Thanks Mr. Abhishek Raj for you help but I want to know which is the best interpolation method in ArcGIS for AOD ? Is spline or krging method? and how you can Statistically concluded that ?

Hello Saadiah.

It's simple to choose and prove the best interpolation method for you data, I mean any kind of 2D or 3D data.

All the thing you want is a "Validation". you should perform interpolation with proposed methods and to choose the best one from validation results.

Kriging based interpolation methods are a set of very useful tools to interpolate unknown blocks of your estimation space as they minimize the variance of estimation (kriging is B.L.U.E (best linear unbiased estimator)). But it is vital to perform a good variogram modelling before running Kriging. A bad variogram modelling may lead you to inaccurate estimations.

If you have high levels of heterogeneity in your data, it's better to use "geostatistical simulations" such as SGS, DSim, CCS and so.

Geostatistical Simulation methods don't have unwanted smoothing effect of Kriging.

Besides, if you aren't able to model the anisotropy via variogram modelling, you have to use some other simpler but more inaccurate methods such as splines and inverse distance weighted.

In order to validating results, you may use below statistics to compare interpolation methods >

cross validation, Jackknife validation and kriging variance, kriging efficiency for kriging based methods.

Remember that "validation" is the essential part of every interpolation.

Hello Hossein Molayemat

Thanks very much for you helpful answer.

When I mapping AOD by using “spatial analysis Tools” / Interpolation /Kriging/(ordinary method)/(spherical  semivariogram model) the result map different from that when I used  “Geostatistical Analysis”/Kriging/(Ordinary method) /(Spherical semivariogram model ) with same lag size!  why ?

Note that in the first way the value of AOD in Map is near to the origin grid data !

Please let me know how much is that "difference"? Is it significant or not?

I think it's because that you're not using the same input data as you mentioned in last line.

 Thanks Mr. Hossein

I used the same input data file. I would like to show you the simple results in the two ways . Please find the attached files.

I think these two maps are the same (means containing same values) but you used "different color scales".

It's obvious that one map with different classification for value won't seem the same.

In addition, it's essential to model the "anisotropy" of your data. If there are different experimental variograms in different azimuths, you "have to" model them and do not consider the data as "isotropic". 

It's a very importanat part of every geostatistical estimation which some of researches forget to perform.

Do not trust the software and its fits, do the job manually. If you use anisotrop variogram for estimations, you may have significant error or biased results.

Also, you should check some other factors of estimation using kriging such as:

- First of all, your data must have normal distribution. Otherwise, you must transform the data using "Normal Transform Functions" such as natural logarithm (Ln), Cox & Box, Johnson and normal score transformations.

- most of the time, you should perform "block kriging" not point kriging. Also you need to choose the proper block size, it's important to reduce the kriging variance.

- "Always", you should check the trend existence in your data. if it exists, perform "Universal Kriging".

- check min. and max number of samples to contribute in a block estiamtion

- Check the search radius

- "Always" validate the results and choose the best one(s)

There may be countless results coming out from software, but only one of them is the correct and you should reach it.

you mean the result maps must be the same in the two ways spatial analyst tools and geostatistical analyst tools if I select the same model and methods

Yes, for sure.

They both use the same performance if estimation parameters are the same.

But they may vary in "legend color scaling", you need to check it in the end.

Thanks Dr.Hossein very much for your helpful information

you're welcome.

feel free to ask about the topic.

Dear Saadiya,

There is no method of interpolation which is best, every method has its own limitation, what u have to do is get interpolation done and compare ur result whichever interpolation gives u nearly correct data opt that one.