ArcGIS 空间分析包括如下内插方法

? 样条（Spline）
样条用一种数学函数来估计值，最小化所有的表面曲率，逼近曲面一种方法。样条函数易操作，计算量不大，它与空间统计方法相比具有以下特点:不需要对空间方差的结构做预先估计；不需要做统计假设，而这些假设往往是难以估
计和验证的；同时，当表面很平滑时，也不牺牲精度。样条函数适合于非常平滑的表面，一般要求有连续的一阶和二阶导数；它适合于根据很密的点内插等值线，特别是从不规则三角网（TIN）内插等值线。样条函数的缺点是难以对误差进行估计，点稀时效果不好。
? Inverse Distance Weighted (IDW)
反距离加权法是最常用的空间内插方法之一。它认为与未采样点距离最近的若干个点对未采样点值的贡献最大，其贡献与距离成反比。以数据点到待求点的距离给予适当的权重，按最小二乘法平差原理求解。权的值应与距离成反比，间距愈近，对待求点测定值的影响应愈大。如取W = 1 / dp 或[(R-d)/d]p式中d 为待定点到数据点间的水平距离， p 是距离的幂，它显著影响内插的结果，它的选择标准是最小平均绝对误差。Husar 等的研究结果表明，幂越高，内插结果越具有平滑的效果。
? Kriging
克里格法是空间统计方法的一种。所谓空间统计方法，其基本假设是建立在空间相关的先验模型之上的。假定空间随机变量具有二阶平稳性，或者是服从空间统计的本征假设（in trinsic hypothesis）。则它具有这样的性质：距离较近的采样点比距离远的采样点更相似，相似的程度或空间协方差的大小，是通过点对的平均方差度量的。点对差异的方差大小只与采样点间的距离有关，而与它们的绝对位置无关。空间统计内插的最大优点是以空间统计学作为其坚实的理论基础，可以克服内插中误差难以分析的问题，能够对误差做出逐点的理论估计；它也不会产生回归分析的边界效应。缺点是复杂；另一个缺点是变异函数。克里格法的优点是以空间统计学作为其坚实的理论基础，物理含义明；不但能估计测定参数的空间变异分布，而且还可以估算估计参数的方差分布。克里格法的缺点是计算步骤较烦琐，计算量大，且变异函数有时需要根据经验人为选定。

ok

这个不错，不过好象等高线的插值总是有那么点不如人意o  

GIS大ＧＧ，等高线插值就是有问题啊，其实只要是插值效果就不会有实测的好，呵呵！不花钱的还可以吧，要不就自己搞新模式。

<P>希望能有个好方法,大家收集些工具和方法,放上来啊</P><P>以后大家就可以节约很多时间了</P>

<img src="images/post/smile/dvbbs/em01.gif" /><img src="images/post/smile/dvbbs/em02.gif" />

<img src="images/post/smile/dvbbs/em01.gif" /><img src="images/post/smile/dvbbs/em02.gif" /><img src="images/post/smile/dvbbs/em07.gif" />

<P>听说澳大利亚国立大学有人开发了个anusplin的插值软件，效果非常好，就是不好用，参数非常多，界面是dos的。</P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><FONT face="Times New Roman">The aim of the ANUSPLIN package is to provide a facility for transparent analysis and interpolation of noisy multi-variate data using thin plate smoothing splines. The package supports this process by providing comprehensive statistical analyses, data diagnostics and spatially distributed standard errors. It also supports flexible data input and surface interrogation procedures.</FONT>  ANUSPLIN软件包的目标是应用薄盘光滑样条函数为嘈杂的多变量数据进行透彻分析和插值提供便利。软件包通过提供综合统计分析、数据诊断和空间分布的标准误实现之。另外还提供了灵活的数据输入和表面审查程序。<p></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; TEXT-ALIGN: left; mso-line-height-rule: exactly; mso-layout-grid-align: none" align=left><p><FONT face="Times New Roman"> </FONT></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><FONT face="Times New Roman">The original thin plate (formerly Laplacian) smoothing spline surface fitting technique was described by Wahba (1979), with modifications for larger data sets due to Bates and Wahba (1982), Elden (1984), Hutchinson (1984) and <st1:City w:st="on"><st1:place w:st="on">Hutchinson</st1:place></st1:City> and de Hoog (1985). The package also supports the extension to partial thin plate splines based on Bates et al. (1987). This allows for the incorporation of parametric linear sub-models (or covariates), in addition to the independent spline variables. This is a robust way of allowing for additional dependencies, provided a parametric form for these dependencies can be determined. In the limiting case of no independent spline variables (not currently permitted), the procedure would become simple multi-variate linear regression. </FONT>薄盘光滑样条函数拟合技术（之前称拉普拉斯算子）最初是<FONT face="Times New Roman">Wahba</FONT>（<FONT face="Times New Roman">1979</FONT>）描述的，其应用于大数据集的改进归于<FONT face="Times New Roman">Bates;Wahba (1982),  Elden (1984),Hutchinson (1984)</FONT>和<FONT face="Times New Roman"> Hutchinson</FONT>及<FONT face="Times New Roman">de Hoog (1985)</FONT>。<p></p></P>
<P 0cm 0cm 0pt; mso-layout-grid-align: none"><p><FONT face="Times New Roman"> </FONT></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><FONT face="Times New Roman">Thin plate smoothing splines can in fact be viewed as a generalisation of standard multivariate linear regression, in which the parametric model is replaced by a suitably smooth non-parametric function. The degree of smoothness, or inversely the degree of complexity, of the fitted function is usually determined automatically from the data by minimising a measure of predictive error of the fitted surface given by the generalised cross validation (GCV). Theoretical justification of the GCV and demonstration of its performance on simulated data have been given by Craven and Wahba (1979). </FONT>实际上光滑薄盘样条函数可以看作是广义的标准多变量线性回归，只是其中的参变量模型被适宜的光滑的非参数函数所代替。拟合函数的光滑度或相反地复杂度通常使用广义交叉验证<FONT face="Times New Roman">(GCV)</FONT>给定的拟合表面的预测误差测度最小而自动确定。<FONT face="Times New Roman">GCV</FONT>的理论证明及其模拟数据的性能的验证已有<FONT face="Times New Roman">Craven</FONT>和<FONT face="Times New Roman">Wahba (1979)</FONT>给出。<p></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><p><FONT face="Times New Roman"> </FONT></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><FONT face="Times New Roman">An alternative criterion is to minimise the generalised maximum likelihood (GML) developed by Wahba (1985,1990). It is based on a Bayesian formulation for the thin plate smoothing spline model and has been found to be superior to GCV in some cases (Kohn et al. 1991). Both criteria are offered in this version of ANUSPLIN. </FONT>另一标准是<FONT face="Times New Roman">Wahba(1985,1990)</FONT>发展的最小广义最大似然法。它依据于光滑薄盘样条函数模型的贝叶斯公式，并已被证明在某些情况下优于<FONT face="Times New Roman">GCV</FONT>法（<FONT face="Times New Roman">Kohn</FONT>等，<FONT face="Times New Roman">1991</FONT>）。本版<FONT face="Times New Roman">ANUSPLIN</FONT>提供了以上两种标准。<p></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><p><FONT face="Times New Roman"> </FONT></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><FONT face="Times New Roman">A comprehensive introduction to the technique of thin plate smoothing splines, with various extensions, is given in Wahba (1990). A brief overview of the basic theory and applications to spatial interpolation of monthly mean climate is given in <st1:City w:st="on"><st1:place w:st="on">Hutchinson</st1:place></st1:City> (<st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="False" SourceValue="1991" UnitName="a">1991a</st1:chmetcnv>). More comprehensive discussion of the algorithms and associated statistical analyses, and comparisons with kriging, are given in <st1:City w:st="on">Hutchinson</st1:City> (1993) and Hutchinson Gessler (1994). Recent applications to annual, monthly and daily precipitation data have been described by <st1:place w:st="on"><st1:City w:st="on">Hutchinson</st1:City></st1:place> (1995, 1998ab) and Price et al. (2000). The book by Schimek (2000) provides a good overview of the subject of smoothing and nonparametric regression with extensive references. Wahba</FONT>（<FONT face="Times New Roman">1990</FONT>）对多种扩展情况下光滑薄盘样条函数技术进行了全面介绍。<FONT face="Times New Roman">Hutchinson</FONT>（<st1:chmetcnv w:st="on" TCSC="0" NumberType="1" Negative="False" HasSpace="False" SourceValue="1991" UnitName="a"><FONT face="Times New Roman">1991a</FONT></st1:chmetcnv>）对其基本原理和月平均气候空间插值应用进行了简要概述。<FONT face="Times New Roman">Hutchinson</FONT>（<FONT face="Times New Roman">1993</FONT>）和<FONT face="Times New Roman">Gessler</FONT>（<FONT face="Times New Roman">1994</FONT>）对其算法与统计分析及与<FONT face="Times New Roman">kriging</FONT>的比较进行了全面探讨。最近<FONT face="Times New Roman">Hutchinson</FONT>（<FONT face="Times New Roman">1995</FONT>，<FONT face="Times New Roman">1998ab</FONT>）和<FONT face="Times New Roman">Price</FONT>等（<FONT face="Times New Roman">2000</FONT>）对其应用于年、月、日降水量数据进行了描述。<FONT face="Times New Roman">Schimelk</FONT>（<FONT face="Times New Roman">2000</FONT>）的著作很好地概述光滑、非参数回归主题。<p></p></P>
<P 0cm 0cm 0pt; LINE-HEIGHT: 20pt; mso-line-height-rule: exactly; mso-layout-grid-align: none"><p><FONT face="Times New Roman"> </FONT></p></P>
<P><FONT face="宋体, MS Song">It is often convenient, particularly when processing climate data, to process several surfaces simultaneously. If the independent variables and the relative weightings of the data are the same for each surface then many surfaces can be calculated for little more computation than one surface. ANUSPLIN allows for arbitrarily many such surfaces with significant savings in computation. ANUSPLIN also introduces the concept of "surface independent variables", to accommodate independent variables that change systematically from surface to surface. ANUSPLIN permits systematic interrogation of these surfaces, and their standard errors, in both point and grid form. ANUSPLIN also permits transformations of both independent and dependent variables and permits processing of data sets with missing data values. When a transformation is applied to the dependent variable ANUSPLIN permits back-transformation of the fitted surfaces, calculates the corresponding standard errors, and corrects for the small bias that these transformations induce. This has been found to be particularly convenient when fitting surfaces to precipitation data and other data that are naturally positive or non-negative. </FONT>同时生成多个表面尤其是处理气候数据时通常十分方便。如果独立变量及数据的相关权重对每一表面均相同，那么多个表面几乎不比单个表面需要更多的计算。<FONT face="宋体, MS Song">ANUSPLIN</FONT>考虑任意多的这种表面显著地减少了计算量。<FONT face="宋体, MS Song">ANUSPLIN</FONT>还引入了“表面独立变量”的概念以适应那些随表面而系统地发生变化的独立变量。<FONT face="宋体, MS Song">ANUSPLIN</FONT>允许以点和栅格两种方式对这些表面及其标准误进行系统审讯。<FONT face="宋体, MS Song">ANUSPLIN</FONT>还允许对独立变量和非独立变量进行转换，允许处理包含有缺失值的数据。当对非独立变量进行转换时，<FONT face="宋体, MS Song">ANUSPLIN</FONT>允许对拟合表面进行逆转换，计算相应的标准误差，并对这些转换引起的微小偏差进行校正。显而易见，这在拟合降水及其它正的或非负的数据表面时尤为方便</P>

<P>大家可以去看楼上兄弟说的</P>
<P><a href="http://cres.anu.edu.au/outputs/anusplin.php" target="_blank" >http://cres.anu.edu.au/outputs/anusplin.php</A></P>