A geostatistical framework for area-to-point spatial interpolation
A geostatistical framework for area-to-point spatial interpolation
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DOI：
10.1111/j.1538-4632.2004.tb01135.x
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发表时间：
2004-07-01
影响因子：
3.6
通讯作者：
Kyriakidis, PC
中科院分区：
文献类型：
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作者：
Kyriakidis, PC
在支持度变化的一般地质统计学框架内，根据相同属性的面数据对点值进行空间预测;术语支持度是指由每个数据或未知值所告知的域。它表明，拟议的地质统计框架可以明确和一致的帐户之间的支持可用的面积数据和抢手的点预测的差异。特别是它被证明是适当的建模所需的地质统计框架产生一致的（质量保留或pycnophylactic）预测的所有区域到区域和区域到点的协方差。换句话说，由面积平均（或面积总和）基准面所通知的任意区域内的点预测的面积平均（或面积总和）等于该特定基准面。此外，拟议的地质统计框架提供了一个独特的优势，提供了一个衡量每个点预测的责任（标准误差）。它还表明，现有的几种方法，面积到点的插值可以被视为在这个地质统计框架。更准确地说，它表明：（i）choropleth地图的情况下，对应于在点支持水平的空间独立性的假设下的地质统计解决方案;（ii）几种形式的核平滑可以被视为替代（尽管有时不连贯）地统计方法的实施;（iii）在无非负性约束的拟无限域上的Tobler光滑密度插值，当在点支撑水平上采用半变异函数模型时，对应于泊松偏微分方程的自由空间绿色函数（一维线性或二维对数）的地质统计学解。在一个正式的案例研究，几个I-D的例子来说明相关的概念。
The spatial prediction of point values from areal data of the same attribute is addressed within the general geostatistical framework of change of support; the term support refers to the domain informed by each datum or unknown value. It is demonstrated that the proposed geostatistical framework can explicitly and consistently account for the support differences between the available areal data and the sought-after point predictions. In particular it is proved that appropriate modeling of all area-to-area and area-to-point covariances required by the geostatistical framework yields coherent (mass-p reserving or pycnophylactic) predictions. In other words, the areal average (or areal total) of point predictions within any arbitrary area informed by an areal-average (or areal-total) datum is equal to that particular datum. In addition, the proposed geostatistical framework offers the unique advantage of providing a measure of there liability (standard error) of each point prediction. It is also demonstrated that several existing approaches for area-to-point interpolation can be viewed within this geostatistical framework. More precisely, it is shown that (i) the choropleth map case corresponds to the geostatistical solution under the assumption of spatial independence at the point support level; (ii) several forms of kernel smoothing can be regarded as alternative (albeit sometimes incoherent) implementations of the geostatistical approach; and (iii) Tobler's smooth pycnophylactic interpolation, on a quasi- infinite domain without non-negativity constraints, corresponds to the geostatistical solution when the semivariogram model adopted at the point support level is identified to the free-space Green's functions (linear in 1-D or logarithmic in 2-D) of Poisson's partial differential equation. In lien of a formal case study, several I-D examples are given to illustrate pertinent concepts.