Kriging - trends and error statistics

[ElizabethYoung]

Hi,

I just had a couple of questions about some of the steps used in kriging in ArcGIS geostatistical analyst.

Firstly, I am working with data that I know has a trend first order trend, so I have chosen to remove this trend.  What are the differences between neighbourhood and global trend removal, and what should I be aiming for when setting the % of each?  Minimising my error?  I am also not sure whether I should use the anisotropy option if I am already removing the trend - my understanding was this was to account for trends in data?

Secondly, I was wondering if someone could explain the error statistics to me in a simple way (I have relatively little knowledge of statistics).  I understand that I want to minimse the mean error, standard error, and rms, and that the rms should be similar to the standard error, but I???m not sure which of these are most useful for communicating the accuracy of my resulting data.  I???m slightly confused as on some datasets I seem to get very low mean error but the other values seem quite high.  Does this mean that high errors in both directions are effectively cancelling each other out when the mean is taken?

[EricKrause]

The global vs local trend removal slide bar in ArcMap 9.3.1 is used to determine how locally the trend will be removed.  100% global will remove trend using global polynomial interpolation, and anything else will use local polynomial interpolation.  Read about these two methods in our help, and feel free to ask questions about anything you have trouble understanding.  Note that in ArcMap 10, you can actually see the trend removal parameters, so you have more control over how the trend is removed.  As for how you decide how locally to remove the trend, there are a couple of things to watch.  First, if you remove the trend too locally, you may find that the semivariogram on the next page is near flat.  That means that you removed too much trend.  You want to remove just enough in order to still fit a good semivariogram.  Second, you can go by crossvalidation statistics, which I'll talk about below. 

The biggest things to look for in crossvalidation is that the average standard error should be similar to the root-mean-square, and the root-mean-square standardized should be close to one.  If you find several models that have these properties, choose the one with the lowest root-mean-square.  You can also see if the mean standardized is close to 0, but if the other statistics are good, this one is usually good too.