融合无人机点云数据的雪岭云杉天然林立地质量评价

Site quality evaluation of natural Picea schrenkiana forests in the Tianshan Mountains integrating UAV point cloud data

摘要

【目的】构建基于立地形法的雪岭云杉天然异龄林树高−胸径关系立地质量评价模型，验证其在无年龄数据条件下评价雪岭云杉天然异龄林立地质量的可行性，为天然林可持续经营与生产力预测提供技术参考。【方法】结合样地实测胸径数据与机载 LiDAR 提取的树高信息，计算 5 种优势木组合的平均树高与平方平均胸径指标，筛选最优导向曲线；以生长量特征确定基准胸径，采用立地形法划分立地等级，并将立地等级作为随机效应纳入树高−胸径非线性混合效应模型，综合评价模型性能。【结果】（1）由调整最大树法与胸径排序得到的 H₅− D_g,5 组合拟合的 Schumacher 导向曲线效果最佳（ R² = 0.794 3，RMSE = 1.309 3）；（2）确定基准胸径为 34 cm，在此基础上含胸径平移倒数项的指数型树高−胸径模型被确定为最优基础模型，其建模集 R² 为 0.833 9，RMSE 为 2.984 3，检验集 R² 为 0.858 5，RMSE 为 2.822 3；（3）构建非线性混合效应模型后，模型精度提高。建模阶段，传统估计法与树高排序形成的 H₂− D_g,2 组合表现最佳（ R² = 0.845 8，RMSE = 2.875 6）；检验阶段，调整最大树法与树高排序形成的 H₆− D_g,6 组合表现最优（ R² = 0.875 6，RMSE = 2.645 5）。【结论】立地形法结合树高−胸径模型可实现缺乏年龄数据条件下雪岭云杉天然异龄林的立地质量分级；优势木筛选方式对导向曲线构建及模型性能具有重要影响；将立地等级作为随机效应引入模型，可有效提高树高−胸径模型的拟合精度和预测能力，该研究方法可为雪岭云杉天然异龄林立地质量评价提供技术支撑。

Abstract

[Objective] This study aims to construct a site quality evaluation model for uneven-aged natural Picea schrenkiana forests in the Tianshan Mountains, based on the site form method and the height-DBH relationship. It also seeks to verify the model’s applicability in the absence of stand age data, thereby providing technical support for sustainable forest management and productivity prediction. [Method] Field-measured diameter at breast height (DBH) data were integrated with tree height data derived from airborne LiDAR point clouds. Five dominant-tree combinations were used to calculate dominant height and quadratic mean diameter, and the optimal guide curve was selected accordingly. The reference diameter was determined based on growth characteristics, and site classes were classified using the site form method. Site class was then incorporated as a random effect into a height-DBH nonlinear mixed-effects model, and model performance was comprehensively evaluated using multiple statistical criteria. [Result] (1) The Schumacher guide curve fitted using the H₅- D_g,5 combination, derived from the adjusted largest trees method with DBH-based ranking, achieved the best performance ( R² = 0.794 3, RMSE = 1.309 3); (2) The reference diameter was determined to be 34 cm. On this basis, the exponential height-DBH model incorporating a shifted reciprocal term of DBH was identified as the optimal base model, with R² = 0.833 9 and RMSE = 2.984 3 for the modeling dataset, and R² =0.858 5 and RMSE = 2.822 3 for the validation dataset; (3) The introduction of the nonlinear mixed-effects model improved model accuracy. The H₂- D_g,2 combination, derived from the conventional estimation method with tree-height-based ranking, performed best during the modeling stage ( R² =0.845 8, RMSE = 2.875 6), whereas the H₆- D_g,6 combination, derived from the adjusted largest trees method with tree-height-based ranking, showed the best performance during the validation stage ( R² = 0.875 6, RMSE = 2.645 5). [ Conclusion] The combination of the site form method and height-DBH models enables reliable site quality classification for uneven-aged natural Picea schrenkiana forests in the absence of age data. The selection of dominant tree combinations significantly influences guide curve construction and model performance. Incorporating site class as a random effect effectively improves the fitting accuracy and predictive ability of height-DBH models, demonstrating that this approach provides a practical and reliable technique for site quality evaluation in uneven-aged forests.

关键词

立地形法 / 树高−胸径模型 / 立地质量 / 雪岭云杉林 / 非线性混合效应模型

Key words

site form method / height-DBH model / site quality / Picea schrenkiana forest / nonlinear mixed-effects model

参考文献

[1] 孟宪宇. 测树学 [M]. 3 版. 北京: 中国林业出版社,2006:101.

[2] Meng X Y. Forest mensuration[M]. 3rd ed. Beijing: China Forestry Publishing House,2006:101.

[3] Vanclay J K, Henry N B. Assessing site productivity of indigenous cypress pine forest in southern Queensland [J].Commonwealth Forestry Review, 1988, 67(1):53-64.

[4] 沈剑波. 基于广东省针阔混交异龄林的立地质量评价方法研究 [D]. 北京: 中国林业科学研究院,2018.

[5] Shen J B. Study on site quality evaluation methods of uneven—aged coniferous and broad—leaved mixed stands in Guangdong Province[D]. Beijing: Chinese Academy of Forestry,2018.

[6] 雷相东, 符利勇, 李海奎, 等. 基于林分潜在生长量的立地质量评价方法与应用 [J].林业科学, 2018, 54(12):116-126.

[7] Lei X D, Fu L Y, Li H K, et al. Methodology and applications of site quality assessment based on potential mean annual increment [J].Scientia Silvae Sinicae, 2018, 54(12):116-126.

[8] 曾翀, 雷相东, 刘宪钊, 等. 落叶松云冷杉林单木树高曲线的研究 [J].林业科学研究, 2009, 22(2):182-189.

[9] Zeng C, Lei X D, Liu X Z, et al. Individual tree height—diameter curves of larch—spruce—fir forests [J].Forest Research, 2009, 22(2):182-189.

[10] 李欣宇, 叶尔江·拜克吐尔汉, 王娟, 等. 基于非线性混合效应模型的东北红松树高−胸径关系 [J].北京林业大学学报, 2025, 47(3):38-48.

[11] Li X Y, Yierjiang B K T H, Wang J, et al. Relationship between tree height and DBH of Pinus koraiensis in northeastern China based on nonlinear mixed effects model [J].Journal of Beijing Forestry University, 2025, 47(3):38-48.

[12] 邓祥鹏, 许芳泽, 赵善超, 等. 基于贝叶斯法的新疆天山云杉树高−胸径模型研究 [J].北京林业大学学报, 2023, 45(1):11-20.

[13] Deng X P, Xu F Z, Zhao S C, et al. Tree height—DBH model for Picea schrenkiana in Tianshan Mountain, Xinjiang of northwestern China based on Bayesian method [J].Journal of Beijing Forestry University, 2023, 45(1):11-20.

[14] Chen Q D, Gao T, Zhu J J, et al. Individual tree segmentation and tree height estimation using leaf—off and leaf—on UAV—LiDAR data in dense deciduous forests [J].Remote Sensing, 2022, 14(12):2787.

[15] 杨军, 王帆, 宋仲禹. 基于背包激光雷达构建天然林蒙古栎胸径−树高模型 [J].森林工程, 2023, 39(5):57-64.

[16] Yang J, Wang F, Song Z Y. Development of natural forest Quercus mongolica diameter—height curve model based on BLS [J].Forest Engineering, 2023, 39(5):57-64.

[17] 胡天祺, 王振锡, 郝康迪, 等. 基于 WorldView—3 遥感影像与机载 LiDAR 的单木树高提取 [J].干旱区资源与环境, 2022, 36(10):166-175.

[18] Hu T Q, Wang Z X, Hao K D, et al. Extraction of individual tree height using WorldView—3 remote sensing images and airborne LiDAR [J].Journal of Arid Land Resources and Environment, 2022, 36(10):166-175.

[19] 于生华. 天然林资源共享保护工程在我区经济社会发展中的地位和重要性 [J].新疆林业, 2015(1):21-23.

[20] Yu S H. The position and importance of natural forest resources sharing and protection project in the economic and social development of our region [J].Forestry of Xinjiang, 2015(1):21-23.

[21] 闫兆杰. 基于机载激光雷达的天山云杉树高估测研究 [D]. 乌鲁木齐: 新疆农业大学,2024.

[22] Yan Z J. Study on tree height estimation of Picea schrenkiana based on airborne lidar[D]. Urumqi: Xinjiang Agricultural University,2024.

[23] 闫兆杰, 苏香玲, 王振锡, 等. 基于不同点云密度 LiDAR 数据的天山云杉单木树高提取 [J].新疆农业科学, 2025, 62(4):917-928.

[24] Yan Z J, Su X L, Wang Z X, et al. Single tree height extraction based on different LiDAR density data of Tianshan spruce [J].Xinjiang Agricultural Sciences, 2025, 62(4):917-928.

[25] 陶薇, 向玮, 陶然, 等. 融合机载 LiDAR 的天然混交林优势高估算方法 [J].北京林业大学学报, 2026, 48(3):165-177.

[26] Tao W, Xiang W, Tao R, et al. Estimation methods of top height in natural mixed forests integrating airborne LiDAR [J].Journal of Beijing Forestry University, 2026, 48(3):165-177.

[27] Zhou M L, Lei X D, Duan G S, et al. The effect of the calculation method, plot size, and stand density on the top height estimation in natural spruce—fir—broadleaf mixed forests [J].Forest Ecology and Management, 2019, 453:117574.

[28] 国家林业和草原局. LY/T 3315—2022 森林立地质量评价技术规程 [S]. 北京: 中国标准出版社, 2022.

[29] National Forestry and Grassland Administration.LY/T 3315−2022 Technical regulation for forest site quality evaluation[S]. Beijing: China Standards Press, 2022.

[30] 《中国森林立地分类》编写组. 中国森林立地分类 [M]. 北京: 中国林业出版社, 1989:42-46.

[31] Editorial Group of Forest Site Classification in ChinForest site classification in China[M]. Beijing: China Forestry Publishing House, 1989:42-46.

[32] 沈国舫, 翟明普. 森林培育学 [M]. 2 版. 北京: 中国林业出版社,2011:21-25.

[33] Shen G F, Zhai M P. Forest cultivation[M]. 2nd ed. Beijing: China Forestry Publishing House,2011:21-25.

[34] 马炜, 孙玉军. 长白落叶松人工林立地指数表和胸径地位级表的编制 [J].东北林业大学学报, 2013, 41(12):21−25,38.

[35] Ma W, Sun Y J. Compilation of site index table and site class table for Larix olgensis plantations [J].Journal of Northeast Forestry University, 2013, 41(12):21−25,38.

[36] Richards F J. A flexible growth function for empirical use [J].Journal of Experimental Botany, 1959, 10(2):290-301.

[37] Korf V. Příspěvek k matematické definici vzrůstového zákona hmot lesních porostů [J].Lesnická Práce, 1939, 18:339-379.

[38] Pearl R, Reed L J. On the rate of growth of the population of the United States since 1790 and its mathematical representation [J].Proceedings of the National Academy of Sciences of the United States of America, 1920, 6(6):275-288.

[39] Peschel W. Die mathematischen Methoden zur Herleitung der Wachstumsgesetze von Baum und Bestand und die Ergebnisse ihrer Anwendung [J].Tharandter Forstliches Jahrbuch, 1938, 89:169-274.

[40] Schumacher F X. A new growth curve and its applications to timber yield studies [J].Journal of Forestry, 1939, 37:819-820.

[41] Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies [J].Philosophical Transactions of the Royal Society of London, 1825, 115:513-583.

[42] Weibull W. A statistical distribution function of wide applicability [J].Journal of Applied Mechanics, 1951, 18(3):293-297.

[43] Stage A R. Prediction of height increment for models of forest growth[M]. Ogden: Intermountain Forest and Range Experiment Station, Forest Service, U. S. Dept. of Agriculture,1975.

[44] Curtis R O. Height—diameter and height—diameter—age equations for second—growth Douglas—fir [J].Forest Science, 1967, 13(4):365-375.

[45] Meyer H A. A mathematical expression for height curves [J].Journal of Forestry, 1940, 38(5):415-420.

[46] Sibbesen E. Some new equations to describe phosphate sorption by soils [J].Journal of Soil Science, 1981, 32(1):67-74.

[47] Winsor C P. The gompertz curve as a growth curve [J].Proceedings of the National Academy of Sciences of the United States of America, 1932, 18(1):1-8.

[48] Ratkowsky D A. Handbook of nonlinear regression models[M]. New York: Marcel Dekker Inc. ,1990.

[49] Wykoff W, Crookston N L, Stage A R. User’s guide to the stand prognosis model[M]. Ogden: U. S. Dept. of Agriculture, Forest Service, Intermountain Forest and Range Experiment Station,1982.

[50] Xu Q G, Yang F, Hu S, et al. Tree height—diameter model of natural coniferous and broad—leaved mixed forests based on random forest method and nonlinear mixed—effects method in Jilin Province, China [J].Forests, 2024, 15(11):1922.

[51] 董自华, 李大勇, 梁宇, 等. 冀北山地杨桦次生混交林地位指数模型构建 [J].林草资源研究, 2024(3):70-78.

[52] Dong Z H, Li D Y, Liang Y, et al. Construction of the site index model of secondary Populus davidiana × Betula platyphylla mingled forest in northern Hebei Mountains [J].Forest and Grassland Resources Research, 2024(3):70-78.

[53] 姜鹏, 孙悦, 许佳明, 等. 基于非线性混合效应的华东地区主要优势树种林分水平树高−胸径模型 [J].自然保护地, 2024, 4(3):65-73.

[54] Jiang P, Sun Y, Xu J M, et al. Tree height—diameter models of main tree species in East China based on nonlinear mixed—effects model [J].Natural Protected Areas, 2024, 4(3):65-73.

[55] 曹晓梅, 苗铮, 郝元朔, 等. 基于树种分类的帽儿山阔叶混交林树高−胸径模型 [J].应用生态学报, 2024, 35(2):307-320.

[56] Cao X M, Miao Z, Hao Y S, et al. Height—diameter model of broad—leaved mixed forest based on species classification in Maoershan, Northeast China [J].Chinese Journal of Applied Ecology, 2024, 35(2):307-320.

[57] Wu B Y, Lei X D, Xu Q G, et al. Forest site classification and grading using mixed—variables clustering and nonlinear mixed—effects modeling based on forest inventory data [J].Forestry: An International Journal of Forest Research, 2025, 98(5):812-826.

[58] Siipilehto J, Sarkkola S, Nuutinen Y, et al. Predicting height—diameter relationship in uneven—aged stands in Finland [J].Forest Ecology and Management, 2023, 549:121486.

[59] Cui K D, Wu X Y, Zhang C Y, et al. Estimating height—diameter relations for structure groups in the natural forests of Northeastern China [J].Forest Ecology and Management, 2022, 519:120298.

[60] Feng Y, Chai Y, Qin Y P, et al. Plant functional traits and tree size inequality improved individual tree height prediction of mid—montane humid evergreen broad—leaved forests in southwest China [J].Forest Ecology and Management, 2024, 551:121526.

[61] 程雯, 武晓昱, 叶尔江·拜克吐尔汉, 等. 基于混合效应和分位数回归的温带针阔混交林树高与胸径关系研究 [J].北京林业大学学报, 2024, 46(2):28-39. Cheng W,

[62] Wu X Y, Yierjiang B K T H, et al. Research on the relationship between tree height and DBH of temperate coniferous and broadleaved mixed forests based on mixed effects and quantile regression [J].Journal of Beijing Forestry University, 2024, 46(2):28-39.

[63] Zhang W M, Xi Y B, Brandt M, et al. Stand structure of tropical forests is strongly associated with primary productivity [J].Communications Earth & Environment, 2024, 5:796.

[64] 冯垚, 周梦丽, 罗光成, 等. 天山云杉天然林优势高估计方法 [J].北京林业大学学报, 2025, 47(12):48-55.

[65] Feng Y, Zhou M L, Luo G C, et al. Estimation methods for dominant height in natural forest of Picea schrenkiana var. tianschanica [J].Journal of Beijing Forestry University, 2025, 47(12):48-55.

[66] 罗光成, 雷相东, 史景宁, 等. 基于潜在生产力的吉林省长白落叶松人工林立地质量评价 [J].北京林业大学学报, 2025, 47(1):1-10.

[67] Luo G C, Lei X D, Shi J N, et al. Site quality evaluation of Larix olgensis plantations based on potential productivity in Jilin Province of northeastern China [J].Journal of Beijing Forestry University, 2025, 47(1):1-10.

基金资助

国家自然科学基金项目(32160366)