我国4种落叶松人工林的林分优势高和平均高转换模型

doi:10.11707/j.1001-7488.LYKX20240804

摘要/Abstract

摘要：

目的: 建立全国4种落叶松人工林的林分优势高和平均高转换模型，为落叶松人工林立地质量评价和生长预测提供依据。方法: 基于2021和2022年2期全国林草生态综合监测落叶松人工林样地调查数据，采用对偶回归和线性混合效应模型方法，建立落叶松人工林的林分优势高和平均高转换模型，选取残差平方和、决定系数（R²）、均方根误差和相对均方根误差等指标对模型进行评价。结果: 1）基于对偶回归模型方法建立的林分优势高和平均高转换模型表现最好，优于线性混合效应模型方法，对偶回归模型方法的平均R²达0.92以上，平均均方根误差1.31~1.34 m，平均相对均方根误差9.63%~9.85%，且可实现优势高与平均高相互预测；2）考虑树种分组和省（市）分组的对偶回归模型均可进一步提升模型精度，但考虑省（市）分组的模型精度更高。结论: 基于对偶回归模型方法和考虑省（市）分组的林分优势高和平均高转换模型具有较好的适用性和预测效果，可为落叶松人工林立地质量评价提供更为精确的基础模型。

关键词: 林分优势高, 林分平均高, 对偶回归模型, 线性混合效应模型, 落叶松人工林

Abstract:

Objective: This study aims to develop conversion models between the stand dominant height and the mean height of the four larch species (Larix spp.), providing a basis for evaluating the site quality and predicting the growth of larch plantations. Method: Based on the survey data of national forest and grass ecological comprehensive monitoring of plantation plots of Larix species from the 2021 and 2022, dual regression and mixed-effects models were applied to develop conversion models for stand dominant height and mean height. Model performance was assessed using residual sum of squares, coefficient of determination (R²), root mean square error (RMSE) and relative root mean square error (rRMSE). Result: 1) The conversion model between stand dominant height and mean height based on the dual regression model method performed the best, outperforming the linear mixed effect model approach. The dual regression model method had average R² exceeding 0.92, average RMSEs between 1.31 m and 1.34 m, and average rRMSEs between 9.63% and 9.85%, and was able to achieve mutual prediction between stand dominant height and mean height. 2) Incorporating tree species and province (city) groups into the dual regression model further improved model accuracy, and the model including province (city) groups showed higher accuracy. Conclusion: The dual regression model in incorporating province (city) groups had good applicability and predictive performance in establishing the conversion relationship between stand dominant height and mean height. This approach offers a more accurate and basic forecasting model for site quality evaluation of larch plantations.

Key words: stand dominant height, stand mean height, dual regression model, linear mixed effect model, Larix spp. plantations

中图分类号:

S757

何潇,曾伟生,陈新云,黄宏超,雷相东. 我国4种落叶松人工林的林分优势高和平均高转换模型[J]. 林业科学, 2026, 62(1): 223-230.

Xiao He,Weisheng Zeng,Xinyun Chen,Hongchao Huang,Xiangdong Lei. Conversion Models of Stand Dominant Height and Mean Height of the Plantations of Four Larix species in China[J]. Scientia Silvae Sinicae, 2026, 62(1): 223-230.

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单元 Classification	变量Variables	平均值 Mean	最小值 Min.	最大值 Max.	变异系数 Coefficient of variation （%）
全部 Total （n=366）	林分平均高Stand mean height （H_m）/m	12.7	3.3	25.7	37.75
	林分优势高Stand dominant height （H_d）/m	14.6	3.9	28.8	33.57
	林分平均林龄 Stand mean age/a	27	5	64	61.65
华北落叶松 Larix gmelinii var. principis- rupprechtii （n=120）	林分平均高Stand mean height （H_m）/m	12.1	4.1	25.7	41.54
	林分优势高Stand dominant height （H_d）/m	14.0	5.7	28.8	36.39
	林分平均林龄 Stand mean age/a	26	7	64	47.91
日本落叶松 Larix kaempferi （n=57）	林分平均高Stand mean height （H_m）/m	11.5	4.8	19.9	36.14
	林分优势高Stand dominant height （H_d）/m	13.3	5	21.5	32.83
	林分平均林龄 Stand mean age/a	27	7	52	43.85
兴安落叶松 Larix gmelinii （n=132）	林分平均高Stand mean height （H_m）/m	13.1	3.3	23.3	34.08
	林分优势高Stand dominant height （H_d）/m	14.9	3.9	24.7	31.07
	林分平均林龄 Stand mean age/a	27	5	60	50.03
长白落叶松 Larix olgensis （n=57）	林分平均高Stand mean height （H_m）/m	14.3	6.3	25.7	36.63
	林分优势高Stand dominant height （H_d）/m	16.3	6.5	26.3	31.39
	林分平均林龄 Stand mean age/a	25	8	61	48.30

指标Index	统计量Statistics	指标Index	统计量Statistics
Q	654	R²	0.923 5
Q₁	669	R₁²	0.923 4
Q₂	639	R₂²	0.923 7
RMSE/m	1.34	rRMSE (%)	9.85
RMSE₁/m	1.35	rRMSE₁ (%)	9.28
RMSE₂/m	1.32	rRMSE₂ (%)	10.41

模型Model	指标Index	统计量Statistics	模型Model	指标Index	统计量Statistics
M1-1	Q	624	M1-2	Q	642
	Q₁	628		Q₁	654
	Q₂	621		Q₂	630
	R²	0.927 0		R²	0.924 9
	R₁²	0.928 1		R₁²	0.925 1
	R₂²	0.925 9		R₂²	0.924 8
	RMSE/m	1.31		RMSE/m	1.32
	RMSE₁/m	1.31		RMSE₁/m	1.34
	RMSE₂/m	1.30		RMSE₂/m	1.31
	rRMSE （%）	9.63		rRMSE （%）	9.76
	rRMSE₁ （%）	8.99		rRMSE₁ （%）	9.18
	rRMSE₂ （%）	10.26		rRMSE₂ （%）	10.34
M2-1	Q	1 061	M2-2	Q	1 060
	Q₁	615		Q₁	640
	Q₂	1 507		Q₂	1 480
	R²	0.874 8		R²	0.875 0
	R₁²	0.929 6		R₁²	0.926 8
	R₂²	0.820 0		R₂²	0.823 3
	RMSE/m	1.66		RMSE/m	1.67
	RMSE₁/m	1.30		RMSE₁/m	1.32
	RMSE₂/m	2.03		RMSE₂/m	2.01
	rRMSE （%）	12.44		rRMSE （%）	12.46
	rRMSE₁ （%）	8.90		rRMSE₁ （%）	9.07
	rRMSE₂ （%）	15.99		rRMSE₂ （%）	15.85
	$ {\delta }_{u({{a}_{0}})} $	0.581 98		$ {\delta }_{u({{a}_{0}})} $	0.486 62
	$ {\delta }_{u({{a}_{1}})} $	0.023 12		$ {\delta }_{u({{a}_{1}})} $	0.022 60
	$ {\delta }_{\text{1}} $	3.067 92		$ {\delta }_{\text{1}} $	3.316 16
M3-1	Q	1 162	M3-2	Q	1 139
	Q₁	1 685		Q₁	1 645
	Q₂	639		Q₂	633
	R²	0.865 4		R²	0.868 0
	R₁²	0.807 1		R₁²	0.811 6
	R₂²	0.923 7		R₂²	0.924 4
	RMSE/m	1.73		RMSE/m	1.72
	RMSE₁/m	2.15		RMSE₁/m	2.12
	RMSE₂/m	1.32		RMSE₂/m	1.32
	rRMSE （%）	12.57		rRMSE （%）	12.46
	rRMSE₁ （%）	14.73		rRMSE₁ （%）	14.55
	rRMSE₂ （%）	10.41		rRMSE₂ （%）	10.36
	$ {\delta }_{u({{b}_{0}})} $	9.008 44×10^?6		$ {\delta }_{u({{b}_{0}})} $	0.088 03
	$ {\delta }_{u({{b}_{1}})} $	3.603 11×10^?6		$ {\delta }_{u({{b}_{1}})} $	0.006 79
	$ {\delta }_{\text{2}} $	0.230 06		$ {\delta }_{\text{2}} $	0.760 51

省（市） Province (city)	$ \hat{H}_{\mathrm{d}}=a_0+a_1H_{\mathrm{m}} $		$ \hat{H}_{\mathrm{m}}=b_0+b_1H_{\mathrm{d}} $
省（市） Province (city)	a₀	a₁	b₀	b₁
甘肃 Gansu	0.015 83	1.173 45	?0.013 49	0.852 19
河北 Hebei	0.865 74	1.081 71	?0.800 35	0.924 46
黑龙江 Heilongjiang	2.315 75	0.987 06	?2.346 11	1.013 11
吉林 Jilin	2.336 10	0.985 64	?2.370 13	1.014 57
辽宁 Liaoning	2.287 00	0.973 84	?2.348 45	1.026 87
内蒙古自治区 Inner Mongolia	0.906 10	1.041 98	?0.869 60	0.959 71
宁夏回族自治区 Ningxia Hui Autonomous Region	1.998 95	0.956 91	?2.088 97	1.045 03
山西 Shanxi	1.232 50	1.056 49	?1.166 60	0.946 53
其他（四川、重庆、青海、湖北） Others （Sichuan， Chongqing， Qinghai， Hubei）	2.708 55	0.955 32	?2.835 22	1.046 77

树种 Tree species	$ \hat{H}\mathrm{_d}=a_0+a_1H_{\mathrm{m}} $		$ \hat{H}\mathrm{_m}=b_0+b_1H\mathrm{_d} $
树种 Tree species	a₀	a₁	b₀	b₁
华北落叶松 Larix gmelinii var. principis-rupprechtii	1.131 71	1.053 02	?1.074 73	0.949 65
日本落叶松 Larix kaempferi	2.496 73	0.959 83	?2.601 23	1.041 85
兴安落叶松 Larix gmelinii	1.716 18	1.021 47	?1.680 11	0.978 98
长白落叶松 Larix olgensis	2.242 67	0.985 53	?2.275 61	1.014 69