樟子松人工固沙林冠幅——胸径模型
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摘要
基于章古台地区22块樟子松(Pinus sylvestris var.mongolica)人工纯林标准地的702棵樟子松立木数据,构建了樟子松固沙林冠幅—胸径关系的基础模型、广义模型及基于混合效应的基础模型和广义模型;比较了随机选择样本木、选择平均胸径树、选胸径较小树和选胸径较大树4种方案,计算混合模型随机参数时的混合模型预测精度;最后分析了不同林木因子和林分变量对冠幅—胸径关系的影响。模型评价指标包括决定系数(R~2)、平均绝对误差(MAE)以及均方根误差(RMSE)。结果表明:枝下高(HCB)、相对植距(RS)和林龄(A)对冠幅—胸径关系影响最为显著;混合模型拟合精度(基础混合模型R~2、MAE和RMSE分别是0.703 0、0.386 6和0.515 4;广义混合模型R~2、MAE和RMSE为0.705 1、0.382 2和0.513 6)高于最小二乘法回归(OLS)模型(基础模型R~2、MAE和RMSE分别为0.587 5、0.469 6、0.607 5;广义模型R~2、MAE和RMSE分别为0.661 8、0.415 5和0.550 0)。基础混合模型和广义混合模型差异较小(2模型R~2、MAE和RMSE均相差1%左右)。冠幅随HCB和A的增大而减小,随RS的增大而增大。进行冠幅预测时,推荐使用基础混合模型并从每块标准地选择2棵平均木冠幅计算其随机参数,或使用方法较为简单的OLS广义模型预测单木冠幅大小。
In this study,the data consisted of 702 individuals of Pinus sylvestris var.mongolica in 22 temporary sample plots of pure plantation in Zhanggutai of Liaoning Province,northeast China,were used to develop the canopy-DBH models,i.e.the basic model(fitted by ordinary least squares,OLS),generalized model(fitted by OLS),nonlinear mixed-effect basic model and nonlinear mixed-effect generalized model.The goodness-of-fits and prediction accuracy of the four models were compared.For the mixed-effect model,four sampling strategies,i.e.,random sampling,large-DBH tree sampling,small-DBH tree sampling and medium-DBH tree sampling,were designed to calculate the random parameters.The effects of individual factor and stand level variables on the canopy-DBH relationship were simulated.Model evaluation indices included the determination coefficient(R~2),mean absolute error(MAE)and root mean square error(RMSE).Results showed that the height to live crown base(HCB),relative spacing index(RS)and stand age(A)were the dominant factors in CW-DBH models.The goodness-of-fits of mixed-effect CW-DBH models(R~2,MAE and RMSE)were 0.703 0,0.386 6 and 0.515 4,and those of mixedeffect generalized model were 0.705 1,0.382 2 and 0.513 6,respectively,which were better than those of the OLS models.However,the difference in goodness-of-fit between the mixed-effect basic and generalized models was not significant(below 1%).Canopy decreased with the increase of A and height of HCB,but increased with the increase of RS.
In this study,the data consisted of 702 individuals of Pinus sylvestris var.mongolica in 22 temporary sample plots of pure plantation in Zhanggutai of Liaoning Province,northeast China,were used to develop the canopy-DBH models,i.e.the basic model(fitted by ordinary least squares,OLS),generalized model(fitted by OLS),nonlinear mixed-effect basic model and nonlinear mixed-effect generalized model.The goodness-of-fits and prediction accuracy of the four models were compared.For the mixed-effect model,four sampling strategies,i.e.,random sampling,large-DBH tree sampling,small-DBH tree sampling and medium-DBH tree sampling,were designed to calculate the random parameters.The effects of individual factor and stand level variables on the canopy-DBH relationship were simulated.Model evaluation indices included the determination coefficient(R~2),mean absolute error(MAE)and root mean square error(RMSE).Results showed that the height to live crown base(HCB),relative spacing index(RS)and stand age(A)were the dominant factors in CW-DBH models.The goodness-of-fits of mixed-effect CW-DBH models(R~2,MAE and RMSE)were 0.703 0,0.386 6 and 0.515 4,and those of mixedeffect generalized model were 0.705 1,0.382 2 and 0.513 6,respectively,which were better than those of the OLS models.However,the difference in goodness-of-fit between the mixed-effect basic and generalized models was not significant(below 1%).Canopy decreased with the increase of A and height of HCB,but increased with the increase of RS.
引文
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[16]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.
[17]朱教君,曾德慧,康宏樟,等.沙地樟子松人工林衰退机制[M].北京:中国林业出版社,2005:10-40.[Zhu Jiaojun,Zeng Dehui,Kang Hongzhang,et al.Decline of Pinus sylvestris var.mongolica Plantations on Sandy Land[M].Beijing:China Forestry Publishing House,2005:10-40.]
[18]Zhu J J,Fan Z P,Zeng D H,et al.Comparison of stand structure and growth between artificial and natural forests of Pinus sylvestiris var.mongolica,on sandy land[J].Journal of Forest Research,2003,14(2):103-111.
[19]雷泽勇,周晏平,赵国军,等.竞争对辽宁西北部樟子松人工固沙林树高生长的影响[J].干旱区研究,2018,35(1):961-966.[Lei Zeyong,Zhou Yanping,Zhao Guojun,et al.Effects of competition on tree height growth of sand fixation plantations of Pinus sylvestris var.mongolica in Northwest Liaoning Province[J].Arid Zone Research,2018,35(1):961-966.]
[20]焦树仁.辽宁省章古台樟子松固沙林提早衰弱的原因与防治措施[J].林业科学,2001,37(2):131-138.[Jiao Shuren.Report on the causes of the early decline of Pinus slyvestris var.mongolica shelterbelt and its preventative and control measures in Zhanggutai of Liaoning Province[J].Scientia Silvae Sinicae,2001,37(2):131-138.]
[21]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].Plo S One,2015,10(4):e0122257.
[22]Fang Z,Bailey R L.Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments[J].Forest Science,2001,47(3):287-300.
[23]Huang S,Douglasp W,Yang Y,et al.Assessing the impacts of species composition,top height and density on individual tree height prediction of quaking aspen in boreal mixedwoods[J].Forest Ecology and Management,2009,258(7):1 235-1 247.
[24]Temesgen H T,Monleon V J M,Hann D W H.Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests[J].Canadian Journal of Forest Research,2008,38(38):553-565.
[25]Sharma R P,Breidenbach J.Modeling height-diameter relationships for Norway spruce,Scots pine,and downy birch using Norwegian national forest inventory data[J].Forest Science and Technology,2015,11(1):44-53.
[26]Gómez-García E,Fonseca T F,Crecente-Campo F,et al.Height-diameter models for maritime pine in Portugal:A comparison of basic,generalized and mixed-effects models[J].Forest-Biogeosciences and Forestry,2015,9:72-78.
[27]Power H,Le May V,Berninger F,et al.Differences in crown characteristics between black(Picea mariana)and white spruce(Picea glauca)[J].Canadian Journal of Forest Research,2012,42(9):1 733-1 743.
[28]Zhao D,Michael K,Brucee B.Development and applications of the relative spacing model for loblolly pine plantations[J].Forest Ecology and Management,2010,259(10):1 922-1 929.
[29]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.[Dong Chen,Wu Baoguo,Han Yanyun,et al.An individual crownwidth model for Chinese fir plantation based on modified function[J].Journal of Northeast Forestry University,2015,43(5):49-53.]
[30]Ishii H,Mcdowell N.Age-related development of crown structure in coastal Douglas-fir trees[J].Forest Ecology and Management,2002,169(3):257-270.
[31]Uzoh F C C,Oliver W W.Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model[J].Forest Ecology and Management,2008,256(3):438-445.
[2]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.[Fu Liyong,Sun Hua.Individual crown diameter prediction for Cuninghamia lanceolata forests based on mixed effects models[J].Scientia Silvae Sinicae,2013,49(8):65-74.]
[3]刘江,徐先英,丁爱强,等.荒漠灌木侧影面积的数字化测定及应用[J].干旱区研究,2017,34(5):1 070-1 076.[Liu Jiang,Xu Xianying,Ding Aiqiang,et al.Application of digitized measurement in upwind project area of desert shrubs[J].Arid Zone Research,2017,34(5):1 070-1 076.]
[4]赵维俊,刘贤德,金铭,等.祁连山青海云杉林群落结构特征分析[J].干旱区研究,2012,29(4):615-620.[Zhao Weijun,Liu Xiande,Jin Ming,et al.Analysis on community structure of picea crassifolia forests in the Qilian Mountains[J].Arid Zone Research,2012,29(4):615-620.]
[5]Pretzsch H,Biber P,Uhl E,et al.Crown size and growing space requirement of common tree species in urban centres,parks,and forests[J].Urban Forestry and Urban Greening,2015,14(3):466-479.
[6]Bechtold W A.Crown-diameter prediction models for 87 species of stand-grown trees in the Eastern United States[J].Southern Journal of Applied Forestry,2003,27(4):269-278.
[7]Gill S J,Biging G S,Murphy E C.Modeling conifer tree crown radius and estimating canopy cover[J].Forest Ecology and Management,2000,126(3):405-416.
[8]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.
[9]Sharma R P,Bílek L,Vacek Z,et al.Modelling crown width-diameter relationship for Scots pine in the central Europe[J].Trees,2017:1-15
[10]Thorpe H C,Astrup R,Trowbridge A,et al.Competition and tree crowns:A neighborhood analysis of three boreal tree species[J].Forest Ecology and Management,2010,259(8):1 586-1 596.
[11]Crecentecampo F,lvarezgonzález J G,Castedodorado F,et al.Development of crown profile models for Pinus pinaster Ait.and Pinus sylvestris L.in northwestern Spain[J].Forestry,2013,86(4):481-491.
[12]Pinheiro J C,Bates D M.Mixed-Effects Models in S and S-PLUS[M].New York:Springer-Verlag,2000:271-395.
[13]臧颢,雷相东,张会儒,等.红松树高—胸径的非线性混合效应模型研究[J].北京林业大学学报,2016,38(6):8-16.[Zang Hao,Lei Xiangdong,Zhang Huiru,et al.Nonlinear mixed-effects height-diameter model of Pinus koraiensis[J].Journal of Beijing Forestry University,2016,38(6):8-16.]
[14]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,2014:1-20.[Jiang Lichun,Li Fengri.Application of Mixed Effects Model in Forestry Modeling[M].Beijing:Science Press,2014:1-20.]
[15]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(6):210-220.
[16]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.
[17]朱教君,曾德慧,康宏樟,等.沙地樟子松人工林衰退机制[M].北京:中国林业出版社,2005:10-40.[Zhu Jiaojun,Zeng Dehui,Kang Hongzhang,et al.Decline of Pinus sylvestris var.mongolica Plantations on Sandy Land[M].Beijing:China Forestry Publishing House,2005:10-40.]
[18]Zhu J J,Fan Z P,Zeng D H,et al.Comparison of stand structure and growth between artificial and natural forests of Pinus sylvestiris var.mongolica,on sandy land[J].Journal of Forest Research,2003,14(2):103-111.
[19]雷泽勇,周晏平,赵国军,等.竞争对辽宁西北部樟子松人工固沙林树高生长的影响[J].干旱区研究,2018,35(1):961-966.[Lei Zeyong,Zhou Yanping,Zhao Guojun,et al.Effects of competition on tree height growth of sand fixation plantations of Pinus sylvestris var.mongolica in Northwest Liaoning Province[J].Arid Zone Research,2018,35(1):961-966.]
[20]焦树仁.辽宁省章古台樟子松固沙林提早衰弱的原因与防治措施[J].林业科学,2001,37(2):131-138.[Jiao Shuren.Report on the causes of the early decline of Pinus slyvestris var.mongolica shelterbelt and its preventative and control measures in Zhanggutai of Liaoning Province[J].Scientia Silvae Sinicae,2001,37(2):131-138.]
[21]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].Plo S One,2015,10(4):e0122257.
[22]Fang Z,Bailey R L.Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments[J].Forest Science,2001,47(3):287-300.
[23]Huang S,Douglasp W,Yang Y,et al.Assessing the impacts of species composition,top height and density on individual tree height prediction of quaking aspen in boreal mixedwoods[J].Forest Ecology and Management,2009,258(7):1 235-1 247.
[24]Temesgen H T,Monleon V J M,Hann D W H.Analysis and comparison of nonlinear tree height prediction strategies for Douglas-fir forests[J].Canadian Journal of Forest Research,2008,38(38):553-565.
[25]Sharma R P,Breidenbach J.Modeling height-diameter relationships for Norway spruce,Scots pine,and downy birch using Norwegian national forest inventory data[J].Forest Science and Technology,2015,11(1):44-53.
[26]Gómez-García E,Fonseca T F,Crecente-Campo F,et al.Height-diameter models for maritime pine in Portugal:A comparison of basic,generalized and mixed-effects models[J].Forest-Biogeosciences and Forestry,2015,9:72-78.
[27]Power H,Le May V,Berninger F,et al.Differences in crown characteristics between black(Picea mariana)and white spruce(Picea glauca)[J].Canadian Journal of Forest Research,2012,42(9):1 733-1 743.
[28]Zhao D,Michael K,Brucee B.Development and applications of the relative spacing model for loblolly pine plantations[J].Forest Ecology and Management,2010,259(10):1 922-1 929.
[29]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.[Dong Chen,Wu Baoguo,Han Yanyun,et al.An individual crownwidth model for Chinese fir plantation based on modified function[J].Journal of Northeast Forestry University,2015,43(5):49-53.]
[30]Ishii H,Mcdowell N.Age-related development of crown structure in coastal Douglas-fir trees[J].Forest Ecology and Management,2002,169(3):257-270.
[31]Uzoh F C C,Oliver W W.Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model[J].Forest Ecology and Management,2008,256(3):438-445.