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- [Teacher] This is the last
of the Module Three Lectures.

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In this lecture, we explore techniques

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through summarizing raster
data within bounded regions.

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Think of this as the raster equivalent

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of the vector operation
reviewed in the last lecture.

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Once again, we're faced
with the same problem

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of determining how much of one thing

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is contained by another,
or how much of each type

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of that one thing is
contained by the other.

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First, a short step back to refresh

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what we know about zonal operations.

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Zonal operations summarize raster values

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within a bounding unit or zone.

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Those zone boundaries can be represented

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with other vector or raster data.

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But in this case, to remain
consistent with the examples

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of the previous lecture,
we'll use polygons

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to define our zone boundaries.

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It's critically important
here that each zone

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feature a unique ID.

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In other words, there are no
two discreet bounding polygons

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that have the same zone ID value.

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Note that you can use a raster dataset

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to represent the zones.

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But in this case, the zone is defined

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by the value of the pixel.

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All pixels in the dataset
with the same value

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make up the zone, regardless
of whether those cells

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are adjacent to one another or not.

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Zonal operations typically
produce either a new table,

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certainly when you run
zonal statistics as table

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or tabulate area.

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Note that the zonal statistics tool

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generates an output raster dataset,

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and it's also only able to
compute a single statistic

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for each run of the tool.

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This slide breaks down the
key details or parameters

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of the two primary approaches
I'd like to focus on,

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zonal statistics as
table and tabulate area.

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In the left column, we
see the characteristics

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of the zonal statistics as
table geo processing tool.

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As I mentioned earlier, input
zones can be either vector

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or raster and must use a
unique ID for the zone field.

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Hopefully you already know why,

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but in case not we'll reconsider
that on the next slide.

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The input data should be a
continuous raster dataset.

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I say should here, because
there is a specific case

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where the thematic dataset could be used

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and the output will still make sense.

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If you want to summarize data
from a continuous raster,

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zonal statistics as table is
the correct tool for the job.

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The output table represents
the summary statistics

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of the input raster for
each of the input zones.

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What about tabulate area?

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The primary difference
here is that the input data

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should be thematic.

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I say should here because
the tool will work

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with continuous data, but
the output table is likely

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to be a mess.

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If you're not sure why consider this again

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after you've reviewed the output

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of a tabulate area operation.

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You still need to specify a
unique value for each zone ID

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and the output will once again be a table.

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So why do we need unique
value for each zone ID?

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Look at the typical workflow
for a zonal operation.

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You compute that summary operation

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and produce a tabular output.

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How do you plan to map your results?

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You're going to join that tabular output

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to the input zone dataset.

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That zone ID comes from the
first step of what is commonly

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a three or more step
geo processing workflow.

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Once the joint is implemented,
you can query the result,

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apply custom symbology or calculate values

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of other attributes from
the summary statistics.

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This is certainly not an exhaustive list

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of what might happen after step two.

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Computing the summary statistics
is just the first step.

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Understanding the what
and how of the operation

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are critical for further
interrogation of the data

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in order to extract the
information you're looking for.

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Let's return to our trail buffers example

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from the Vector Lecture.

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This time however, we'll use
zonal statistics as table

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to make our calculations.

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We're once again using
trail buffers shown in blue

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and town boundaries,
gray with black outlines.

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I converted the polygon trail
buffer data to raster data.

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If we zoom in a bit
closer, we get confirmation

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that this is indeed a raster dataset.

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I can see that stair-step outer edge

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of what used to be the polygon boundaries.

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In this case, our input data,

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that raster that defines whether something

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is a trail buffer or not,
takes on a value of zero,

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not a buffer or one as a buffer.

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Look to the right to
evaluate the parameters

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of the zonal statistics
as table operation.

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Not surprisingly, I'm going
to use that FIPS six code

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as my zone ID.

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We run the tool to produce a
table of summary statistics,

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one record for each of the FIPS six codes

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in my input zone data.

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At this point, you might be
scratching your head saying,

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wait a minute, you just introduced

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zonal statistics as table
as the appropriate tool

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for summarizing continuous raster data

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and then the first example you show us

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is not a continuous raster dataset.

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And you're absolutely right.

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This is the special case
I alluded to earlier.

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In this instance, it's important
to remember that a pixel

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in my input dataset is
either a trail buffer

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of value of one, or it's
not, a value of zero.

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The output here has a particularly
useful interpretation.

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Not surprisingly, we see
a minimum value of zero

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and a maximum value of one.

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The count represents the
number of pixels in that zone

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and the sum is the sum of
all values in that zone.

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If you divide the sum by
the count, you get the mean.

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The mean value in this case represents

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the percent of the zone that
is covered by that phenomenon.

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In this case, we interpret
the first record in the table

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to mean that 58% of the town
with FIPS six code 23040

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is covered by the 500 meter trail buffer.

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It's important to understand
that this interpretation

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only works when you
specify a raster dataset

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with values of zero and
one for your input values.

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Let's take a look at a
slightly different example

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with a more traditional continuous raster.

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In this case, a digital elevation model.

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We see the input data in
the image on the left,

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which includes the town
boundaries and a DEM with values

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that range between 548 and 4,064 feet.

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I set up the zonal
statistics as table tool

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exactly like I did before,
but the key difference being

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the input raster and
the output table name.

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When we look at the output table,

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we notice that it's got
all the same statistics

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we saw last time, the
min, max, mean and so on

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but the way to interpret
this is different.

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Let's review the top record in the table.

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The mean value of that top record

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is approximately 1,720 feet.

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That means the mean elevation
in that particular town

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is 1,720 feet.

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We can't tell how much of the town is at

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or above that elevation.

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Obviously the output is
still valid and useful,

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but it's important to understand
that the interpretation

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of the outputs for these two
different instances does vary.

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One other things to mention
here is this warning

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you might receive when
running a zonal operation.

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The warning states that some zones

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may not have been rasterized.

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That's okay, it simply
means that one or more

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of the zone boundaries are
so small or oddly shaped

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that they did not contain the center point

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of any of the pixels in
your input raster dataset.

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As a result, that particular
zone will be ignored

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in the calculations.

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Okay, now back to our regularly
scheduled programming.

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Let's look at another case here.

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We use zonal statistics as table again,

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but this time we've got multiple
buffers around the trails,

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one at 500 meters with
a pixel value of 500

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and the other at 1000 meters
with a pixel value of 1000.

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What do you think?

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Is this the right tool for the job

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if we're trying to compute
the amount of each town

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that is comprised of each buffer type?

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Let's look at the output table.

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Once again, as expected,
we see the same listing

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of statistical summary information,

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but what can we tell from the output?

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Remember the 500 meter buffer
has a pixel value of 500

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and the 1000 meter buffer
has a pixel value of 1000.

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What does a mean value of
574 actually mean here?

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Not much really.

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It's certainly not the mean
buffer with in each town.

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If you've got some
well-developed math skills,

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you could probably back your
way into something meaningful.

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But for the rest of us, what's the point?

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My point here is simply to
illustrate that this is not

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the right tool for the job.

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However, if you use raster calculator

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to query your raster
inputs, to, for example,

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identify all pixels of
the 1000 meter buffer

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or elevations above 1700 feet in the DEM,

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you produce datasets
that meet the criteria

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of the special case raster
that only contains values

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of either zero or one,
where zero means the pixel

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did not meet the criteria
1000 meter buffer

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or 1700 foot elevation
and one means that it did.

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We've already reviewed
an approach to summarize

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this type of data so I won't
go into that again here.

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Let's move on to the tabulate
area geo processing tool

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to address the same questions.

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We've got our 500 meter trail buffers

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and town boundaries once again.

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I set up the tabulate
areas geo processing tool

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as you see on the right.

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And, not surprisingly, I
need to specify a zone field

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as well as the input raster.

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The tool produces a table as its output.

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The review of the output table
reveals the FIPS six code

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as expected and the columns
for values of zero and one.

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Of course, the zero and
one represent the classes

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of the input raster where
zero means the pixel

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is not a trail buffer and vice versa.

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Now it's important to note
here that these numbers

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represent the area of
each pixel class or value

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within that particular zone boundary.

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If we look at that top row, we
see that the value one number

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for the FIPS six code 23040

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is about 54.5 million square meters.

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You can always review the layer properties

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to determine the linear
and arrow units of the data

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you're working with.

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Okay, that was a simple example.

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Let's muddy the waters a bit.

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This time, we'll evaluate
two trail buffers,

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one at 500 meters and
the other 1000 meters.

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Of course, we also have
the non buffer pixels

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with value zero.

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If I set up the tabulate area
tool in the exact same way,

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what do you suppose will happen here?

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After I run the geo processing operation

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and open the resulting table,

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I see a format that looks very
similar to the previous one

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with the addition of
the 1000 meter buffer.

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That's great.
One more quick aside here,

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in this example, I illustrate the use

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of the tabulate area tool

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on the National Land Cover Dataset.

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That's automatic raster

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with more than 25 pixel classes or values.

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I set the tool parameters
just like we've seen before

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and run the operation.

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The output is as expected.

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I only show this example to
point out that it doesn't matter

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how many different values are represented

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in your input raster.

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In the end, each value will
have a corresponding column

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in the output table where
the cell value represents

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the area of that pixel class
within a given boundary.

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If we compare the outputs from
the zonal statistics as table

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and tabulate area operations,
we know similarities

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and differences in the two approaches.

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Of course, it doesn't make sense

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to calculate summary
statistics on thematic values.

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00:11:39,730 --> 00:11:41,740
They're not really numbers.

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00:11:41,740 --> 00:11:45,420
The primary similarity here
is the zone field definition.

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00:11:45,420 --> 00:11:47,880
And we can see the FIPS six
code throughout all four

256
00:11:47,880 --> 00:11:49,680
of the tables that are present here.

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00:11:52,250 --> 00:11:54,490
Let's look at just two of the outputs,

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00:11:54,490 --> 00:11:57,200
the two that dealt with a
special class of input raster

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00:11:57,200 --> 00:11:59,520
with values of zero and one.

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00:11:59,520 --> 00:12:02,900
Can you see any similarities
between the two tables?

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00:12:02,900 --> 00:12:04,300
Look at the top row in each,

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00:12:04,300 --> 00:12:06,410
they both refer to the same town,

263
00:12:06,410 --> 00:12:08,460
which you can tell by the FIPS six codes.

264
00:12:09,470 --> 00:12:13,010
If we multiply the area by the mean,

265
00:12:13,010 --> 00:12:16,363
I derive a value of 54.5
million square meters.

266
00:12:17,270 --> 00:12:19,560
If we look instead at
the tabulate area result,

267
00:12:19,560 --> 00:12:22,260
we see almost exact same value.

268
00:12:22,260 --> 00:12:23,680
We wondered to the same result,

269
00:12:23,680 --> 00:12:25,780
along two very different paths,

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00:12:25,780 --> 00:12:28,703
zonal statistics as
table and tabulate area.

271
00:12:30,130 --> 00:12:32,630
So where do we go from here?

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00:12:32,630 --> 00:12:35,860
Remember that a joint operation
joining the resulting table

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00:12:35,860 --> 00:12:39,190
from a zonal operation
to the input zone data

274
00:12:39,190 --> 00:12:43,000
is a common following step
after zonal calculation.

275
00:12:43,000 --> 00:12:47,170
After that, query the data,
apply custom symbology,

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00:12:47,170 --> 00:12:50,190
calculate attribute values,
recreate new attributes

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00:12:50,190 --> 00:12:52,080
based on your findings.

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00:12:52,080 --> 00:12:54,160
That's it for Module Three Lectures.

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00:12:54,160 --> 00:12:55,810
We covered a lot of ground this week.

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00:12:55,810 --> 00:12:59,280
Hopefully some of it was
review and some of it was new.

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00:12:59,280 --> 00:13:01,550
If any of this remains a mystery to you,

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00:13:01,550 --> 00:13:03,240
one, don't panic

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00:13:03,240 --> 00:13:05,800
and two, post questions
and comments to Yellowdig

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00:13:05,800 --> 00:13:07,700
and let's keep the conversation going.