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Does anybody have experiences about Geostatistical Simulation in ArcGIS (Gaussian Geostatistical Simulation)?

CarineSilva

I have used Gaussian Geostatistical Simulation in ArcGIS , but I would like to understand better how the method works. When the number of simulation is increased, the global mean from the output map is almost constant when the “mean output”; and the global mean from the output map is increasing when the “maximum output”.

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Eric6346

Hi Carine,

What you are seeing is to be expected. The Gaussian Geostatistical Simulations tool works by creating many different rasters that are all simulated from the same geostatistical model. When you output the mean raster, you are creating a raster where each cell is the average of all the simulated values in that raster cell. This average value should not change drastically as you increase the number of simulations because the mean value will stabilize fairly quickly. When you output a maximum raster, you are creating a raster where each cell is the maximum of all the simulated values in that raster cell. Unlike the mean, the maximum will keep getting bigger and bigger as you increase the number of simulations.

Please let me know if you need more clarification, but what you are seeing is what is supposed to happen.

SteveLynch

To add to what Eric said...

On the far left we have the simple kriging layer that is used as input, then you create N realizations. The N=8 image is the average of 8 of these realizations. As N increases so will the mean get closer to the input simple kriging layer. This is true for conditional simulations.

CarineSilva

Thanks, Eric Krause and Steve Lynch! The answers are helpful.

I am just have a question about spatial pattern distribution. Using ordinary or universal kriging we can see some pattern. But, using GGS the spatial pattern looks like "sand points", without a pattern.
Maybe, this spatial pattern is because the simple kriging or the model is not well ajusted?
Thank you!

SteveLynch

Are you doing conditional or unconditional simulation?

Eric6346

I think Steve is right. You are probably doing unconditional simulation when you want to be doing conditional simulation.

To do conditional simulation, you must provide the dataset and the field that you use to create the kriging layer into the Gaussian Geostatistical Simulations tool. You provide them in the "Input conditioning features" and "Conditioning field" parameters.

The idea here is that there are an infinite number of surfaces that all have the same covariance structure (ie, the same semivariogram). When you do an unconditional simulation, you simply create several of them at random. However, these surfaces do not pass through the same set of points, and their high/low values will not occur in the same places. When you average over all these simulations, you will get close to a constant raster.

But there are also an infinite number of surfaces that all have the same covariance structure and are conditioned to pass through a given set of points. You can specify these conditioning points to be anything that you want, but the most common thing to do is to condition that the simulations must pass through the input points from the kriging layer. When you do this, all simulations will resemble the original kriging layer, and when you take an average of the simulations, you will get something close to the original layer. The more simulations that you perform, the closer the average will look to the original layer. Steve's picture shows how this works.

Both conditional and unconditional simulations have uses, but it can sometimes be tricky to tell which one you should use. In your case, it sounds like you want to be doing conditional simulations and conditioning on the features that were used to create the kriging layer.

CarineSilva

Thanks, Steve! I am doing unconditional simulation.

CarineSilva

Thanks, Eric. The explanation is really helpful.

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