topic Re: Geostat_Bimodal data in ArcGIS GeoStatistical Analyst Questions

Geostat_Bimodal data

EifLeffie — Wed, 16 Nov 2011 00:27:32 GMT

Hi,

I am using geostat analysis to particularly kriging to interpolate my data but I cant seem to get a better result. I am new to kriging and geostat and am doing some readings and research about it but its taking so much time that I cant finish the interpolation as early as planned.

I would highly appreciate if anyone could give me an advise on this. The data that I am interpolating is bimodal and I wonder if there is an appropriate procedure for this. Thank u so much for any advise you can give.

Eif

Re: Geostat_Bimodal data

EricKrause — Wed, 16 Nov 2011 14:41:39 GMT

For bimodal data like this, I suggest using Simple kriging, then apply a Normal Score Transformation. Change the "Approximation method" to Gaussian Kernels. Also, if your data is clustered, consider cell declustering before the normal score transformation.

Re: Geostat_Bimodal data

EifLeffie — Mon, 21 Nov 2011 03:47:05 GMT

Hi Eric,

Thanks for the help Eric.
I got a result showing a high root mean square (239) and average standard error (234.16), mean error is also high (-7). I wonder if there is a technique to reduce these. I have tried changing the model type like Hole effect and other types hoping to at least reduce the errors but they are all resulting to high error values. Would there be some other trick here to reduce the error? My apology as I am not familiar with this method. I would be glad if there is any procedure on how to reduce errors in this type of processing.

I would highly appreciate any help on this. Thanks.

Best regards,

Eif

Re: Geostat_Bimodal data

EricKrause — Mon, 21 Nov 2011 13:26:08 GMT

The optimal model parameters completely depend on your data. There isn't any one technique that is guaranteed to work.

Have you tried the Optimize Model button at the top? Try using K-Bessel or Stable semivariogram types, then press the optimize model button. Also, try changing Variable to semivariogram and optimize the model again.

If that doesn't work, you may want to try to remove trends (the option appears on the Wizard page right before the semivariogram).

Re: Geostat_Bimodal data

EifLeffie — Wed, 23 Nov 2011 09:37:21 GMT

Hi Eric,

The datasets that I am working with has a trend and the plan is to remove it. The trend is a U shape which can be removed using the second order polynomial. However, I have confusion in identifying the directional influence in the datasets. For instance, in page 104 of the manual of geostat analyst (Which I just found and is very useful indeed), the image (attached here) shows a strong influence on the southeast to northwest. I wonder how the strength of directional influence was detected. X axis is west-east (left-right) direction while Y-axis is the north-south (up-down) heading. Directional info on the image says: Location - 30 degrees; Horizontal - 120 degrees; Vertical - -27degrees. Please kindly elaborate on this. Thank you.

Regards,
Eif

Re: Geostat_Bimodal data

EricKrause — Wed, 23 Nov 2011 13:40:02 GMT

The Trend Analysis ESDA tool has a horizontal and vertical slide bar that allows you to rotate the graph. As you move these sliders, you'll see the projected points (the green and blue points) change accordingly, and the trend lines will change to fit the new projected points. By aligning the graph at different angles, you can see how the trend changes in different directions.

When you use trend removal in the Geostatistical Wizard, these directional trends will be automatically detected using local polynomial interpolation, and it will do its best to remove them before fitting the semivariogram.

One caveat is that it is often difficult (if not impossible) to differentiate trend, autocorrelation, and anisotropy. They can all present themselves in ways that look identical.

Does that answer your question?

Re: Geostat_Bimodal data

EifLeffie — Mon, 28 Nov 2011 00:24:08 GMT

Thanks Eric, but not really. I was wondering how the strength of the anisotropy can be detected. I have found an article regarding that clearly explained with the use of other software and I sorted it out already. I am also wondering if once the anisotropy is set to "TRUE", does the software automatically removes the effect of the directional influences or we need to do

Pardon me for the many questions, but it's actually taking me months already before I can finalize the kriging procedure as I am doing also some readings and research about the geostat and variograms. I am new to this geostat and semivariogram stuff. I don't want to give up on these and am keen to learn how I could minimize the errors so I could end up with the very good kriging results.

Cheers,
Eif

Re: Geostat_Bimodal data

EifLeffie — Mon, 28 Nov 2011 00:26:25 GMT

Eric, sorry about my former post..

ERRATA ....OR WE NEED TO DO SOME FURTHER MODIFICATIONS...

Eif

Re: Geostat_Bimodal data

EricKrause — Mon, 28 Nov 2011 14:08:19 GMT

When you set anisotropy to True, then hit the Optimize Model button at the top, the software will find the best angle and major/minor semiaxes based on cross-validation (lowest root-mean-square). You can then manually alter these parameters if you want to.

Re: Geostat_Bimodal data

EifLeffie — Wed, 30 Nov 2011 14:19:59 GMT

Thanks Eric. That's a big help!

Cheers,
Eif

Re: Geostat_Bimodal data

JeffreyEvans — Wed, 30 Nov 2011 15:54:07 GMT

Have you checked "stationarity" assumptions? It sounds like you may have some serious nonstationarity in your data. A polynomial trend removal will not account for second-order effects. Violation of even the most relaxed model of stationarity can have a negative effect on Kriging estimates. ArcGIS has the LISA model available, in the Spatial Statistics Toolbox, for testing stationarity.

Re: Geostat_Bimodal data

EricKrause — Thu, 01 Dec 2011 15:23:02 GMT

The Local Moran's I test in spatial statistics has the potential to detect nonstationarity, but it's really looking for local outliers. If the data is stationary, you won't find local outliers; however, the lack of local outliers does not imply stationarity, so be careful.

For investigating stationarity, I suggest using the Voronoi Map ESDA tool with Type set to Entropy or StDev. One advantage of the Voronoi Map is that it works with quantiles, so it's nonparametric. Local Moran's I comes with distributional assumptions.

Re: Geostat_Bimodal data

EifLeffie — Fri, 02 Dec 2011 01:09:01 GMT

Have you checked "stationarity" assumptions? It sounds like you may have some serious nonstationarity in your data. A polynomial trend removal will not account for second-order effects. Violation of even the most relaxed model of stationarity can have a negative effect on Kriging estimates. ArcGIS has the LISA model available, in the Spatial Statistics Toolbox, for testing stationarity.

Thanks for the reply Jevans. I have not checked yet for the "stationarity" of the dataset. The dataset is actually annual growth of trees. Pardon me but I am not yet that well verse in GIS processing. What is LISA model?

Thanks,
Eif

Re: Geostat_Bimodal data

EifLeffie — Fri, 02 Dec 2011 01:32:57 GMT

The Local Moran's I test in spatial statistics has the potential to detect nonstationarity, but it's really looking for local outliers. If the data is stationary, you won't find local outliers; however, the lack of local outliers does not imply stationarity, so be careful.

For investigating stationarity, I suggest using the Voronoi Map ESDA tool with Type set to Entropy or StDev. One advantage of the Voronoi Map is that it works with quantiles, so it's nonparametric. Local Moran's I comes with distributional assumptions.

Thanks Eric. I am not familiar with how the Voronoi map works and this is sort of abstract to me. Is there a paper on how this works? I have attached the image of the voronoi for both entropy and stDev and I am confused on how to interpret it.

Any help is highly appreciated.

Thanks,
Eif

Re: Geostat_Bimodal data

EricKrause — Fri, 02 Dec 2011 01:35:09 GMT

LISA = Local Indicators of Spatial Association

He is referring to this geoprocessing tool:
http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//005p0000000z000000.htm

Re: Geostat_Bimodal data

EricKrause — Fri, 02 Dec 2011 01:54:13 GMT

Thanks Eric. I am not familiar with how the Voronoi map works and this is sort of abstract to me. Is there a paper on how this works?

If your data is stationary, you expect to see randomness in the colors of the Voronoi polygons when they're symbolized by entropy or standard deviation. The idea is that the local variation should be roughly constant across the surface; you should not have areas with much more erratic data than others.

Looking at your two Voronoi maps, it looks like you have some nonstationarity, but it doesn't look very drastic. The StDev symbolization seems more clustered, but the Entropy symbolization doesn't look too bad, and I prefer to use Entropy when looking for stationarity.

If you want, you can send your data to ekrause@esri.com, and I'll see if I can fit a good kriging model.

Re: Geostat_Bimodal data

EifLeffie — Mon, 12 Dec 2011 07:35:43 GMT

If your data is stationary, you expect to see randomness in the colors of the Voronoi polygons when they're symbolized by entropy or standard deviation. The idea is that the local variation should be roughly constant across the surface; you should not have areas with much more erratic data than others.

Looking at your two Voronoi maps, it looks like you have some nonstationarity, but it doesn't look very drastic. The StDev symbolization seems more clustered, but the Entropy symbolization doesn't look too bad, and I prefer to use Entropy when looking for stationarity.

Thanks much Eric.

If you want, you can send your data to ekrause@esri.com, and I'll see if I can fit a good kriging model.

I have sent you the file via email. I highly appreciate the help.

Best regards,

Eif

Re: Geostat_Bimodal data

JeffreyEvans — Mon, 12 Dec 2011 16:11:23 GMT

Eric,
I am curious to why you prefer entropy as a measure of nonstationarity? Since the the empirical semivariogram is based on binned variance/2 and the standard model of nonstationarity is based on mean and variance, would not the standard deviation better represent how this assumption is violated?

Without looking at the data this is pure conjecture, but I am wondering if the data is limited to two distinct modes is there a possibility that it is assuming a binomial form? There is a possibility that indicator Kriging may be more appropriate. Since indicator Kriging is nonparametric, how sensitive is it to nonstationarity and distributional assumptions, compared to the linear form?

Re: Geostat_Bimodal data

EricKrause — Mon, 12 Dec 2011 18:47:57 GMT

I prefer Entropy because it works with classified bin values rather than the raw data. You're right that using Standard Deviation more directly checks the assumption of stationarity, but I've found that it is often too sensitive to deviations. A couple relatively non-extreme outliers will often completely throw off the Voronoi map, giving the impression that the dataset is highly nonstationary when the deviation from stationarity is not actually very extreme.

I took a look at the data, and it isn't binomial data. I couldn't fit a good kriging model to the data in the graphics, but I found a seemingly good model using Kernel Smoothing.