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한국농림기상학회지, 제 16 권제 4 호 (2014) (pissn 1229-5671, eissn 2288-1859) Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4, (2014), pp. 327~335 DOI: 10.5532/KJAFM.2014.16.4.327 c Author(s) 2014.

1 한국농림기상학회지, 제 16 권제 4 호 (2014) (pissn , eissn ) Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4, (2014), pp. 327~335 DOI: /KJAFM c Author(s) CC Attribution 3.0 License. 수간곡선모델을이용한소나무의지방별수간재적표개발 강진택 * 손영모 김소원 이선정 박현국립산림과학원기후변화연구센터 (2014 년 10 월 31 일접수 ; 2014 년 11 월 7 일수정 ; 2014 년 11 월 7 일수락 ) Development of Local Stem Volume Table for Pinus densiflora S. et Z. Using Tree Stem Taper Model Jin-Taek Kang*, Yeong-Mo Son, So-Won Kim, Sun-Jeoung Lee and Hyun Park Center for Forest & Climate Change, Hoegi-ro, Dongdaemen-gu, Seoul , Korea (Received October 31, 2014; Revised November 7, 2014; Accepted November 7, 2014) ABSTRACT Current volume tables might underestimate or overestimate the volumes of individual trees in a specific region because the tables were made using the data from broad regions within South Korea. Therefore, to solve this problem, this study was conducted to develop local stem volume tables reflecting the local growth pattern and properties using stem taper equations in the regions of Hongcheon and Yeongju. We developed the local stem volume table for Pinus densiflora, which is the widely planted species in South Korea. To derive the most suitable taper equation for estimating the stem volume of region, three models of Max & Burkhart, Kozak and Parresol et al. were applied and their fitness were statistically analyzed by using the Fitness Index, Bias, and Standard Error of Bias. The result showed that there is a significant difference among the three models, and the Fitness Index of the Kozak model was highest compared to the other models. Therefore, the Kozak model was chosen for generating stem taper equation and stem volume tables for P. densiflora. The result from the developed stem volume tables of each region was compared to the current stem volume tables with driven by the data of tree growth obtained throughout the nation. The result showed that there is a significant difference (0.000<α=0.05) in two regions, Hongcheon and Yeongju, and also there is a significant difference (0.000<α=0.05) between the two regions. Key words: Stem volume table, Stem taper equations, Local stem volume table, Kozak model I. 서론임목은지리적환경에따라형태적, 해부학적, 생리적형질변이를나타내는지리적변이를갖는다. 우리나라의대표적수종인소나무의분포는수직적으로북위 43 o 20' 의함북에서부터북위 33 o 20' 의제주한라산에이르고있으며, 수직적으로는표고 10m에서최고 1,300m까지분포하고있다 (Jung and Lee, 1965). Uyeki(1928) 는우리나라소나무를수형에따라 6개군으로분류한바있으며, 이러한분류는외부환경요인의지리적 지역별차이에따른임목생장차이도같은수종이라할지라도크게나타날수있음을증명해주는것이라볼수있다. Park and Lee(1990) 은우리나라소나무의 4개지역형소나무 30-40년생천연림전체의현존량이안강형은 29.77t/ha인반면금강형은 t/ ha로큰차이를보인다고보고한바있다. 산림은목재 * Corresponding Author : Jin-Taek Kang (beg8bune@forest.go.kr)

2 328 Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4 생산을위한경제적기능과생태계의유지및보건문화휴양기능과더불어탄소흡수원으로서의공익적기능을가지고있다. 다양한산림의다목적기능을최대로발휘될수있도록하려면최적의산림경영이이루어져야한다. 이러한최적의산림경영을위해서는산림의임목에대한정확한재적추정은필수적이다. 임목의재적은보통그임목의흉고직경 (DBH), 수고 (H), 그리고형수 (F) 를포함하는함수에의하여추정된다. 그러나형수의변이가임목재적에미치는영향은흉고직경이나수고의변이가재적에미치는영향보다적고, 또한수종에따라서는임목의크기에관계없이형수는상대적으로큰차이가없는것으로알려져있어 (Clutter et al., 1983) 흉고직경과수고의 2변수만을이용하여재적을추정하는것이일반적인방법이다. 그동안임목재적추정식에대한많은연구가국내외적으로진행되 었으며방법론으로는형수에의한방법 (Park and Chung, 1985; Seo, 1998), 간곡선식이나임목의완만도표조제에의한방법 (Kim et al., 1994; Kim, et al., 1986) 등이있다. 초기의재적표는독립변수흉고직경및수고의값과상응하는재적에대한관련식 (Chapman and Meyer, 1949; Amateis and Burkhart, 1987; Jeon et al., 2007) 이일반적방법이었으나, 근래통계이론및분석기법의발달은많은표본자료를이용하여정도가더높은개별임목재적식을개발할수있게되었다. 현재우리나라에서사용하고있는몇가지수종에대한재적표는이러한통계모형기법과분석을위한컴퓨터의사용이일반화되기이전에조제된것으로소나무를제외하고는모두전국에적용시키도록조제되었다 (Korea Forest Service, 1981). 1970년대에집중적으로조성된우리나라의산림은현재성숙화단계에있으며, 임목자원과관련된산림정책및경영의목표도다각화되는추세에있다. 그러나임목자원평가와관련된경영제표와임목간재적표는 1960대에만들어진이후, 1980년대와최근 2009년에일부수종에대해서보완되었으나대부분 40년전에작성되어현재의성숙된임목자원을대표하지못하고있어경영 목표에부합되는정보를제공하지못하고있다. 현재우리나라산림은유령기에해당하는영급과영급의임목축적이차지하는비율이 1964년 69.4% 에서 2010년에는 23% 에불과한반면, 청 장년기에해당하는영급과영급이차지하는임목축적의비율은 22.7% 에서 65.6% 로증가하였다 (Korea Forest Service, 2013). 이러한사실은결과적으로기존의재적표가우리나라산림의초장기유령임분상태의전국평균치자료로추정되었기때문에오늘날의대부분중 장령림임분특성을가진특정지역의재적을추정하기위해적용시킬경우, 지역에따라통계적으로인정할수없는과소또는과대추정치를제공할수도있다. 본연구는최근우리나라산림의영급, 경급구조가장령기에접어들면서지역간의임목재적의차이가나타나고있고, 기존의임목재적표의적용으로는지역의생장특성및현실재적을반영하기에는한계가있어지역의특성을반영한지방별재적표를조제하고자수행하였다. 대상수종은현재우리나라에서가장많은면적을차지하고있는소나무를대상으로하였으며, 강원도홍천과경북영주지역에대한지방별재적표를작성하기위한최적수간곡선식을도출하여지방별재적표를작성하고자하였다. II. 재료및방법 2.1. 공시재료본연구는소나무분포범위가넓고, 지역을대표하는수종이소나무인강원홍천과경북영주지역의소나무를대상으로각지역별로경급을다양하게하여 100여본의개체목생장자료를이용하였다. 분석에이용된개체목의생장특성은 Table 1에서보는바와같다 분석방법최근수간재적표는 70-80년대재적표개발에주로이용한 Logarithmic 모형등지수식에의한방법이아니라, 수간곡선식을도출하여이를적분하는방법을 Table 1. Data summary of stem analysis by survey regions of pinus densiflora used in this study Region No. of Trees DBH(cm) Height(m) Min. Max. Mean Min. Max. Mean Hongcheon Yeongju

3 Jin-Taek Kang: Development of Local Stem Volume Table for Pinus densiflora S. et Z. Using Tree Stem Table 2. Taper equations selected for this study Model Taper Equation Max and Burkhart d DBH b h h 2 h = H + b b 3 a H 2 I + b a --- h H I 2 where d = diameter outside bark at height (cm) DBH = diameter at breast height outside bark (cm) h = height along stem (m) H = total height (m) b i = parameters = inflection points (i=1; upper, i=2; lower) a i H 2 I i = 1, if h --- < α H 1 0, otherwise b 1 Z d a 0 DBH a1 DBH = a 2 X Kozak where Z = relative height (= h --- ) H h X = H (p = HI -----, Hi; inflection point) 1 p H a i, b i = parameters 2 + b 2 ln( Z ) + b 3 Z+ b 4 e 2 + b DBH H Parresol et al. d i = dz ( 2 ( b 1 + b 2 Z) + ( Z a) 2 ( b 3 + b 4 ( Z+ 2a) )I) 0.5 Z = (h-h i )/h, a: join point, I = 1, if Z a = 0. if Z a Table 3. Statistics for evaluating performance of taper equations Statistics Fitness index (FI) Bias Standard error of estimate as percent of the mean (SEE%) Mean absolute difference (MAD) Equation FI = 1 Σ( Y i Yˆ 2 ) 2 ( Y i Y) D = Σ( Y i Ŷ) n SEE% = ( ( e i D) 2 ( N 1) ) Y 100 D = Σ ( Y i Ŷ) n 2 많이이용하고있다. 후자의방법이좋은것은개체목재적을말구직경및원구직경등을자유롭게조정하여이용재적을산출할수있게하여주기때문이다. 또한몇 m 간격으로절단하여이용할수있는정보도바로제공할수있다 (Lee et al., 1999). 이에많은연구자들은임목수간곡선을추정할수있는다양한모형을개발한바있다 (Son et al., 2009, 2012; Shin et al., 1996, Kim et al., 1994). 본연구에서는임목재적표를조제하기에앞서최적수간곡선식을도출하기위하여 Max & Burkhart 모델, Kozak 모델그리고 Parresol et al. 모델의 3가지수간곡선모델중 분석을통해나타난검정통계량을이용하여최적모형을판정하였다. 그리고여기에서도출된최적모델을이용하여수간곡선모양을구하고이를수간중심선중심으로회전시켜수간재적을산출하였다 (Lee et al., 2003; Kozak, 1988; Max and Burkhart, 1976). 각수간곡선식의수간높이별수간직경추정이행능력을평가하기위해 적합도지수 (Fit index, FI), 편의 (Bias), 추정치표준오차 (Standard error of estimate, SEE%), 평균절대편차 (Mean absolute deviation, MAD) 등의검정통계량을이용하였다 (Son et al., 2009; Lee et al., 1999).

4 330 Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4 검정통계량중적합도지수 (FI) 는회귀분석에서의결정계수와같은성격의지수이며, 비선형회귀분석에서의결정계수는의미가없으므로실측치와추정치와의관계정도를구명하기위하여나타내는것이며, 편의 (Bias) 는추정량이평균적으로모수의참값에대해어느정도과소치혹은과대치를주는지를나타내준다. 추정치표준오차 (SEE%) 는모델의상대적인정도 (accuracy) 를평가하고, 평균절대편차 (MAD) 는각추정치잔차의절대값을평균한값으로각추정치의평균적인편차크기를나타내주는것이다. III. 결과및고찰 3.1. 수간곡선식파라미터도출 3가지수간곡선모델을이용하여소나무수간곡선식을추정한바, Table 4와같이각모델별파라미터및검정통계량을도출할수있었다. Table 4에서적합도지수, 편의 (Bias) 등기타검정 통계량값으로모델의적합성을검토하였으며, 또한잔차도를그려평균범위를벗어나는지를검토하였다. Kozak 모델에의해추정된수간곡선식의적합성은홍천 92%, 영주 97% 였으며, 편의 (Bias) 역시 Kozak 모델이타모델보다적어모델의적합성을입증해주었다 (Son et al., 2009, 2012; Chung et al., 2010). Kozak 모델의수간곡선모형적합성을좀더정밀하게알아보기위하여잔차를도식한결과, 2지역모두에서잔차는 0 을중심으로하여고르게분포하고있었다 (Fig. 1). 따라서 Kozak 모델이두지역의소나무수간곡선을설명하는데우수함을알수있어, 이모델이소나무의수간곡선을추정하는데있어가장적합한식임을알수있었다. 그러므로본수간곡선을재적표도출에이용하여도무방할것으로판단하였다. Kozak 모델에서이용자가결정하는변곡점은홍천과영주지역모두가 20%( 변곡점 0.2) 높이의상대수고에서결정됨을알수있었다 (Fig. 2). 한편, Kozak (1988) 에의한연구결과를보면, 소나무류 0.25, 가 Table 4. Parameter estimates for three taper equations by regions of Hongcheon and Yeongju for Pinus densiflora Region Model Max and Burkhart Kozak Parresol et al. Hongcheon Yeongju a a a a a b b a b Parameter b b b b b b b b b b FI SEE Bias MAD a a a a a b b a b Parameter b b b b b b b b b b FI SEE Bias MAD

5 Jin-Taek Kang: Development of Local Stem Volume Table for Pinus densiflora S. et Z. Using Tree Stem Fig. 3. Stem taper curve pattern by regions of Hongcheon and Yeongju for Pinus densiflora. Fig. 1. Residual distribution of estimated diameter by relative height of regions, Hongcheon and Yeongju for Pinus densiflora. 나무는 0.22라고밝혀, 동일수종이라도지역에따라변곡점이달리형성될수있음을밝힌바있다 (Son et. al., 2007) 수간곡선형의비교 Kozak 모델의파라미터를이용하여각지방별소나무의수간형을상대수고 (Relative height, RH) 를토대로도식화하였다 (Fig. 3). 정밀한수간곡선형의비교는그림상에서식별하기곤란하나, 홍천지역의소나무수간형의수간고별직경급이영주지역보다높은것으로나타났으며, 수간형초살도는영주지역이다소높은것으로나타났다. 초살도가높다는것은임목의부피, 즉재적이그만큼적게나타날수있음을의미한다. Fig. 2. Distribution of estimated diameter by relative height of regions, Hongcheon and Yeongju for Pinus densiflora. 문비나무 0.30, 사시나무 0.20 등을수간변곡점이라보고한바있다. 국내에서는 Son et al. (2012) 은 Kozak 모델을이용하여아까시나무의수간곡선식도출에있어 0.25를변곡점으로정하였으며, 또한전남완도지역의붉가시나무변곡점은 제주지역붉가시 3.3. 지방별낙엽송수간재적표조제각표본목의수피포함수간재적추정은먼저측정된수간고와직경에의해모델별수간곡선식을도출한후, 이를이용하여수간고 10cm 간격으로직경을추정하고, Smalian식에의한구분구적법으로산출하였다 (Son et. al., 2012). 최적수피포함수간곡선식인 Kozak 모델을이용하여소나무의지방별수간재적표를작성한결과아래 Table 5와같다. Kozak 모델에의해작성된각지방별수간재적표와기존의전국단위의단일수간재적표와의차이그리고지방별수간재적표간의차이를알아보기위하여 T-test

6 332 Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4 Table 5. Local stem volume table within bark by region of, Hongcheon(a), and Yeongju(b) for Pinus densiflora (a) D(cm) H(m) *H: Height, D: DBH (b) D(cm) H(m)

7 Jin-Taek Kang: Development of Local Stem Volume Table for Pinus densiflora S. et Z. Using Tree Stem Table 6. Analysis of T-test between local stem volume table and standard stem volume table Region Class N Mean SD t p-value MD Hongcheon Standard Local < Yeongju Standard Local < Table 7. Analysis of T-test between local stem volume table and standard stem volume table Region Mean SD F p-value Hongcheon <0.000 Yeongju 검정을실시한결과는 Table 6, 7과같다. Table 6에서홍천과영주지역모두에서기존의전국단위의단일재적표 (Korea Forest Research Institute, 2009) 의수고및직경별평균재적값의차이는모두유의적인 (p-value:0.000<α=0.05) 것으로나타났다. 또한두지역간지방별재적표의평균재적도통계적으로유의한차이를보였다 (Table 7). 이와같이, 실제개별임목의재적차이는기존의재적표및추정치와는그차이가크지않을수있지만, ha당재적을추정할경우는상당한차이를보인다. 이러한결과는합리적경영을위한기초자료로부실하고목재자원량의저평가로국가혹은개인의재산평가에대한손실의결과를초래할수있을것이다. Kim et al.(1997) 은전국의대표적소나무 6곳의산지별소나무를전국 8곳에시험지를조성하여지역간생장특성변이연구에서수고, 직경및뿌리생장등에서산지및지역간생장차이가뚜렷이나타났다고하였으며, Matziris (1995) 와 Alia(1995) 도산지별생장시험에서지역별로차이가크다고보고하였다. 또한 Park and Lee(1990) 는한국산 4개지역형별로전형적인수형을보이는소나무천연림의 30-40년생임분을대상으로물질생산현존량을추정하여비교분석한결과, 안경형 29.87t/ha, 중남부평지형 t/ha, 중남부고지형 t/ha, 금강형 t/ha로지역형별로큰차이를보이고있었다. 한편, Song et al.(1995) 은강원도 9개지역의소나무목편을채취하여직경생장패턴에따른강원도소나무의생장권역구분연구에서지역간의근접성분석을위하여 cluster 분석을한결과영동지방 ( 명주, 양양, 고성, 삼척 ) 과영서지방 ( 횡성, 영월, 평창 ) 으로연년생장패턴이유사하며두집단으로구분함으로써같은강원지역소나무라도지역내에서도지리적환경등에따라생장이달라짐을알수있었다. IV. 결론우리나라에소나무를대상으로수간고별직경측정자료와일반적으로많이이용되는 3가지수간곡선모델을이용하여지방별수간재적표를작성하고적합성검정을실시한결과는다음과같다. Max & Brukhart, Kozak, Parresol et al. 의 3가지수간곡선모델중지방별소나무의수간곡선을가장잘나타내는식선정을위하여적합도지수및기타검정통계량을비교분석한결과 Kozak 모형이가장우수함을알수있어, 이모형이소나무의지방별수간곡선을추정하는데있어최적의식으로판단하였다. Kozak 수간곡선추정모델을이용하여각개체목의수간고별직경을추정하고이를구분구적하여수간재적을산출하였는데, 각지방의추정된수간재적표와전국단위의기존수간재적표와비교 분석한결과, 2지역모두에서기존재적표보다높은값의재적을보였으며, 통계적으로유의한차이가있는것으로나타났다. 또한추정된두지역의지방별수간재적표간의재적평균값에서도지역간에통계적으로유의한차이를보이는것으로나타났다. 이와같이, 본연구에서기존의재적표와유의적인차이를보이고있고지역간에도차이를보이고있어지방별재적표의필요성에대한설득력을얻을수있었다. 수간재적표는임목의매매시경제적가치를판단하는기준이되며, 해당임목의축적통계등을계산할때도필수적인요소이다. 또한지역별입지환경및생육환경이다르기때문에같은수종이라도재적생장차이를보이고있다. 따라서향후지방별수간재적표가임목의매매또는매각, 국가또는지자체산림통계작성시가장기본이되

8 334 Korean Journal of Agricultural and Forest Meteorology, Vol. 16, No. 4 는경영제표로수요가많아질것으로기대되며, 목재이용측면과정확한탄소저장량계산등에서도반드시필요할것으로판단된다. 적 요 현재사용하고있는임목재적표는전국공용으로제작되어있기때문에, 특정지역에적용할경우재적을과소또는과대추정하는문제점을가지고있다. 따라서, 본연구는이러한문제점을해결하기위하여수간곡선식을이용하여지역의재적생장을잘반영할수있도록홍천과영주지역의지방별임목수간재적표를개발하고자수행하였으며, 우리나라에서가장많은분포를보이고있는소나무를대상으로개발하였다. 추정에적합한수간곡선식의도출을위해서 Max & Burkhart, Korzak 그리고 Parresol et al. 의세가지수간곡선모델을적용하였으며, 적합도, 편의, 잔차의표준오차등의통계량을분석하여각모델의적합성을평가하였다. 그결과 3개의수간곡선모델간에는정확성에대한유의적인차이가없으나, 소나무의수간생장을표현하는데에는 Kozak 모델이가장적합한것으로나타났다. 따라서 Kozak 모형을이용하여소나무의지방별수간재적표를조제하였다. 새롭게개발된지방별수간재적표와전국단위의소나무수간재적표와비교한결과, 홍천과영주 2지역모두에서현재재적표보다재적이높은것으로나타났으며 (0.000<α=0.05), 또한두지역간지방별재적표의재적에서도통계적으로유의한차이를보였고 (p-value: 0.000<α=0.05) 홍천이영주에비해재적이높게나타났다. REFERENCES Alia, R., Gil and J. A. Parods Performance of 43 Pinus pinaster Ait. Provenances on 5 Locations in central Spain. Silvae Genetica 44(2-3), Amateis, R. L. and H. E. Burkhart, 1987: Cubic-foot volume equations for loblolly pine trees in cutover, site prepared plantations. St Jeanne Antide Foundation, pp Bennett, F. A., C. E. McGee and J. L. Clutter Yield of old-field slash pine plantations. USDA U.S. Dept. of Agriculture, Forest Service, Southeastern Forest Experiment Station, Paper No Bonnor, G. M. and P. Boudewyn Taper-volume equations for major tree species of the Yukon Territory. Forestry Canada Pacific and Yukon Region-Information Report BC-X-323, 18pp. Burkhart, H. E., R. C. Parker, M. R. Strub. and R. G. oderward Yield of old-field loblloy pine plantations. Virginia Polytechnic Institute and State University Pub. FWS-3-72, 51. Chapman, H. H. and W. H. Meyer Forest Mensuration. McGraw-Hill, New York. Chung, Y. G., D. H. Kim and C. M. Kim Development of Stem Profile and Taper Equation for Quercus acuta in Jeju Experiment Forests. Journal of Korean Forestry Society 99(1), Clutter, J. R., J. C. Fortson, L. V. Pienaar, G. H. Brister, and R. L. Bailey Timber management: a quantitative approach. John Wiley & Sons, Inc Gal, J. and I. E. Bella New stem taper functions for 12 Saskatchewan timber species. Natural Resources Canada, Canadian Forest Service, Northwest Region, Northern Forestry Centre, Information Report Nor-x-338. Jeon, B. H., S. H. Lee, Y. J. Lee, H. Kim, and H. M. Kang Estimation of Site Index and Stem Volume Equations for Larix leptolepis Stand in Jinan, Chonbuk. Journal of Korean Forestry Society 96(1), Jung, T. H. and W. C. Lee The Korean forest vegetation zone and theory of the suitable tree on a site tree. Journal of SungKyunKwan University. pp Kim, J. S., W. K. Lee and W. H. Byun Regional Stem Curve and Volume Function Model of Pinus densiflora in Kangwon-Province. Journal of Korean Forestry Society 83(4), Kim, K. S. and Y. C. Han Variation in Growth characteristics of Pinus densiflora S. et Z. at Eight Experimental Plantations of Korea. Journal of Korean Forestry Society 86(2), Kim, Y. W. and H. K. Lee Study of Stem Volume Table of Pinus thunbergii in the southern Part of Korea. Journal of Korean Forestry Society 33, Korea Forest Research Institute Stem Volume Table. 261pp. Korea Forestry Service Assessment of the Korea Forest Resources. 59pp. Korea Forest Service Statistical Yearbook of forestry. p88. Kozak, A A variable-exponent taper equation. Can. J. For. Res. 18, Lee, K. H., Y. M. Son, Y. G. Chung and W. K. Lee A Taper and Volume Prediction System for Pinus densiflora in Kangwon Province, Korea. Korea Forestry Research Institute 62, Lee, W. K., J. H., Seo, Y. M. Son, K. H. Lee and K. V. Gadow Modelling stem profiles for Pinus densiflora in Korea. Forest Ecology and Management 172(1), Max, T. A. and H. E. Burkhart Segmented polynomial regression applied taper equations. Forest Science 22(3),

9 Jin-Taek Kang: Development of Local Stem Volume Table for Pinus densiflora S. et Z. Using Tree Stem Matziris, D. I Provenance variation of Pinus radiate grown in Greece. Silvae Genetica 44(2-3), Park, I. H. and S. M. Lee Biomass and Net Production of Pinus densiflora Natural forests of Four Local Forms in Korea. Journal of Korean Forestry Society 79(2), Park, N. C. and Y. G. Chung Studies on the Determination of the Breast-Height Form Factors for Stem of Pinus thunbergii and Cryptomeria japonica. Journal of Korean Forestry Society 70, Seo. J. W Studies on Estimation of Stand form Factor for Red Pine (Pinus densiflora S. et Z.) Stands Focusing on Stands in Kwangwon Province. Jour. Korean For. Measur 1, Shin, M, Y., J. W. Yun and D. S. Cha Local Correction of Tree Volume Equation for Larix leptolepis by Rati-of- Means Estimator. Journal of Korean Forestry Society 85(1), Smalley, G. W. and D. R. Bower Volume tables and point factors for loblloly pines in plantations on abandoned fields in Tennessee, Alabama, and Georgia highlands, USDA, U.S. Dept. of Agriculture, Forest Service, Southeastern Forest Experiment Station, Paper SO-32, 13. Son, Y. M., H. Kim, H. Y. Lee, C. M. Kim, C. S. Kim, J. W. Kim, R. W. Joo and K. H. Lee Taper Equations and Stem Volume Table of Eucalyptus pellita and Acacia mangium Plantations in Indonesia. Journal of Korean Forestry Society 98(6), Son, Y. M., J. H. Jeon, J. K. Pyo, K. N. Kim, S. W. Kim, S. J. Lee and K. H. Lee Development of Stem Volume Table for Robinia Pseudoacacia Using Kozak s Stem Profile Model. Journal of Agriculture & Life Science 46(6), Song, C. C., W. H. Byun and W. K. Lee Districting the Growth Zone by Diameter Growth Pattern for Pinus densiflora in Kangwon Province. Journal of Korean Forestry Society 84(10), Uyeki, H On the physiognomy of Pinus densiflora growing in Korea and silvicultural reatment for its improvement. Bulletin of the Agricultural and Forestry College Suigen (Suwon). Korea. 263pp.

03-서연옥.hwp

03-서연옥.hwp 농업생명과학연구 49(4) pp.31-37 Journal of Agriculture & Life Science 49(4) pp.31-37 Print ISSN 1598-5504 Online ISSN 2383-8272 http://dx.doi.org/10.14397/jals.2015.49.4.31 국가산림자원조사 자료를 적용한 충남지역 사유림경영율 추정 서연옥