Latest Contributions by EricKrause

Hi @Lacin_Ibrahim,  The Visualize Space Time Cube in 2D tool will re-create the most recent result of Emerging Hot Spot Analysis for the analysis variable.  If you rerun EHSA on the same variable, the Visualize STC in 2D tool will start creating the output of the most recent EHSA tool run.   Please let me know if you have any other questions or need any clarifications. -Eric ... View more

Hi Elijah, I'll try with an example of Inverse Distance Weighting with five points: p1, p2, p3, p4, and p5.  Each of these points have a location and a measured value.   Cross validation would start by removing p1.  It would then use p2, p3, p4, and p5 to predict the value of p1.  In IDW, this means taking the weighted average of the values of p2 to p5 (weighted by inverse distance). This will result in some prediction (called the cross validation prediction) that can be compared to the measured value of p1.  Next, p2 would be removed, and p1, p3, p4, and p5 would be used to predict to the location of p2 (note that p1 is added back to the dataset after being cross validated). The same is done for p3, p4, and p5, each using the other four points. This would produce five cross validation errors that would be used to calculate, among other things, the root mean square error of the IDW model. But when actually making the prediction surface (after cross validation), all points are used to make the predictions.  The surface also predicts values everywhere, including at the input point locations.  So, what will it predict at, say, the location of p3? The prediction is the weighted average of all the points p1, p2, p3, p4, and p5, weighted by the inverse distance to p3.  But the distance from p3 to itself is zero, which gives the value of p3 a weight of infinity.  This forces the predicted value to be exactly equal to the measured value at p3.  This is what makes IDW an "exact" interpolation method.   Please let me know if that still is not clear. -Eric   ... View more

@Elijah  Each horizontal line of points in the graph appears to have the same Measured value on the y-axis (or very close to equal).  However, they each have a different Predicted value on the x-axis.  Having many repeated values in the field you used to interpolate would produce this kind of graph.  This isn't necessarily a problem, but you should look into it and confirm that the repeated values are expected in your data. ... View more

Hi @ArnieWaddell1  The graph is showing the distribution each field in the cross validation Table (change the field with the Field pulldown) using a kernel density estimation.  Think of it like a smoothed histogram of the Measured values, Predicted values, or Errors.   Overlaying the Measured and Predicted fields is the most important use of the Distribution tab.  This lets you compare the distribution of true values and the cross validated predictions.  Ideally, the two should have very similar distributions, and big deviations might indicate problems in the interpolation model. -Eric ... View more

This seems like a pretty reasonable study outline to me.   If I had to nitpick, I would suggest simulating data from the interpolation model rather than extracting the results of a single interpolation.  This allows you to do multiple repetitions for each gridding, where the data for each repetition comes from the same model and differs only in their random components. That being said, in Geostatistical Analyst, you can only simulate from univariate Simple Kriging models, so that might not be an option.  I'm definitely interested in the results, I've done some ad hoc experimentation along these lines but not enough to draw any solid conclusions.   ... View more

Hi Elijah, I'm not aware if this has been specifically researched by anyone, but I have a few thoughts about EBK with low and varying sampling density.  For the same subset size, the area of a subset will be larger for a low-density area than a high-density area (ie, 100 points would be spread out over a larger area for lower densities).  EBK assumes stationarity within each subset, so to get best results, you should configure the subset size so that the resulting subsets are small enough in area to assume each is stationarity.   EBK (when a transformation is used) and EBKRP are based on Simple Kriging, so they assume a uniform density within each subset.  It's ok if the density of the samples varies globally (ie, some areas are densely sampled, and others aren't), but it's important that the density of the points be relatively consistent within each subset.  Again, this may require configuring the subset size.  EBK Regression Prediction, however, has a clear advantage for low density sampling, but it's the regression part, not the EBK part.  The better the regression model predicts the dependent variable on its own, the less need there is for including autocorrelation from neighbors with EBK. Hope that's all clear, Eric ... View more

Hi @Elijah, "Small" is of course relative, but this generally means datasets between ~20 and 100 input points.  Most other kriging methods estimate a single semivariogram for the entire study area, and this presents two problems.  First, it is difficult to estimate semivariogram for small datasets, and the uncertainty in the semivariogram model will not be propagated to the prediction standard errors.  Second, one semivariogram (even if correctly estimated) may not fit well everywhere in the study area; some areas may need different semivariograms than other areas. By simulating data and semivariograms locally, EBK/EBKRP better captures uncertainty in the semivariogram model, and it allows the models to change within the study area.  This results in, among other things, better "coverage probabilities" for EBK.  For example, when creating 95% confidence intervals for kriging (not EBK) predictions, it is common for only 75% of validation data to fall within the confidence interval because the standard errors do not accurately reflect the prediction uncertainties.  But you should generally expect confidence intervals from EBK to be much closer to 95%.   -Eric ... View more

Hi @Elijah , The tool is estimating the effect of each explanatory variable with a regression-kriging equation.  Each explanatory variable comes with a coefficient that indicates the expected change of the dependent variable for a one-unit increase in the explanatory variable.  For distance to roads, it is trying to estimate the effect on CO2 by moving one distance unit (maybe 1 meter) further from a road. This can become a problem because if all of your data are sampled on or near a road, all of the distances used to estimate the coefficient come from a narrow range of distances, likely all under 10 meters.  But when you are predicting, you are predicting to areas relatively far from a road.  The patterns that the tool detected in the narrow set of distances likely will not hold up for larger distances. Generally speaking, you should be cautious when extrapolating outside the range of the explanatory variables of the input points.  Specifically, if all of your points are near a road, I would not use distance to roads as an explanatory variable because there isn't enough variation to reliably estimate and extrapolate the effect.  To do this, you would need samples of points at varying distances from roads. Hope that helps, Eric   PS, I'm also concerned that the distances to roads you're providing aren't accurate.  If all points are truly on the road, that distance should always be 0.  I'm wondering if the distance to roads of the input points are just an artifact of the cells of the Euclidean Distance raster not landing exactly on the road.  If so, the "distance" of each point will be somewhat random and not correspond to any correlation between roads and CO2.   ... View more

@Bill_Thayer No, I'm sorry, but this information cannot be extracted.  One thing to know, however, is that the semivariogram is estimated using no more than 1000 input features.  If the input features have more than 1000 valid records, a random sample of 1000 is taken, and only these features are binned for semivariogram estimation*.  So even if you could extract the actual number of binned pairs, it would not match the number you expect, unless you have fewer than 1000 points. If this information is something that would help you in your work or research, your best bet is submit the idea through ArcGIS Ideas.   *After estimating the semivariogram from the random sample, all input points are used when making predictions, not just the 1000 point sample. ... View more

Hi Christina, There is a lot going on with that equation, probably too much to summarize in a post.  The idea is that the red dots and blue crosses are estimated directly from the data, and the smooth blue semivariogram model is fit to this data (similar to fitting a regression line to a scatterplot).  The equation under the curve is the equation for the smooth blue line.   Some of the formulas used in Geostatistical Analyst are slightly different than used in 3D Analyst and Spatial Analyst (the help page you linked to).  You can find the exact formulas used in Geostatistical Analyst on page 263 of this document: https://dusk.geo.orst.edu/gis/geostat_analyst.pdf However, I would highly suggest that you project your data to a projected coordinate system and perform kriging on the projected data.  In general, you cannot convert semivariograms calculated in one coordinate system to another coordinate system.  This problem is especially bad for data with latitude-longitude coordinates because there is no standard conversion between degrees and other linear units like kilometers. Hope that helps, -Eric ... View more