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张旭臣. 空间变异函数的数学模型及参数反演[J]. 科学技术与工程, 2010, (18): .
Zhang Xuchen.The Mathematical Model of Spatial Variogram and Parameters Inversion[J].Science Technology and Engineering,2010,(18):.
空间变异函数的数学模型及参数反演
The Mathematical Model of Spatial Variogram and Parameters Inversion
投稿时间:2010-04-01  修订日期:2010-04-07
DOI:
中文关键词:  空间变异函数  数学模型  参数反演  克里格方程组  交叉检验  方差  降水量空间插值
英文关键词:Spatial Variogram  mathematical model  parameter inversion  kriging equation set  cross-examination  variance  precipitation spatial interpolation
基金项目:河北省2009年水利科研与推广计划项目(2009-62)
  
作者单位
张旭臣 河北省承德水文水资源勘测局
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中文摘要:
      空间变异函数在克里格估计中占有重要地位。基于椭圆分布函数可导出两类空间变异函数的数学模型。一类是只考虑变程各项异性的模型,本文称之为AE模型;一类是只考虑拱高各项异性的模型,称之为CE模型。传统的方法需要先进行空间变异函数的拟合,然后进行克里格估计。交叉检验方差是评价估计精度的一项重要指标。根据克里格方程组的重要性质,克里格估值仅与标准变异函数有关,对标准变异函数进行线性变换得到新的变异函数不会改变克里格估值和交叉检验方差。因此,用拟合方法获得的最优变异函数进行交叉检验,通常并不能有效地降低交叉检验方差。如果直接以交叉检验方差为目标函数进行参数反演,则可以有效地解决这个问题。变异函数数学模型一般含有5个参数,其中2个是线性变换作用。进行交叉检验时只需研究标准变异函数的3个参数,从而可以降低参数反演的复杂度。研究表明:较之AE类模型CE类模型具有更强的适应性,通常可获得更小的交叉检验方差;鉴于评价面非常复杂,将遗传算法(GA)应用于参数反演是可行和有效的。滦河流域降水量空间插值实例表明,交叉检验均方差降幅分别为11.7%和29.8%。
英文摘要:
      The Spatial Variogram plays an important role in Kriging estimation. Two types of the mathematical models of Spatial Variogram are inferred based on the elliptic distribution function. One type only considers the anisotropy of variable-range(A) in the model, which is called the AE model in this paper. Another only considers the anisotropy of high arch(C) in the model, which is called the CE model. Traditional methods need to fit the Spatial Variogram and then deal with the kriging estimation. The cross-examination variance is an important indicator to evaluate the estimation accuracy. According to the important characteristic of Kriging equation set, Kriging estimation is only related to the standard Spatial Variogram, and for the linear change from standard Spatial Variogram to a new Spatial Variogram , it will not change the result of kriging estimation and the cross-examination. Thus, doing the cross-examination by the Spatial Variogram from optimal fitting method can not usually reduce the cross-examination variance effectively. If directly process parameters inversion within the cross-examination variance as the objective function, we can solve this problem effectively. The spatial variogram model generally contains five parameters in which two play linear effect on the function. We need only study three parameters of the standard spatial Variogram on the cross-examination in order to make it easy to progress parameter inversion. Studies have shown that CE model has more flexibility than AE model, and it is usually get smaller cross-examination variance. Because of the complexity of evaluation surface, Genetic Algorithms (GA) being applied to parameter inversion is feasible and effective. The case of spatial interpolation of precipitation on the Basin of Luan River shows that the standard deviation reduced 11.7% and 29.8% separately.
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