Latest Contributions by EricKrause

Do the zero and non-zero values cluster together?  In other words, does your map seem to be divided between regions of zeros and regions of non-zeros?  For example, we often see this with rainfall data: large areas of all zero (where it didn't rain) and large areas of all non-zero (where it did rain). ... View more

Based on the semivariogram, your data looks somewhat categorical. I think this is just due to the small major range (look at the semivariogram surface on the bottom-left).  I would suggest increasing the range, but if there is no spatial correlation, increasing the range won't fix the underlying problem. ... View more

Kriging can work fine on data sampled on a grid.  However, your semivariogram does look a bit strange.  The biggest problem I see is that the semivariogram is basically flat, meaning that there is little spatial correlation in the data.  If the data is not spatially correlated, it does not make sense to interpolate at all. Try using this geoprocessing tool on your data: http://webhelp.esri.com/arcgiSDEsktop/9.3/index.cfm?TopicName=Spatial_Autocorrelation_%28Morans_I%29_%28Spatial_Statistics%29 Find the p-value from the output.  The lower the p-value, the more spatially correlated your data is.  You'd like to see something below 0.05. ... View more

You can do this with the GA Layer to Points geoprocessing tool: http://webhelp.esri.com/arcgisdesktop/9.3/index.cfm?TopicName=GA_Layer_to_Points_%28Geostatistical_Analyst%29 Build your model with the training data, then use GA Layer to Points.  Supply the kriging geostatistical layer you created with the training data, then give the validation dataset and the z-field with the measured values to compare against. ... View more

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. ... View more

Does the geostastical wizard used the first or the second model equation to compute data? It uses both.  When you do cokriging, you have to model the primary variable (Var 1), the secondary variable (Var 2), and the cross-covariance between the primary and secondary variable (Var1 - Var 2).  The cokriging equations require you to model all three processes to make predictions. ... View more

The first graphic is the semivariogram for variable 2 (elevation), and the second graphic is for variable 1 (precipitation).  You can see this at the top-right of each graphic: "Between: Var2 - Var2" and "Between: Var1 - Var1".  The first graphic is pulling Nugget[1][1] and Partial Sill[1][1] from all models.  Graphic 2 is pulling Nugget[0][0] and Partial Sill[0][0].  The cross-covariance (not pictured) between elevation and precipitation is from Nugget[0][1] and Partial Sill[0][1]. I'm not seeing any problems with the graphics you posted.  Can you try to clarify your question? ... View more

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. ... View more

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 ... View more

There are a lot of different techniques you could try, but the simplest is to use the "Optimize Model" button.  It's on the semivariogram screen in the Geostatistical Wizard, at the top.  It will find the optimal lag size (among other parameters) that minimizes the root-mean-square prediction error. ... View more

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. ... View more

You can get choppy results like that at the boundary of searching neighborhoods, and having data that is not normally-distributed will generally make this worse.  I suggest you stick with the Simple Kriging results, but if you want to use Ordinary Kriging, try using a Smooth searching neighborhood, or increase the minimum number of neighbors (these options appear in the Geostatistical Wizard on the screen after the semivariogram). ... View more

The raster looks fine to me.  What is concerning you about the raster? One thing to keep in mind is that the geostatistical layer will look different after exporting to raster.  This is because the geostatistical layer uses a quick contouring algorithm to give fast results.  The contours are not exact.  If you want to make the contours more exact, you can right-click the geostatistical layer and choose "Properties..."  On the Symbology tab, there's a checkbox for "Presentation quality". When you export to raster, the software makes a prediction at the center of every raster cell.  Depending on the data and the kriging model, the raster surface may appear different than the geostatistical layer. ... View more

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. ... View more

The empirical semivariogram is created by averaging the squared differences between pairs of points that are approximately the same distance apart.  Even a few outliers can heavily influence this average (particularly because you're squaring the difference).  Outliers are almost always problematic for kriging, but they're particularly bad when the outliers are scattered randomly throughout the study region (rather than being clustered together).  This is because randomly scattered outliers will affect the empirical semivariances at small distances (because they might be right next to low values), but if the outliers are clustered, the squared difference between two outliers might still be small, allowing for accurate semivariogram estimation at small distances (which is the most important part of the semivariogram because closer neighbors get the highest weights). ... View more