Remote sensing estimation of aboveground biomass of spruce-fir forests in Diqing based on mixed effect models
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摘要:
目的 确定云冷杉林生物量光学遥感估测饱和值，探索提高生物量遥感估测精度。 方法 以云南省迪庆藏族自治州云冷杉林为研究对象，根据森林资源二类调查数据，结合同时期Landsat 8 OLI遥感影像，利用随机选取的小班样本数据提取遥感因子反射率统计值，并与生物量进行曲线拟合，求解云冷杉林生物量饱和值，建立云冷杉生物量回归估测模型、BP神经网络模型。同时基于回归模型构建考虑区域、龄组效应的单水平和嵌套两水平(区域+龄组)混合效应模型，反演研究区云冷杉林地上生物量。 结果 利用幂函数拟合迪庆藏族自治州云冷杉林生物量饱和值为233 t∙hm−2；最优回归估测模型调整决定系数(Ra2)为0.606，高于BP神经网络模型的Ra2(0.542)，各个效应水平混合模型的拟合精度与独立性检验指标均优于回归模型。考虑两水平的混合效应模型有最优的拟合精度，而考虑龄组效应水平的混合模型有最优的独立性检验指标。混合效应模型在低生物量段(＜100 t∙hm−2)和高生物量段(＞233 t∙hm−2)均显著降低了回归模型和BP神经网络模型的估测平均残差。 结论 混合效应模型有更宽的估测范围，在一定程度上减小低值高估与数据饱和造成的高值低估影响，提高了预估精度。图3表12参28 Abstract:Objective The objective of this study is to determine the saturation value of optical remote sensing estimation of spruce-fir forest biomass, and to improve the accuracy of remote sensing estimation of biomass. Method Taking the spruce-fir forests in Diqing Tibetan Autonomous Prefecture as the research object, the saturation value of the spruce-fir biomass was calculated by curve fitting, Tibetan Autonomous and the regression estimation model and BP neural network model of the spruce-fir biomass were established using the forest management inventory (FMI) data combined with Landsat 8 OLI remote sensing image in the contract period and the statistical value of remote sensing factor reflectance extracted from the randomly selected small class sample data. At the same time, based on the regression model, single level and nested two-level(region+age group)mixed effect models considering regional and age group effects were constructed to estimate the aboveground biomass of spruce-fir forests in the study area. Result The biomass saturation value of the spruce-fir forests in Diqing Tibetan Autonomous Prefecture was 233 t·hm−2 by power function fitting. The adjusted determination coefficient of the optimal regression estimation model $R_{\rm{a}}^{2}$ was 0.606, which was higher than$R_{\rm{a}}^{2}$ (0.542) of the BP neural network model. The fitting accuracy and independence test indexes of the mixed model of each effect level were better than those of the regression model. The two-level mixed effect model had the best fitting accuracy, while the mixed model with age group effect level had the best independence test index. The mixed effect model significantly reduced the average residual error of regression model and BP neural network model in the low biomass section (＜100 t∙hm−2), especially in the high biomass section (＞233 t∙hm−2).Conclusion The mixed effect model has a wider estimation range, which can reduce the impact of low overestimation and high underestimation caused by data saturation, and improve prediction accuracy.[Ch, 3 fig. 12 tab. 28 ref.] -
图 1 幂函数拟合云冷杉林生物量饱和曲线
Figure 1 Power function fitting curve of spruce-fir forest biomass saturation
图 2 基于回归模型和混合效应模型生物量估测残差分布
A.基本模型；B. 区域效应混合模型；C. 龄组效应混合模型；D. 两水平混合效应模型
Figure 2 Biomass estimation residual distribution based on regression model and mixed effect model
图 3 研究区云冷杉林地上生物量反演示意图
A. 回归模型；B. BP神经网络模型；C. 区域效应混合模型；D. 龄组效应混合模型；E. 两水平混合效应模型
Figure 3 Biomass inversion of spruce-fir forests in the study area
表 1 研究区Landsat 8 OLI影像基本信息
Table 1. Basic information of Landsat 8 OLI images in study area
影像ID 获取时间 条带号 太阳方位角/(°) 太阳高度角/(°) 平均云量/% LC81310412016341LGN00 2016-12-06 131/041 56.524 36.313 1.04 LC81320402016348LGN00 2016-12-13 132/040 156.677 34.220 0.73 LC81320412016348LGN00 2016-12-13 132/041 156.001 35.443 0.76 
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表 2 云冷杉蓄积量—生物量转换因子信息指数
Table 2. Spruce and fir storage—biomass conversion factor information index
树种 模型公式 FBE DSV 幼龄林 中龄林 近熟林 成熟林 过熟林 乔木层 云杉 MA=VFBEDSV 2.326 5 1.516 4 1.473 0 1.427 4 1.264 2 0.342 冷杉 1.327 9 1.339 3 1.333 6 1.309 7 1.285 9 0.366 说明：MA为单位面积生物量；V为单位面积蓄积量；FBE为蓄积生物量转换系数；DSV为木材基本密度
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表 3 建模及检验数据基本情况
Table 3. Modeling and testing data
统计量 建模/训练数据(n=983) 检验数据(n=245) 单位面积蓄积
量/(m3∙hm−2)单位面积生物
量/(t∙hm−2)单位面积蓄积
量/(m3∙hm−2)单位面积生物
量/(t∙hm−2)最小值 8.33 5.74 28.57 14.37 最大值 651.82 314.83 598.92 287.88 平均值 294.73 141.66 298.78 143.57 标准差 137.54 65.43 122.51 58.65
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表 5 生物量与遥感因子各统计值相关性
Table 5. Significant Pearson correlation coefficients between remote sensing factors and AGB
遥感因子 MEAN MAX MIN 遥感因子 MEAN MAX MIN ALBEDO −0.555** −0.065* −0.449** ND67 0.439** 0.160** 0.317** ARVI 0.469** 0.251** 0.193** NDVI 0.329** 0.216** 0.069* B −0.540** −0.055 −0.430** NLI 0.165** 0.207** 0.091** B1 −0.168** 0.010 −0.092** PC1-A −0.682** −0.154** 0.323** B2 −0.187** 0.008 −0.097** PC1-B −0.711** −0.165** 0.337** B3 −0.238** 0.001 −0.095** PC1-P 0.616** 0.383** −0.180** B4 −0.334** −0.018 −0.096** PC2-A 0.440** 0.172** −0.110** B5 −0.296** 0.003 −0.100** PC2-B 0.099** 0.040 −0.097** B6 −0.762** −0.333** −0.101** PC2-P 0.670** 0.349** 0.085** B7 −0.705** −0.345** −0.219** PC3-A −0.094** 0.016 −0.004 DVI −0.050 0.036 −0.220** PC3-B −0.039 0.049 −0.470** G 0.057 0.051 −0.203** PC3-P −0.197** 0.006 −0.531** KT1 −0.555** −0.060* −0.203** PVI −0.237** 0.004 0.163** KT2 0.070* 0.053 −0.521** RVI 0.102** −0.002 0.325** KT3 0.534** 0.126** −0.523** SARV −0.036 −0.041 0.176** MSAVI 0.326** 0.215** −0.430** SAV12 0.326** 0.215** 0.361** MSR 0.269** 0.009 −0.430** SAVI 0.329** 0.216** 0.043 MVI5 0.626** 0.436** −0.057* SR 0.102** −0.002 −0.016 MVI7 0.619** 0.363** −0.018 TVI 0.329** 0.217** −0.052 ND43 −0.490** −0.251** −0.441** W 0.497** 0.114** −0.174** ND563 −0.075* 0.010 −0.015 说明：**表示极显著相关(P＜0.01)；*表示显著相关(P＜0.05)
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表 6 基于不同曲线拟合饱和值结果
Table 6. Results of fitting saturation values based on different curves
函数 R2 显著性(P) 对数函数 0.555 0.000 二次项函数 0.583 0.000 三次项函数 0.584 0.000 幂函数 0.590 0.000
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表 7 基于单水平混合参数选择拟合结果
Table 7. Selection of fitting results based on single-level mixing parameters
模型 混合参数 区域效应 龄组效应 AIC BIC logLik AIC BIC logLik 基础模型 无 10 129.57 10 154.04 −5 059.787 10 129.57 10 154.04 −5 059.787 模型1 a1 10 093.99 10 133.10 −5 038.993 10 011.61 10 050.73 −4 997.806 模型2 a2 10 102.12 10 141.24 −5 043.062 10 016.07 10 055.18 −5 000.034 模型3 a3 不收敛 10 023.89 10 063.00 −5 003.943 模型4 a1, a2 10 099.99 10 153.78 −5 038.996 10 017.62 10 071.41 −4 997.812 模型5 a1, a3 10 100.01 10 153.80 −5 039.007 10 017.66 10 071.44 −4 997.829 模型6 a2, a3 10 108.13 10 161.92 −5 043.066 10 022.21 10 075.99 −5 000.105 模型7 a1, a2, a3 10 108.00 10 181.34 −5 038.998 10 023.67 10 053.00 −5 005.834
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表 8 基于两水平混合参数选择拟合结果
Table 8. Selection of fitting results based on two levels of mixing parameters
模型 区域效应 龄组效应 AIC BIC logLik a1 a2 a3 a1 a2 a3 模型1 √ √ 9 956.50 10 010.29 −4 967.250 模型2 √ √ √ 9 958.93 10 012.71 −4 968.464 模型3 √ √ √ √ 9 957.83 10 045.84 −4 960.915 模型4 √ √ √ √ √ 9 963.75 10 066.43 −4 960.872 模型5 √ √ √ √ √ √ 9 971.72 10 093.96 −4 960.862 说明：带√的变量表示模型包含这个随机参数
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表 9 基于随机参数不同组间方差-协方差结构混合模型拟合结果
Table 9. Mixed model fitting results of variance-covariance structure between groups based on random parameters
方差-协方差结构 自由度 AIC BIC logLik 似然比检验(LRT) P 广义正定矩阵(UN) 11 9 956.50 10 010.29 −4 967.250 − − 复合对称(CS) 10 9 958.34 10 012.24 −4 969.170 18.396 56 ＜0.000 1 对角矩阵(UN1) 9 9 965.69 10 009.70 −4 973.846 13.190 81 0.001 4
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表 10 考虑组内协方差结构矩阵后各个效应混合模型比较结果
Table 10. Comparison results of mixed effects models considering intra-group covariance matrix
随机效应 协方差结构 AIC BIC logLik LRT P 区域效应 10 093.99 10 133.10 −5 038.993 − − 指数函数 10 095.75 10 139.76 −5 038.877 0.233 1 0.629 0 高斯函数 10 095.99 10 139.99 −5 038.993 0.000 8 0.999 3 球面函数 10 093.70 10 137.71 −5 037.850 2.287 1 0.130 4 龄组效应 10 011.61 10 050.73 −4 997.806 − − 指数函数 10 000.52 10 044.53 −4 991.262 13.088 0 ＜0.000 1 高斯函数 10 002.22 10 046.23 −4 992.110 0.040 2 0.841 0 球面函数 10 002.23 10 046.24 −4 992.117 11.378 0 0.000 7 两水平效应 9 956.50 10 010.29 −4 967.250 − − 指数函数 9 956.43 10 015.10 −4 966.213 2.074 6 0.149 8 高斯函数 9 958.47 10 017.15 −4 967.237 0.027 3 0.870 1 球面函数 9 956.49 10 015.17 −4 966.248 2.003 7 0.156 9 说明：−表示无此项
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表 11 生物量混合效应模型拟合参数及独立性检验结果
Table 11. Biomass mixed effect model fitting parameters and independence test results
变量 区域效应混合模型 龄组效应混合模型 两水平混合效应模型 估计值 P 估计值 P 估计值 P 常量 278.430 ＜0.000 1 208.410 ＜0.000 1 220.590 ＜0.000 1 a1 −0.259 ＜0.000 1 −0.187 ＜0.000 1 −0.208 ＜0.000 1 a2 0.201 ＜0.000 1 0.143 ＜0.000 1 0.164 ＜0.000 1 a3 132.054 ＜0.000 1 107.874 ＜0.000 1 120.942 ＜0.000 1 残差 39.883 38.172 36.526 总相对误差 −4.564 −1.609 −7.539 平均相对误差 −0.462 −0.163 −0.765 说明：区域效应D矩阵(组间方差-协方差结构)为0.0010；龄组效应D矩阵为0.0007，R矩阵(组内方差-协方差结构)为0.465；两水平 D矩阵分别为0.0003和0.0002
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表 12 生物量分段残差检验
Table 12. Biomass segmentation residual test
生物量分段/(t∙hm−2) 拟合模型 回归模型 BP神经网络模型 区域效应混合模型 龄组效应混合模型 两水平混合效应模型 0~50 −25.77 −26.39 −27.14 −25.34 −23.43 50~100 −15.35 −15.15 −13.87 −15.47 −14.85 100~150 −17.76 −10.69 −13.62 −12.63 −10.33 150~200 2.68 4.26 5.34 1.12 2.41 200~233 42.27 41.20 36.77 40.13 33.55 ＞233 79.39 72.37 70.69 68.65 55.43
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