﻿ 林分断面积组合预测模型权重确定的比较
 林业科学  2011, Vol. 47 Issue (7): 36-41 PDF
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#### 文章信息

Zhang Xiongqing, Lei Yuancai, Chen Xinmei

Comparison of Weight Computation in Stand Basal Area Combined Model

Scientia Silvae Sinicae, 2011, 47(7): 36-41.

### 作者相关文章

Comparison of Weight Computation in Stand Basal Area Combined Model
Zhang Xiongqing, Lei Yuancai , Chen Xinmei
Research Institute of Forest Resources Information Techniques, CAF Beijing 100091
Abstract: In this paper, forecast combination was introduced to improve stand basal area prediction accuracy and compatibility.A linear combination of two or more predictions may often yield more accurate forecasts than using a single model to the extent that the component forecasts contain useful and independent information.But it is very important to calculate weight coefficients for improving forecast combination.Based on the data of the Chinese pine in Beijing mountains, sum of squared errors method, variance-covariance method and optimal weight method were used to calculate weight coefficients of combined model.Results show that forecast combination for predicting stand basal area outperformed over the stand-level and tree-level models respectively, and meanwhile, stand basal area model based on the optimal weight method(R2 = 0.929 2) is superior to other two methods, and variance-covariance method(R2 = 0.929 1) is better than the sum of squared errors method(SSE) (R2 = 0.929 1).
Key words: stand basal area    forecast combination    sum of squared errors method(SSE)    variance-covariance method    optimal weight method

1 数据来源

2 研究方法 2.1 组合预测权重确定的方法 2.1.1 误差平方和法

Newbold等(1974)提出在单个预测模型之间不存在相关性的前提下利用误差平方和法确定组合预测模型的权重, 预测精度较高; Winkler等(1983)研究表明:误差平方和法在对实际问题的预测研究中具有很好的预测精度。其原理为:对误差平方和小的模型赋予较大的权重, 误差平方和大的模型赋予较小的权重。权重公式为:

 (1)
 (2)

2.1.2 方差协方差法

Bates等(1969)在提出组合预测方法的同时, 利用方差协方差法来确定组合预测的权重。方差协方差法利用加权平均的方法, 对较精确的预测值赋予较大的权重。这种方法从理论上得到最佳的权值系数组合, 如果这个权值可以保持稳定, 则此方法就有较大的稳定性; 但是在实际情况下权值常不稳定, 因此有局限性(张艳等, 2006)。单木水平模型和林分水平模型的权重分别为(Granger et al., 1977; Yue et al., 2008) :

 (3)
 (4)

2.1.3 最优加权法

J = (e1, e2), 则。用Z表示林分断面积预测的误差平方和, 则Z = WTEW。由约束条件ω1 + ω2 = 1, 可以得到:

 (5)

 (6)

 (7)

2.2 单木胸高断面积模型及林分断面积模型的建立

Cao(2002)在对单木生长模型进行年生长预测时, 提出了可变生长率法(variable rate method), 该方法考虑了单木每年生长的变化, 而不是按每年固定生长率进行的。那么, 林分每年的生长量也是有变化的, 不应该固定不变。

 (8a)
 (8b)
 (8c)
 (8d)
 (8e)
 (8f)
 (9a)
 (9b)
 (9c)
 (9d)
 (9e)
 (9f)

3 模型评价

 (10)
 (11)
 (12)
 (13)

4 结果与分析

 图 1 3种不同方法的林分断面积预测值与实际值线性相关图 Figure 1 Correlations of predicted and observed stand basal area based on three different methods a.误差平方和法SSE; b.方差协方差法Variance-covariance; c.最优加权法Optimal weight

5 结论

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