Most appropriate interpolation method?

[RebeccaSlepkov]

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]

   We basically need to connect regions with the lowest z values, then those with the next lowest, etc, with interpolation between our points.

Can you try explaining this again? I think you lost us here.

[RebeccaSlepkov]

Ok, let me try again.  We have about 20 of sites in Africa, each defined by lat, long and a third variable.  Instead of elevation our 'z' variable is a measurement of the ecological distance between each site and an archaeological site.  We want to display this visually by plotting contours on a map, but we aren't sure what interpolation method to use to plot the contours between the sites.  One suggestion we have gotten is nearest neighbour, but I've also tried IDW and Global Polynomial.
Does that help at all?

[curtvprice]

Ok, let me try again.  We have about 20 of sites in Africa, each defined by lat, long and a third variable.  Instead of elevation our 'z' variable is a measurement of the ecological distance between each site and an archaeological site.  We want to display this visually by plotting contours on a map, but we aren't sure what interpolation method to use to plot the contours between the sites.  One suggestion we have gotten is nearest neighbour, but I've also tried IDW and Global Polynomial.
Does that help at all?

There really is no hard and fast rule about which is most appropriate, it kind of depends on what you're trying to do.

Global Polynomial is normally used to find overall trends (so you can isolate local effects). However, with really noisy data, overall trends (although unlikely to pass through your points if you choose a low order polynomial) may be exactly what you want to calculate -- the trend will be smooth and obvious.

IDW is the simplest interpolator (really a family of interpolators based on neighborhood and power choices). Nearest neighbor is a special case of IDW (when you choose to use only 1 neighbor for each estimate) -- and is equivalent to creating Thiessen polygons. It doesn't always make very pretty surfaces. "Natural Neighbor" is a nice general-purpose interpolator Esri provides that is sort of a hybrid of IDW and a nearest-neighbor approach - it weights by shared "territory" as defined by the thiessen polygons instead of merely distance.

If your data show a clear pattern and you want your contours to completely agree with your input points, spline interpolators are a worth trying. You can tweak splines to model the amount of local variablity in your data. Since they are a curve fit through points, outliers can give you some very unhelpful surfaces (doing a spline can help you identify such unhelpful points, as they can warp your surface horribly).

Kriging is more for parameter estimation than making contours, say if you are estimating values that go into another model and you want the best linear unbiased estimate at every gridcell. (This is usually not a very "pretty" trend suface.)

Your mileage may vary, but I hope this quick overview helps! Its best to read up on each interpolator so you have a better idea of their strengths and weaknesses for your task and your dataset.

[EricKrause]

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?

[curtvprice]

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."

[curtvprice]

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.pd... July 2004: Interpolating Surfaces in ArcGIS Spatial Analyst