Dear Raphael'

The accuracy of interpolation method depending (partially) on the data types. for example see the following paper

Article Integrating WAsP and GIS Tools for Establishing Best Positio...

the IDW method was used in the wind data. while in the solar data , some papers recommended kriging method , such as

Data Iraqi Solar Maps/ Optimal Inclination

So, the accuracy is relative .

The criteria to determined which is better is is depend on the performance of each method . Each method was assessed quantitatively in terms of mean-absolute-percentage-error, root-mean-square-error, and goodness-of-prediction statistic .

Regards

Thank you so much for your responses.

Neither IDW nor kriging is a unique "black box" interpolation method. In the case of IDW it is very sensitive to the pattern of the data locations as well as the exponent in the weighted linear interpolator and also to choice of the number of data locations used for each interpolator.

As for kriging there is the question of whether Simple kriging, Ordinary kriging, Universal kriging was used. Each of these implies some statistical assumptions and they are not the same. For each it is necessary to use the data to estimate/model the covariance function/variogram and its parameters. Then when actually using kriging you must make some choices, e.g. the search neighborhood (circular vs elliptical, minimum/maximum number of data locations in the neighborhood.

There have been a number of papers published with empirical studies comparing different interpolators, see for example

1994, Myers,D.E., Spatial Interpolation: An Overview Geoderma 62, 17-28

1990, A.W. Warrick, R. Zhang, M.M. Moody and D.E. Myers, Kriging Versus Alternative Interpolators: Errors and Sensitivity to Model Inputs - in Field-Scale Water and Solute Flux in Soils (Monte Verita),(eds)Roth, Fl�hler, and Jury � Birkhauser Verlag Basel

1991, Myers,D.E.Interpolation and Estimation with Spatially Located Data Chemometrics and Intelligent Laboratory Systems 11, 209-228

It would be nice to be able to say with some degree of certainty which interpolation method is "best" but that is a fallacy, in part because there is no single definition of "best". Terms such as "predictive accuracy" are misleading, this should mean a comparison of the "true value" with the interpolated value but if the "true value" were known then it would not be necessary to interpolate. Note that the various forms of kriging are "exact" interpolators, i.e. if you include the value at the interpolation point then the interpolated value will match the data value. You can't do this with IDW.

PS

Both IDW and kriging generate interpolated values at a set of points, you still need other software to produce "maps", e.g. contour plots. The software actually involves a further form of interpolation.

I second Myers answers. There is no such thing as best method. Check this example notebook for a quantitative comparison of Kriging and IDW with k-fold cross-validation: http://nbviewer.jupyter.org/github/juliohm/GeoStats.jl/blob/master/examples/SolverComparison.ipynb

The software as well as the example are open source and you can run them yourself to experiment with the concepts.

Using IDL for interpolating precipitation I prefer Kriging. We use Kriging since years and those maps look really better than any other. But you have to choose the parameters well. Precipitation is very sensitiv to interpolate for drawing in a map. Flood event maps of the precipitation is done fpr publication: http://www.hnd.bybn.de/files/berichte/Bericht-HW99.pdf, see examples

All answers are in place, however, the best interpolator is that minimizes the residual error to the lowest at each point while maintaining a pleasant regonalized smooth surface, i.e., approximated smooth surface with min. error., many reference sources are mentioned in previous answers.

Drar Raphael Mwiti Gikunda

In ArcGIS software so many Interpolation methods. you can understand batter in details according your work need from following link.

http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/an-introduction-to-interpolation-methods.htm

http://desktop.arcgis.com/en/arcmap/latest/extensions/geostatistical-analyst/an-introduction-to-interpolation-methods.htm

I recommend Alaa's answer

Best Regards

"All answers are in place, however, the best interpolator is that minimizes the residual error to the lowest at each point while maintaining a pleasant regonalized smooth surface, i.e., approximated smooth surface with min. error., many reference sources are mentioned in previous answers. "

If at each point refers to data locations then kriging always reproduces the data values at each data location, i.e. the residual errors are all zero (unlike regression). What is a "pleasant regionalized smooth surface", i.e. how do you quantify "pleasantness". The thin plate spline is derived as an interpolator that minimizes the second derivative of the interpolated surface, i.e. maximum smoothness, however it is well known that the thin plate spline is equivalent to kriging (See G. Matheron, ~1981)