基于线性分位数组合的兴安落叶松冠幅预测

doi:10.12302/j.issn.1000-2006.202003088

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南京林业大学学报（自然科学版） ›› 2021, Vol. 45 ›› Issue (5): 161-170.doi: 10.12302/j.issn.1000-2006.202003088

基于线性分位数组合的兴安落叶松冠幅预测

王君杰(), 姜立春*^*()

东北林业大学林学院,森林生态系统可持续经营教育部重点实验室, 黑龙江哈尔滨 150040

收稿日期:2020-03-31 接受日期:2020-06-18 出版日期:2021-09-30 发布日期:2021-09-30
通讯作者: 姜立春*
基金资助:
国家自然科学基金项目(31570624);黑龙江省应用技术研究与开发计划项目(GA19C006);中央高校基本科研业务费专项资金资助项目(2572019CP15)

Predicting crown width for Larix gmelinii based on linear quantiles groups

WANG Junjie(), JIANG Lichun^*()

Key Laboratory of Sustainable Forest Ecosystem Management-Ministry of Education, School of Forestry, Northeast Forestry University, Harbin 150040, China

Received:2020-03-31 Accepted:2020-06-18 Online:2021-09-30 Published:2021-09-30
Contact: JIANG Lichun

摘要/Abstract

摘要：

【目的】 使用线性分位数回归和分位数组合对兴安落叶松(Larix gmelinii)冠幅进行建模和预测,为准确模拟和预测冠幅生长提供技术支持。【方法】 利用大兴安岭兴安落叶松天然林实测数据,采用线性回归和分位数回归构建基础和多元冠幅模型。比较7种分位数组合:三分位数组合(τ=0.1, 0.5, 0.9和τ=0.3, 0.5, 0.7)、五分位数组合(τ=0.1,0.3,0.5,0.7,0.9和τ=0.3,0.4,0.5,0.6,0.7)、七分位数组合(τ=0.1,0.2,0.3,0.5,0.7,0.8,0.9和τ=0.1,0.3,0.4,0.5,0.6,0.7,0.9)和九分位数组合(τ=0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9)的预测效果。分析4种抽取方案(随机抽样、选择最大树、平均木、最小树)和9种抽样数量(1~9株)对预测精度的影响。同时使用K折交叉验证对线性回归、最优分位数回归和最优分位数组合进行比较。【结果】 线性和分位数回归都能对冠幅模型进行拟合,中位数回归的拟合结果与线性回归相似,且在所有分位数中拟合能力最好。多元冠幅模型和分位数回归的拟合及检验效果都优于基础模型,冠幅与胸径和样地平均高(立地质量)呈正相关,与枝下高(树木大小)和样地内落叶松断面积(竞争)呈负相关。使用分位数组合可以提高模型的预测能力,7种分位数组合的差异很小,三分位数组合(τ=0.3, 0.5, 0.7)的预测能力最好。对于基础和多元分位数组合在实际应用时,最优抽取方案都为选取最大树,每个样地建议选取6株样木。【结论】 基于线性分位数组合的冠幅模型可以提高预测精度,建议使用三分位数组合和选取最大树及抽取数量为6株的方案对冠幅进行预测。

关键词: 冠幅预测, 分位数回归, 线性分位数组合, 抽取方案, 兴安落叶松

Abstract:

【Objective】 Linear quantile regression and quantile groups were used in this study to model and predict crown width, which provides a valuable method for accurately simulating and predicting crown growth. 【Method】 Data in this study were collected from the natural forests of Larix gmelinii of Greater Khingan Mountains. Linear regression and quantile regression were used to build the basic and multivariate models of crown width. Prediction effects of seven quantiles groups were compared, namely three quantiles groups (τ=0.1, 0.5, 0.9 and τ=0.3, 0.5, 0.7), five quantiles groups (τ=0.1, 0.3, 0.5, 0.7, 0.9 and τ=0.3, 0.4, 0.5, 0.6, 0.7), seven quantiles groups (τ=0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9 and τ=0.1, 0.3, 0.4, 0.5, 0.6, 0.7, 0.9), and nine quantiles groups (τ=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9). Effects of four sampling methods (random sampling, largest DBH tree selection, mean DBH tree selection and smallest DBH tree selection) and nine sampling sizes (1-9 trees per plot) on prediction accuracy were analyzed. K-fold cross validation was used to compare the prediction effects of linear regression, optimal quantile regression and optimal quantile groups. 【Result】 Linear regression and quantile regression fit the crown width models. The fitting results of the median regressions were similar to those of the linear regressions and were the best of all quantiles. The fitting and validation results of the multivariate model and quantile regressions were better than those of the basic model. Crown width was positively correlated with DBH and average tree height (site quality) and negatively correlated with height under banch (tree size) and basal area of larch (competition). Quantile groups could improve the predictive ability of the model. The seven quantile groups showed little difference. The three quantile groups (τ=0.3, 0.5, 0.7) had the best prediction ability. For the practical application of the basic and multivariate quantile groups, the optimal sampling design was to select the largest trees. A recommendation was to select six sample trees for each plot.【Conclusion】 Crown width models based on linear quantile groups can improve the prediction accuracy. A recommendation is to use three quartile groups and a sampling design of the six largest trees to predict crown width.

Key words: crown width prediction, quantile regression, linear quantile groups, sample method, Larix gmelinii

中图分类号:

S757

王君杰,姜立春*. 基于线性分位数组合的兴安落叶松冠幅预测[J]. 南京林业大学学报（自然科学版）, 2021, 45(5): 161-170.

WANG Junjie, JIANG Lichun. Predicting crown width for Larix gmelinii based on linear quantiles groups[J].Journal of Nanjing Forestry University (Natural Science Edition), 2021, 45(5): 161-170.DOI: 10.12302/j.issn.1000-2006.202003088.

图/表 8

表1

表2

候选冠幅基础模型"

模型编号 model designation	模型 model	模型形式 model form
M1	$W C = β 0 + β 1 D BH$	线性 Linear
M2	$W C = β 0 / [1 + β 1 exp (- β 2 D BH)]$	逻辑斯蒂Logistic
M3	$W C = β 0 / [1 + exp (β 1 + β 2 log (D BH + 1))]$	逻辑斯蒂Logistic
M4	$W C = β 0 D BH β 1$	幂函数 Power
M5	$W C = β 0 [1 - exp (- β 1 D BH)] β 2$	理查德Richards
M6	$W C = β 0 [1 - exp (- β 1 D BH β 2)]$	威布尔Weibull

表2

表3

候选冠幅基础模型拟合统计量"

模型编号 model number	$σ ME$	$σ RMSE$	R²
M1	0.000 0	0.595 6	0.384 4
M2	-0.000 3	0.596 2	0.383 3
M3	0.000 8	0.596 4	0.382 8
M4	0.000 7	0.596 7	0.382 1
M5	0.001 2	0.596 8	0.382 0
M6	0.001 8	0.596 8	0.381 9

表3

表4

图1

图2

表5

线性回归、中位数回归和三分位数组合的K折交叉验证统计量"

模型 model	参数估计方法 parameter estimate method	$σ MPE$				$σ MAPE$	$σ RMSE$	R²
基础模型 basic model	线性回归linear regression	-7.821 7				20.834 9	0.569 6	0.369 1
	中位数回归median regression	-7.870 8				20.836 7	0.569 5	0.369 5
	分位数组合 τ=0.1,0.5,0.9 quantiles group τ=0.3,0.5,0.7	-4.956 2				16.895 4	0.476 9	0.558 8
	分位数组合 τ=0.1,0.5,0.9 quantiles group τ=0.3,0.5,0.7	-4.550 5				16.872 1	0.477 2	0.558 4
多元模型 multivariate model	线性回归linear regression	-7.541 7	19.450 3	0.536 2	0.443 7
	中位数回归median regression	-7.162 6	19.281 9	0.534 7	0.447 0
	分位数组合 τ=0.1,0.5,0.9 quantiles group τ=0.3,0.5,0.7	-1.688 9	16.311 1	0.472 6	0.567 3
	分位数组合 τ=0.1,0.5,0.9 quantiles group τ=0.3,0.5,0.7	-1.517 0	16.164 3	0.470 5	0.571 4

表5

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统计量 statistics	D_BH/ cm	W_C/ m	H_T/ m	H_CB/ m	R_C	R_HD	H_mean/ m	H_DOM/ m	D_DOM/ cm	A_B/ (m²·hm^-2)	N/ (株·hm^-2)	S_R	B_AL/ m²	G_larch/ m²
平均值 mean	10.8	2.5	10.8	5.3	0.5	1.0	10.8	15.7	19.5	18.7	1 837	0.9	0.4	0.6
标准差 SD	4.2	0.8	3.2	2.3	0.1	0.2	1.7	2.2	2.6	8.0	834	0.2	0.3	0.2
最小值 min	5.0	0.4	3.4	0.6	0.1	0.4	7.0	11.1	14.0	4.5	528	0.5	0.0	0.2
最大值 max	32.5	6.4	23.3	14.4	0.9	2.0	14.0	20.2	27.1	37.5	4 400	1.4	1.4	1.4

模型 model	参数估计方法 parameter estimate method	β₀	β₁	σ(MAE)	σ(RMSE)
基础模型 basic model	线性回归 linear regression	1.287 0 (0.028 0)	0.112 4 (0.002 4)	0.464 1	0.595 6
	分位数回归 quantile regression
	τ=0.1	0.911 4 (0.040 0)	0.079 6 (0.003 5)	0.791 8	0.951 8
	τ=0.2	0.940 0 (0.049 4)	0.100 0 (0.004 3)	0.616 1	0.766 9
	τ=0.3	1.068 4 (0.032 6)	0.105 3 (0.002 8)	0.522 9	0.665 4
	τ=0.4	1.169 8 (0.036 3)	0.109 9 (0.003 4)	0.478 7	0.612 8
	τ=0.5	1.255 9 (0.033 5)	0.115 6 (0.002 9)	0.464 0	0.595 8
	τ=0.6	1.357 1 (0.033 2)	0.119 1 (0.002 9)	0.477 8	0.613 1
	τ=0.7	1.426 5 (0.035 2)	0.126 5 (0.003 0)	0.523 0	0.666 1
	τ=0.8	1.555 6 (0.040 0)	0.131 9 (0.003 5)	0.617 2	0.769 3
	τ=0.9	1.779 7 (0.053 1)	0.135 1 (0.004 6)	0.799 5	0.953 6

模型 model	参数估计方法 parameter estimate method	β₀	β₁	β₂	β₃	β₄	σ(MAE)	σ(RMSE)
多元模型 multivariate model	线性回归 linear regression	1.043 3 (0.068 4)	0.139 5 (0.002 7)	-0.099 8 (0.052 6)	0.082 2 (0.008 3)	-0.699 5 (0.005 6)	0.432 2	0.558 3
	分位数回归 quantile regression
	τ=0.1	0.647 3 (0.099 7)	0.112 4 (0.003 9)	-0.067 7 (0.076 7)	0.074 8 (0.012 0)	-0.878 9 (0.008 1)	0.755 7	0.902 3
	τ=0.2	0.606 8 (0.089 4)	0.127 1 (0.003 5)	-0.092 3 (0.068 7)	0.098 5 (0.010 8)	-0.847 8 (0.007 3)	0.571 8	0.712 9
	τ=0.3	0.772 7 (0.081 7)	0.133 1 (0.003 2)	-0.094 2 (0.062 8)	0.088 9 (0.009 9)	-0.767 0 (0.006 6)	0.489 7	0.623 3
	τ=0.4	0.880 7 (0.084 8)	0.139 5 (0.003 3)	-0.101 0 (0.065 2)	0.085 2 (0.010 2)	-0.684 4 (0.010 2)	0.444 5	0.572 4
	τ=0.5	0.892 1 (0.068 6)	0.145 0 (0.002 7)	-0.106 8 (0.052 8)	0.093 0 (0.008 3)	-0.684 5 (0.005 6)	0.431 6	0.558 9
	τ=0.6	0.971 4 (0.076 9)	0.148 7 (0.003 0)	-0.106 6 (0.059 1)	0.097 0 (0.009 3)	-0.735 7 (0.006 3)	0.445 2	0.574 9
	τ=0.7	1.055 7 (0.081 9)	0.153 3 (0.003 2)	-0.110 0 (0.063 0)	0.094 0 (0.009 9)	-0.631 5 (0.006 7)	0.488 5	0.625 4
	τ=0.8	1.111 7 (0.100 3)	0.153 0 (0.003 9)	-0.107 3 (0.077 2)	0.105 2 (0.012 1)	-0.666 3 (0.008 2)	0.573 4	0.716 0
	τ=0.9	1.532 5 (0.099 3)	0.155 1 (0.003 9)	-0.112 2 (0.076 4)	0.083 1 (0.012 0)	-0.577 6 (0.008 1)	0.735 0	0.876 8

基于线性分位数组合的兴安落叶松冠幅预测

Predicting crown width for Larix gmelinii based on linear quantiles groups

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[1]	韩新宇, 高露双, 秦莉, 庞荣荣, 刘鸣谦, 朱一泓, 田益雨, 张金. 林分密度对兴安落叶松径向生长-气候关系的影响[J]. 南京林业大学学报（自然科学版）, 2024, 48(2): 182-190.
[2]	左壮, 张韫, 崔晓阳. 火烧对兴安落叶松林土壤氮形态和含量的初期影响[J]. 南京林业大学学报（自然科学版）, 2024, 48(1): 147-154.
[3]	路文燕, 董灵波, 田园, 汪莎杉, 曲宣怡, 魏巍, 刘兆刚. 基于树种组成的大兴安岭天然林主要树种树高-胸径曲线研究[J]. 南京林业大学学报（自然科学版）, 2023, 47(4): 157-165.
[4]	高羽, 李静, 刘洋, 乌雅瀚, 巩家星, 辛启睿. 结构方程模型在兴安落叶松林生长中的应用[J]. 南京林业大学学报（自然科学版）, 2023, 47(1): 38-46.
[5]	谢立红, 黄庆阳, 曹宏杰, 杨帆, 王继丰, 倪红伟. 气候变暖对黑龙江省五大连池兴安落叶松径向生长的影响[J]. 南京林业大学学报（自然科学版）, 2022, 46(2): 150-158.
[6]	王冰, 张鹏杰, 张秋良. 不同林型兴安落叶松林土壤团聚体及其有机碳特征[J]. 南京林业大学学报（自然科学版）, 2021, 45(3): 15-24.
[7]	何培, 夏宛琦, 姜立春. 基于非参数方法的落叶松树干削度方程[J]. 南京林业大学学报（自然科学版）, 2020, 44(6): 184-192.
[8]	周司涵, 张韫, 崔晓阳. 兴安落叶松林火烧迹地土壤速效钾时空动态分析[J]. 南京林业大学学报（自然科学版）, 2020, 44(5): 141-147.
[9]	魏玉龙, 张秋良. 兴安落叶松林缘天然更新与立地环境因子的相关分析[J]. 南京林业大学学报（自然科学版）, 2020, 44(2): 165-172.
[10]	宋浩,满秀玲,段北星,刘家霖. 兴安落叶松天然林新老枝叶光合能力及水分利用效率研究[J]. 南京林业大学学报（自然科学版）, 2018, 42(05): 53-58.
[11]	石磊,盛后财,满秀玲,蔡体久. 兴安落叶松林降雨再分配及其穿透雨的空间异质性[J]. 南京林业大学学报（自然科学版）, 2017, 41(02): 90-96.
[12]	刘玉杰,满秀玲. 修正Gash模型在兴安落叶松天然林林冠截留中的应用[J]. 南京林业大学学报（自然科学版）, 2016, 40(04): 81-88.
[13]	郭莹洁,赵荣军,钟永,任海青. 兴安落叶松成熟材单一年轮顺纹力学模型[J]. 南京林业大学学报（自然科学版）, 2015, 39(01): 177-180.
[14]	郭莹洁,赵荣军,钟永,任海青. 兴安落叶松成熟材指接材抗拉破坏载荷力学模型[J]. 南京林业大学学报（自然科学版）, 2014, 38(05): 20-24.
[15]	马利强,玉宝,王立明,张秋良. 兴安落叶松天然林单木高生长模型[J]. 南京林业大学学报（自然科学版）, 2013, 37(02): 169-172.