Most appropriate interpolation method?

Question

Hi,
    I have a map of a number of modern sites that are used as comparisons for a fossil site.  They are all plotted with x,y,z coordinates, with the z being a measure of the 'distance' between that modern site's environment and that hypothesized for the fossil site.  My colleague plotted the points out in SAS using a joining linear interpolation, and we are trying to figure out the best way to plot this in ArcMap so that the results can be displayed on a map.  We basically need to connect regions with the lowest z values, then those with the next lowest, etc, with interpolation between our points. 
Any thoughts on which techniques would be the most appropriate?  We first thought the global polynomial, but that doesn't look at all like our stats results.
Thank you so much for any advice...

curtvprice · Answer

Here's a great summary of ArcGIS Spatial Analyst interpolators. (Colin Childs rocks.)

ArcUser" rel="nofollow" target="_blank">http://www.esri.com/news/arcuser/0704/files/interpolating.pdf]ArcUser July 2004: Interpolating Surfaces in ArcGIS Spatial Analyst

curtvprice · Answer

If kriging is the optimal interpolator (under certain conditions), wouldn't it also be the optimal method for making contour maps?

If the point of your contour map is to demonstrate a trend, you may want random noise or the effect of outliers to be removed from your contours -- as this would obstruct what you're trying to show with the contours.

However, the cell by cell unbiased estimate of value, although it may make very ugly and maybe even nonsensical contours, may be what you want if you want a best estimate of a value over a drainage basin or over a groundwater model cell.

Remember for every output gridcell that doesn't land exactly on a point of input data (pretty much everywhere, in most cases!)  you will be "making up data" -- the surface you are generating is a model, and as one of my colleagues likes to say: "all models are wrong, some are useful."

Eric6346 · Answer

Kriging is more for parameter estimation than making contours

Can you explain what you mean here?  Which parameters are you talking about? If kriging is the optimal interpolator (under certain conditions), wouldn't it also be the optimal method for making contour maps?