how does kriging arrive at areal level prediction?

[annfeng1]

I have searched the ESRI kriging-related documentation but cannot seem to find relevant information on this. It's rather straightforward with the prediction feature from the geostatistical analysis extention to predict an areal-level value from a continuous surface interplated from kriging (e.g. ordinary kriging). But what are the maths behind this process? Is it some sort of moving average based on continous values for each areal unit? How is the average calculated? I only find the basic formula for point-location predicted values, but not for areal level values. Any help or pointers in this regard is greatly appreciated.

[EricKrause]

Good to hear you found the tool.  I highly recommend using it to aggregate predictions to polygons.

When researchers talk about block kriging, they're usually talking about things that are a lot more complicated than just averaging to polygons.  They usually are talking about analyzing how the point-to-point semivariogram compares to the polygon-to-polygon semivariogram after doing areal averaging of the discretized surface.  But if you just want to aggregate kriging predictions to polygons, you don't really need to worry about all that.

[annfeng1]

Thanks Eric but i want to properly interpret the difference between block prediction and block kriging, if there is any. A fellow researcher of mine is pretty adamant block kriging is NOT post hoc block prediction. I don't think block kriging is included in the kriging methods available in GA though. You seem to suggest block kriging is synonymous with block prediction. please entertain my curiosity and thrash this out if you could. Thanks so much!

[EricKrause]

For block predictions, it's just an areal average.  Block standard errors are more complicated than that, and I think that's what your colleague is getting at.

GA Layer to Grid performs block predictions from a kriging model you've already made.  It does not calculate block standard errors, which is the big difference from true "block kriging".  True block kriging tries to reduce calculations by incorporating the areal units into the kriging step, and it handles the standard errors for the polygons differently (the calculation of block standard errors is not a simple areal average of the point standard errors).  Sorry for the terminology issues; I probably should have consistently said "block prediction" rather than "block kriging."

Again, we decided not to implement full block kriging because geostatistical simulations do the same job a lot better.

[annfeng1]

Thanks Eric for clarifying this. I doubt if i can apply GGS though since the input layer must be from Simple kriging which is not the case here. But i have a better understanding of block kriging. Thanks for your help.