Comparison of crown width models and estimation methods of natural spruce fir forest in Jingouling Forest Farm of northeastern China
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摘要:
目的 对比不同冠幅预测方法对云冷杉幼树不同方向冠幅（东、西、南、北、东西、南北、平均冠幅）的预测精度的差异，为天然云冷杉林经营提供一定的理论依据。 方法 利用2013年金沟岭云冷杉3块1 hm2固定样地中云冷杉幼树各向冠幅实测数据，以逻辑斯蒂模型为基础模型，以非线性最小二乘法为基础方法进行模型初步拟合。以1/D、1/D0.5、1/D2作为模型的权函数进行模型异方差的消除。以不加权非线性似乎不相关法、加权非线性似乎不相关法、分位数回归法、非线性最小二乘法分别构建了云冷杉幼树冠幅各组分预测模型。 结果 模型拟合结果显示，分位数回归模型的拟合效果在云冷杉幼树冠幅预测模型中拟合精度最低；相较于分位数回归而言，加权非线性似乎不相关回归模型拟合效果与加权最小二乘模型拟合效果相当。模型拟合效果排序为：加权NSUR ≈ 加权OLS > OLS > QR。以1/D2作为模型的权函数时，模型残差图的异方差趋势被消除最明显，该权函数为最优权函数。 结论 本文中非线性分位数回归模型拟合效果不一定比非线性最小二乘法更好。加权NSUR模型（权函数为1/D2）可以为金沟岭林场云冷杉幼树冠幅的预测提供一定的理论基础。 -
关键词:
- 冠幅模型 /
- 幼树 /
- 权函数 /
- 非线性似乎不相关回归 /
- 分位数回归
Abstract:Objective Different crown prediction methods were used to predict varied crown components (east, west, south, north crown width and east-west crown width, south-north crown width, average crown width) of young spruce fir, and the prediction accuracy was compared in order to provide a theoretical basis for the tending of spruce fir management. Method The measured data of different crown components in permanent spruce fir sample plots was got from three 1 ha sample plots on Jingouling Forest Farm of northeastern China in 2013, the logistic model was chosen as base model and the ordinary least square method was used to fit crown radii of east, west, south, north and crown width of east-west, south-north, and mean direction. 1/D, 1/D0.5, and 1/D2 were used as weight function to eliminate the heteroscedasticity of model residuals. The unweighted nonlinear seemingly unrelated regression method, weighted nonlinear seemingly unrelated regression method, quantile regression method, and ordinary least square method were applied to develop different crown component prediction model. Result The fitting results indicated that, quantile regression model had the lowest fitting accuracy, compared with quantile regression, weighted nonlinear seemingly unrelated regression and weighted ordinary least square regression had nearly same fitting effectiveness. The accuracy order arrangement was weighted NSUR ≈ weighted OLS > OLS > QR, 1/D2 was the best choice to eliminate heteroscedasticity by residuals plot. Conclusion In this paper, the fitting effect of nonlinear quantile regression model was not necessarily better than that of nonlinear least square method, the weighted nonlinear seemingly unrelated regression model (1/D2 as weight function) developed in this essay can provide some theory basis for different crown components of young spruce fir. -
图 1 不同冠幅组分与胸径、树高之间关系图
SCR：南冠幅South crown width；NCR：北冠幅North crown width；ECR：东冠幅 East crown width；WCR：西冠幅 West crown width；EWCW：东西冠幅 East-west crown width；SNCW：南北冠幅South-north crown width；CW：平均冠幅 Average crown width；DBH：胸径 DBH；H：树高Tree height. YLK-6、YLK-7、YLK-12分别代表云冷杉阔叶混交林第6号、7号、12号样地YLK-6，YLK-7，YLK-12 represent the 6th, 7th, 12th sample plots of spruce-fir broadleaved mixed forest
Figure 1. Relationship between different crown components and DBH, H
表 1 数据描述性统计分析
Table 1. Statistics of modeling data and validation data
项目 Item 变量 Variable 最大值 Max. 最小值 Min. 均值 Mean 标准差 Std. 建模数据
Model-fitting data (n = 548)胸径 DBH/cm 5.00 1.00 2.99 1.14 树高 Tree height (H)/m 11.90 1.50 3.60 1.55 南冠幅 South crown width (SCR)/m 2.96 0.29 1.08 0.44 北冠幅 North crown width (NCR)/m 3.66 0.00 1.11 0.50 西冠幅 West crown width (WCR)/m 3.23 0.00 1.13 0.51 东冠幅 East crown width (ECR)/m 2.87 0.06 1.06 0.40 南北冠幅 South-north crown width (SNCW)/m 5.35 0.61 2.19 0.80 东西冠幅 East-west crown width (EWCW)/m 6.40 0.68 2.19 0.83 平均冠幅 Average crown width (CW)/m 5.35 0.68 2.19 0.77 检验数据
Model-validation data (n = 235)胸径 DBH/cm 5.00 1.00 3.01 1.18 树高 Tree height (H)/m 11.10 1.50 3.56 1.47 南冠幅 South crown width (SCR)/m 2.90 0.00 1.05 0.45 北冠幅 North crown width (NCR)/m 3.12 0.00 1.06 0.50 西冠幅 West crown width (WCR)/m 3.06 0.33 1.13 0.51 东冠幅 East crown width (ECR)/m 2.81 0.22 1.03 0.37 南北冠幅 South-north crown width (SNCW)/m 5.26 0.99 2.16 0.80 东西冠幅 East-west crown width (EWCW)/m 6.02 0.90 2.11 0.83 平均冠幅 Average crown width (CW)/m 5.13 1.01 2.13 0.77 
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表 2 基础模型拟合指标统计
Table 2. Fitting results of basic models
模型 Model $\overline e$ R2 RMSE CWS −0.000 3 0.298 3 0.369 8 CWN −0.000 2 0.278 0 0.421 1 CWE −0.000 2 0.309 8 0.329 3 CWW −0.000 2 0.267 4 0.439 5 CWEW −0.000 4 0.368 9 0.635 8 CWSN −0.000 5 0.369 1 0.656 8 CW −0.000 5 0.411 6 0.590 4
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表 3 加入权函数后基础模型拟合指标统计
Table 3. Fitting index statistics of basic models by addition of weight function
模型 Model 1/D 1/D2 1/D0.5 R2 RMSE R2 RMSE R2 RMSE CWS 0.372 4 0.205 1 0.416 1 0.122 6 0.336 9 0.273 4 CWN 0.342 4 0.233 2 0.368 7 0.140 2 0.312 7 0.310 8 CWE 0.360 1 0.195 5 0.363 6 0.128 3 0.339 3 0.250 9 CWW 0.345 4 0.244 0 0.382 2 0.147 4 0.309 0 0.324 9 CWSN 0.446 0 0.361 4 0.471 7 0.225 5 0.411 9 0.475 0 CWEW 0.444 0 0.365 4 0.479 7 0.219 5 0.409 4 0.486 4 CW 0.492 5 0.331 0 0.527 5 0.201 0 0.455 9 0.439 1
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表 4 可加性冠幅模型参数估计
Table 4. Parameter estimation of additivity crown model
CWS CWN CWE CWW 参数
Parameter估计值
Estimation参数
Parameter估计值
Estimation参数
Parameter估计值
Estimation参数
Parameter估计值
Estimationa0 0.875 (0.112) b0 1.040 (0.184) c0 0.741 (0.102) d0 0.855 (0.133) a1 0.096 (0.018) b1 0.098 (0.022) c1 0.112 (0.018) d1 0.118 (0.021) a2 1.770 (0.352) b2 1.653 (0.324) c2 1.389 (0.423) d2 1.835 (0.421) a3 0.977 (0.237) b3 0.659 (0.188) c3 1.119 (0.378) d3 0.977 (0.265) 注: 括号内的数值是标准差。Note: value in brackets is the standard deviation.
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表 5 可加性冠幅模型拟合精度
Table 5. Fitting accuracy of additivity crown model
评价指标 Evaluation index CWS CWN CWE CWW CWSN CWEW CW R2 0.416 1 0.368 8 0.363 7 0.382 3 0.479 5 0.471 6 0.527 3 RMSE 0.122 6 0.140 2 0.128 3 0.147 4 0.219 5 0.225 6 0.201 0
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表 6 参数估计的残差方差−协方差矩阵
Table 6. Variance-covariance matrix of parameter estimation
CWS CWN CWE CWW CWSN CWEW CW CWS 0.015 0 0.006 7 0.006 8 0.009 5 0.021 7 0.016 2 0.019 0 CWN 0.006 7 0.019 6 0.005 9 0.008 6 0.026 4 0.014 6 0.020 5 CWE 0.006 8 0.005 9 0.016 5 0.006 3 0.012 7 0.022 8 0.017 8 CWW 0.009 5 0.008 6 0.006 3 0.021 7 0.018 1 0.028 0 0.023 1 CWSN 0.021 7 0.026 4 0.012 7 0.018 1 0.048 2 0.030 9 0.039 6 CWWE 0.016 2 0.014 6 0.022 8 0.028 0 0.030 9 0.050 9 0.041 0 CW 0.019 0 0.020 5 0.017 8 0.023 1 0.039 6 0.041 0 0.040 4
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表 7 不同分位数模型拟合统计结果
Table 7. Fitting results of various quantile crown models
模型 Model 分位数 Quantile (τ) $\overline e$ R2 RMSE CWS 0.3 0.189 4 0.083 8 0.422 5 0.4 0.127 8 0.194 9 0.396 1 0.5 0.041 4 0.287 2 0.372 7 0.6 −0.028 2 0.293 8 0.371 0 0.7 −0.147 4 0.167 2 0.402 9 CWN 0.3 0.198 4 0.093 7 0.471 7 0.4 0.124 4 0.204 0 0.442 1 0.5 0.042 9 0.264 7 0.424 9 0.6 −0.025 0 0.273 7 0.422 3 0.7 −0.134 6 0.182 8 0.447 9 CWE 0.3 0.164 6 0.106 3 0.374 7 0.4 0.096 6 0.221 5 0.349 7 0.5 0.019 7 0.282 6 0.335 7 0.6 −0.063 3 0.278 5 0.336 7 0.7 −0.148 2 0.159 0 0.363 5 CWW 0.3 0.239 7 0.019 1 0.508 4 0.4 0.153 4 0.163 0 0.469 7 0.5 0.075 9 0.241 2 0.447 3 0.6 −0.039 8 0.247 6 0.445 4 0.7 −0.153 7 0.150 7 0.473 1 CWSN 0.3 0.339 9 0.171 1 0.752 7 0.4 0.211 4 0.287 7 0.697 8 0.5 0.072 5 0.350 9 0.666 1 0.6 −0.097 6 0.348 4 0.667 4 0.7 −0.284 0 0.229 9 0.725 5 CWEW 0.3 0.341 6 0.162 2 0.732 4 0.4 0.229 9 0.267 2 0.685 0 0.5 0.046 5 0.365 3 0.637 6 0.6 −0.087 0 0.351 4 0.644 5 0.7 −0.288 4 0.212 4 0.710 1 CW 0.3 0.319 1 0.212 1 0.683 0 0.4 0.209 9 0.321 6 0.633 9 0.5 0.046 0 0.405 6 0.593 7 0.6 −0.107 9 0.388 4 0.601 9 0.7 −0.284 9 0.243 4 0.669 4
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表 8 0.55分位数模型参数估计
Table 8. Parameter estimation at 0.55 tau
参数 Parameter 方法 Method CWS CWN CWE CWW CWSN CWEW CW a0 QR 1.177 1.573 1.469 1.191 4.386 2.195 2.561 a1 QR 0.072 0.040 0.032 0.082 0.148 0.160 0.122 a2 QR 1.748 2.422 2.048 1.988 3.363 1.912 2.115 a3 QR 0.580 0.518 0.521 0.620 0.332 0.725 0.628 注：QR为分位数回归。下同。Notes: QR is quantile regression. The same below.
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表 9 0.55分位数回归模型拟合结果
Table 9. Fitting results of 0.55 quantile models
模型 Model 方法 Method $\overline e$ R2 RMSE CWS QR −0.000 9 0.298 3 0.369 8 CWN QR −0.008 5 0.274 4 0.422 1 CWE QR −0.025 9 0.295 4 0.332 7 CWW QR 0.015 5 0.264 4 0.440 4 CWSN QR −0.022 7 0.360 4 0.661 3 CWEW QR −0.022 1 0.366 3 0.637 1 CW QR −0.028 3 0.408 6 0.591 9
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表 10 模型检验结果
Table 10. Validation results of models
评价指标
Evaluation index方法
MethodCWS CWN CWE CWW CWSN CWEW CW $\overline e$ OLS −0.031 2 −0.050 0 −0.032 2 −0.000 2 −0.081 3 −0.032 5 −0.056 7 加权OLS Weighted OLS −0.025 9 0.046 9 −0.027 3 0.002 7 −0.073 0 −0.024 8 −0.048 3 加权NSUR Weighted NSUR −0.025 2 −0.046 2 −0.027 3 0.002 9 −0.071 4 −0.024 4 −0.047 9 QR −0.031 9 −0.059 8 −0.060 4 0.014 7 −0.109 7 −0.054 3 −0.086 0 R2 OLS 0.275 4 0.140 8 0.266 2 0.270 9 0.265 3 0.329 0 0.333 5 加权OLS Weighted OLS 0.277 2 0.130 9 0.273 1 0.271 4 0.258 0 0.330 9 0.329 0 加权NSUR Weighted NSUR 0.389 3 0.229 4 0.345 7 0.303 9 0.373 5 0.407 7 0.429 9 QR 0.275 2 0.142 5 0.223 8 0.281 2 0.251 5 0.329 8 0.322 8 RMSE OLS 0.385 6 0.462 5 0.320 7 0.435 8 0.714 6 0.658 3 0.630 5 加权OLS Weighted OLS 0.385 1 0.465 1 0.319 1 0.435 6 0.718 1 0.657 4 0.632 7 加权NSUR Weighted NSUR 0.121 6 0.166 6 0.121 9 0.159 1 0.243 2 0.233 3 0.219 8 QR 0.385 6 0.462 0 0.329 8 0.432 7 0.721 2 0.657 9 0.635 6 注 Notes：OLS：最小二乘法 Least square method；加权OLS：加权最小二乘法 Weighted least square method；加权NSUR：加权非线性似乎不相关回归 Weighted nonlinear seemingly unrelated regression.
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[1] Assmann E, Davis P W. The principles of forest yield study[M]. Oxford: Pergamon Press Ltd., 1970. [2] Hasenauer H, Monserud R A. Biased predictions for tree height increment models developed from smoothed ‘data’[J]. Ecological Modelling, 1997, 98(1): 13−22. doi: 10.1016/S0304-3800(96)01933-3 [3] Monserud R A, Sterba H. A basal area increment model for individual trees growing in even- and uneven-aged forest stands in Austria[J]. Forest Ecology & Management, 1996, 80(1−3): 57−80. [4] Carvalho J P, Parresol B R. Additivity in tree biomass components of Pyrenean oak (Quercus pyrenaica Willd.)[J]. Forest Ecology & Management, 2003, 179(1−3): 269−276. [5] Fu L Y, Lei Y C, Wang G X, et al. Comparison of seemingly unrelated regressions with error-in-variable models for developing a system of nonlinear additive biomass equations[J]. Trees, 2016, 30(3): 839−857. doi: 10.1007/s00468-015-1325-x [6] Pukkala T, Becker P, Kuuluvainen T, e al. Predicting spatial distribution of direct radiation below forest canopies[J]. Agricultural and Forest Meteorology, 1991, 55: 295−307. doi: 10.1016/0168-1923(91)90067-Z [7] 贾炜玮, 解希涛, 姜生伟, 等. 大兴安岭新林林业局3种林分类型天然更新幼苗幼树的空间分布格局[J]. 应用生态学报, 2017, 28(9):2813−2822.Jia W W, Xie X T, Jiang S W, et al. Spatial distribution pattern of seedlings and saplings of three forest types by natural regeneration in Daxin’an Mountains Xinlin Forestry Bureau, China[J]. Chinese Journal of Applied Ecology, 2017, 28(9): 2813−2822. [8] EerikäInen K, Valkonen S, Saksa T. Ingrowth, survival and height growth of small trees in uneven-aged Picea abies stands in southern Finland[J]. Forest Ecosystems, 2014, 1(1): 1−10. doi: 10.1186/2197-5620-1-1 [9] Lei Y K, Li Y F, Affleck D L R, et al. Additivity of nonlinear tree crown width models: aggregated and disaggregated model structures using nonlinear simultaneous equations[J]. Forest Ecology and Management, 2018, 427: 372−382. doi: 10.1016/j.foreco.2018.06.013 [10] Fu L Y, Sun H, Sharma R P, et al. Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China[J]. Forest Ecology and Management, 2013, 302: 210−220. doi: 10.1016/j.foreco.2013.03.036 [11] Sharma R P, Vacek Z, Vacek S. Individual tree crown width models for Norway spruce and European beech in Czech Republic[J]. Forest Ecology and Management, 2016, 366: 208−220. doi: 10.1016/j.foreco.2016.01.040 [12] 贺梦莹, 董利虎, 李凤日. 长白落叶松−水曲柳混交林冠幅预测模型[J]. 北京林业大学学报, 2020, 42(7):23−32. doi: 10.12171/j.1000-1522.20190250He M Y, Dong L H, Li F R. Crown width prediction models for Larix olgensis and Fraxinus mandshurica mixed plantations[J]. Journal of Beijing Forestry University, 2020, 42(7): 23−32. doi: 10.12171/j.1000-1522.20190250 [13] 李凤日, 王治富, 王保森. 落叶松人工林有效冠动态研究(Ⅰ): 有效冠的确定[J]. 东北林业大学学报, 1996, 24(1):1−8.Li F R, Wang Z F, Wang B S. Studies on the effective crown development of Larix olgensis (Ⅰ): determination of the effective crown[J]. Journal of Northeast Forestry university, 1996, 24(1): 1−8. [14] Kajihara M. Estimation of stem-volume increment by using sunny crown-surface area and stem-surface area[J]. Journal of the Japanese Forestry Society, 2008, 67: 501−505. [15] Koenker R, Bassett G W. Regression quantiles[J]. Econometrica, 1978, 46(1): 211−244. [16] 马岩岩, 姜立春. 基于非线性分位数回归的落叶松树干削度方程[J]. 林业科学, 2019, 55(10):68−75.Ma Y Y, Jiang L C. Stem taper function for Larix gmelinii based on nonlinear quantile regression[J]. Scientia Silvae Sinicae, 2019, 55(10): 68−75. [17] 辛士冬, 姜立春. 利用分位数回归模拟人工樟子松树干干形[J]. 北京林业大学学报, 2020, 42(2):1−8. doi: 10.12171/j.1000-1522.20190014Xin S D, Jiang L C. Modeling stem taper profile for Pinus sylvestris plantations using nonlinear quantile regression[J]. Journal of Beijing Forestry University, 2020, 42(2): 1−8. doi: 10.12171/j.1000-1522.20190014 [18] Özçelik R, Cao Q V, Trincado G, et al. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey[J]. Forest Ecology and Management, 2018, 419−420: 240−248. doi: 10.1016/j.foreco.2018.03.051 [19] Bohora S B, Cao Q V. Prediction of tree diameter growth using quantile regression and mixed-effects models[J]. Forest Ecology and Management, 2014, 319: 62−66. doi: 10.1016/j.foreco.2014.02.006 [20] 陈科屹, 张会儒, 雷相东, 等. 基于目标树经营的抚育采伐对云冷杉针阔混交林空间结构的影响[J]. 林业科学研究, 2017, 30(5):718−726.Chen K Y, Zhang H R, Lei X D, et. al. Effect of thinning on spatial structure of spruce-fir mixed broadleaf-conifer forest base on crop tree management[J]. Forest Research, 2017, 30(5): 718−726. [21] 陈科屹, 张会儒, 雷相东, 等. 云冷杉过伐林垂直结构特征分析[J]. 林业科学研究, 2017, 30(3):450−459.Chen K Y, Zhang H R, Lei X D, et. al. Analysis of vertical structure characteristics for spruce-fir over-cutting forest[J]. Forest Research, 2017, 30(3): 450−459. [22] 孟宪宇. 测树学[M]. 3版. 北京: 中国林业出版社, 2006.Meng X Y. Forest mensuration[M]. 3rd ed. Beijing: China Forestry Publishing House, 2006. [23] 曾伟生, 骆期邦, 贺东北. 论加权回归与建模[J]. 林业科学, 1999, 35(5):5−11. doi: 10.3321/j.issn:1001-7488.1999.05.002Zeng W S, Luo Q B, He D B. Research on weighting regression and modeling[J]. Scientia Silvae Sinicae, 1999, 35(5): 5−11. doi: 10.3321/j.issn:1001-7488.1999.05.002 [24] Khurra S M, 韩斐斐, 姜立春. 不同抽样方法对兴安落叶松立木材积方程预测精度的影响[J]. 林业科学, 2018, 54(8):99−105. doi: 10.11707/j.1001-7488.20180811Khurra S M, Han F F, Jiang L C. Effects of different sampling methods on predict precision of individual tree volume equation for Dahurian larch[J]. Scientia Silvae Sinicae, 2018, 54(8): 99−105. doi: 10.11707/j.1001-7488.20180811 [25] 关静. 分位数回归理论及其应用[D]. 天津: 天津大学, 2009.Guan J. Quantile regression theory and its application[D]. Tianjin: Tianjin University, 2009. [26] 段光爽, 王秋燕, 宋新宇, 等. 竞争环境下红松单木树高与胸径的相对生长关系[J]. 林业科学, 2020, 56(10):108−115.Duan G S, Wang Q Y, Song X Y, et. al. Relative growth relations between height and diameter of individual Korean pine under competitive environment[J]. Scientia Silvae Sinicae, 2020, 56(10): 108−115. [27] 张冬燕, 王冬至, 李晓, 等. 基于分位数回归的针阔混交林树高与胸径的关系[J]. 浙江农林大学学报, 2020, 37(3):424−431.Zhang D Y, Wang D Z, Li X, et al. Relationship between height and diameter at breast height (DBH) in mixed coniferous and broadleaved forest based on quantile regression[J]. Journal of Zhejiang A&F University, 2020, 37(3): 424−431. [28] 董灵波, 刘兆刚, 李凤日, 等. 基于线性混合模型的红松人工林一级枝条大小预测模拟[J]. 应用生态学报, 2013, 24(9):2447−2456.Dong L B, Liu Z G, Li F R, et. al. Primary branch size of Pinus koraiensis plantation: a prediction based on linear mixed effect model[J]. Chinese Journal of Applied Ecology, 2013, 24(9): 2447−2456. [29] 沈钱勇, 汤孟平. 浙江省毛竹竹秆生物量模型[J]. 林业科学, 2019, 55(11):181−188. doi: 10.11707/j.1001-7488.20191120Shen Q Y, Tang M P. Stem biomass models of Phyllostachys edulis in Zhejiang Province[J]. Scientia Silvae Sinicae, 2019, 55(11): 181−188. doi: 10.11707/j.1001-7488.20191120 [30] 沈钱勇, 汤孟平. 浙江省毛竹竹秆材积模型[J]. 林业科学, 2020, 56(5):89−96.Shen Q Y, Tang M P. Stem volume models of Phyllostachys edulis in Zhejiang Province[J]. Scientia Silvae Sinicae, 2020, 56(5): 89−96. -
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