CHOOSING FUNCTIONS FOR SEMI-VARIOGRAMS OF SOIL PROPERTIES AND FITTING THEM TO SAMPLING ESTIMATES
CHOOSING FUNCTIONS FOR SEMI-VARIOGRAMS OF SOIL PROPERTIES AND FITTING THEM TO SAMPLING ESTIMATES
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DOI：
10.1111/j.1365-2389.1986.tb00392.x
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发表时间：
1986-12-01
期刊：
影响因子：
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通讯作者：
WEBSTER, R
中科院分区：
文献类型：
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作者：
MCBRATNEY, AB;WEBSTER, R
半变异函数是地质统计学的核心，也是土壤地质统计学应用中最重要的工具。半变函数的数学函数必须是条件负半定的，满足这一要求的简单函数族很少。其中包括由移动平均过程导出的具有有限先验方差的传递模型。球形格式和指数格式是最常遇到的成员。另一大类是无界模型，其中方差似乎没有限制地增加。线性模型是这一组中最常见的。如果需要更复杂的模型，它们可以通过组合两个或更多的简单模型来形成。通常的半方差估计通常被认为是低效的，并且对数据偏离正态性很敏感。它与稳健估计量进行了比较，并表明在无偏和具有不宽的置信区间方面通常更可取。对于常规分析，通过加权最小二乘近似拟合模型到样本半方差，其权重与期望的半方差成正比，比更复杂和计算要求更高的广义最小二乘和最大似然统计过程更可取。赤池信息准则被推荐用于从几个似是而非的模型中选择最佳模型来描述观察到的土壤变化，尽管对于克里格来说，可能需要验证所选模型。给出了拟合土壤半变差函数的模型实例并进行了比较。
The semi-variogram is central to geostatistics and the single most important tool in geostatistical applications to soil. Mathematical functions for semi-variograms must be conditional negative semi-definite, and there are only a few families of simple function that meet this demand. These include the transitive models with finite a priori variance deriving from moving average processes. The spherical and exponential schemes are the most often encountered members. The other major group is that of unbounded models in which the variance appears to increase without limit. The linear model is the most common in this group. If more complex models are needed they can be formed by combining two or more simple models. The usual estimator of the semi-variance is often considered inefficient and to be sensitive to departures from normality in the data. It is compared with a robust estimator and shown to be generally preferable in being unbiased and having confidence intervals that are no wider. For routine analysis, fitting models to sample semi-variograms by weighted least squares approximation, with weights proportional to the expected semivariance, is preferred to the more elaborate and computationally demanding statistical procedures of generalized least squares and maximum likelihood. The Akaike information criterion is recommended for selecting the best model from several plausible ones to describe the observed variation in soil, though for kriging it may be desirable to validate the chosen model. Examples of models fitted to soil semi-variograms are shown and compared.