基于机载激光雷达的崇礼冬奥核心区林分地上生物量反演

doi:10.11707/j.1001-7488.20221004

摘要/Abstract

摘要：

目的: 基于机载激光雷达数据建立结构稳定的林分地上生物量预测模型, 考虑最小二乘、混合效应和贝叶斯等参数估计方法对最优生物量预测模型选择进行探讨, 为生物量建模方法研究、生物量估测提供科学依据, 为冬奥核心区实现"双碳"目标和生物量模型计算提供技术支撑。方法: 基于崇礼冬奥核心区2种森林类型(华北落叶松和白桦)62块实测样地及对应的激光雷达数据, 通过变量筛选分别建立最小二乘、混合效应和贝叶斯生物量模型, 应用确定系数(R²)、均方根误差(RMSE)、残差、总体相对误差(TRE)评价模型, 采用留一交叉法验证模型精度。结果: 筛选出相关性较高的激光雷达变量共20个, 最终进入模型的自变量3个。拟合效果最好的是Logistic混合效应模型(RMSE=22.99 t·hm^-2, R²=0.768, TRE=6.08%), 分树种建立模型后华北落叶松模型拟合效果提升(RMSE=22.92 t·hm^-2, R²=0.795, TRE=7.45%), 白桦模型预测精度提高(RMSE=23.34 t·hm^-2, R²=0.440, TRE=4.35%)。利用训练好的模型预测崇礼冬奥核心区生物量并制图。结论: 基于机载激光雷达和地面实测数据估测林分地上生物量, 非线性模型优于线性模型; 以龄组为随机效应的非线性混合效应模型预测精度最高; 贝叶斯估计受先验条件影响较大, 本研究样本量偏少, 贝叶斯估计具有进一步探讨的价值。

关键词: 机载激光雷达, 林分地上生物量, 混合效应模型, 贝叶斯模型

Abstract:

Object: This study was implemented to develop the stand aboveground biomass model with stable structure based on light detection and ranging(LiDAR) data, considering the ordinary least squares, mixed effects and Bayesian parameter estimation method, and then discussed the selection of the optimal biomass prediction model with the aims to provide a scientific basis for biomass modeling method and biomass estimation and to provide a technical support for achieving the "double carbon" target and biomass model calculation in the core area of the Winter Olympics. Method: Based on the LiDAR data and field measurement of 62 sample plots distributed across the Larix principis-rupprechtii and Betula platyphylla forest stands in the core areas of the Winter Olympics, ordinary least squares (OLS), mixed effects and Bayesian biomass models were established by variable screening.Determination coefficient (R²), root mean square error(RMSE), residual error and total relative error(TRE) were used to evaluate the model, and reserve-one crossover method was used to verify the accuracies of the models. Result: A total of 20 LiDAR variables with high correlations were filtered out, and 3 independent variables were finally entered into the models. The best fitting was the Logistic mixed effect model(RMSE = 22.99 t·hm^-2, R² = 0.768, TRE = 6.08%). After establishing the model by tree species, the accuracy of larch model was improved(RMSE = 22.92 t·hm^-2, R² = 0.795, TRE = 7.45%), and the accuracy of birch model decreased(RMSE = 23.34 t·hm^-2, R² = 0.440, TRE = 4.35%). Using the trained model, the biomass of Chongli Winter Olympic core area was predicted and mapped. Conclusion: As for the estimation of the stand aboveground biomass based on the LiDAR and field measurement data, the nonlinear model was superior to the linear model. The nonlinear mixed effect model with age group as random effects might have the highest prediction accuracy of biomass. Bayesian estimation may be greatly affected by prior conditions and might have further discussion values although with a small sample size in this study.

Key words: arborne LiDAR, forest aboveground biomass, mixed effect model, Bayesian model

中图分类号:

陈星京,冯林艳,张宇超,刘清旺,杨朝晖,符利勇,白晋华. 基于机载激光雷达的崇礼冬奥核心区林分地上生物量反演[J]. 林业科学, 2022, 58(10): 35-46.

Xingjing Chen,Linyan Feng,Yuchao Zhang,Qingwang Liu,Zhaohui Yang,Liyong Fu,Jinhua Bai. Inversion of Aboveground Biomass in the Core Area of Chongli Winter Olympics Based on Airborne LiDAR[J]. Scientia Silvae Sinicae, 2022, 58(10): 35-46.

图/表 13

表1

图1

表附表

机载激光雷达变量"

变量 Variable	名称 Name	原理 Principle
x₁	高度平均绝对偏差 Average absolute deviation of height	$v=\frac{\sum_\limits{i=1}^n\left(\left\|z_i-\bar{z}\right\|\right)}{n}$，其中，z_i为每一统计单元内第i个点的高度值，${\bar z}$为每一统计单元内所有点的平均高度，n为每一统计单元内的总点数 $v=\frac{\sum_\limits{i=1}^n\left(\left\|z_i-\bar{z}\right\|\right)}{n}$, where z_i is the height of the i point in each statistical unit, ${\bar z}$ is the average height of all points in each statistical unit, n is the total number of points in each statistical unit
x₂	冠层高度起伏率 Canopy height fluctuation rate	$v=\frac{\operatorname{mean}-\min }{\max -\min }$，其中，mean为每一统计单元内所有点的平均高度，min为每一统计单元内所有点的最小高度值，max为每一统计单元内所有点的最大高度值 $v=\frac{\operatorname{mean}-\min }{\max -\min }$，where, mean is the average height of all points in each statistical unit, min is the minimum height of all points in each statistical unit, and max is the maximum height of all points in each statistical unit
x₃-x₁₇	累计高度百分位数(AIH) Cumulative height percentile(AIH)	某一统计单元内，将其内部所有归一化的激光雷达点云按高度进行排序并计算所有点的累积高度，每一统计单元内x%的点所在的累积高度，即为该统计单元的累积高度百分位数。 In a statistical unit, all normalized LiDAR point clouds within it are sorted by height and the cumulative height of all points is calculated. The cumulative height of x% points in each statistical unit is the percentile of the cumulative height of the statistical unit.
x₁₈	累积高度百分位数四分位数间距 Cumulative height percentile quartile spacing	V=AIH75%-AIH25%
x₁₉	高度三次幂平均值 Average height of cubic power	$V=\sqrt[3]{\frac{\sum_\limits{i=1}^n Z_i^3}{n}}$, 其中，z_i为每一统计单元内第i个点的高度值，n为每一统计单元内的总点数 $V=\sqrt[3]{\frac{\sum_\limits{i=1}^n Z_i^3}{n}}$, where z_i is the height of point i in each statistical unit and n is the total number of points in each statistical unit
x₂₀	变异系数 Coefficient of variation	$V=\frac{Z_{\text {std }}}{Z_{\text {mean }}} \times 100 \%$, 其中，Z_std为每一统计单元内所有点高度值的标准差，Z_mean为每一统计单元内所有点的平均高度 $V=\frac{Z_{\text {std }}}{Z_{\text {mean }}} \times 100 \%$, where Z_std is the standard deviation of the height of all points in each statistical unit, and Z_mean is the average height of all points in each statistical unit
x₂₁	高度百分位数四分位数间距 Height percentile quartile spacing	V=Elcv75%-Elcv25%
x₂₂	高度峰度 Height kurtosis	$\text { Kurtosis }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(z_i-\bar{z}\right)^4}{\sigma^4}$, 其中，z_i为每一统计单元内第i个点的高度值，${\bar z}$为每一统计单元内所有点的平均高度，n为每一统计单元内的总点数，σ为统计单元内点云高度分布的标准差 $\text { Kurtosis }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(z_i-\bar{z}\right)^4}{\sigma^4}$，where z_iis the height of the first point in each statistical unit, ${\bar z}$ is the average height of all points in each statistical unit, n is the total number of points in each statistical unit, σ is the standard deviation of the height distribution of point clouds in each statistical unit
x₂₃	高度中位数绝对偏差的中位数 Median of absolute deviation of height median	高度中位数绝对偏差的中位数 The median of absolute deviation of height median
x₂₄	高度最大值 Maximum height	某一统计单元内，所有点的Z值的最大值 In a statistical unit, the maximum Z value of all points
x₂₅	高度最小值 Minimum height	某一统计单元内，所有点的Z值的最小值 Minimum Z value for all points in a statistical unit
x₂₆	高度平均值 Average height	某一统计单元内，所有点的Z值的平均值 In a statistical unit, the average Z value of all points
x₂₇	高度中位数 Height median	某一统计单元内，所有点的Z值的中位数 In a statistical unit, the median of Z value of all points
x₂₈-x₄₂	高度百分位数(Elcv) Height percentile (Elcv)	某一统计单元内，将其内部所有归一化的激光雷达点云按高度进行排序，然后计算每一统计单元内x%的点所在的高度，即为该统计单元的高度百分位数 In a statistical unit, all normalized LiDAR point clouds inside it are sorted by height, and then the height of x% points in each statistical unit is calculated, which is the height percentile of the statistical unit
x₄₃	高度偏斜度(偏态) Height skewness (skewness)	某一统计单元内，所有点的Z值分布的对称性, $\text { Skewness }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(z_i-\bar{z}\right)^3}{\sigma^3}$, 其中，z_i为每一统计单元内第i个点的高度值，n为每一统计单元内的总点数 The symmetry of Z-value distribution of all points in a statistical unit, $\text { Skewness }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(z_i-\bar{z}\right)^3}{\sigma^3}$, where z_i is the height of point i in each statistical unit and n is the total number of points in each statistical unit
x₄₄	高度二次幂平均值 Average value of height quadratic power	$V=\sqrt[2]{\frac{\sum_\limits{i=1}^n Z_i{ }^2}{n}}$, 其中，z_i为每一统计单元内第i个点的高度值，${\bar z}$为每一统计单元内所有点的平均高度, n为每一统计单元内的总点数 $V=\sqrt[2]{\frac{\sum_\limits{i=1}^n Z_i{ }^2}{n}}$, where z_i is the height of the i point in each statistical unit, ${\bar z}$ is the average height of all points in each statistical unit, n is the total number of points in each statistical unit
x₄₅	高度标准差 Height standard deviation	某一统计单元内，所有点的Z值的标准差 The standard deviation of Z value of all points in a statistical unit
x₄₆	高度方差 Height variance	某一统计单元内，所有点的Z值的方差 In a statistical unit, the variance of Z value of all points
x₄₇-x₅₆	密度变量 Density variable	将点云数据从低到高分成十个相同高度的切片，每层回波数的比例就是相应的密度变量 The point cloud data is divided into ten slices of the same height from low to high, and the ratio of echo number per layer is the corresponding density variable
x₅₇	强度平均绝对偏差 Average absolute deviation of intension	$v=\frac{\sum_\limits{i=1}^n\left(\left\|I_i-\bar{I}\right\|\right)}{n}$，其中，I_i为每一统计单元内第i个点的高度值，${\bar I}$为每一统计单元内所有点的平均高度，n为每一统计单元内的总点数 $v=\frac{\sum_\limits{i=1}^n\left(\left\|I_i-\bar{I}\right\|\right)}{n}$，where I_iis the height of the i point in each statistical unit, ${\bar I}$ is the average height of all points in each statistical unit, and n is the total number of points in each statistical unit
x₅₈	强度变异系数 Tension variance	$V=\frac{I_{\mathrm{std}}}{I_{\text {mean }}} \times 100 \%$, 其中，I_std为每一统计单元内所有点高度值的标准差，I_mean为每一统计单元内所有点的平均高度 $V=\frac{I_{\mathrm{std}}}{I_{\text {mean }}} \times 100 \%$, where I_std is the standard deviation of the height of all points in each statistical unit, and I_mean is the average height of all points in each statistical unit
x₅₉-x₇₃	累计强度百分位数 Cumulative intension percentiles	某一统计单元内，将其内部所有归一化的激光雷达点云按强度进行排序并计算所有点的累积强度，每一统计单元内x%的点的累积强度，即为该统计单元的累积强度百分位数 All normalized LiDAR point clouds within a statistical unit are sorted by intension and the cumulative intension of all points is calculated. The cumulative intension of x% points in each statistical unit is the percentile of the cumulative intension of the statistical unit
x₇₄	强度峰度 Peak intension	$\text { Kurtosis }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(I_i-\bar{I}\right)^4}{\sigma^4}$, 其中，I_i为每一统计单元内第i个点的高度值，${\bar I}$为每一统计单元内所有点的平均高度，n为每一统计单元内的总点数，σ为统计单元内点云高度分布的标准差 $\text { Kurtosis }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(I_i-\bar{I}\right)^4}{\sigma^4}$，where I_i is the height of the i point in each statistical unit, ${\bar I}$ is the average height of all points in each statistical unit, n is the total number of points in each statistical unit, σ is the standard deviation of the height distribution of point clouds in each statistical unit
x₇₅	强度中位数绝对偏差的中位数 Median of absolute deviation of median intension	强度中位数绝对偏差的中位数 Median of absolute deviation of median intension
x₇₆	强度最大值 Intension maximums	某一统计单元内，所有点的强度值的最大值 In a statistical unit, the maximum intension value of all points
x₇₇	强度平均值 Average intension	某一统计单元内，所有点的强度值的平均值 Average intension of all points in a statistical unit
x₇₈	强度中位数 Intension median	某一统计单元内，所有点的强度值的中位数 Median intensit of all points in a statistical unit
x₇₉	强度最小值 Minimum intension	某一统计单元内，所有点的强度值的最小值 Minimum intension of all points in a statistical unit
x₈₀	强度偏斜度 Intension skewness	某一统计单元内，所有点的强度值分布的对称性, $\text { Skewness }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(I_i-\bar{I}\right)^3}{\sigma^3}$, 其中，I_i为每一统计单元内第i个点的高度值，${\bar I}$为每一统计单元内所有点的平均强度n为每一统计单元内的总点数 Symmetry of intension distribution of all points in a statistical unit, $\text { Skewness }=\frac{\frac{1}{n} \sum_\limits{i=1}^n\left(I_i-\bar{I}\right)^3}{\sigma^3}$, where I_i is the height of the i point in each statistical unit, and ${\bar I}$ is the average intension n of all points in each statistical unit
x₈₁	强度方差 Variance of intension	某一统计单元内，所有点的强度值的方差 Variance of intension values of all points in a statistical unit
x₈₂	强度标准差 Standard deviation of intension	某一统计单元内，所有点的强度值的标准差 Standard deviation of intension values of all points in a statistical unit
x₈₃-x₉₇	强度百分位数 Intension percentiles	某一统计单元内，将其内部所有归一化的激光雷达点云按强度进行排序，然后计算每一统计单元内x%的点的强度，即为该统计单元的强度百分位数 In a statistical unit, all normalized laser radar point clouds inside it are sorted by intension, and then the intension of x% points in each statistical unit is calculated as the intension percentile of the statistical unit
x₉₈	强度百分位数四分位数间距 Intension percentile quartile spacing	V=Int75%-Int25%

表附表

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树种 Species	异速生长方程 Allometric growth equation	来源 Source
华北落叶松 Larix principis-rupprechtii	AGB=0.027 7×DBH^{2.793 26}	国家林业局，2017a; 2017b State Forestry Administration，2017a; 2017b
白桦 Betula platyphylla	AGB=0.1905×DBH^{2.243 22}

树种 Species	样地数 Number of plots	平均胸径DBH/cm		平均树高Mean tree height/m		生物量Biomass/(t·hm^-2)
树种 Species	样地数 Number of plots	最小值Min.	最大值Max.	最小值Min.	最大值Max.	最小值Min.	最大值Max.
华北落叶松Larix principis-rupprechtii	40	2	41.4	7.2	16.8	4.91	197.62
白桦Betula platyphylla	22	2.3	41.2	6.4	14.3	26.32	165.15

序号 No.	模型 Model	模型来源 Model source
Ⅰ	AGB=b₀+b₁X₁+b₂X₂+b₃X₃+…+b_nX_n+ε_AGB	Linear
Ⅱ	AGB=b₀/[1+b₁exp(-b₂X₁-b₃X₂-b₄X₃-…-b_n+1X_n)]+ε_AGB	Logistic
Ⅲ	AGB=b₀exp(-b₁X₁-b₂X₂-b₃X₃-…-b_nX_n)+ε_AGB	Exponential
Ⅳ	AGB=b₀X₁^b₁X₂^b₂X₃^b₃…X_n^b_n+ε_AGB	Empirical

变量 Variable	相关系数 Correlation coefficient	变量 Variable	相关系数 Correlation coefficient	变量 Variable	相关系数 Correlation coefficient	变量 Variable	相关系数 Correlation coefficient
x₁₂	0.889 52	x₁₆	0.883 15	x₂₆	0.877 50	x₅₀	-0.696 09
x₁₃	0.888 53	x₁₉	0.882 68	x₁₇	0.875 29	x₄₇	-0.706 26
x₁₄	0.887 56	x₄₄	0.880 84	x₄₂	0.873 65	x₄₉	-0.761 40
x₁₅	0.886 27	x₁₀	0.879 22	x₉	0.871 94	x₄₈	-0.800 81
x₁₁	0.885 50	x₂₇	0.879 18	x₂₄	0.871 90	x₄₃	-0.819 34

模型 Model	参数 Parameter	解释变量 Explainable variable	参数估计值 Parameter estimate	P
Ⅰ	b₁	x₄₆	8.82	1.84E-07
	b₂	x₄₇	-298.89	1.84E-07
	b₃	x₅₆	300.42	0.040 4
Ⅱ	b₀		152.27	8.30E-11
	b₁		3.35	0.005 948
	b₂	x₄₆	0.32	0.000 253
	b₃	x₄₇	-11.87	0.000 472
	b₄	x₅₆	10.70	0.112 488
Ⅲ	b₀		14.80	0.06
	b₁	x₄₆	0.71	1.07E-06
	b₂	x₄₇	-0.23	1.72E-05
	b₃	x₅₆	0.05	0.456 8
Ⅳ	b₀		59.98	6.51E-11
	b₁	x₄₆	-0.11	3.31E-07
	b₂	x₄₇	6.52	2.93E-06
	b₃	x₅₆	-1.13	0.467 0