Growth model of carbon storage and driving force of carbon sequestration capacity of natural secondary forests
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摘要:目的 针对采伐干扰后天然恢复的次生林，建立其碳储量生长模型及对应的碳汇模型，分析不同因子对固碳能力的驱动作用，为固碳能力量化评价提供科学依据。方法 基于吉林省第9次森林资源连续清查固定样地数据筛选出的111个采伐后形成的天然次生林样地数据，采用Richards理论生长方程，以样地平均木的碳储量为因变量，以样地平均年龄为自变量，通过对年龄分组和迭代算法建立碳储量分级生长模型，通过对碳储量分级生长模型中的年龄求导得到碳汇分级生长模型。采用决定系数（R2）和均方根误差（RMSE）评价模型拟合效果。以地理因子、地形因子、气候因子、土壤因子和林分因子为自变量，基于一般线性模型，引入定性和定量因子交互作用，分析固碳能力的驱动力。结果 （1）天然次生林碳储量分级生长模型的R2为0.965 6，RMSE为2.61 kg，具有很好的拟合优度。（2）各个分级碳汇量最大的年龄分别为8、10、13、17和29年，以1 000株/hm2的密度计算，5年时间的阈值为1.84 t/hm2，到30年时增加到10.78 t/hm2，各级间的阈值随年龄的增加而增加。（3）一阶定性和一、二阶定量交互的模型对平均木碳储量的解释最高，R2为0.919 2，与不含交互项的主效应模型相比，R2提高了0.088 5。（4）对于平均木碳储量，地理因子（经度和纬度）、地形因子（海拔、地貌、坡向、坡位和坡度）、枯枝落叶层厚度、气候因子（年均气温、极端最低温度、湿度指数、无霜期天数）、土壤因子（土壤厚度）和林分因子（年龄和优势树种）等因子有显著性影响；对于不同立地分级20年时碳密度，地理因子（纬度）、地形因子（地貌、坡度和坡向）、气候因子（极端最高温度、最热月平均温度和湿度指数）、土壤因子（土壤类型和砾石含量）和林分因子（优势树种）等因子有显著性影响，而海拔和腐殖质厚度等变量存在于交互项中，其主效应并不显著。结论 天然次生林不同等级的碳密度在不同的时间段，等级间的阈值不同，随着年龄的增加，各级间的阈值不断增加，但不同等级间碳储量的相对差距随着年龄的增加而减小。引入交互作用可以提高模型对森林固碳的解释程度。纬度等地理因子，坡度、坡向等地形因子，湿度指数等气候因子和优势树种等林分因子是影响天然次生林固碳能力因素的关键因子。Abstract:Objective This paper aims to establish a growth model of carbon storage of the natural secondary forests after logging disturbance and the corresponding carbon sink model, so as to analyze the driving effect of different factors on carbon sequestration capacity, which can provide references for quantitative evaluation of carbon sequestration capacity.Method Totally 111 sample plot data for the natural secondary forests were selected based on the data of the 9th National Forest Inventory in Jilin Province of northeastern China. Based on the Richards theoretical growth equation, taking the average tree carbon storage of the sample plot as the dependent variable and the average age of the sample plot as the independent variable, a carbon storage classified growth model was established by grouping the age and iterative algorithm, and the carbon sink classified growth model was obtained by deriving the age in the carbon storage classified growth model. The coefficient of determination (R2) and the root mean square error (RMSE) were used to evaluate the effect of model fitting. Based on a linear model, taking geographical factors, topographic factors, climate factors, soil factors and forest stand factors as independent variables, the interactions of qualitative and quantitative factors were introduced to analyze the driving force of carbon sequestration capacity.Result (1) The R2 of the natural secondary forest carbon storage classified growth model was 0.965 6, and the RMSE was 2.612 7 kg, this model had a good goodness of fit. (2) The ages of the largest carbon sinks in each level were 8, 10, 13, 17 and 29 years. Calculated at a density of 1 000 plants per hectare, the threshold between levels in 5 years was 1.84 t/ha, and by 30 years increased to 10.78 t/ha, the threshold between each level increased with age. (3) The first-order qualitative, first-order, and second-order quantitative interaction model had the highest explanation for the average tree carbon storage, and R2 was 0.919 2. Compared with the main effect model without interaction terms, R2 was increased by 0.088 5. (4) For the average tree carbon storage, geographic factors (longitude and latitude), topographic factors (altitude, landform, slope aspect, slope position and slope degree), litter layer thickness, climate factors (annual average temperature, extreme minimum temperature, humidity index, frost-free days), soil factor (soil thickness) and stand factors (age and dominant tree species) had significant effects. For 20 years of carbon density by different classifications, geographic factor (latitude), topographic factors (landform, slope degree and slope aspect), climate factors (extreme maximum temperature, hottest monthly average temperature and humidity index), soil factors (soil type and gravel content) and stand factor (dominant tree species) had significant effects, while factors such as altitude and humus thickness existed in the interaction terms, and their main effects were not significant.Conclusion The carbon density of different level thresholds of the natural secondary forests is different in varied time periods. With the increase of age, the thresholds between levels continue to increase, but the relative magnitudes in carbon storage between different levels are decreasing. The introduction of interaction could help improve the interpretation degree of forest carbon sequestration. Geographical factors such as latitude, topographical factors such as slope degree and slope aspect, climate factors such as humidity index, and stand factors such as dominant tree species are the key factors affecting the carbon sequestration capacity of the natural secondary forests.
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图 1 平均木碳储量实测值和估计值的散点图
Figure 1. Scatter plot of measured and estimated values of average tree carbon storage
表 1 吉林天然次生林样地统计量
Table 1 Statistics of the natural secondary forest sample plots in Jilin Province
调查因子 Survey factor 平均值 Mean 标准差 SD 最小值 Min. value 最大值 Max. value 平均年龄/a
Average age/year18 6 5 20 平均胸径
Mean DBH/cm9.2 2.2 5.7 16.6 株密度/（株·hm−2）
Tree density/(plant·ha−1)1 015 698 17 4 000 蓄积量/（m3·hm−2）
Volume/(m3·ha−1)35.82 31.58 0.22 146.25 碳密度/（t·hm−2）
Carbon density/(t·ha−1)18.52 15.77 0.14 82.56 
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表 2 样地非生物环境因子以及优势树种统计量
Table 2 Statistics of abiotic environmental factors and dominant tree species in the sample plots
调查因子Survey factor 属性 Attribute 说明 Description 东经 East longitude/(°) 定量 Quantitative 127.42 ± 1.70 (125.31 ~ 130.76) 北纬 North latitude/(°) 定量 Quantitative 42.41 ± 0.86 (40.96 ~ 44.89) 海拔 Altitude/m 定量 Quantitative 494 ± 205 (90 ~ 1 140) 地貌 Landform 定性 Qualitative 中山 Mid-mountain (3) 低山 Low-mountain (65)
丘陵 Hill (35) 平原 Plain (8)坡向 Slope aspect 定性 Qualitative 北坡 North slope (9) 东北坡 Northeast slope (13) 东坡 East slope (8)
东南坡 Southeast slope (11)南坡 South slope (8)
西南坡 Southwest slope (20) 西坡 West slope (15)
西北坡 Northwest slope (14) 无坡向 No aspect (13)坡度 Slope degree 定性 Qualitative 平坡 Flat slope (20) 缓坡 Gentle slope (48) 斜坡 Slope (27)
陡坡 Steep slope (13) 急坡 Escarpment (3)坡位 Slope position 定性 Qualitative 脊部 Ridge (2) 上坡 Up slope (29) 中坡 Middle slope (31)
下坡 Down slope (39) 山谷 Valley (7) 平地 Flat (3)腐殖质厚度 Humus layer thickness/cm 定量 Quantitative 3.05 ± 2.14 (0.00 ~ 12.00) 枯枝落叶厚 Litter layer thickness/cm 定量 Quantitative 3.20 ± 1.80 (0.00 ~ 10.00) 土壤类型 Soil type 定性 Qualitative 灰黑土 Gray black soils (106) 白浆土 Albic soils (1)
风沙土 Aeolian sandy soils (1) 草甸土 Meadow soils (2) 沼泽土 Bog soils (1)砾石含量 Gravel content/% 定量 Quantitative 6.70 ± 9.48 (0.00 ~ 40.00) 土壤厚度 Soil thickness/cm 定量 Quantitative 38.54 ± 12.11 (10.00 ~ 60.00) 年降水量 Annual precipitation/mm 定量 Quantitative 734 ± 134 (486 ~ 1 059) 年平均气温 Annual average temperature/℃ 定量 Quantitative 4.94 ± 0.98 (0.79 ~ 6.91) 极端最低温
Extreme minimum temperature/℃定量 Quantitative −29.72 ± 1.79 (−34.80 ~ −24.30) 极端最高温
Extreme maximum temperature/℃定量 Quantitative 33.34 ± 0.72 (30.50 ~ 34.50) 湿度指数 Humidity index 定量 Quantitative 21.62 ± 4.40 (11.75 ~ 32.48) 无霜期天数 Frost-free days/d 定量 Quantitative 182 ± 9 (141 ~ 199) 最冷月平均温度
Mean temperature in the coldest month/℃定量 Quantitative −15.04 ± 1.17 (−17.87 ~ −11.13) 最热月平均温度
Mean temperature in the hottest month/℃定量 Quantitative 21.69 ± 1.01 (17.55 ~ 23.73) 优势树种 Dominant tree species 定性 Qualitative 云杉Picea asperata (2) 落叶松Larix spp. (21)
栎类Quercus spp. (10)
白桦Betula platyphylla (3)
胡桃楸Juglans mandshurica (5)
榆树Ulmus pumila (3)
杨树Populus simonii (4)
泡桐Paulownia fortune (5)
其他软阔 Other soft-broadleaved (10)
阔叶混交林 Broadleaved mixed forest (41)
针阔混交林 Coniferous and broadleaved mixed forest (7)注：对定量数据，说明为：平均值 ± 标准差（最小值 ~ 最大值）；对定性数据，说明为：定性变量值（样本数）。Notes: for quantitative data, it is explained as: average ± SD (minimum to maximum); for qualitative data, it is explained as qualitative variable value (sample size).
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表 3 不同碳储量生长等级的样地数量
Table 3 Number of sample plots with different carbon storage growth grades
等级
Grade样地数
Sample plot number比例
Proportion/%1 16 14 2 11 10 3 14 13 4 34 31 5 36 32
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表 4 碳储量生长模型拟合参数和模型评价指标
Table 4 Fitting parameters and evaluation indexes of carbon storage growth model
参数 Parameter 估计值 Estimate value T 值 T-value 显著性 Sig. a 228.093 282 2.221 265 0.028 400 b1 0.011 314 2.608 114 0.010 381 b2 0.008 498 2.242 808 0.026 932 b3 0.006 704 2.183 002 0.031 181 b4 0.004 997 2.310 217 0.022 759 b5 0.002 965 2.199 555 0.029 950 c 1.090 761 12.525 250 0.000 000 注：参数b的下标表示分级等级，下标越小表示生长越快，碳储量也越大。Notes: the subscript of parameter b indicates the grading grade, and the smaller of the subscript is, the faster the growth is and the greater the carbon reserves are.
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表 5 不同林分年龄不同分级的次生林碳密度估计值 t/hm2
Table 5 Estimated carbon storage density of the natural secondary forests in different stand ages and classifications
t/ha 林分年龄/a
Stand age/year分级 Classification 1 2 3 4 5 5 9.64 7.11 5.52 4.02 2.29 10 19.92 14.80 11.54 8.45 4.84 15 30.08 22.51 17.64 12.98 7.47 20 39.96 30.12 23.71 17.52 10.14 25 49.49 37.57 29.71 22.05 12.83 30 58.63 44.83 35.60 26.55 15.52
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表 6 样地平均木碳储量不同交互项选择模式的拟合结果和统计量
Table 6 Fitting and statistics results of the sample plot average tree carbon storage model on different interactive item selection patterns
指标
Index交互项选择模式 Interactive item selection mode M-All DDI DDIA D12D D12DA 样本数 Number of sample 111 111 111 111 111 参数个数 Number of parameter 53 59 60 66 59 筛选次数 Screening time 0 16 12 16 13 最终因子数 Final factor number 24 13 14 14 15 主效应因子数 Number of main effect factor 24 11 14 11 13 交互项个数 Number of interaction item 0 3 2 3 2 决定系数 Coefficient of determination (R2) 0.833 4 0.899 8 0.918 0 0.917 3 0.919 2 修正决定系数
Adjusted coefficient of determination (R2 adj)0.684 1 0.787 9 0.823 1 0.797 7 0.829 2 均方根误差
Root mean square error (RMSE)/kg7.696 7 6.306 3 5.759 1 6.158 9 5.660 4 注：M-All表示所有因子的主效应；DDI表示显著因子一阶定性一阶定量交互；DDIA表示所有因子一阶定性一阶定量交互；D12D表示显著因子一阶定性一、二阶定量交互；D12DA表示所有因子一阶定性一、二阶定量交互。Notes: M-All represents the main effect of all factors; DDI represents the first-order qualitative and first-order quantitative interaction of significant factors; DDIA represents the first-order qualitative and first-order quantitative interaction of all factors; D12D represents the first-order qualitative first-order and second-order quantitative interaction of significant factors; D12DA represents the first-order qualitative first-order and second-order quantitative interaction of all factors.
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表 7 含交互项的样地平均木碳储量方差分析
Table 7 Variance analysis of the sample plot average tree carbon storage with interactive terms
因子 Factor 显著性 Sig. 年龄 Age < 0.001 优势树种 Dominant tree species 0.004 纬度 Latitude < 0.001 经度 Longitude 0.025 地貌 Landform 0.081 坡向 Slope aspect < 0.001 坡位 Slope position 0.003 坡度 Slope degree 0.007 枯枝落叶厚度 Litter layer thickness 0.064 年平均气温 Annual average temperature 0.002 极端最低温 Extreme minimum temperature 0.105 湿度指数 Humidity index < 0.001 无霜期天数 Frost-free days 0.001 海拔 × 坡向 × 土壤厚度
Altitude × slope aspect × soil thickness< 0.001 海拔 × 枯枝落叶厚 × 优势树种
Altitude × litter layer thickness × dominant tree species0.023
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表 8 不同立地分级20年时碳密度的含交互项的方差分析
Table 8 Variance analysis of carbon storage density with interactive terms in different site grades for 20 years
因子 Factor 显著性 Sig. 优势树种 Dominant tree species < 0.001 纬度 Latitude 0.026 地貌 Landform < 0.001 坡度 Slope degree < 0.001 坡向 Slope aspect < 0.001 湿度指数 Humidity index < 0.001 最热月平均温度
Mean temperature in the hottest month< 0.001 极端最高温度
Extreme maximum temperature< 0.001 极端最低温
Extreme minimum temperature0.124 土壤类型 Soil type 0.012 砾石含量 Gravel content 0.004 株数密度 × 砾石含量
Tree density × gravel content< 0.001 坡向 × 最冷月平均温度 × 最热月平均温度
Slope aspect × mean temperature in the coldest
month × mean temperature in the hottest month< 0.001 腐殖质厚度 × 海拔 × 坡向
Humus layer thickness × altitude × slope aspect0.008
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