基于最优权重的落叶松单木叶面积组合预测模型
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摘要
最优权重组合预测模型是将各种模型组合起来并分配它们适当的权重系数进行组合预测的模型,减少单项模型预测的风险性,提高预测精度。以落叶松单木叶面积为例,通过拟合一元线性、多元非线性和多元线性等各种单项基础模型,构建最优权重组合预测模型。结果表明,胸径是预测落叶松单木叶面积的最佳变量,增加树冠率或高径比可提高模型解释力,改进异速生长方程是最佳单项模型,R~2达0.927;最优权重算法组合模型优于单项模型及平均值组合模型,落叶松叶面积最优权重组合模型的估测值与实测值之间的平均绝对相对误差和均方根误差均低于单项模型,R~2达0.930。构建的最优权重组合预测模型适合估测落叶松单木叶面积,估测精度高,可应用于长白落叶松人工林叶面积指数估测。
Optimal weighted combinatorial model can reduce predicting risk of single model and improve the predicting precision.Fifty five larch( Larix olgensis) trees were collected randomly at the Xiaoxing' an Mountains in Northeast China for fitting the univariate( or multivariate) variable nonlinear and linear leaf area model,and the optimal weights of combination forecasting model determined by the optima tool box in Matlab 2010 b software. Results showed diameter at breast height( D1.3) is the best prediction variable for estimating larch leaf area. The modified allometric equation with adding the ratio of tree height to D1.3,with a higher explanation ability( R~2= 0.927). The index of accuracy evaluation for optimal weighted combinatorial model( OW) was better than the single model and the mean weighted combinatorial model,and the OW-M3 M8 M12 forecasting model improved accuracy for predicting leaf area of individual tree. The optimal weighted combination forecasting model suit for estimating leaf area. The leaf area model would be used for estimating the leaf area index for pure larch plantation.
Optimal weighted combinatorial model can reduce predicting risk of single model and improve the predicting precision.Fifty five larch( Larix olgensis) trees were collected randomly at the Xiaoxing' an Mountains in Northeast China for fitting the univariate( or multivariate) variable nonlinear and linear leaf area model,and the optimal weights of combination forecasting model determined by the optima tool box in Matlab 2010 b software. Results showed diameter at breast height( D1.3) is the best prediction variable for estimating larch leaf area. The modified allometric equation with adding the ratio of tree height to D1.3,with a higher explanation ability( R~2= 0.927). The index of accuracy evaluation for optimal weighted combinatorial model( OW) was better than the single model and the mean weighted combinatorial model,and the OW-M3 M8 M12 forecasting model improved accuracy for predicting leaf area of individual tree. The optimal weighted combination forecasting model suit for estimating leaf area. The leaf area model would be used for estimating the leaf area index for pure larch plantation.
引文
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[18]戴钰.最优组合预测模型的构建及其应用研究[J].经济数学,2010,27(1):92-98.
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[20]张雄清,雷渊才,陈新美.林分断面积组合预测模型权重确定的比较[J].林业科学,2011,47(7):36-41.
[21]郭孝玉.长白落叶松人工林树冠结构及生长模型研究[D].北京:北京林业大学,2013:28-115.
[22]SHINOZAKI K,YODA K,HOZUMI K,et al.A quantitative analysis of plant form the pipe model theory I.basic analyses[J].Japanese Journal of Ecology,1964,14(3):97-105.
[23]RENNOLL K.Pipe-model theory of stem-profile development[J].Forest Ecology and Management,1994,69(1/2/3):41-55.
[24]曾伟生,唐守正.立木生物量方程的优度评价和精度分析[J].林业科学,2011,47(11):106-113.
[25]董利虎,张连军,李凤日.立木生物量模型的误差结构和可加性[J].林业科学,2015,51(2):28-36.
[26]WWISKITTEL A R,KERSHAW Jr J A,HOFMEYER P V,et al.Species differences in total and vertical distribution of branch-and tree-level leaf area for the five primary conifer species in Maine,USA[J].Forest Ecology and Management,2009,258(7):1 695-1 703.
[27]MONSERUD R A,MARSHALL J D.Allometric crown relations in three northern Idaho conifer species[J].Canadian Journal of Forest Research,1999,29(5):521-535
[28]ZHI X,HAI X Q,BAI Y,et al.A comparison of three kinds of multi-model ensemble forecast techniques based on the TIGGE data[J].Journal of Meteorological Research,2012,26(1):41-51.
[2]朱宏光,阳永泉,温远光,等.广西巨尾桉立木与林分叶面积估测模型[J].安徽农业科学,2009,37(30):15 069-15 070.
[3]JONCKHEERE I,FLECK S,NACKAERTS K,et al.Review of methods for in-situ leaf area index determination:part I.theories,sensors and hemispherical photography[J].Agricultural and Forest Meteorology,2004,121(13):19-35.
[4]苏宏新,白帆,李广起.3类典型温带山地森林的叶面积指数的季节动态:多种监测方法比较[J].植物生态学报,2012,36(3):231-242.
[5]马泽清,刘琪璟,曾慧卿,等.南方人工林叶面积指数的摄影测量[J].生态学报,2008,28(5):1 971-1 980.
[6]向洪波,郭志华,赵占轻,等.不同空间尺度森林叶面积指数的估算方法[J].林业科学,2009,45(6):139-144.
[7]RYU Y,SOMMENTAG O,NILSON T,et al.How to quantify tree leaf area index in an open savanna ecosystem:a multiinstrument and multi-model approach[J].Agricultural and Forest Meteorology,2010,150(1):63-76.
[8]刘志理,金光泽.光学仪器法测定叶面积指数季节变化的误差分析[J].林业科学,2016,52(9):11-21.
[9]ZELLERS C E,SAUNDERS M R,MORRISSEY R C,et al.Development of allometric leaf area models for intensively managed black walnut(Juglans nigra L.)[J].Annals of Forest Science,2012,69(8):907-913.
[10]赵东,杨喜田,樊巍,等.杨树农田防护林带单木叶面积的变化[J].林业科学,2011,47(4):107-113.
[11]NELSON A S,WEISKITTEL A R,WAGNER R G.Development of branch,crown,and vertical distribution leaf area models for contrasting hardwood species in Maine,USA[J].Trees,2014,28(1):17-30.
[12]ZHANG W,GE M,LIU X,et al.Optimal weighted combinatorial forecasting model of QT dispersion of ECGs in Chinese adults[J].International Journal of Biometeorology,2016,60(7):1-10.
[13]刘纯,范高锋,王伟胜,等.风电场输出功率的组合预测模型[J].电网技术,2009,33(13):74-79.
[14]DURAI V R,BHARDWAJ R.Forecasting quantitative rainfall over India using multi-model ensemble technique[J].Meteorology and Atmospheric Physics,2014,126(1):31-48.
[15]LUCA G D,CARFORA A.Predicting U.S.recessions through a combination of probability forecasts[J].Empirical Economics,2014,46(1):127-144.
[16]李际平,刘素青.基于最小偏差的林分生长组合预测模型及其应用[J].中南林业科技大学学报,2004,24(5):80-83.
[17]张雄清,雷渊才,陈新美,等.组合预测法在林分断面积生长预估中的应用[J].北京林业大学学报,2010,32(4):6-11.
[18]戴钰.最优组合预测模型的构建及其应用研究[J].经济数学,2010,27(1):92-98.
[19]WAND J,SUN Z H,XU B J.Optimal weighted combinatorial forecasting model in the airport cargo prediction[C]∥The24th Chinese Control and Decision Conference.Taiyuan:[s.n.],2012:1 556-1 561.
[20]张雄清,雷渊才,陈新美.林分断面积组合预测模型权重确定的比较[J].林业科学,2011,47(7):36-41.
[21]郭孝玉.长白落叶松人工林树冠结构及生长模型研究[D].北京:北京林业大学,2013:28-115.
[22]SHINOZAKI K,YODA K,HOZUMI K,et al.A quantitative analysis of plant form the pipe model theory I.basic analyses[J].Japanese Journal of Ecology,1964,14(3):97-105.
[23]RENNOLL K.Pipe-model theory of stem-profile development[J].Forest Ecology and Management,1994,69(1/2/3):41-55.
[24]曾伟生,唐守正.立木生物量方程的优度评价和精度分析[J].林业科学,2011,47(11):106-113.
[25]董利虎,张连军,李凤日.立木生物量模型的误差结构和可加性[J].林业科学,2015,51(2):28-36.
[26]WWISKITTEL A R,KERSHAW Jr J A,HOFMEYER P V,et al.Species differences in total and vertical distribution of branch-and tree-level leaf area for the five primary conifer species in Maine,USA[J].Forest Ecology and Management,2009,258(7):1 695-1 703.
[27]MONSERUD R A,MARSHALL J D.Allometric crown relations in three northern Idaho conifer species[J].Canadian Journal of Forest Research,1999,29(5):521-535
[28]ZHI X,HAI X Q,BAI Y,et al.A comparison of three kinds of multi-model ensemble forecast techniques based on the TIGGE data[J].Journal of Meteorological Research,2012,26(1):41-51.