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I am working with existing groundwater borehole data (borehole location data plus the water quality data) to plan for the future monitoring of the groundwater water using spatially balanced sampling techniques. Thus obtaining sampling points from the existing points for the monitoring of groundwater quality in the future.

I have not used the create spatially balanced point sampling tool before. I have read a bit about it and my understanding is as follow:

The input file should be raster file which contain the inclusion probability and the input file can be a point or polygon file.

These means, I can input an interpolated file (say the water quality Index Interpolation file) or individual water quality index as point data in raster.

My question is which of the raster data is more appropriate to use, the interpolated data or the point data? The software I am using is ArcGIS 10.2

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    Welcome to GIS SE. As a new user, please take the Tour, which emphasizes the importance of asking one question per Question. In addition, you have tagged this with three different versions of ArcGIS software, two of which are already in Retired status, and didn't specify the software in use within the body of the question. Please Edit you question. – Vince Jun 3 '18 at 20:15
  • Thanks for your comments. I have edited the question, however, if there is any issues with the question again, kindly alert me. Thanks – PublishingK3 Jun 4 '18 at 6:49
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This particular algorithm (Stevens & Olsen 2004) uses a recursive quadrant randomization based on tessellation of the data. The "inclusion probability" raster is used to normalize sampling intensity, functioning as sample weights. If your data is spatially random you can provide a uniform weights raster (all 1).

The issue here is that, theoretically, the inclusion probabilities should represent an intensity function. Not exactly sure why the authors of the tool did not include this, seemingly obvious, component to the model as an option. Without coding it in Python/NumPy I do not think that you can produce a spatial intensity function in ArcGIS. The spatial intensity is akin to a Kernel Density but, represents the expected frequency/density of the observed point process.

Ideally, the probability weights would be based on a model of your process. If you have the data to support it, a method such as probability kriging would produce a surface that could be used as an inclusion probability raster.

It is not entirely valid but, I imagine you could derive a Kernal Density estimate, scaling it to [0-1] using ( d / max(d) ) to use as the probability weights however, the results will be highly dependent on the parameters used for the density estimate (ie., bandwidth). The trick here is to decide on what order of spatial variation you want to target. This will be entirely dependent on the bandwidth used for the KDE. A small distance bandwidth will converge on second-order (local) spatial variation whereas large distances will represent a first-order (global) spatial process and notably smooth the data. A KDE can be created in ArcGIS (with a Spatial Analyst license) using the the "ArcToolbox > Spatial Analyst toolbox > Density > Kernel Density".

Stevens, D.L., & A.R. Olsen (2004). Spatially balanced sampling of natural resources. Journal of the American Statistical Association 99(465):262–278.

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