落叶松人工林单木胸高断面积生长差分模型及驱动因素分析

doi:10.11707/j.1001-7488.LYKX20250423

Abstract

Abstract:

Objective: This study aims to construct an age-independent differential model to simulate the growth dynamics of individual Larix gmelinii (larch) trees' basal area at breast height in larch plantations, analyze the nonlinear regulatory mechanisms of topographic, climatic, stand, and competition factors on growth, and explore the interaction among these factors on tree growth, providing a scientific basis for the formulation of forest management strategies. Method: Larch plantation data from the seventh and eighth national forest resource consecutive inventories in north and northeast China were used to construct an age-independent differential model to simulate the growth process of individual larch trees' basal area at breast height. During the model construction, a dummy variable representing solar radiation based on topographic calculations was introduced, and climate factors (annual precipitation), stand factors (basal area at breast height per hectare), and individual tree competition factors were used as driving variables. Reparameterization analysis was performed to assess the nonlinear impacts of these factors on the growth of basal area at breast height. In addition, sensitivity analysis and interaction effect analysis were conducted on the variables to quantify the contributions of different factors to individual tree growth and to explore the interactive effects among these factors on tree growth. Result: 1) The age-independent differential model had a significant advantage in simulating the growth of individual tree basal area at breast height. The model incorporating climate, stand, and competition factors (Model 4) performed the best, with an R² of 0.956 4 and an RMSE of 0.002 272 m². Compared to the baseline model (Model 2), Model 4 showed an R² increase of 0.51%, and RMSE decrease of 5.18%. 2) Sensitivity analysis showed that competition factors had the most significant impact on individual tree basal area growth, with dominant trees exhibiting higher growth efficiency in resource competition. Secondly, there was a significant positive correlation between the mean annual precipitation and basal area at breast height. Thirdly, the stand basal area per hectare and stand density exhibited an inhibitory effect on individual tree growth. Finally, solar radiation intensity had the least impact, with moderate solar radiation being most favorable for growth, while excessive radiation could lead to heat stress. 3) Interaction effect analysis indicated that climate factors, stand structure, and individual tree competition jointly influenced growth. The promoting effect of precipitation on growth was moderated by competition pressure and stand density, with more pronounced under low competition and low-density conditions. Conclusion: This study simulated the growth process of individual larch trees' basal area at breast height in larch plantations using an age-independent differential model, and evaluated the nonlinear effects of climate, stand, and competition factors. The results show that competition factors have the most significant impact on growth, with dominant trees exhibiting higher growth efficiency in resource competition. Annual mean precipitation, basal area per hectare, and solar radiation also play important roles in growth. Meanwhile, climate factors, stand structure, and individual tree competition jointly influence individual tree growth.

Key words: age-independent difference model, basal area at breast height, basal area of larger trees, precipitation, solar radiation, interactive effect

CLC Number:

S718.5

Kailun Zou,Zhanyin Wang,Kexin Zhang,Xiangdong Lei,Xiaoxue Guo,Lu Yang,Xianzhao Liu. Differential Model of Basal Area Growth at Breast Height for Individual-Tree in Larch Plantations and Analysis of Its Driving Factors[J]. Scientia Silvae Sinicae, 2026, 62(8): 97-105.

Figures/Tables 6

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References 0

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因子 Factor	最小值 Minimum	最大值 Maximum	均值 Mean	标准差 Standard deviation
期初单木断面积 Initial basal area per tree/m²	0.002 0	0.120 7	0.010 3	0.009 2
期末单木断面积 Final basal area per tree/m²	0.002 1	0.136 6	0.013 6	0.010 9
期初单木胸径 Initial DBH/cm	5.0	39.2	10.6	4.3
期末单木胸径 Final DBH/cm	5.2	41.7	12.3	4.5
大于对象木的胸高断面积 Basal area of larger trees/(m²·hm^?2)	0.000 0	41.181 8	8.569 6	7.212 5
林分每公顷断面积 Stand basal area per hectare/(m²·hm^?2)	0.110 0	41.210 0	14.353 3	8.962 4
林分株树密度 Stand tree density/(stems·hm^?2)	50	4 083	1 585	842
林分密度指数 Stand density index	6	1 594	571	326

因子 Factor	最小值 Minimum	最大值 Maximum	均值 Mean	标准差 Standard deviation
夏季平均最高温度 Summer mean maximum temperature/℃	18.64	28.48	23.98	1.74
冬季平均最低温度 Winter mean minimum temperature/℃	?33.06	?8.04	?20.98	5.71
最暖月平均温度 Mean warmest month temperature/℃	15.62	24.06	19.16	1.69
最冷月平均温度 Mean coldest month temperature/℃	?27.94	?6.06	?17.24	5.54
年均降水量 Mean annual precipitation/mm	385.40	808.40	526.01	91.45
年均太阳辐射总量 Annual mean total solar radiation/(kWh·m^?2)	62.64	3 044.00	1 920.60	795.09

编号 No.	基础模型来源 Basic model derivation source	表达式 Expression
模型 1 Model 1	Logistic	$ Y_{t+n}=\dfrac{Y_ta\mathrm{\rm e}^{bn}}{Y_t\mathrm{\rm e}^{bn}+a-Y_t} $
模型 2 Model 2	Gompertz	$ Y_{t+n}=a\cdot\mathrm{\rm e}^{\mathrm{\rm e}^{-bn}\cdot\ln\dfrac{Y_t}{a}} $

模型 Model	$ \mathrm{\mathit{R}}^2 $	$ \text{RMSE} $
基于Logistic的无关年龄差分模型（模型1） Logistic-based age-independent difference model (Model 1)	0.947 9$ \pm $0.005 1	0.002 483$ \pm $0.000 064
基于Gompertz的无关年龄差分模型（模型2） Gompertz-based age-independent difference model (Model 2)	0.951 5$ \pm $0.005 0	0.002 396$ \pm $0.000 067
含年太阳辐射量哑变量的模型（模型3） Model with annual solar radiation dummy variable (Model 3)	0.951 6$ \pm $0.005 0	0.002 393$ \pm $0.000 067
含林分因子、单木竞争因子、气候因子和哑变量的模型（模型4） Model incorporating stand factors, individual tree competition factors, climate factors， and dummy variables (Model 4)	0.956 4$ \pm $0.004 0	0.002 272$ \pm $0.000 045

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Differential Model of Basal Area Growth at Breast Height for Individual-Tree in Larch Plantations and Analysis of Its Driving Factors

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