| Kriging插值和序贯高斯条件模拟算法的对比分析 |
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| 引用本文： | 赵彦锋,孙志英,陈杰.Kriging插值和序贯高斯条件模拟算法的对比分析[J].地球信息科学,2010,12(6):767-776. |
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| 作者姓名： | 赵彦锋 孙志英 陈杰 |
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| 作者单位： | 1. 郑州大学水利与环境学院, 郑州 450001;
2. 河南省国土资源调查规划院, 郑州 450016 |
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| 基金项目： | 国家自然科学青年基金项目（40801080） 国家自然科学基金项目（40971128） |
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| 摘 要： | 本文对Kriging插值与序贯高斯条件模拟值的算法联系进行了推导,并将两种计算结果和原始数据的统计参数作了对比。结果表明,Monto-carlo方法求得的序贯高斯条件模拟值经数学变换后等同于已知数据和此前模拟数据共同参与的Kriging插值结果与一个随机偏差的和,该随机偏差的均值为0,方差为Kriging误差方差。最优性条件导致Kriging插值结果的方差较原始数据降低了1个Kriging误差方差,造成Kriging平滑效应,其空间变异函数值降低,但自协方差函数值不变。序贯高斯条件模拟避免了平滑效应,其方差、变异函数和自协方差函数均不变,而其模拟值的误差方差较Kriging误差方差增加了1倍,表明1次随机模拟值的误差比Kriging插值大。然而,多次随机模拟值的平均值与Kriging插值的地理制图效果近似,可以弥补局部估值误差大的不足。因此,在应用中,Kriging插值是提供局部最优估计的方法,但却低估了全局的空间变异。而序贯高斯条件模拟的优点,在于提供若干等可能概率的模拟结果以进行估值的不确定性评价,并再现全局的空间可变性。
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| 关 键 词： | 算法联系 Kriging插值 序贯高斯条件模拟(SGCS) |
| 收稿时间： | 2010-08-29; |
Analysis and Comparison in Arithmetic for Kriging Interpolation and Sequential Gaussian Conditional Simulation |
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| ZHAO Yanfeng,SUN Zhiying,CHEN Jie.Analysis and Comparison in Arithmetic for Kriging Interpolation and Sequential Gaussian Conditional Simulation[J].Geo-information Science,2010,12(6):767-776. |
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| Authors: | ZHAO Yanfeng SUN Zhiying CHEN Jie |
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| Institution: | 1. School of Environment and Water Conservancy,Zhengzhou University,Zhengzhou 450001,China;
2. Academy of Land Surveying and Planning,Zhengzhou 450016,China |
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| Abstract: | In this paper,the relation in arithmetic between Kriging interpolation and sequential Gaussian conditional simulation（SGCS）were inferred and the statistical parameters for Kriging interpolation,for SGCS and for the original data were compared.It demonstrated that a stochastic realization of SGCS calculated by Monte Carlo Method could be divided into two parts by mathematic transform,one was Kriging value,and the other was a stochastic deviation which followed a normal distribution with the mean = 0 and the variance equal to Kriging error variance.The comparison among Kriging interpolation,SGCS and the origin data showed that the variance of Kriging interpolation value was lower than that of the original data with a reduction equal to one Kriging error variance.This was a result of demanding for optimal weights in estimating,which was attributed to the smoothing effect during Kriging interpolation.And because of the smoothing effect,the variogram for Kriging interpolation was lower than that of the original data,though it kept no change in autocovariance.By adding the missing variance back into the SGCS,the smoothing effect was corrected,and it kept no change in variance,variogram and covariance.But the error variance caused by SGCS was as 2 times as Kriging error variance which showed that the precision of local estimate of a single SGCS was lower than that of Kriging.However,SGCS could correct the shortage by adequate repeats because the mean SGCS and Kriging interpolation share a same expectation in theory.And then,in the function of geography mapping mean SGCS was comparable with Kriging.In practice it could be concluded that the advantage of Kriging method was to provide accurate estimate in a local zone though it underestimated spatial variation in the whole area.While the advantage of SGCS was to carry out uncertainty assessment for spatial estimate by providing multiple results about probability and reproduce the spatial variability in the whole area. |
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| Keywords: | Kriging interpolation sequential Gaussian conditional simulation（SGCS） relation in arithmetic |
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