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- Welcome back to module six.

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It's come down to this.

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We're at the the last of the four lectures

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for this learning module.

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And I've saved the best for last.

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Well, depending on how you look at it.

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What I can guarantee you is
this is the most technical

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of the approaches that
we've looked at so far.

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So there was a time when
Kriging was essentially

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geostatistical analysis.

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Now that branch of statistics has expanded

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in the recent past to
cover a lot more ground

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than just Kriging.

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But just note that Kriging
is the most well-developed

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of all of the approaches
that we've seen so far.

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It's a collection of
advanced interpolation

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methods that can assess the quality

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of the prediction and
provide estimated errors.

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Now, kriging assumes that
the distance or the direction

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between sample points reflects
spatial autocorrelation

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that can be used to explain
the variation in the data.

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So the spatial variation
of the attributes is

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neither totally random nor deterministic

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but that auto correlation
can be expected to explain

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some of that variation.

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There are three components
to a Kriging model,

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the spatially correlated
component, the drift structure

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or trends in the data

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something larger than local
autocorrelation might capture

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and the random error term.

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Now, Kriging is a two-step
process where first

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you need to get to know your data.

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Uncover any dependencies that might exist

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by using variograms and
covariance functions

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to estimate the spatial autocorrelation

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that's present in the data.

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Then once you've uncovered
those dependencies

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in the dataset, you're
able to make predictions

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by predicting those unknown values

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within some area of interest.

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There are two different types of Kriging,

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ordinary and universal.

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In ordinary approach, this
assumes that the constant mean

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is an unknown value.

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Universal assumes that
there's some overriding trend

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in the data.

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Again, really important
to understand the data

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that you're using and
how you'll be using it

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in order to make decisions
about these approaches.

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Now, the semivariogram is where things

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get really complicated.

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This is a function that
describes the difference

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between the samples separated by distance.

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So, there's a low variance
for small distances

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and a larger variance
expected at greater distances.

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Again, indicator of positive
spatial autocorrelation.

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This function is fit through the points

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of the model that's known
as the semivariogram model.

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Now, again, this is mapping the
distance between every point

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and every other point in the data set.

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In order to narrow down
the computation time

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that would be required,

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the data can actually be binned
into these distance ranges

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and we'll see an example of
that here in a few minutes.

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Now, a few other terms to note

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about the semivariogram.
There's the range,

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this is the distance over
which the model flattens out.

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The sill, this is the value
obtained at the range,

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so the Y axis value where that model fit

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has started to flatten out.

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And then lastly, the nugget,
and this is the value

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where the semivariogram
intercepts the Y axis.

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Now it's assumed to be zero

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but that's typically not the case.

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So, up on top we see an example

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of what a series
semivariogram would look like

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with all the constituent parts labeled.

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Down below we see five different options

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for the types of curves we could try

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to fit through our data.

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Once again, we're using that
recreational site's dataset

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over on the left-hand side,
just to point locations

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over on the right hand
side, graduated symbols

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by that acreage attribute
contained within the dataset.

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Now, I can start out with ordinary kriging

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from the spatial analyst toolkit.

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Using my recreation sites
and that acreage attribute,

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I'm inputting point features

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and specifying some numeric
attribute for my Z value field.

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I need to choose between ordinary

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and universal for my methods

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and then specify the area
of the neighborhood itself.

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The default lag size in this case,

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those bins that I was mentioning

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in the previous slide, is
equal to the default cell size.

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You can of course change
that value if you see fit.

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And then all of the advanced parameters,

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all those other blanks that we see

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in the Kriging dialog box
are computed internally

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if the user doesn't specify those.

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Here's the output from my
ordinary kriging approach.

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If I move on to the
universal kriging, again,

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all the same parameters
that need to be specified

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but in this case you choose
the semivariogram model

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that you would like to produce as well.

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Here's the output from that

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universal Kriging implementation.

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Now, I can take this one step further

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and take the more complicated route

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by using the geostatistical wizard.

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I choose my Kriging, co-kriging option

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up in the geostatistical methods

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and input my recreation sites

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with acreage as my data field.

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Note that I have the option
here to input a second data set.

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So if I know something
about an overarching trend

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in the data, I can use information
from that second dataset

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in conjunction with the sample
points of the first data set

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to produce my raster surface.

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I click next and I have options

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for doing data transformations here

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or specifying my trend removal order.

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I'll just leave those for none right now

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and click next once again.

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Now we see the first look
at the semivariogram.

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Note that we have the point location

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with the search neighborhood
identified in that lower image.

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The semivariogram is set up then

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with all of the data
points in the dataset.

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I can click that optimize model icon

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over on the right hand side

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and RTIs will compute some of
those advanced metrics for me.

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Alternatively, I could calculate

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those advanced metrics
individually or use functions

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within RGIS to calculate those one by one.

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For now, I'll just click the
optimized mode to take care

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of all factors within the model

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and now we see the revised semivariogram.

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If I click next,

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I can get more details about
the search neighborhood

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for individual locations
within the output surface area.

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I can click anywhere in this map

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RGIS will show me which
neighbors have been selected

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and the relative weights of each

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of those neighbors in
the output calculation.

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Once again, we see cross validation here

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with a pretty mediocre model.

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I can look at the table over

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on the right hand side to
see the predicted value,

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the measured value and
that error calculation

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a little bit further over to the right.

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Lastly, I can produce my
output that we see over here

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on the right hand side and
review my method report.

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That's all the details that went

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into setting up my Kriging operation.

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You can refer back to that at any time.

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It's sort of like a metadata document

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for the data layer that you create.

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Just as a reminder,

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when you're using the
geostatistical wizard,

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it produces a geostatistical
analyst layer.

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If you wanna use that layer
in further calculations

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say for, Raster calculator
or Aecon operation

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or even zonal statistics,

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you'll need to export that
to a raster file format,

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right click on the
geostatistical analyst layer

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of interest, choose export

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and I think you know the
rest of the way from there.

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Well, that does it for this
week's lecture materials.

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Hope you're not too overwhelmed
by what you've just heard.

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This is a technical topic
within a very technical subject.

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So don't beat yourself up too much

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if some of this seemed a bit elusive.

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I'm certainly happy to
discuss this in more detail

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with those of you that are interested.

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For the rest of you,

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it's enough to know these techniques exist

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and how to find them if you
ever need to employ them.

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However, if you're working

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in a discipline that employs
field sampling methods

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for data collection, you should
plan to spend some more time

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with background materials to
dig deeper into the content.

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Enjoy the lab assignment and like always

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let me know how I can help.