# Interpolation of Three Data Points

I have three location points with weather data. It's a 10-year composite of temperature values which means I only have three values for three locations for ten years. The distance between points is approximately 100 kilometers.

I want to interpolate these points to create a temperature map for the area. So, which method should I use and how?

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Results from remote sensing are promising. I guess I'll stick to this one and thank you for those kind replies. Have a great day! – Joseph15 Jan 14 '11 at 0:09

Would your map be better than using the average temperature for the whole area? Unless you know that there is a physical reason why temperature differences occur I would use the average value everywhere, and not make an interpolation. It may well be that the prediction is more accurate if you do that than if you use an interpolated map. Local differences may be causing the temperature changes rather than a large scale spatial trend.

What do you need the map for?

Where is your study area located? Are you sure you cannot get other data for the area?

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Good point! ... – underdark Jan 13 '11 at 10:12
thanks. i've read through some journals. i guess i'll be using satellite images. says here it's good for regional studies with limited data source. thank you for the replies. – Joseph15 Jan 13 '11 at 11:43
+1 for a good and thoughtful response. – whuber Jan 13 '11 at 19:46

For only 3 points, a simple linear interpolation for each date might be suitable. You just need to compute the equation of the plane defined by your three points. See here, section "define a plane through three points".

However, any kind of interpolation on 3 points will provide only a very schematized trend of the temperature variation over space. Depending on the question you want to answer to with your data, more detailed data may be required.

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+1 Linear interpolation makes most sense for only three points. – underdark Jan 13 '11 at 9:07
Thanks for that. Will be able, however, to get values using linear interpolation outside of my extent? Further reading suggests extrapolation instead of interpolation and I am having hard time doing that in ArcGIS 9.3 – Joseph15 Jan 13 '11 at 9:13
Please be aware that extrapolating will lead to very unreliable values. QGIS' IDW interpolation will allow for extrapolation. The TIN interpolation doesn't. Don't know about Arc. – underdark Jan 13 '11 at 9:45
Whether or not your software allows you to extrapolate, extrapolation will be erroneous, regardless of the method used. There simply aren't enough data here to assess the accuracy of any estimate. – whuber Jan 13 '11 at 19:47

Im no expert in interpolation, but surely 3 points is too little? Creating a layer from these 3 points will unlikely be that spatially realistic to the real world?

That aside, you have what you have. Perhaps an Inverse Distance Weighting interpolation, setting the max search radius to be the max distance between any two of the points.

(You dont mention a specific software package, hence no specific links to relevant how-to topics)

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I am using ArcGIS 9.3. – Joseph15 Jan 13 '11 at 3:55
A quadratic interpolation has six unknowns. Solving it for three points wouldn't make much sense I think. – underdark Jan 13 '11 at 9:10
u might be right - edited. – Simon Jan 13 '11 at 10:05