[ArcGIS小白记]Kriging插值

ArcToolBox>>Spatial Analyst Tools>>Interpolation>>Kriging

引用来源:http://bbs.esrichina-bj.cn/ESRI/viewthread.php?tid=55815

地统计与确定性插值的最大区别在于,地统计插值引入了概率模型,即地统计插值认为从一个统计模型不可能完全精确地得出预测值,所以在进行预测时,应该给出预测值的误差,即预测值在一定概率内合理。

通常所说的地统计插值是指克里格插值法(Kriging)
Z
(s)=μ(s)+ε(s)
S表示不同的位置点,可以是用经纬度表示的空间坐标。
Z(s)是该位置点的属性值。μ(s)为确定趋势值,ε(s)
为自相关随机误差。

当要考虑多个协同变量的情况下,可采用协克里格插值法(Co-Kriging).则其计算公式将变为:
Zj(s)=μj(s)+εj(s)
表示的是第j个变量的情况。在协克里格中,只对主变量进行预估,但将在插值预估时引入不同变量间的随机误差项εj(s)的交叉相关性值,从而构建协同克里格模型。

克里格插值是一个最优的无偏估计法。

获得预测图并不要求数据呈正态分布。但当数据呈正态分布时,克里格插值法将是无偏估计法中效果最好的一种方法。

因此,在进行克里格插值前,可先对非正态分布的数据进行转换,包括Log对数转换,Box-Cox转换,使之呈正态分布,然后再进行插值。
根据样点数据统计特征的不同可将克里格分成多种不同的插值法:

当样点数据是二进制值时,用指示克里格插值法进行概率预测;

对样点数据进行了未知函数变换后,可用该变换函数进行析取克里格插值;

当样点数据的趋势值μ(s)是一个未知常量时,用普通克里格;

当样点数据的趋势可用一个多项式进行拟合,但回归系数未知时,用泛克里格插值法;

当样点数据的趋势已知时,用简单克里格插值法;

其中最常用的是普通克里格与泛克里格插值法;当加入了协变量进行插值时,则叫作协同普通克里格插值法和协同泛克里格插值法。

同反距离权重插值法IDW一样,克里格插值法同样可以表示为:
Z(x0)=
∑λi Z(xi)
Z(x0)
为待估点的值, Z(xi) 为待估点周围的已知样点值,λi为第i个已知点的权重

所不同之处在于,IDW的权重为待估点与已知样点间距离的u次幂的倒数,而克里格的权重值不仅考虑待估点与已知样点、已知样点之间的距离,还考虑了其空间分布的方位。通过半变异函数来赋权重值。

4,135 thoughts on “[ArcGIS小白记]Kriging插值

  1. Thanks for the sensible critique. Me & my neighbor were just preparing to do some research on this. We got a grab a book from our local library but I think I learned more from this post. I am very glad to see such fantastic info being shared freely out there.

  2. I really like your blog.. very nice colors & theme. Did you design this website yourself or did you hire someone to do it for you? Plz respond as I’m looking to create my own blog and would like to find out where u got this from. cheers

  3. When I originally commented I clicked the -Notify me when new comments are added- checkbox and now each time a comment is added I get four emails with the same comment. Is there any way you can remove me from that service? Thanks!

  4. Hi Bro, hairstyles picture Thank you very much for your writing and your article and I wish you continued success. Please try to produce such valuable content in the following processes. In addition to this article, I am very happy to see your unique content.

  5. Sizin de diğer tüm yurt dışına hizmet vermek isteyen şirketlerimiz gibi gostr belgesi ne ihtiyacınız varsa bunu bizim hocalarımız ile artık çok kolay bir şekilde yapabileceğinizi iddia ediyoruz. Gostr sertifikası özellikle Rusya başta olmak üzere birçok firmanın da en önemli hassas noktalarından olan bir belgedir. Sizin de gostr veya eac belgesi veya da birçok başka belgelere ihtiyacınız varsa bunu şirketimiz tarafından artık daha hızlı bir şekilde temin edebileceğinizi hatırlatmak isteriz. Şirketimiz sizin adınıza ihtiyaç duyduğunuz belgelerin hepsini eksiksiz bir şekilde tamamlamanız konusunda size çok yardımcı olacaktır. Detaylı bilgi için bizi arayabilirsiniz.

  6. Hi Bro, hairstyles picture Thank you very much for your writing and your article and I wish you continued success. Please try to produce such valuable content in the following processes. In addition to this article, I am very happy to see your unique content.

  7. My wife and i got now contented that John managed to do his homework by way of the ideas he discovered through your weblog. It is now and again perplexing to just happen to be giving away tips and tricks a number of people have been trying to sell. And now we know we need the blog owner to appreciate because of that. All of the illustrations you have made, the simple site menu, the friendships you can assist to foster – it’s most exceptional, and it’s really assisting our son and us imagine that that content is amusing, and that’s really fundamental. Thank you for the whole lot!

Leave a Reply

Your email address will not be published. Required fields are marked *