Hello Uzzal.

Please let me know if the max. range of 261 km is provided by software modelling or not?

If it's so, deny the auto variogram modelling and take the control yourself (I mean fit a reasonable model to the experimental variogram individually).

Sometimes when I use GS+ to perform 2D geostatistical estimations I face with such problems. 

It occurs because the fitting algorithm of the software is seeking for minimum standard error (SE) of fitting a model to expermental variogram and maximizing R (correlation coefficient of experimental and model variograms).

So, it is highly probable for a software to calculate an invalid long range distance for variograms.

My advice: never trust auto variogram modellings. Do it manually.

Yeah, that's right. but I needed to plot thousands of variogram. so I plotted it by autokrige.

an addition to the above feedback.

Take the half of the maximum inter-station distance of all stations. In most case, it would work fine. However, apply the obtained variogram in kriging and if it satisfy the cross-validation criteria, then you can use it. As long as the criteria is satisfied, you can claim the variogram works fine since it is the one which indicates the spatial correlation among data points.

Hope it would help you.

fundamentally, you have to limit the long range, but if you're using a dense data grid, I suggest you to reduce "the number of sample points" which are taken into account for interpolation.

It will reduce the Lagrange coefficient for distant samples.

Also, as Sajal said, if there is no significant problem with "cross validation" it is allowed to consider that invalid long range for your models.

I agree with Hossein.

Surfer also overestimates range when you use the auto fitting function.

To the comment: "to reduce "the number of sample points" which are taken into account for interpolation"

But then you have to keep in mind that you need around at least 25 to 30 measurement pairs per lag to get a stable experimental variogram (rule of thumb).

Thanks for your comment Christian and yes you're right about sample size in experimental variogram calculation. 

But I mean number of samples for interpolation using block kriging.

Beside these things, the max. and min. number of samples should been observed to reduce the unwilling smoothing effect of kriging.

In some cases of using block kriging in lithogeochemical studies, I found that 12 ... 15 samples results the best CV and block variance and a reasonable degree of smoothing effect.

In this case, I have no suggestion for number of samples as I have no idea about the nature of data.

It means you should not believe the numbers the software is generating.  Typically, variograms should only be interpreted (or modelled) to one-half or one-third the distance of the most widely separated data point pair. 

Jennifer is right, if your software permits it look at the numbers of pairs used to compute the sample variogram for different lag distances and you will see that the numbers begin to decrease for lag distances that exceed about half the maximum distance between data locations. You may want to consider whether there are other hidden problems in the software if it produces  clearly wrong results like this. It is certainly possible that the range is actually greater than the maximum distance but you can't determine that from the sample variogram. There are multiple possible algorithms for auto fitting of the variogram parameters but no one choice is best possible for all data sets. Also if your software permits it, look at the kriging weights. In gereral you don't want any negative weights, those would indicate too oarge a search neighborhood and/or too large a range

I think it means that the automatic variogram fitting software is wrong and not reliable. I suggest you change software, e.g. try the R package gstat where you can see the source code if you want to. It is also possible as Mohammad says that you have a non-constant mean and fitting a Trend surface to the data and re-computing the empirical variogram may resolve the problem.

It is not a question of the diameter of the study area but rather the it is the maximum distance between data locations and then how you use the empirical variogram to determine/choose the range of the variogram.

There are variogram models, e.g. a power model, which do not have a range.

Because the size of the experimental domain and the decorrelation length of the data are two completely different quantities. You can easiliy examine some data within 200x200 km domain that have 1500 km decorelation length. Just imagine that you have a data that are known to have 1500km range. Then imagine you take a sample of the surface which is 200x200km. The range is still 1500km, although you deal with a smaller area. The question of whether it is possible to accurately estumate range given smaller domain is different question. In principle, you estimate the range using one of the parametric theoretical variogram models fitted into experimental or raw variograms and if the domain is not too much smaller than the decorrelation length, you might still be able to relatively accurately estimate variogram parameters, including range parameter.

Jovan

You shouldn't confuse "decorrelation length" with the range of a variogram. You also have to recognize the distinction between a "true" range, e.g. a spherical variogram and an "effective" range, e.g. an exponential or gaussian variogram.

How are you determining the "decorrelation length" prior to estimating and fitting a variogram model? To speak of the "decorrelation length" of the data is nonsense, especially prior to collecting the data.