accessed on 20 November 2016
<http://biological-diversity.info/Downloads/NPAPSP/Prot_area_analysis.pdf>
(16) Programm for Belize (PFB), Annual Plan of Operation, 2013.
(17) Sánchez-González, M., Cañellas, I., & Montero, G., "Generalized height-diameter and crown diameter prediction models for cork oak forests in Spain," Investigación Agraria: Sistemas y Recursos Forestales, 16(1):76-88, 2007.
(18) Sharma, M., & Parton, J., "Height-diameter equations for boreal tree species in Ontario using mixed-effects modelling approach," Forest Ecology and Management, 249: 187-198, 2007.
(19) Shoman, A., Thirteen Chapters of a History of Belize, 1st edition, The Angelus Press Limited, 1994.
(20) Shugart, H. H., Saatchi, S., & Hall, F. G., "Importance of structure and its measurements in quantifying function of forest ecosystem," Journal of Geophysical Research, Vol. 115, G00E13, 2010.
(21) Soares, P., & Tomé, M., "Height-diameter equation for firest rotation eucalyt plantations in Portgual," Forest Ecology and Management, 166: 1, 99-109, 2002.
(22) Statistical Institute of Belize, Population of Belize, accessed on 1 June 2017, < http://www.sib.org.bz/>
(23) Synnott, T. J., A manual of permanent plot procedures for tropical forests, Tropical Foresty Papers, Commonwealth Foresty Institute, University of Oxford, No. 14: 67, ISBN:0 85074 031 2, 1979.
(24) Thornley, J. H. M., "Modelling Stem Height and Diameter Growth in Plants," Annals of Botany, 84: 195 - 2-5, 1999.
(25) Thornley, J. H. M., "Dynamic model of leaf photosynthesis with acclimation to light and nitrogen," Annals of Botany, 81: 421-430, 1998.
(26) Thornley, J. H. M., & Cannell, M. G. R., "Nitrogen relations in a forest plantation-soil organic matter ecosystem model," Annals of Botany, 70: 137-151, 1992.
(27) Vargas-Larreta, B., Castedo-Dorado, F., Álvarez-González, J. G., Barrio-Anta, M., & Cruz-Cobos, F., "A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto Durango (Mexico)," Forestry Advance Access, 2009.
(28) Vilppo, T., Mola-Yudego, B., Diáz-Yañez, O., Haapala, A., Melin, M., Heistakene, J., Packalen, P., Valbuena, R., Mononen, K., Pitkänen, S., Rodriguez, Y. P., Ramcilovik-Suominen, S., Torssonen, P., & Pykäläinen, J., Sustainable Fuelwood Management in West Africa, p. 37, University of Eastern Finland, 2016.
(29) West, P. W., Tree and Forest Measurement, Second Edition, Springer, 2009.