[1] Shinozaki K, Yoda K, Hozumi K, et al. A quantitative analysis of plant form: the pipe model theory basic analysis[J]. Japanese Journal of Ecology, 1964, 14 (3): 97−105.
[2] Oohata S, Shinozaki K. A statical model of plant form: further analysis of the pipe model theory[J]. Japanese Journal of Ecology, 1979, 29(4): 323−335.
[3] 城田徹央, 作田耕太郎. 「樹形のパイプモデル」は「樹形」をどこまで説明できるだろうか?―スギとヒノキの場合[J]. 生物科学(日本), 2003, 54(3):163−171.

Tetsuoh S, Kotaro S. Can ‘the pipe model of tree form’ explain ‘the tree form’ in the case of Cryptomeria Japonica andChamaecyparis obtuse[J]. Bioscience (Japan), 2003, 54(3): 163−171.
[4] 马钦彦, 刘盛, 刘志刚. 树形管道模型原理[J]. 北京林业大学学报, 1991, 13(3):84−91.

Ma Q Y, Liu S, Liu Z G. The pipe theory of tree form (a review)[J]. Journal of Beijing Forestry University, 1991, 13(3): 84−91.
[5] 马钦彦, 刘盛, 刘志刚, 等. 华北落叶松单木管道模型[J]. 北京林业大学学报, 1992, 14(2):11−16.

Ma Q Y, Liu S, Liu Z G, et al. Pipe model of individual trees for prince rupprecht ’s larch[J]. Journal of Beijing Forestry University, 1992, 14(2): 11−16.
[6] 刘盛. 华北落叶松树形管道模型的研究[D]. 北京: 北京林业大学, 1991.

Liu S. The pipe theory of tree form of Larix principis-rupprechtii[D]. Beijing: Beijing Forestry University, 1991.
[7] 刘盛, 宋彩民, 李国伟. 4种林木年轮水分输导模式研究[J]. 北京林业大学学报, 2011, 33(2):14−18.

Liu S, Song C M, Li G W. Patterns of water transport in tree rings of four tree species[J]. Journal of Beijing Forestry University, 2011, 33(2): 14−18.
[8] 马菁, 郭建斌, 刘泽彬, 等. 六盘山华北落叶松林分蒸腾日内变化及其对环境因子的响应[J]. 北京林业大学学报, 2020, 42(5):1−11.

Ma J, Guo J B, Liu Z B, et al. Diurnal variations of stand transpiration of Larix principis-rupprechtii forest and its response to environmental factors in Liupan Mountains of northwestern China[J]. Journal of Beijing Forestry University, 2020, 42(5): 1−11.
[9] 刘盛, 宋全民. 华北落叶松边材在树干中垂直分布的探讨[J]. 吉林林学院学报, 1992, 8(2):57−60.

Liu S, Song Q M. The discussion of the vertical distribution in the stem of the sapwood area of Larix principis-rupprechtii Mayi[J]. Journal of Jilin Forestry Institute, 1992, 8(2): 57−60.
[10] 刘盛, 郝广明, 拱化国. 应用管道模型原理估测华北落叶松叶量叶面积的方法[J]. 吉林林学院学报, 1993, 9(2):25−32.

Liu S, Hao G M, Gong H G. A measure to estimate the leaf biomass and leaf area of Larix Principis-rupprechtii with pipe model principle[J]. Journal of Jilin Forestry Institute, 1993, 9(2): 25−32.
[11] 刘盛, 李国伟. 基于管道模型理论的树形结构分析[J]. 东北林业大学学报, 2006, 34(6):15−16. doi:  10.3969/j.issn.1000-5382.2006.06.006.

Liu S, Li G W. Tree structure based on pipe model theory[J]. Journal of Northeast Forestry University, 2006, 34(6): 15−16. doi:  10.3969/j.issn.1000-5382.2006.06.006.
[12] Hinckley R, 曾兆芬. 栎树叶重和叶面积与当年边材面积的关系[J]. 四川林业科技, 1981(2):94−97.

Hinckley R, Zeng Z F. Relationship between leaf biomassleaf area and sapwood area of Quercus variabilis[J]. Sichuan Forestry Science and Technology, 1981(2): 94−97.
[13] 杨洪国, 李治宇. 应用管道模型原理建立柏木桤木叶面积叶量估测模型[J]. 四川林勘设计, 2012(1):35−37.

Yang H G, Li Z Y. Estimation models for leaf area and amount of cedarwood and alder based on the pipeline model[J]. Sichuan Forestry Exploration and Design, 2012(1): 35−37.
[14] 刘盛, 刘成. 长白落叶松水分输导模式及叶生物量估测方法[J]. 东北林业大学学报, 2005, 33(5):35−37. doi:  10.3969/j.issn.1000-5382.2005.05.013.

Liu S, Liu C. The model of water transportation and the estimation methods of leaf biomass for Larix olgensis[J]. Journal of Northeast Forestry University, 2005, 33(5): 35−37. doi:  10.3969/j.issn.1000-5382.2005.05.013.
[15] 钱能志. 杉木叶量叶面积与边材面积关系研究[J]. 南京林业大学学报, 1989, 13(4):75−79.

Qian N Z. The relationship of leaf and foliage biomass to sapwood area in Chinese fir[J]. Journal of Nanjing Forestry University, 1989, 13(4): 75−79.
[16] 项文化, 田大伦, 闫文德. 森林生物量与生产力研究综述[J]. 中南林业调查规划, 2003, 22(3):57−60, 64. doi:  10.3969/j.issn.1003-6075.2003.03.020.

Xiang W H, Tian D L, Yan W D. Review of researches on forest biomass and productivity[J]. Central South Forest Inventory and Planning, 2003, 22(3): 57−60, 64. doi:  10.3969/j.issn.1003-6075.2003.03.020.
[17] 胡屾, 郭海沣, 刘国成, 等. 不同林分条件下落叶松人工林生物量研究[J]. 林业科技情报, 2017, 49(1):24−27. doi:  10.3969/j.issn.1009-3303.2017.01.009

Hu S, Guo H F, Liu G C, et al. Study on biomass of Larix gmelinii plantation of different forest[J]. Forestry Science and Technology Information, 2017, 49(1): 24−27. doi:  10.3969/j.issn.1009-3303.2017.01.009
[18] 罗云建, 张小全, 侯振宏, 等. 我国落叶松林生物量碳计量参数的初步研究[J]. 植物生态学报, 2007, 31(6):1111−1118.

Luo Y J, Zhang X Q, Hou Z H, et al. Biomass carbon accounting factors of Larix forests in China based on literature data[J]. Chinese Journal of Plant Ecology, 2007, 31(6): 1111−1118.
[19] Trugman A T, Anderegg L D L, Wolfe B L, et al. Climate and plant trait strategies determine tree carbon allocation to leaves and mediate future forest productivity[J]. Global Change Biology, 2019, 25(10): 3395−3405. doi:  10.1111/gcb.14680.
[20] 董利虎, 李凤日, 贾炜玮, 等. 含度量误差的黑龙江省主要树种生物量相容性模型[J]. 应用生态学报, 2011, 22(10):2653−2661.

Dong L H, Li F R, Jia W W, et al. Compatible biomass models for main tree species with measurement error in Heilongjiang Province of Northeast China[J]. Chinese Journal of Applied Ecology, 2011, 22(10): 2653−2661.
[21] 贾炜玮, 李凤日, 董利虎, 等. 基于相容性生物量模型的樟子松林碳密度与碳储量研究[J]. 北京林业大学学报, 2012, 34(1):6−13.

Jia W W, Li F R, Dong L H, et al. Carbon density and storage for Pinus sylvestris var. mongolica plantation based on compatible biomass models[J]. Journal of Beijing Forestry University, 2012, 34(1): 6−13.
[22] 董利虎, 李凤日, 宋玉文. 东北林区4个天然针叶树种单木生物量模型误差结构及可加性模型[J]. 应用生态学报, 2015, 26(3):704−714.

Dong L H, Li F R, Song Y W. Error structure and additivity of individual tree biomass model for four natural conifer species in Northeast China[J]. Chinese Journal of Applied Ecology, 2015, 26(3): 704−714.
[23] 郭孝玉, 孙玉军, 刘凤娇. 不同估算树冠生物量方法的比较: 以长白落叶松林为例[J]. 林业资源管理, 2010(5):41−47. doi:  10.3969/j.issn.1002-6622.2010.05.009.

Guo X Y, Sun Y J, Liu F J. Study on different methods of estimating crown biomass, take Larix olgensis forest as an example[J]. Forest Resources Management, 2010(5): 41−47. doi:  10.3969/j.issn.1002-6622.2010.05.009.
[24] 王华田, 马履一, 孙鹏森. 油松、侧柏深秋边材木质部液流变化规律的研究[J]. 林业科学, 2002, 38(5):31−37. doi:  10.3321/j.issn:1001-7488.2002.05.006.

Wang H T, Ma L Y, Sun P S. Sap flow fluctuations of Pinus tabulaeformis and Platycladus orientalis in late autumn[J]. Scientia Silvae Sinicae, 2002, 38(5): 31−37. doi:  10.3321/j.issn:1001-7488.2002.05.006.
[25] 刘志刚, 马钦彦, 潘向丽. 华北落叶松边材透水性与叶面积空间分布的相关性的探讨[J]. 林业科学, 1995, 31(3):269−274.

Liu Z G, Ma Q Y, Pan X L. An approach to relationship between sapwood permeability and distribution of leaf area for Larix principis-rupprechtii[J]. Scientia Silvae Sinicae, 1995, 31(3): 269−274.
[26] 马履一, 王华田. 油松边材液流时空变化及其影响因子研究[J]. 北京林业大学学报, 2020, 24(3):23−27.

Ma L Y, Wang H T. Spatial and chronic fluctuation of sapwood flow and its relevant variables of Pinus tabulaeformis[J]. Journal of Beijing Forestry University, 2020, 24(3): 23−27.
[27] 郭孝玉. 长白落叶松人工林树冠结构及生长模型研究[D]. 北京: 北京林业大学, 2013.

Guo X Y. Crown structure and growth model for Larix olgensis plantation[D]. Beijing: Beijing Forestry University, 2013.
[28] 闫明准, 刘兆刚. 樟子松人工林单木叶量垂直分布规律[J]. 东北林业大学学报, 2009, 37(7):16−19, 24. doi:  10.3969/j.issn.1000-5382.2009.07.006.

Yan M Z, Liu Z G. Foliage vertical distribution of Mongolian pine plantations[J]. Journal of Northeast Forestry University, 2009, 37(7): 16−19, 24. doi:  10.3969/j.issn.1000-5382.2009.07.006.