Universal Kriging with External Drift

[Tae-Jung_JonathanKwon]

Hi

I am looking for a way to use UK with external drift and the external drift. Or in others words, is there any way to perform a regression kriging on ArcGIS? (i.e., kriging with underlying trend..).
Thanks for your input in advance.

[EricKrause]

I'll look into why the top-right and lower-left cells are being ignored, but after asking around, I think the tool you want to use is Focal Statistics.  It gives lots of options for defining cell neighbors, and you can calculate the standard deviation of these neighbors. 

And I'm not surprised at the fairly weak R^2 between standard deviation and entropy.  Because entropy works with classified values (rather than raw values), the entropy map tends to be smoother.  Entropy also has a maximum, but standard deviation has no maximum.  So, two cells can have the same entropy value but still have very different standard deviations.  If you look at your scatterplot, you can even see this; there are clear vertical columns that all have the same entropy, but the standard deviations vary a lot.  This variance is what is pulling down the R^2.

[EricKrause]

I've looked into why the Voronoi map is ignoring the top-right and lower-left cells.  The problem is that when you have gridded points, the Delaunay triangulation is not unique.  Since we define polygon neighbors at the triangulation step (the first step of creating the Voronoi polygons), our algorithm drops the top-right and lower-left neighbors.  A different but analogous implementation would drop the upper-left and lower-right polygons.  We could fix this by defining neighbors after the polygons are created, but this would slow down the tool.  We'll have to think whether this hit in performance is worth it, especially considering that Focal Statistics is specifically built to deal with gridded data.

[Tae-Jung_JonathanKwon]

Thank you very much for your kind explanations. Yes I understood why those cells are dropped.
Yes use of Focal Statistics would do the job since it gives standard deviation (which really indicates the local variability with its neighbours. I will go ahead and try it out!

Again, thanks a lot for all your support! Your support truly helped very much!!!
I will come back with more question if I have any 😄

Have a good weekend.

Jonathan

I've looked into why the Voronoi map is ignoring the top-right and lower-left cells.  The problem is that when you have gridded points, the Delaunay triangulation is not unique.  Since we define polygon neighbors at the triangulation step (the first step of creating the Voronoi polygons), our algorithm drops the top-right and lower-left neighbors.  A different but analogous implementation would drop the upper-left and lower-right polygons.  We could fix this by defining neighbors after the polygons are created, but this would slow down the tool.  We'll have to think whether this hit in performance is worth it, especially considering that Focal Statistics is specifically built to deal with gridded data.

[EricKrause]

Glad I could help.  Feel free to ask more questions if anything else comes up.

[Tae-Jung_JonathanKwon]

[ATTACH=CONFIG]20608[/ATTACH]
Hi Eric,
One quick question; following the steps mentioned above, I have krigged the residuals using 40 points (appeared as black pin). But as you can see in the attached image, the krigged region does not cover the entire study area. I know that it only allows to krig to the extent where the known points are.. Is there any way to extend this and to cover the entire study area? So far I have not found any option to do so.. Thanks!

Jonathan

The steps you've outlined are correct. 

Unfortunately, there's no way to make a continuous OLS surface.  You'll need to make separate rasters for each resolution you want to test, but you only need to krig on the residuals once.  You can export the interpolated residual surface to any cell size and extent that you want.

I now understand what you're trying to do with the correlation coefficient.  However, I don't think a correlation coefficient will work here because if you want to correlate a single point to the mean of its neighbors, you'll only be able to calculate a single coefficient for the entire surface (since you need repeated samples), so it won't help you in deciding which particular locations should be given preference. 

The first thing that comes to mind is the Voronoi Map tool.  It's an interactive graphical tool, and if you use Standard Deviation, Entropy, or Interquartile Range, you'll get an estimate of the local variability.  A small local variability indicates that the predictions are more constant in that area, so they might be good candidates for new sites because the area can be better represented by a single value.  Note that you'll need to convert your rasters to points to run the tool.

[EricKrause]

Yes, you can change the extent of a geostatistical layer.  Right-click the layer in ArcMap's Table of Contents and choose "Properties."  Go to the Extent tab and specify the new extent.

[Tae-Jung_JonathanKwon]

Sorry I didn't know it was that simple.. I should have looked into more closely.. I thought such feature would be available when running the kriging..

Thank you!

Yes, you can change the extent of a geostatistical layer.  Right-click the layer in ArcMap's Table of Contents and choose "Properties."  Go to the Extent tab and specify the new extent.

[SteveLynch]

Such features are available through the geoprocessing environment. I.e. when using GP tools. The Wizard, however, does not honor these environment settings.

You could, however, use the layer that you created in the GALayerToGrid tool and specify an output extent in the environment and your output raster will then have this new extent.

Steve

[Tae-Jung_JonathanKwon]

Steve,

Thanks for providing additional info. Yes it is definitely worthwhile using it since I have equal-sized grids (MLR surface), and I will assign a single value to each and every grid by taking the average of the converted raster data to get the final output of "regression-Kriging"...
Have a good weekend.

Jonathan

Such features are available through the geoprocessing environment. I.e. when using GP tools. The Wizard, however, does not honor these environment settings.

You could, however, use the layer that you created in the GALayerToGrid tool and specify an output extent in the environment and your output raster will then have this new extent.

Steve

[MERLINDAVIS]

Hello

I would like to know how exactly we can do the external drift kriging using ArcGIS. I couldnot figure it out(got confused) from the above discussion.
Also can anyone tell whether it is possible to do it for a time series of data. I have the hourly precipitation data for some staions. I would like to interpolate it for the entire area.

Thanks in advance! 🙂