适于GlobalAllomeTree国际数据平台的标准化中国主要树种树高-胸径方程研建

doi:10.13304/j.nykjdb.2023.0116

摘要/Abstract

摘要：

GlobalAllomeTree作为共享异速方程的国际网络平台，逐渐受到全球高度关注。当前，为促进该项国际合作，针对当前该平台缺乏中国主要树种生长异速方程的现状，系统性更新标准化中国主要树种树高-胸径方程。由于树冠和下部灌木及草丛遮挡，树高相对于胸径测量具有一定的难度，因此需要使用数学工具进行计算。选取了36个树种为材料构建树高-胸径关系方程，以全国主要树种的二元材积模型、各地区一元材积表为基础材料，以取样径阶为1 cm间隔所生成1 692组树高-胸径数据作为建立方程样本，1 238组外业调查数据为验证样本。建模结果表明：36个主要树种的1 692组树高-胸径数据建立的全国通用性树高-胸径方程拟合相关系数（R² ）为0.801，方程拟合结果较好，说明可以通过测定胸径，带入树高（H，m）-胸径（D，cm）方程（ $H = a D b)$ 预估树高；对36个主要树种的树高-胸径方程进行拟合，决定系数R²值均大于0.916，平均误差（ME）、平均绝对误差（MAE）和均方根误差（RMSE）相对较小，方程整体精度较高，可广泛推广；将外业采集的1 238组树高-胸径数据，根据36个主要树种树高-胸径方程拟合公式及参数估计值a、b进行方程精度验证，方程预测的平均相对误差为16.86%，在误差允许范围内，并且模型形式规范，可为GlobalAllomeTree平台用户提供科学参考。

关键词: GlobalAllomeTree, 主要树种, 树高, 胸径, 树木生长方程

Abstract:

GlobalAllomeTree is an international network platform that shares differential equations， which has gradually received high global attention. Currently， aiming at the lack of growth differential equations for major tree species in China on this platform， this study updated the standardized tree height-diameter relationship equation for major tree species in China. Due to the canopy and lower shrubs and grass cover， the measurement of tree height relative to diameter at breast height （DBH） is difficult， so mathematical tools need to be used for regression calculations. 36 tree species were selected as materials to construct a tree height-diameter relationship equation. Based on the binary volume model of major tree species in China and the one-dimensional volume table of each region， 1 692 sets of tree height-diameter data generated with a sampling diameter order of 1 cm interval were used as equation samples， and 1 238 sets of field survey data were used as validation samples. The modeling results showed as followed： the correlation coefficient （R²） of the national universal tree height-diameter equation fitting based on 1 692 sets of tree height diameter data from 36 main tree species was 0.801， indicating that the equation fitting results were good， so the tree height can be estimated by measuring the diameter at breast height （H，m） - diameter at breast height （D，cm） square $H = a D b$ ； using the equation to fit 36 main tree species， the results showed that the determination coefficients （R²） of the tree height-diameter at breast height equation for 36 main tree species were all greater than 0.916， and the values of mean error （ME）， mean absolute error （MAE）， and root mean square error （RMES） were relatively small. The overall accuracy of the equation was high， which could be widely promoted； using 1 238 analytical tree data collected from field work， the accuracy of the equation was verified based on the fitting formulas and parameter estimates a and b of the tree height diameter equation for 36 main tree species. The results showed that the average relative error of the equation prediction was 16.86%， within the allowable range of error， and the model format was standardized. Above results provided scientific reference for users of the GlobalAllomeTree platform.

Key words: GlobalAllomeTree, 36 main tree species, tree height, chest diameter, tree growth equation

中图分类号:

S711

杨飞, 冯仲科, 周杨杨, 程文生, 王智超. 适于GlobalAllomeTree国际数据平台的标准化中国主要树种树高-胸径方程研建[J]. 中国农业科技导报, 2024, 26(9): 62-71.

Fei YANG, Zhongke FENG, Yangyang ZHOU, Wensheng CHENG, Zhichao WANG. Construction of A Standardized Height-diameter Equation for the Main Tree Species in China Suitable for the GlobalAllomeTree International Data Platform[J]. Journal of Agricultural Science and Technology, 2024, 26(9): 62-71.

图/表 5

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地区 Region	序号 No.	树种 Species	a	b
华北地区 North China	1	落叶松Larix principis-rupprechtii	1.488	0.708
	2	云杉 Picea asperata Mast	1.917	0.562
	3	侧柏Platycladus orientalis （Linn.） Franco	1.614	0.601
	4	山杨Populus davidiana Dode	2.875	0.550
	5	桦木Betulaceae	3.341	0.419
	6	阔叶树North Sinis durae	2.586	0.400
东北地区 Northeast China	7	红松Pinus koraiensis	2.363	0.576
	8	落叶松Larix principis-rupprechtii	3.574	0.498
	9	云杉、冷杉Picea asperata Mast，Abies fabri	2.363	0.576
	10	大兴安岭樟子松Pinus sylvestris Linn. var. mongolica Litv.	2.681	0.515
	11	白桦Betula platyphylla Suk	3.902	0.440
华东地区 East China	12	黄山松Pinus taiwanensis Hayata	4.736	0.429
华东地区 East China	13	华山松Pinus armandii Franch	2.425	0.607

地区 Region	序号 No.	树种 Species	a	b
华北地区 North China	1	落叶松Larix principis-rupprechtii	1.488	0.708
	2	云杉 Picea asperata Mast	1.917	0.562
	3	侧柏Platycladus orientalis （Linn.） Franco	1.614	0.601
	4	山杨Populus davidiana Dode	2.875	0.550
	5	桦木Betulaceae	3.341	0.419
	6	阔叶树North Sinis durae	2.586	0.400
东北地区 Northeast China	7	红松Pinus koraiensis	2.363	0.576
	8	落叶松Larix principis-rupprechtii	3.574	0.498
	9	云杉、冷杉Picea asperata Mast，Abies fabri	2.363	0.576
	10	大兴安岭樟子松Pinus sylvestris Linn. var. mongolica Litv.	2.681	0.515
	11	白桦Betula platyphylla Suk	3.902	0.440
华东地区 East China	12	黄山松Pinus taiwanensis Hayata	4.736	0.429
华东地区 East China	13	华山松Pinus armandii Franch	2.425	0.607

地区 Region	序号 No.	树种 Species	a	b
华南地区 South China	16	桉树Eucalyptus robusta Smith	4.846	0.341
华南地区 South China	17	杉木Cunninghamia lanceolata （Lamb.） Hook	1.946	0.610
西南地区 Southwest China	18	云南松Pinus yunnanensis Franch	2.820	0.527
	19	云杉（四川适用）Picea asperata Mast （for Sichuan）	2.633	0.544
	20	云杉（云南适用）Picea asperata Mast （for Yunnan）	2.352	0.561
	21	冷杉（四川适用）Abies fabri （Mast.） Craib（for Sichuan）	2.529	0.533
	22	冷杉（云南适用）Abies fabri （Mast.） Craib （for Yunnan）	2.340	0.528
	23	柏、杉类Cupressaceae， Taxodiaceae	2.910	0.461
	24	桦木Betulaceae	3.960	0.365
	25	栎类Quercus	2.836	0.494
	26	丝栗、高山栎Castanea，Quercus semicarpifolia Smith	3.137	0.418
西北地区 Northwest China	27	冷杉Abies fabri （Mast.） Craib	3.081	0.420
	28	云杉（天山、祁连山、六盘山等适用）Picea asperata Mast （for Tianshan， Qilian， and Liupan Mountains etc.）	2.998	0.476
	29	云杉（阿尔泰适用）Picea asperata Mast （for Altai）	3.205	0.472
	30	云杉（青海适用）Picea asperata Mast （for Qinghai）	3.158	0.460
	31	山杨Populus davidiana Dode	2.671	0.507
	32	桦木Betulaceae	3.808	0.366
	33	阔叶树Ventus broadleaf	3.122	0.340
	34	落叶松（天山适用）Larix gmelinii （Ruprecht） Kuzeneva （for Tianshan Mountain）	3.293	0.440
	35	落叶松（阿尔泰适用）Larix gmelinii （Ruprecht） Kuzeneva （for Altai）	3.081	0.484
	36	栎类Quercus	2.592	0.458

地区 Region	序号 No.	树种 Species	a	b
华南地区 South China	16	桉树Eucalyptus robusta Smith	4.846	0.341
华南地区 South China	17	杉木Cunninghamia lanceolata （Lamb.） Hook	1.946	0.610
西南地区 Southwest China	18	云南松Pinus yunnanensis Franch	2.820	0.527
	19	云杉（四川适用）Picea asperata Mast （for Sichuan）	2.633	0.544
	20	云杉（云南适用）Picea asperata Mast （for Yunnan）	2.352	0.561
	21	冷杉（四川适用）Abies fabri （Mast.） Craib（for Sichuan）	2.529	0.533
	22	冷杉（云南适用）Abies fabri （Mast.） Craib （for Yunnan）	2.340	0.528
	23	柏、杉类Cupressaceae， Taxodiaceae	2.910	0.461
	24	桦木Betulaceae	3.960	0.365
	25	栎类Quercus	2.836	0.494
	26	丝栗、高山栎Castanea，Quercus semicarpifolia Smith	3.137	0.418
西北地区 Northwest China	27	冷杉Abies fabri （Mast.） Craib	3.081	0.420
	28	云杉（天山、祁连山、六盘山等适用）Picea asperata Mast （for Tianshan， Qilian， and Liupan Mountains etc.）	2.998	0.476
	29	云杉（阿尔泰适用）Picea asperata Mast （for Altai）	3.205	0.472
	30	云杉（青海适用）Picea asperata Mast （for Qinghai）	3.158	0.460
	31	山杨Populus davidiana Dode	2.671	0.507
	32	桦木Betulaceae	3.808	0.366
	33	阔叶树Ventus broadleaf	3.122	0.340
	34	落叶松（天山适用）Larix gmelinii （Ruprecht） Kuzeneva （for Tianshan Mountain）	3.293	0.440
	35	落叶松（阿尔泰适用）Larix gmelinii （Ruprecht） Kuzeneva （for Altai）	3.081	0.484
	36	栎类Quercus	2.592	0.458

地区 Region	序号 No.	树种 Species	方程决定系数 R²	平均绝对误差 MAE/m	平均误差 ME/m	均方根误差 RMSE/m
华北地区 North China	1	落叶松Larix principis-rupprechtii	0.989	0.079	0.076	0.028
	2	云杉 Picea asperata Mast	0.990	0.130	-0.083	0.361
	3	侧柏Platycladus orientalis （Linn.） Franco	0.998	0.030	-0.006	0.173
	4	山杨Populus davidiana Dode	0.868	0.027	-0.006	0.166
	5	桦木Betulaceae	0.979	0.071	0.040	0.266
	6	阔叶树North Sinis durae	0.989	0.082	1.839	0.287
东北地区 Northeast China	7	红松Pinus koraiensis	0.985	0.057	-0.056	0.239
	8	落叶松Larix principis-rupprechtii	0.993	0.135	0.118	0.367
	9	云杉、冷杉Picea asperata Mast，Abies fabri	0.993	0.166	0.134	0.407
	10	大兴安岭樟子松Pinus sylvestris Linn.var. mongolica Litv.	0.991	0.123	0.087	0.351
	11	白桦Betula platyphylla Suk	0.918	0.097	-0.009	0.312
华东地区 East China	12	黄山松Pinus taiwanensis Hayata	0.994	0.176	-0.147	0.419
华东地区 East China	13	华山松Pinus armandii Franch	0.982	0.075	-0.046	0.273
华中地区 Central China	14	马尾松Pinus massoniana Lamb	0.993	0.129	0.109	0.360
华中地区 Central China	15	油松Pinus tabulaeformis Carr	0.996	0.213	-0.212	0.461
华南地区South China	16	桉树Eucalyptus robusta Smith	0.988	0.092	0.069	0.303
华南地区South China	17	杉木Cunninghamia lanceolata （Lamb.） Hook	0.982	0.062	0.046	0.251
西南地区Southwest China	18	云南松Pinus yunnanensis Franch	0.930	0.092	0.012	0.304
	19	云杉（四川适用）Picea asperata Mast （for Sichuan）	0.993	0.184	0.129	0.429
	20	云杉（云南适用）Picea asperata Mast （for Yunnan）	0.994	0.179	0.142	0.421
	21	冷杉（四川适用）Abies fabri （Mast.） Craib（for Sichuan）	0.979	0.094	-0.041	0.307
	22	冷杉（云南适用）Abies fabri （Mast.） Craib （for Yunnan）	0.874	0.084	0.006	0.291
	23	柏、杉类Cupressaceae， Taxodiaceae	0.994	0.174	0.145	0.417
	24	桦木Betulaceae	0.997	0.308	0.301	0.556
	25	栎类Quercus	0.990	0.109	0.081	0.331
	26	丝栗、高山栎Castanea，Quercus semicarpifolia Smith	0.979	0.082	0.040	0.286
西北地区Northwest China	27	冷杉Abies fabri （Mast.） Craib	0.995	0.225	0.187	0.474
	28	云杉（天山、祁连山、六盘山等适用）Picea asperata Mast （for Tianshan， Qilian， and Liupan Mountains）	0.916	0.092	0.046	0.304
	29	云杉（阿尔泰适用）Picea asperata Mast （for Altai）	0.952	0.091	0.016	0.301
	30	云杉（青海适用）Picea asperata Mast （for Qinghai）	0.987	0.146	0.065	0.383
	31	山杨Populus davidiana Dode	0.994	0.332	0.291	0.568
	32	桦木Betulaceae	0.995	0.213	0.200	0.461
	33	阔叶树Ventus broadleaf	0.996	0.255	0.247	0.506
	34	落叶松（天山适用）Larix gmelinii （Ruprecht） Kuzeneva （for Tianshan Mountain）	0.963	0.104	0.021	0.323
	35	落叶松（阿尔泰适用）Larix gmelinii （Ruprecht） Kuzeneva （for Altai）	0.755	0.093	0.003	0.306
	36	栎类Quercus	0.989	0.127	0.072	0.357