Minimum 10-20 datasets you can analysis then you get better results

Well,

That depends on used scale and homogeneity of observed points, I test 4 data set, the result was not satisfied with weak accuracy.

Regards

In Geostatistics, Kriging relies on the semi-variogram which calculate (spatial or non-spatial) auto-correlation from the variance obtained from the number of samples / locations. Therefore, the closer the points are related to each other often determine the level of semi-variance obtained.

Some authors had often set a range of minimum sample points/locations between 25 -40, some use 28 as their minimum sample points,but specifically there is no minimum number required. The more the number of points within the specified study area, determines the better the krigging interpolation outputs.

Therefore, the minimum number of sample locations required depends on the total number of data samples/locations and their respective distribution spatial pattern being used to fit the variogram model.

read through the attached article for further explanations.

You need to start with a good book on geostatistics, see the book with that title by J.P. Chiles and P. Delfiner, J. Wiley & sons

For a brief intro, written in the form of a tutorial using an actual data set see

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

Thank you @all for the help.

Thank you Samuel Akande and Donald Myers for the references. I will look at them.

Kind regards,

when you are using interpolation techniques more point and equally distribution of point is required. 1 or 2 point not giving proper results for analysis. if your study area having less point it is difficult..then use in and around point data to interpolate

@ patrik silva

Higher number of point and equally distribution of point are best suitable for this techniques. There is no minimum threshold limit. It also based on your study area geometry.

Kalyan & Subhash

1. No, you do not want "equally distribution of point" unless you have an exceeding large number of data locations (so that the distance between two adjacent data locations is quite small).

2. "minimum threshold limit", are you talking about the number of data locations or the distance between data locations? In either case your comment is nonsense

The shape of the sample variogram for short distances/lags is one of the most important pieces of information.

You are right that the geographical extent and shape of the study region is important with respect to the number of data locations and also the spatial distribution of the data locations but the connection is not simple.

There is NO minimum number of data locations that is sufficient for all applications.

You must distinguish between the number of data locations (and the spatial pattern) for variogram estimation and modeling VS using the data in the kriging estimator. Any discussion of the number of data locations is irrelevant without this recognition.

There is no one-size-fits-all criterion for this, however, some rules of thumbs were provided. In addition to the sample size, their spatial distribution pattern is also discussed. In general, the quality of the OK results will be improved with increasing data density and more regular spatial distribution.

This will depend on what you are researching, the size of your study area and the size of the pixel you want. There is no minimum number of observations. My advice is to choose a small area and make the most observations in it. Kriging is the best interpolator we have, however it can fail if you don't have the correct number of samples. In other words, the result may not correspond to the spatial reality.

Hi Patrik,

I believe it depends on multi-factors such as (the size of the study area, the studied phenomena, the points distribution). So, a specific answer will not help.

The geographical pattern of the output interpolation will give primary visual evidence of the accuracy.

Best wishes.

It depends on the distribution of the data set and the distance between samples. In order to get a proper result, the number of samples should be at least 25 samples according to my experience.

You may want to avoid unequal distribution of points or, for instance, you could fail capturing adequately the underlying microvariability. Regarding the extent of your domain, make sure you do not have sub-regions within your domain characterized by dramatically different patterns, suggesting generation by significantly different physical processes. If this is the case you may want to identify first the sub-regions and estimate different variogram for each of them.

number of point data must be greater t o 30 and confirmably 50 to establish the variogram and the kriging techniques.

Webster and Oliver believe that the sampling points are greater than or equal to 150, and at least not less than 100.

(Oliver M.A., Webster R. (2015) The Variogram and Modelling. In: Basic Steps in Geostatistics: The Variogram and Kriging. Page-22. SpringerBriefs in Agriculture. Springer, Cham. https://doi.org/10.1007/978-3-319-15865-5_3)

You need to separate two questions, first there is the number and spatial pattern of the data locations used in estimating and modeling the variogram. Secondly there is the number and spatial pattern of the data locations used in applying the kriging estimator/interpolator. These are two entirely different problems. The system of equations used to determine the coefficients in the kriging estimator only requires ONE data location but the results will not be very useful or reliable. Now you must decide whether to use a "unique" search neighborhood to determine the data locations used in the kriging equations or a "moving" neighborhood. Most geostatistical software will use a "moving" neighborhood, if you use a moving neighborhood then about 25 data locations is adequate, using more may result in negative weights and larger kriging variances. Depending on the total number of data locations and the spatial pattern there may be interpolation locations where there are less than 25 data locations. Using a "unique" search neighborhood will likely result in a very large coefficient matrix to invert.

With respect to estimating and modeling the variogram you must first consider how you are going to do this. Usually this will include computing empirical/experimental variograms but for a given data set the empirical variogram is NOT unique. It will depend on various choices made by the user such as the maximum lag distance, the width of the lag classes and whether it is directional or omnidirectional. An empirical variogram does not directly determine the variogram model type, e.g. spherical, gaussian, exponential, etc. It also does not directly determine the model parameters such as sill, range.

Silva's question may seem like a reasonable one to ask but it does NOT have a simple answer. Asking it implies a lack of understanding about geostatistics and kriging.

1991, Myers,D.E., On Variogram Estimation in Proceedings of the First Inter. Conf. Stat. Comp., Cesme, Turkey, 30 Mar.-2 April 1987, Vol II, American Sciences Press, 261-281

• 1987, A. Warrick and D.E. Myers, Optimization of Sampling Locations for Variogram Calculations Water Resources Research 23, 496-500

Kalyan & Subhash

The shape of the sample variogram for short lags is one of the most important pieces of information.

You are right that the geographical extent and shape of the study region is important with respect to the number of data locations and also the spatial distribution of the data locations but the connection is not simple.

There is NO minimum number of data locations that is sufficient for all applications. You must distinguish between the number of data locations (and the spatial pattern) for variogram estimation and modeling VS using the data in the kriging estimator.

the zonal anisotropy is affected by the lags and point of interest and should be fitted correctely if dataset are not sparsed to but homogeineously distrution.

Dear Silva,

Your concerns are valid.

I think Empirical Bayesian Kriging (EBK) could be helpful in this regard. EBK automatically calculates the required kriging parameters through a process of subsetting and simulation. One advantage of EBK with small (not less than 20) and sparse datasets is that EBK is able to change the subset size to obtain valid number of samples for variogram estimation. For instance, where sample data set is sparse, EBK could expand the subset size and vice-versa. EBK is typically more accurate than other Kriging models especially where sample size is relatively small.

Patrik

You need to start with a good book on geostatistics, e.g. J.P Chiles and P. Delfiner so you can really understand the underlying statistical assumptions for kriging. The derivation of the equations used to determine the weights in the kriging estimator does not depend on any probability distribution assumptions but does presume that the variogram model is known (functional type i.e spherical, exponential, Gaussian etc as well as the parameter values). "SEMIvariogram" is outdated terminology. You have to be careful to distinguish between a variogram model and an empirical variogram. Estimating and fitting a variogram model to data is completely separate from using the kriging estimator, don't mix them up.

If you consult the geostatistical literature (which crosses many disciplines) you will see that the question of how many data locations (as well as the spatial pattern of the locations) continues to attract interest but there are NO absolute answers. To ensure that the system of linear equations (to determine the weights) has a unique solution one location is sufficient but the results would not be useful. As posed your question is nonsensical, partly because you mix up the two different parts of the problem.

Dear @all

Sorry for the late reply. Thank you for the help!

Donald Myers I appreciated your contribution and advice. Kriging requires a strong statistical and math background.

Regards