Predicting crown width for Larix gmelinii based on linear quantiles groups

doi:10.12302/j.issn.1000-2006.202003088

JOURNAL OF NANJING FORESTRY UNIVERSITY ›› 2021, Vol. 45 ›› Issue (5): 161-170.doi: 10.12302/j.issn.1000-2006.202003088

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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 E-mail:631789354@qq.com;jlichun@nefu.edu.cn

Abstract

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

CLC Number:

S757

WANG Junjie, JIANG Lichun. Predicting crown width for Larix gmelinii based on linear quantiles groups[J]. JOURNAL OF NANJING FORESTRY UNIVERSITY, 2021, 45(5): 161-170.

Figures/Tables 8

Table 1

Table 2

Candidate basic crown width models"

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

Table 2

Table 3

Fitting statistics with candidate basic crown width models"

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

Table 3

Table 4

Fig.1

Fig.2

Table 5

K-fold cross validation statistics of linear regression, median quantile regression and three quantiles groups"

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

Table 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

Predicting crown width for Larix gmelinii based on linear quantiles groups

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