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I'm trying to create a DEM using point data spaced very regularly about 10m apart. The area I am interpolating is an educational facility with many flat parking lots and football fields but still has some fairly steep hills that will often plateau to a parking lot. Due to these known plateaus, I have ruled out the Splining method; However, I'm still not sure between using IDW and Kriging methods. I can't see much of a difference after trying both of them and still haven't made my decision after a little research. Anyone got some words of wisdom to clear this up for me? Much appreciated!

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I think you need somthing as "conditioned DME modeling", when Kriging is a good choice... To take into account the different sources of error that you facing in your problem. –  Peter Krauss Jan 18 at 17:36
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Welcome to GIS.SE. Were the points selected intelligently by a field surveyor, as one usually does? I.e., did they choose points at breaks in slope? Also, what is the purpose of the DEM -- contouring, volumes? Such matters can affect our advice. –  martin f Jan 18 at 18:18
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Kriging ought to work better than IDW but requires a lot of expertise and care in this situation, because your description of the topography indicates the spatial correlation will not be stationary, which is a crucial assumption behind kriging. (Without this assumption one cannot even estimate a valid variogram.) If you have the option, you might look into creating a TIN. –  whuber Jan 18 at 22:40
    
+1 for the TIN, it is really worth taking into account in your case. –  radouxju Jan 19 at 19:31
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1 Answer 1

up vote 13 down vote accepted

Both forms rely on Toblers first law of geography: things that are close are more related than things that are further apart.

IDW is the simpler of the two techniques. It involves using known z values and weights determined as a function of distances between the unknown and known points. As such in IDW points that are far away have far less influence than points that are close. The effect of the inverse distance weights have can often be determined by the user by changing the power that the inverse distance is raised to.

IDW using a search radius

As seen in this diagram you can determine the limits of which data points (z values) IDW should take into consideration using a search radius.

IDW differs from Kriging in that no statistical models are used. There is no determination of spatial autocorrelation taken into consideration (that is to say how correlated variables are at varying distances is not determined). In IDW only known z values and distance weights are used to determine unknown areas.

IDW has the advantage that it is easy to define and therefore easy to understand the results. It may be inadvisable to use Kriging if you are unsure of how the results were arrived at. Kriging also suffers when there are outliers (see here for an explanation.).

ESRI states:

Kriging is most appropriate when you know there is a spatially correlated distance or directional bias in the data. It is often used in soil science and geology.

Kriging is a statistical method that makes use of a variograms to calculate the spatial autocorrelation between points at graduated distances (A nice introduction can be found here Statios Variogram Introduction and Washington Intro to Variograms). It uses this calculation of spatial autocorrelation to determine the weights that should be applied at various distances. Spatial autocorrelation is determined by taking squared differences between points. To clarify Kriging is similar to IDW in that:

Like IDW interpolation, kriging forms weights from surrounding measured values to predict unmeasured locations. As with IDW interpolation, the measured values closest to the unmeasured locations have the most influence. (Source)

But differs in that weights are helped determined by the semi variogram.

Variogram Equation

“where n is the number of pairs of sample points of observations of the values of attribute z separated against distance h” (Burrough and McDonnell, 2004: 134).

The Semivariogram

There are various different niche types of Kriging.

Further reading:

  1. How IDW works.
  2. How Kringing works:
  3. How to use Kriging:
  4. Types of Interpolation:
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(+1) Thank you--your additions are a great improvement! –  whuber Jan 19 at 15:22
    
This was helpful for me and I appreciate the effort put in. –  Calavin Jan 19 at 19:56
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