摘要: 目的目前关于林分碳储量随年龄动态变化的模型研究较少，本研究通过建立林分水平的碳储量生长模型系，为区域尺度的森林碳储量动态预估提供方法、�/sec> 方法以吉林省长白落叶松人工林为对象，使用立地质量分级算法将所有样地划分为3个立地等级，并将其作为哑变量引入模型系中，使用联立方程组的方法将林分平均高、断面积生长模型和林分碳储量模型3个方程进行联合估计，建立林分碳储量生长模型系。采用调整确定系数（ $ {{R}}_{{\text{adj}}}^2 $ ）、估计值的标准误（SEE）和平均预估误差（MPE）来评价模型的表现，分析不同立地等级和林分密度指数（SDI）下林分碳储量的生长过程，及林分断面积和平均高对林分碳储量的影响、�/sec> 结果�?）林分碳储量生长模型系中林分平均高生长模型、林分断面积生长模型和林分碳储量模型皃�inline-formula> $ {{R}}_{{\text{adj}}}^2 $ 分别�?.879�?.977�?.953，MPE� < 2%，具有较好的拟合优度。（2）直接利用林分平均高和断面积或由生长模型得到林分平均高和断面积的这两种途径都可以准确估计林分碳储量，结果仅相差0.02 t/hm ²，模型系具有良好的通用性与稳定性。（3）林分碳储量生长量随立地质量的提高而增加；立地等级相同时，SDI < 1 500�?hm ²时生长较慢，SDI > 1 500�?hm ²时，�?0年以后的林分密度对碳储量生长过程基本无影响；林分密度指数控制�? 500 ~ 2 000�?hm ²时可实现较快的碳储量生长。（4）林分碳储量随林分断面积和平均高的增加而增加，林分断面积与林分碳储量的关系更为密切、�/sec> 结论林分碳储量的生长和立地等级、林分平均年龄、密度、断面积、平均高等因子有密切联系，采用联立方程组方法是建立林分碳储量生长模型系的有效方法。本研究建立的林分碳储量生长模型系可以对林分碳储量动态进行有效预测，为了解林分碳储量的生长过程和森林碳汇评估提供了工具、�/sec>

关键诌�
• 林分碳储量模垊�/a> /
• 生长过程/
• 立地等级/
• 林分密度/
• 长白落叶松人工林

Abstract: ObjectiveThere are knowledge gaps on stand carbon stock growth model at present. This study developed a stand-level carbon stock growth model system to provide a method for dynamic estimation of regional forest carbon storage with time. MethodTaking Larix olgensisplantation in Jilin Province of northeastern China as the research object, the site quality classification algorithm was used to divide all sample plots into three site grades, which were introduced into the model system as dummy variables. The stand carbon stock growth model system was established by simultaneous equations to link stand average height, basal area growth model and stand carbon stock model. The adjusted coefficient of determination ( $ {{R}}_{{\text{adj}}}^2 $ ), the standard error of the estimated value (SEE) and the average prediction error (MPE) were used to evaluate model performance. The growth process of stand carbon stock under different site grades and stand density index (SDI), and the influence of stand basal area and average height on stand carbon stock were analyzed. Result(1) The $ {{R}}_{{\text{adj}}}^2 $ of stand average height growth model, basal area growth model and carbon stock model were 0.892, 0.979 and 0.960, respectively, and the MPEs were both less than 2%. (2) Both procedures in the model system (inventory- and model-derived stand average height and basal area) could accurately estimate the stand carbon stock, and the difference was only 0.02 t/ha, so the model system had great generality and stability. (3) Stand carbon stock growth increased with the increasing site grade of sample plots. When the site grade was the same, the growth was slow with SDI less than 1 500 plant/ha; but there were no differences in the growth process among different SDIs larger than 1 500 plant/ha after 40 years, and the optimal SDI for maximum stand carbon stock was about 1 500�? 000 plant/ha. (4) The stand carbon stock increased with the increase of stand basal area and average height, and stand basal area had larger effects on stand carbon than stand average height. ConclusionThe growth of stand carbon stock is closely related to the site grade, stand average age, density, basal area and average height. The modeling approach of simultaneous equations is a feasible method for developing the stand carbon stock growth model system. The stand carbon stock growth model system developed by this study could effectively predict stand carbon stock, which providing a tool for understanding the growth of stand carbon stock and forest carbon sink assessment.

Key words:
• stand carbon stock model/
• growth process/
• site grade/
• stand density/
• Larix olgensisplantation

�?nbsp; 1吉林省落叶松人工林样地分布图

Figure 1.Distribution of sample plots of larch plantation in Jilin Province

下载: 全尺寸图牆�/a> 幻灯牆�/a>

�?nbsp; 2林分碳储量生长过稊�/p>

Figure 2.Growth process of stand carbon stock

下载: 全尺寸图牆�/a> 幻灯牆�/a>

�?nbsp; 3林分碳储量与林分断面积、平均高的关糺�/p>

Figure 3.Relationship between stand carbon stock andstand basal area as well as average height

下载: 全尺寸图牆�/a> 幻灯牆�/a>

�?nbsp; 1林分因子概况(n= 150)

Table 1.Summary statistics of stand variables (n= 150)

变量 Variable	平均� Mean	最小� Min.	最大� Max.	标准� SD
林分平均� Stand average height (H)/m	13.2	5.0	22.0	3.8
林分公顷断面�?(m2·hm�?) Stand basal area (Ba)/(m2·ha�?)	13.41	3.67	27.97	6.28
林分公顷蓄积/(m3·hm�?) Stand volume (V)/(m3·ha�?)	90.75	16.92	229.78	49.97
平均胸径 Average DBH (Dg)/cm	13.6	6.7	26.1	3.8
林分碳储�?(t·hm�?) Stand carbon stock (C)/(t·ha�?)	37.64	8.11	91.79	19.80
林分密度指数/(株·hm�?) Stand density index (SDI)/(tree·ha�?)	494	159	1 086	212
林分平均年龄/a Stand average age (A)/year	30	11	50	10

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�?nbsp; 2不同立地等级的林分平均高生长模型结果

Table 2.Results of stand average height growth model with different site grades

模型 Model	参数� Parameter	标准� SD	$ {{R}}_{{\text{adj}}}^2 $	SEE/m	MPE/%
$ {{\hat H}} = {a_{}}{\left[ {1 - \exp\left( -\left(\displaystyle\sum {{b_i} \cdot {\text{SIT}}{{\text{E}}_i}} \right){A}\right)} \right]^{{\text{ }}c}} $ (i= 1, 2, 3)	a= 27.247	3.800	0.889	1.261	1.547
	b1= 0.027	0.011
	b2= 0.019	0.007
	b3= 0.012	0.004
	c= 0.789	0.107

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�?nbsp; 3划分立地等级后的样地林分因子概况

Table 3.A summary of stand factor characteristics after site classification

林分因子 Stand factor	立地等级 Site grade	样地� Sample plot number	平均� Mean	最小� Min.	最大� Max.	标准� SD	F
H	1	38	16.7a	11.0	22.0	2.9	55.652
	2	70	13.2b	7.0	19.0	3.0
	3	42	9.9c	5.0	15.0	2.5
Ba	1	38	16.58a	6.22	27.09	4.96	17.547
	2	70	14.16b	3.79	27.97	6.61
	3	42	9.29c	3.67	19.90	4.45
C	1	38	48.53a	15.90	87.69	16.96	19.417
	2	70	39.69b	9.29	91.79	20.39
	3	42	24.36c	8.11	54.95	12.95
注：H、Ba�?i>C的单位分别为m、m2/hm2、t/hm2。不同小写字母表示各林分因子在不同立地等级下的差异显�?P< 0.05)。Notes: the units ofH, Ba,Care m, m2/ha, t/ha, respectively. Different lowercase letters indicate significant differences for varied stand factors under different site grades (P< 0.05).

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�?nbsp; 4林分碳储量生长模型式(1)的结枛�/p>

Table 4.Results of growth model equation (1) of stand carbon stock

模型 Model	参数� Parameter value	标准� SD	$ {{R}}_{{\text{adj}}}^2 $	SEE/(t·hm�?) SEE/(t·ha�?)	MPE/%
${{\hat C}} = \left( {\displaystyle\sum {{a_i} \cdot {\rm{SIT}}{{\rm{E}}_i}} } \right){\left[ {1 - \exp ( - {b_1}{{\left( {\dfrac{{{\rm{SDI}}}}{{1\;000}}} \right)}^{{b_2}}} \cdot {{A}})} \right]^{{\rm{ }}c}}(i = 1, 2, 3) $	a1= 155.893	45.193	0.962	3.876	1.662
	a2= 145.708	41.691
	a3= 120.919	34.778
	b1= 0.012ns	0.008
	b2= 1.23	0.109
	c= 0.561	0.038
注：ns表示模型参数�?.05水平不显著。Note: ns indicates that parameters of the model are not significant at 0.05 level.

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�?nbsp; 5独立林分断面积生长模型结枛�/p>

Table 5.Growth model results of independent stand basal area

模型 Model	参数� Parameter value	标准� SD	$ {{R}}_{{\text{adj}}}^2 $	SEE/(m2·hm�?) SEE/(m2·ha�?)	MPE/%
$ \widehat {{\text{Ba}}} = {a_{}}{\left[ {1 - \exp\left( - {b_1}{{\left(\dfrac{{{\text{SDI}}}}{{1\;000}}\right)}^{{b_2}}} \cdot {{A}}\right)} \right]^{{\text{ }}c}} $	a= 32.340	2.232	0.979	0.911	1.097
	b1= 0.023	0.007
	b2= 3.888	0.268
	c= 0.275	0.019

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�?nbsp; 6林分碳储量生长模型系的参数估计与刀切法验证结果

Table 6.Parameter estimation on growth model system of stand carbon stock and validation results by jackknife method

模型 Model	参数 Parameter	平均� Mean	最小� Min.	最大� Max.	标准� SD	${{R} }_{ {\text{adj} } }^2 $	SEE	MPE/%
林分平均高生长模垊�br/>Stand average height growth model (4-1)	a1	29.010	26.866	31.869	0.491	0.889	1.261	1.548
	b11	0.022	0.017	0.028	0.001
	b12	0.016	0.013	0.020	0.001
	b13	0.009	0.007	0.012	0.000
	c1	0.747	0.716	0.820	0.010
林分断面积生长模垊�br/>Stand basal area growth model (4-2)	a2	32.171	31.051	34.333	0.286	0.979	0.912	1.097
	b21	0.023	0.017	0.027	0.001
	b22	3.863	3.791	3.948	0.023
	c2	0.275	0.267	0.281	0.002
林分碳储量模垊�br/>Stand carbon stock model (4-3)	d1	4.867	4.762	5.028	0.026	0.957	4.108	1.762
	d2	10.124	9.593	10.972	0.134
注：模型4-1�?-2�?-3的SEE单位分别为m、m2/hm2、t/hm2。Notes: the SEE units of model 4-1, 4-2 and 4-3 are m, m2/ha and t/ha, respectively.

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�?nbsp; 72种林分碳储量生长模型系林分碳储量估计途径的结枛�/p>

Table 7.Estimation results of stand carbon stock by different methods using stand carbon stock growth model system

龄组 Age group	途径1/(t·hm�?) Method 1/(t·ha�?)	途径2/(t·hm�?) Method 2/(t·ha�?)	相对差异 Relative difference/%
幼龄� Young stand	25.93	26.32	1.51
中龄� Middle-aged stand	32.84	32.46	�?.17
近熟� Near-mature stand	44.43	44.19	�?.54
成熟� Mature stand	53.00	53.89	1.67
总体 Total	37.51	37.53	0.07
注：建模样本中没有过熟林。Note: there are no over-mature stand in modeling samples.

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