黑龙江省东部地区天然椴树单木冠幅预测模型
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摘要
以东北林业大学帽儿山实验林场46块样地共2009株天然椴树为研究对象,从已有的10个冠幅预测模型中选出较好的冠幅直径模型作为基础模型,且考虑样地、林木因子、立地因子、竞争和其它因素等对冠幅大小的影响,构建基于样地水平的非线性混合效应模型。结果表明:逻辑斯蒂形式的冠幅直径模型拟合效果较好;第一活枝高(HCB)、优势木平均高(Ht)和椴树的树种组成系数(P)是影响冠幅的主要因子,且冠幅均随着变量HCB、Ht和P的增加而减少;混合效应模型的调整决定系数(R_(adj)~2)和均方根误差(R_(MSE))分别为0.525 0和0.424 7 m,平均误差、平均绝对误差和相对平均绝对误差分别为-0.004 7 m、0.355 7 m和17.936 5%。与基础模型相比,混合效应模型的R_(adj)~2提高了17.6%,R_(MSE)降低了7.4%。此外,基于数据结构的特点,构建的椴树单木冠幅模型,只适用于对阔叶混交林中小径阶椴树的冠幅进行预测,而不适用于对大径阶椴树的冠幅进行预测。
An individual crown diameter model was developed based on a data set consisting of 2009 natural Tilia tuan Szyszyl.trees from 46 plots located in Maoershan Experimental Forestry Farm of Northeast Forestry University. Because of the problem of high correlation among observations taken from the different sample plot,the random effects of sample plots to crown diameter were considered,namely,developing the nonlinear mixed effect crown width model. Base model used in developing mixed model was selected from 10 models reported in the literatures,and the effects of tree factors,site factors,competition and other factors to crown diameter were considered. The crown width-diameter model of logistic form had a better fit effect and was selected as base model. The height to live crown base Tilia tuan Szyszyl( HCB),dominant height of plot( Ht) and the basal area proportion of T. tuan( P) were significant factors in crown width model,and the crown width all decreased with the increase of( HCB),Htand P; The adjusted coefficient of determination(R_(adj)~2) and the root mean square error( RMSE) of the mixed effect model were 0.525 0 and 0.424 7 m,respectively,and the mean error,mean absolute error and relative average absolute error of the mixed effect model were-0.004 7 m,0.355 7 m and 17.936 5%,respectively. Compared to the basic model,the R2 adjof the mixed effect model increased 17. 6%,while RMSE decreased 7.4%. In addition,based on the characteristics of the data structure,the developing individual tree crown width nonlinear mixed effect model for T. tuan were only applied to the crown width of the small diameter classes within the broad leaved mixed forest,and not to the crown width of the large diameter classes Tilia.
An individual crown diameter model was developed based on a data set consisting of 2009 natural Tilia tuan Szyszyl.trees from 46 plots located in Maoershan Experimental Forestry Farm of Northeast Forestry University. Because of the problem of high correlation among observations taken from the different sample plot,the random effects of sample plots to crown diameter were considered,namely,developing the nonlinear mixed effect crown width model. Base model used in developing mixed model was selected from 10 models reported in the literatures,and the effects of tree factors,site factors,competition and other factors to crown diameter were considered. The crown width-diameter model of logistic form had a better fit effect and was selected as base model. The height to live crown base Tilia tuan Szyszyl( HCB),dominant height of plot( Ht) and the basal area proportion of T. tuan( P) were significant factors in crown width model,and the crown width all decreased with the increase of( HCB),Htand P; The adjusted coefficient of determination(R_(adj)~2) and the root mean square error( RMSE) of the mixed effect model were 0.525 0 and 0.424 7 m,respectively,and the mean error,mean absolute error and relative average absolute error of the mixed effect model were-0.004 7 m,0.355 7 m and 17.936 5%,respectively. Compared to the basic model,the R2 adjof the mixed effect model increased 17. 6%,while RMSE decreased 7.4%. In addition,based on the characteristics of the data structure,the developing individual tree crown width nonlinear mixed effect model for T. tuan were only applied to the crown width of the small diameter classes within the broad leaved mixed forest,and not to the crown width of the large diameter classes Tilia.
引文
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[18]RITCHIE M W,HAMANN J D.Individual-tree height-,diameter-and crown-width increment equations for Young Douglas-fir plantations[J].New Forests,2008,35(2):173-186.
[19]符利勇,孙华.基于混合效应模型的杉木单木冠幅预测模型[J].林业科学,2013,49(8):65-74.
[20]FU L Y,SUN H,SHARMA R P,et al.Nonlinear mixed-effects crown width models for individual trees of Chinese fir(Cunninghamia lanceolata)in south-central China[J].Forest Ecology and Management,2013,302:210-220.
[21]FU L Y,SHARMA R P,WANG G X,et al.Modelling a system of nonlinear additive crown width models applying seemingly unrelated regression for Prince Rupprecht larch in northern China[J].Forest Ecology and Management,2017,386:71-80.
[22]LEI Y K,FU L Y,AFFLECK D L R,et al.Additivity of nonlinear tree crown width models:Aggregated and disaggregated model structures using nonlinear simultaneous equations[J].Forest E-cology and Management,2018,427:372-382.
[23]XU H,SUN Y J,WANG X J,et al.Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian province,southeast China[J].PLoS One,2015,10(4).doi:10.1371/journal.pone.0122257.
[24]RAPTIS D,KAZANA V,KAZAKLIS A,et al.A crown widthdiameter model for natural even-aged Black pine forest management[J].Forests,2018,9(10).doi:10.3390/f9100610.
[25]董晨,吴保国,韩焱云,等.基于修正函数的杉木人工林单木冠幅预测模型[J].东北林业大学学报,2015,43(5):49-53.
[26]SHARMA R P,VACEK Z,VACEK S.Individual tree crown width models for Norway spruce and European beech in Czech Republic[J].Forest Ecology and Management,2016,366:208-220.
[27]SHARMA R P,BLEK L,VACEK Z,et al.Modelling crown width-diameter relationship for Scots pine in the central Europe[J].Trees,2017,31(6):1875-1889.
[28]卢军.帽儿山天然次生林树冠结构和空间优化经营[D].哈尔滨:东北林业大学,2008.
[29]关玉秀,张守攻.竞争指标的分类及评价[J].北京林业大学学报,1992,14(4):1-8.
[30]唐守正,李勇,符利勇.生物数学模型的统计学基础[M].北京:高等教育出版社,2015.
[31]姜立春,李凤日.混合效应模型在林业建模中的应用[M].北京:科学出版社,2014.
[32]祖笑锋,倪成才,GORDEN N,等.基于混合效应模型及EBLUP预测美国黄松林分优势木树高生长过程[J].林业科学,2015,51(3):25-33.
[2]KNOEBEL B R,BURKHART H E,BECK D E.A growth and yield model for thinned stands of yellow-poplar[J].Forest Science,1986,32(Monograph 27):1-41.
[3]MONSERUD R A,STERBA H.A basal area increment model for individual trees growing in even-and uneven-aged forest stands in Austria[J].Forest Ecology and Management,1996,80(1/2/3):57-80.
[4]MONSERUD R A,STERBA H.Modeling individual tree mortality for Austrian forest species[J].Forest Ecology and Management,1999,113(2/3):109-123.
[5]TAHVANAINEN T,FORSS E.Individual tree models for the crown biomass distribution of Scots pine,Norway spruce and birch in Finland[J].Forest Ecology and Management,2008,255(3/4):455-467.
[6]涂宏涛,孙玉军,吴明钦,等.杉木人工林树冠表面积及体积模型的研究[J].中南林业科技大学学报,2015,35(9):88-92,103.
[7]惠刚盈,张连金,胡艳波,等.林分拥挤度及其应用[J].北京林业大学学报,2016,38(10):1-6.
[8]MARSHALL D D,JOHNSON G P,HANN D W.Crown profile equations for stand-grown western hemlock trees in northwestern Oregon[J].Canadian Journal of Forest Research,2003,33(11):2059-2066.
[9]BIGING G S,DOBBERTIN M.Evaluation of competition indices in individual tree growth models[J].Forest Science,1995,41(2):360-377.
[10]李永亮,鞠洪波,张怀清,等.参数化林木个体及林分场景可视化模拟技术[J].林业科学研究,2013,26(6):704-709.
[11]蒲莹,曾伟生.基于树高和树冠因子的立木材积模型研究[J].林业科学研究,2016,29(2):196-201.
[12]李赟,温小荣,佘光辉,等.基于UAV高分影像的杨树冠幅提取及相关性研究[J].林业科学研究,2017,30(4):653-658.
[13]FU L Y,SHARMA R P,HAO K J,et al.A generalized interregional nonlinear mixed-effects crown width model for Prince Rupprecht larch in northern China[J].Forest Ecology and Management,2017,389:364-373.
[14]周志翔,徐永荣,王鹏程,等.不同密度湿地松纸浆原料试验林早期冠幅生长模型研究[J].华中农业大学学报,1998,17(3):289-293.doi:10.13300/j.cnki.hnlkxb.1998.03.019.
[15]BECHTOLD W A.Largest-crown-width prediction models for 53species in the western United States[J].Western Journal of Applied Forestry,2004,19(4):245-251.
[16]雷相东,张则路,陈晓光.长白落叶松等几个树种冠幅预测模型的研究[J].北京林业大学学报,2006,28(6):75-79.
[17]RUSSELL M A,WEISKITTEL A R.Maximum and largest crown width equations for 15 tree species in Maine[J].Northern Journal of Applied Forestry,2011,28(2):84-91.
[18]RITCHIE M W,HAMANN J D.Individual-tree height-,diameter-and crown-width increment equations for Young Douglas-fir plantations[J].New Forests,2008,35(2):173-186.
[19]符利勇,孙华.基于混合效应模型的杉木单木冠幅预测模型[J].林业科学,2013,49(8):65-74.
[20]FU L Y,SUN H,SHARMA R P,et al.Nonlinear mixed-effects crown width models for individual trees of Chinese fir(Cunninghamia lanceolata)in south-central China[J].Forest Ecology and Management,2013,302:210-220.
[21]FU L Y,SHARMA R P,WANG G X,et al.Modelling a system of nonlinear additive crown width models applying seemingly unrelated regression for Prince Rupprecht larch in northern China[J].Forest Ecology and Management,2017,386:71-80.
[22]LEI Y K,FU L Y,AFFLECK D L R,et al.Additivity of nonlinear tree crown width models:Aggregated and disaggregated model structures using nonlinear simultaneous equations[J].Forest E-cology and Management,2018,427:372-382.
[23]XU H,SUN Y J,WANG X J,et al.Linear mixed-effects models to describe individual tree crown width for China-fir in Fujian province,southeast China[J].PLoS One,2015,10(4).doi:10.1371/journal.pone.0122257.
[24]RAPTIS D,KAZANA V,KAZAKLIS A,et al.A crown widthdiameter model for natural even-aged Black pine forest management[J].Forests,2018,9(10).doi:10.3390/f9100610.
[25]董晨,吴保国,韩焱云,等.基于修正函数的杉木人工林单木冠幅预测模型[J].东北林业大学学报,2015,43(5):49-53.
[26]SHARMA R P,VACEK Z,VACEK S.Individual tree crown width models for Norway spruce and European beech in Czech Republic[J].Forest Ecology and Management,2016,366:208-220.
[27]SHARMA R P,BLEK L,VACEK Z,et al.Modelling crown width-diameter relationship for Scots pine in the central Europe[J].Trees,2017,31(6):1875-1889.
[28]卢军.帽儿山天然次生林树冠结构和空间优化经营[D].哈尔滨:东北林业大学,2008.
[29]关玉秀,张守攻.竞争指标的分类及评价[J].北京林业大学学报,1992,14(4):1-8.
[30]唐守正,李勇,符利勇.生物数学模型的统计学基础[M].北京:高等教育出版社,2015.
[31]姜立春,李凤日.混合效应模型在林业建模中的应用[M].北京:科学出版社,2014.
[32]祖笑锋,倪成才,GORDEN N,等.基于混合效应模型及EBLUP预测美国黄松林分优势木树高生长过程[J].林业科学,2015,51(3):25-33.