- Welcome back to module six.
It's come down to this.
We're at the the last of the four lectures
for this learning module.
And I've saved the best for last.
Well, depending on how you look at it.
What I can guarantee you is this is the most technical
of the approaches that we've looked at so far.
So there was a time when Kriging was essentially
geostatistical analysis.
Now that branch of statistics has expanded
in the recent past to cover a lot more ground
than just Kriging.
But just note that Kriging is the most well-developed
of all of the approaches that we've seen so far.
It's a collection of advanced interpolation
methods that can assess the quality
of the prediction and provide estimated errors.
Now, kriging assumes that the distance or the direction
between sample points reflects spatial autocorrelation
that can be used to explain the variation in the data.
So the spatial variation of the attributes is
neither totally random nor deterministic
but that auto correlation can be expected to explain
some of that variation.
There are three components to a Kriging model,
the spatially correlated component, the drift structure
or trends in the data
something larger than local autocorrelation might capture
and the random error term.
Now, Kriging is a two-step process where first
you need to get to know your data.
Uncover any dependencies that might exist
by using variograms and covariance functions
to estimate the spatial autocorrelation
that's present in the data.
Then once you've uncovered those dependencies
in the dataset, you're able to make predictions
by predicting those unknown values
within some area of interest.
There are two different types of Kriging,
ordinary and universal.
In ordinary approach, this assumes that the constant mean
is an unknown value.
Universal assumes that there's some overriding trend
in the data.
Again, really important to understand the data
that you're using and how you'll be using it
in order to make decisions about these approaches.
Now, the semivariogram is where things
get really complicated.
This is a function that describes the difference
between the samples separated by distance.
So, there's a low variance for small distances
and a larger variance expected at greater distances.
Again, indicator of positive spatial autocorrelation.
This function is fit through the points
of the model that's known as the semivariogram model.
Now, again, this is mapping the distance between every point
and every other point in the data set.
In order to narrow down the computation time
that would be required,
the data can actually be binned into these distance ranges
and we'll see an example of that here in a few minutes.
Now, a few other terms to note
about the semivariogram. There's the range,
this is the distance over which the model flattens out.
The sill, this is the value obtained at the range,
so the Y axis value where that model fit
has started to flatten out.
And then lastly, the nugget, and this is the value
where the semivariogram intercepts the Y axis.
Now it's assumed to be zero
but that's typically not the case.
So, up on top we see an example
of what a series semivariogram would look like
with all the constituent parts labeled.
Down below we see five different options
for the types of curves we could try
to fit through our data.
Once again, we're using that recreational site's dataset
over on the left-hand side, just to point locations
over on the right hand side, graduated symbols
by that acreage attribute contained within the dataset.
Now, I can start out with ordinary kriging
from the spatial analyst toolkit.
Using my recreation sites and that acreage attribute,
I'm inputting point features
and specifying some numeric attribute for my Z value field.
I need to choose between ordinary
and universal for my methods
and then specify the area of the neighborhood itself.
The default lag size in this case,
those bins that I was mentioning
in the previous slide, is equal to the default cell size.
You can of course change that value if you see fit.
And then all of the advanced parameters,
all those other blanks that we see
in the Kriging dialog box are computed internally
if the user doesn't specify those.
Here's the output from my ordinary kriging approach.
If I move on to the universal kriging, again,
all the same parameters that need to be specified
but in this case you choose the semivariogram model
that you would like to produce as well.
Here's the output from that
universal Kriging implementation.
Now, I can take this one step further
and take the more complicated route
by using the geostatistical wizard.
I choose my Kriging, co-kriging option
up in the geostatistical methods
and input my recreation sites
with acreage as my data field.
Note that I have the option here to input a second data set.
So if I know something about an overarching trend
in the data, I can use information from that second dataset
in conjunction with the sample points of the first data set
to produce my raster surface.
I click next and I have options
for doing data transformations here
or specifying my trend removal order.
I'll just leave those for none right now
and click next once again.
Now we see the first look at the semivariogram.
Note that we have the point location
with the search neighborhood identified in that lower image.
The semivariogram is set up then
with all of the data points in the dataset.
I can click that optimize model icon
over on the right hand side
and RTIs will compute some of those advanced metrics for me.
Alternatively, I could calculate
those advanced metrics individually or use functions
within RGIS to calculate those one by one.
For now, I'll just click the optimized mode to take care
of all factors within the model
and now we see the revised semivariogram.
If I click next,
I can get more details about the search neighborhood
for individual locations within the output surface area.
I can click anywhere in this map
RGIS will show me which neighbors have been selected
and the relative weights of each
of those neighbors in the output calculation.
Once again, we see cross validation here
with a pretty mediocre model.
I can look at the table over
on the right hand side to see the predicted value,
the measured value and that error calculation
a little bit further over to the right.
Lastly, I can produce my output that we see over here
on the right hand side and review my method report.
That's all the details that went
into setting up my Kriging operation.
You can refer back to that at any time.
It's sort of like a metadata document
for the data layer that you create.
Just as a reminder,
when you're using the geostatistical wizard,
it produces a geostatistical analyst layer.
If you wanna use that layer in further calculations
say for, Raster calculator or Aecon operation
or even zonal statistics,
you'll need to export that to a raster file format,
right click on the geostatistical analyst layer
of interest, choose export
and I think you know the rest of the way from there.
Well, that does it for this week's lecture materials.
Hope you're not too overwhelmed by what you've just heard.
This is a technical topic within a very technical subject.
So don't beat yourself up too much
if some of this seemed a bit elusive.
I'm certainly happy to discuss this in more detail
with those of you that are interested.
For the rest of you,
it's enough to know these techniques exist
and how to find them if you ever need to employ them.
However, if you're working
in a discipline that employs field sampling methods
for data collection, you should plan to spend some more time
with background materials to dig deeper into the content.
Enjoy the lab assignment and like always
let me know how I can help.