kriging results to raster

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02-08-2013 01:52 AM
AstridHarendza
New Contributor III
Hello,

I have a question regarding the export of kriging results into a raster. I've seen a few threads related to this question, but unfortunately could not find the right answer.

The problems:
1. The raster's min and max values differ from the min and max values of the input data.
Max and min values (which are actually real measured max and min) change by nearly 10% when the kriging result is exported to a raster, which is not acceptable for my data and study purpose. I've seen that this problem is linked to the cell size. Is there anyway around it - recalculating the raster values in some way and trying to correct them manually? I really need the min and max values to not be changed in my dataset.

2. The isolines of classes as shown in kriging do not match with the ones in the raster.
As far as I understand is the problem the conversion of the on-the-fly, hence fairly coarse, interpolated GA layer into a much finer raster. So I played around with the cell size and did notice that the result improved when increasing the cell size, but I didn't manage to match the output of the GA layer. I also read in a few threads that the coordinate system could be a problem, so I converted it from degrees to metre, but didn't notice any improvements. My sampling area is only 6m^2, so I guess this makes the degree problem neglectable. Any suggestions on how to improve the raster output if a fairly fine grid is required?

I need a raster output (ideally a fine grid) as I would like to perform further analysis on these data.

Any suggestions and tips on how to deal with this and hopefully improve the end result are highly appreciated!

Best regards,
Astrid
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EricKrause
Esri Regular Contributor
The thing to understand is that the geostatistical layer is a continuous surface.  It has infinite resolution (up to the precision of your computer).  The best way to think of a geostatistical layer is that it is a function that takes an (x,y) location and returns a value.  It doesn't know its own values until you ask it to calculate them.  The contours that you see are drawn from a course grid in order to give an idea what the surface looks like, and the symbology comes from min/max of the input points (since there's no way to calculate a histogram of a continuous surface).

When you export to raster, you are calling the function at the center of each cell, and the symbology is based on the histogram of the output raster.  If you change the number of points in the horizontal/vertical directions, you will call the function multiple times within each raster cell, and the output cell will be assigned the average of these values. 

The visual difference between the geostatistical layer and the raster is due entirely to the different contouring and symbology, but they do contain the same values at the same locations.

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EricKrause
Esri Regular Contributor
The geostatistical layer and the output raster may look very different, but I assure you that they have the same values at the same locations.  Please read this blog and let me know if it still isn't clear.

http://blogs.esri.com/esri/arcgis/2008/09/29/understanding-geostatistical-analyst-layers/
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AstridHarendza
New Contributor III
Hi Eric,

thanks for your prompt reply. I've seen this blog entry before and yes...I guess I'm a bit stupid here.

So when converting a GA layer to a raster, an average value for each raster cell (which is different to the resolution of GA layer) is calculated. If I define only to take into account 1 point in x and y direction, this one will be placed in the centre of the cell. Whilst calculating the average of the cell a weighted distance value will be assigned to all neighbouring points within the cell. In case of the max value not being located in the centre of the cell, it will be weighted according to its distance from the centre of the cell and nearby points. Hence the max value does not show up as the final cell value. Is this right? 

If not, I guess a slightly more in detail explanation would be very much appreciated.

Many thanks for your help,
Astrid
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MichaelAugust
Occasional Contributor III

"Whilst calculating the average of the cell a weighted distance value will be assigned to all neighboring points within the cell. In case of the max value not being located in the center of the cell, it will be weighted according to its distance from the center of the cell and nearby points. Hence the max value does not show up as the final cell value. Is this right?"

I'm interested in knowing the answer to this specific part of this person's question, and what if my point is a physical sample location with analytical results (i.e. metals, petroleum, etc.) and I need to preserve these values?

I believe in my case, by making the measurement error = 0 during kriging I've made it an exact interpolator - is that a correct assumption?

And if so what's the process to preserve these "exact" values at my sample locations in the exported raster then if there's always going to be some averaging going on to get to a cell size, what if my sample point is not exactly in the center - is there a way to center them? It seems I've seen this in my resultant rasters where the values at my sample locations are not honored but "averaged over" during cell creation/export - could someone explain the process in this context, wherein I can preserve the exact max/min of and values of my samples at their locations?

Thanks!

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EricKrause
Esri Regular Contributor
The thing to understand is that the geostatistical layer is a continuous surface.  It has infinite resolution (up to the precision of your computer).  The best way to think of a geostatistical layer is that it is a function that takes an (x,y) location and returns a value.  It doesn't know its own values until you ask it to calculate them.  The contours that you see are drawn from a course grid in order to give an idea what the surface looks like, and the symbology comes from min/max of the input points (since there's no way to calculate a histogram of a continuous surface).

When you export to raster, you are calling the function at the center of each cell, and the symbology is based on the histogram of the output raster.  If you change the number of points in the horizontal/vertical directions, you will call the function multiple times within each raster cell, and the output cell will be assigned the average of these values. 

The visual difference between the geostatistical layer and the raster is due entirely to the different contouring and symbology, but they do contain the same values at the same locations.

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MonicaHaddad
New Contributor

Dear Eric,

I read your explanation.  My simple kriging surface gives values ranging from -5.1  to  2.17.  When I transform my simple kriging surface into a raster the values range from -3.59  to  1.49.  That is OK because it is within the range above (i.e.  -5.1  to  2.17).

My universal kriging surface gives values ranging from -5.1  to  2.17.  When I transform my universal kriging surface into a raster the values range from - 29.17  to 37.83.  That is not OK because it is out of the range above  (I.e., -5.1  to  2.17).  For this one the ranges are too different.  Any comments?

Thank you.

Best regards, Monica.

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TroyMullins
New Contributor

Eric,

Are there settings/environments/etc to maintain original value of input points.  Important for analysis.  For example, we have input point file that has a maximum value of 218, yet the resultant GA Layer and exported raster cell values at that point are in the 90's.  And the maximum value of the raster is 108 - half of the original point data : 

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EricKrause
Esri Regular Contributor

In order for the geostatistical layer to pass through the input points perfectly, you can use IDW or Radial Basis Functions.  They are exact interpolators, and they will always pass through the input points.  If you are using kriging (other than Empirical Bayesian Kriging), you can force it to be an exact interpolator by turning off the nugget effect.  In the Geostatistical Wizard on the semivariogram page, look for the "Model Nugget" section and disable the nugget effect.

However, you should know that forcing an interpolation method to be exact can sometimes result in strange artifacts in the surface.  Make sure to look at your surface carefully.

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AstridHarendza
New Contributor III
Thanks a lot for this brilliant reply Eric! It definitely helped me understanding whats going on with the kriging output and the conversion to rasters. Much appreciated! THANKS!
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EricKrause
Esri Regular Contributor
Glad I could help.  You're definitely not the first person to be confused by this.
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