Dear Sitender

It is difficult to say which method is best.  The performance of each method depends on the data used. Generally, Kriging is found to be more robust and suggested by many researchers. 

Thanks

Dear Kamal Ahmed,

Thanks for interaction but my basic curiosity is to know the experiences of other researchers on using these methods in different parts.

Dear Pujol

I am translating it and reading it, hope it will give some better understanding.

thanks

Hi Sitender,

as mentioned by Kamal, you can't say which of interpolation methods is the best one. It always depends on the context, data, usage, etc. Besides the methods you mentioned, you can also consider others like RBF, GWR ....

Anyway, from my experience the IDW is the least suitable for the complex case study. It usually performs well in the case that initial points are the source of phenomena and its influence declines with the distance continually. The spline is more complex but often provides too smooth results. The kriging (especially in the combination with regression model and/or simulation) gives you the almost countless amount of possibilities but need to be well defined (type of structural function, type of kriging, etc.)

In case you would be interested I can recommend you two (free) books (please see links below). They might be bit kriging-oriented but definitely gives you the overview of interpolation possibilities.

Regards

Lukas

http://spatial-analyst.net/book/system/files/Hengl_2009_GEOSTATe2c1w.pdf

http://eusoils.jrc.ec.europa.eu/ESDB_Archive/eusoils_docs/other/EUR22904en.pdf

Let me just echo what others have said. There is no single best. There is only the best method for the data being analyzed. IDW is rather specialized and not recommended as a first cut for most data. Krieging can be very useful but attention needs to be paid to the parameters which will depend on the precise data and its geography. So experientially, those of us who work with these will all probably say there is no single best. There is only best for a dataset. In teaching these things we usually teach krieging first, especially where we can demonstrate how parameters set incorrectly may effect the outcome. But all work for different problems and the challenge is to have the right dataset and correct geography to express where each best serves. 

Dear Dr Tom!

Thanks for your comments. Your comments are much valuable for all of us. Can you please guide us how to  set the parameters for  Kriging? Or do you have any publication related to this?

Thanks in Advance.

I generally like Kriging, and as I understand it, works best when the area being interpolated isn't that large.  Also, there is more than one type of Kriging that you can choose from besides the number of parameters you have to set for each type..  There's ordinary, universal, simple, dijunctive, indicator, and even Co-kriging (two variables interpolated together).  Kriging also gives you a lot more in the way of statistics - like error analysis.  The text I like to use to explain this topic to my students (and myself) is O'Sullivan and Unwin (2010). Geographic Information Analysis - 2nd ed. (Wiley & Sons: Hoboken, NJ) especially chapters 5, 6 and 9 and 10.  Chapter 10 gives a good treatment of ordinary kriging.  This text especially explains how some of the parameters you set affect the results.  

@Sitendar

I believe you might have already read about basics of IDW and spline. They are methods of displaying data but without any feedback for accuracy of interpolation. Throughout the literature, IDW or spline is used to show the data spatially. The spline give exact values of parameter interpolated at its locations where as IDW will average it out. The krigging does that too, but it can describe the mechanism of estimating values at points other than input data. So check fitting of semi variogram after which you will be more confident about fitting of semi variogram model.

I think it will help you.

One  question I like to ask to friends here.

Location A has say GW table 3 meters, Location B has 6 meters. So how we can assume, that GW will have uniform trend between A & B which are separated by distance. Is there any proxy parameter other than DEM.?

As noted by the preceding commenters, there is no "best" method and there are many reasons for this

1. You must first have a criterion for quantifying the quality of the interpolation results, otherwise the question does not make sense

2. IDW is not based on any theory and there are no underlying assumptions to check. It could be used on essentially any data set but the method does not give you any way of judging whether the results are good or bad. IDW does not provide a way to incorporate non-point support.

3. Some methods appear to be different but in fact are not or are special cases of other methods. E.g. the thin plate spline is a special case of Radial Basis functions which in turn are equivalent to kriging (perhaps with a generalized covariance function)

4. Having "interpolated" the data you may have different possible uses in mind,  not all methods have the same flexibilities and may impose different requirements on the data.