interpolation - Picking coefficient in Inverse Distance Weighted method of QGIS?

I'm using QGIS 1.8.0 to interpolate weather data. This is, I have a weather station located in say, A and C. With the Inverted Distance Weighting or Triangular Interpolation methods, I can know/interpolate information in B. When using the IDW method, I have to choose a coefficient.

Does anyone know in which range the coefficients should be?

Say from 1 to 10 or .1 to .99 or 100 to 1000?

Any ideas?

Answer

It is partially explained here http://www.gistutor.com/quantum-gis/20-intermediate-quantum-gis-tutorials/51-inverse-distance-weighting-idw-interpolation-using-qgis.html by first showing examples of using coefficient values of 1 and 3, and then

As you can see, a larger coefficient means it takes a larger distance for the values of the surface to become dissimilar from nearby points. A small coefficient means the values of the surface will quickly change as distant increases. This can produce an abrupt change in values and is prone to the “bull’s-eye effect” creating circular regions in your surface. It is best to create a few different surfaces and adjust this number to suit your analysis. Set this value to 2.70.

Unfortunately, QGIS use of "coefficient" seems to be the opposite of the classical notion of "power" in inverted distance weighting methods. (See http://linfiniti.com/dla/worksheets/10_interpolation.pdf)

In either case, the overall theory is sound (if not specific): the influence of nearby data points becomes weaker the further away they are. The weight, in early IDW methods, was inversely proportional to the squared distance. This theory, where the distance power is 2, was convenient in two respects: a) it matched accepted theories in physics, and b) it was computationally cheap. For interpolation, however, the value of 2 for the distance power is actually arbitrary. Using a value of 1 means a slower distance decay while a value of 3 means a rapid distance decay.

Returning to QGIS, a coefficient of 1 means faster decay and 3 means slower decay. (Coefficient is opposite of power.) Please try different values in the range 1 to 3 and tell us which looks best. And also, if a value of 2 is noticeably faster.