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- [Instructor] Hi, and
welcome to module six

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of advanced geographic
information systems.

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This week we'll cover two primary topics

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spread out over four lectures.

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The first topic relates
to density calculations.

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And we'll hear about
that here in lecture one.

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From there, we'll move on to interpolation

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and we'll hear about that in
lectures two, three, and four.

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Let's get started.

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A density calculation
is a focal operation,

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meaning that it computes the
value of a cell of interest

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based on the value of the cells

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within a neighborhood that
surrounds that location.

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It's up to you to specify
that search region,

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that area over which the
algorithm looks for other values,

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and it's what is considered
the neighborhood.

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So think about it this way.

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You've got a blank slate
for your raster dataset,

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and you've got a point
data set is your input

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that you want to use to
calculate the density.

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For each one of those
cells in the new raster

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ArcGIS draws a circle and
sums the number of points

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and writes that
information into that cell.

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So it's sort of like a buffer

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and select by location operation

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for identifying the neighbors
for a specific cell.

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Cells with no neighbors are assigned

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a no data value in the output.

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Let's walk through an example here.

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As (indistinct) has populates
the values of the raster

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that identifies a cell,

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draws a neighborhood around that cell,

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then counts or sums the observations

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within that neighborhood.

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Once that's done,

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that value from number two is divided

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by the area of the neighborhood.

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Again, that's something

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that you specify for the calculation.

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And then that result
from step number three

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is assigned to that cell from number one.

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From there ArcGIS just
continues across the raster

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and continues to make those calculations.

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So why do this?

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Density calculations are nice

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to help us identify areas of concentration

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and they can create a
predicted distribution

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of the population.

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The total value, or the sum
of all values of the neighbors

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for each individual cell.

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Now we've heard a little bit about the how

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in terms of summing those observations

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within the neighborhood
and dividing by that area

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of the neighborhood to produce
that density calculation.

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You can also use a kernel.

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And in this case we're fitting
a curve over each cell.

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And the kernel supplies the weights.

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So closer to the center point

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that cell of interest,
the weight is highest.

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And that weight diminishes
with increased distance

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from that center point.

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If you were to compute the
volume under that curve,

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and I urge caution here

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because now we're getting
into the realm of calculus.

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That volume would equal the sum

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of the population within
that search limit.

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So within the neighborhood
that you specify.

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Let's look at a graphical example

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to see if that helps.

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First, here's a number of different types

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of curves for fitting.

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And in this case, we're
talking about a quartic curve.

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So that's the cyan blue that you see

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about halfway down in the legend.

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If we were to look from above,

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imagine that the dark
green cell in the center

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is our cell of interest, and
we fit the curve over that.

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The lighter the green
color, the lower the weight.

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You can see how that
weight factor tapers off

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as you get further and further out

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closer to the edge of the neighborhood.

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Now, we'll look at three

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different density type calculations.

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A kernel density, a line
density, and a point density.

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The kernel density measures
the magnitude per unit area

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for point or line inputs
using that kernel function

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that we just heard about fit
to each one of the features.

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Line density measures a magnitude per area

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from a line feature within
some user-specified radius

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around each cell.

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And then lastly, a point density

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measures the magnitude per unit area

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from a point feature within a
user-specified neighborhood.

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Now, when you're working
with the density operations

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you have the option for not
specifying a population field.

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So in that case it really
is just a hotspot analysis

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identifying clusters of the presence

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of some specific point feature.

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In this case, we'll work with
the recreation sites dataset

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we've seen before.

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We'll use that as our
input point features.

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For now we'll hold off on
specifying a population field.

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So we'll leave the default value of none.

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And then we'll choose
a circular neighborhood

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with a radius of 25,000.

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Now that 25,000 I should note,
is reported in native units

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to the input dataset, which
is also the coordinate system

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of the output raster
that will be produced.

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Here's the distribution
of the input points,

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and the resulting raster from
that tool parameterization.

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Let's take a look at another.

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In this case, I've used the same setup

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except for I've specified
a rectangular neighborhood.

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And based on some theory that I have

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about a trend in the data

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I've decided to create a
rectangular neighborhood

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7,500 meters wide and 15,000 meters tall.

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Let's look at that output

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and then compare the two outputs.

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So you can see that the
definition of the neighborhood,

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that size and shape of the neighborhood

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can have pretty dramatic impact

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on the resulting surface
that you estimate.

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Of course, if you're going to specify

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something other than a circular pattern,

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it's better to know about
those trends ahead of time

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or plan to do some work
in data exploration mode

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to better understand the potential

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for those trends in your data set.

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If we zoom in on the same
location in each image

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we also see that those values
are drastically different

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even at the local scale.

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Now, let's do the same thing

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with a circular neighborhood
in our 25,000 meter radius.

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And this time for our population field

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we'll use the acreage.

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And if you recall, that's the size

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of each one of the recreation sites

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that's recorded in that point dataset.

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So this leads us to believe
that there's more acreage

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in the Southern recreation sites

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than there are in the
Northern recreation sites.

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Again, the darker the purple,

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the higher the value of
that particular cell.

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If we compare the two, the
result is even more interesting.

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Not surprisingly by sheer numbers

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there are more recreation opportunities

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in the Burlington area,

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but by total acreage we
see a definite pattern

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that emerges along the spine
of the Green Mountains.

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If we move over to line
density we'll start again

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with withholding a population factor.

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And in this case, we're using the matter

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of Valley trails data set
that we've looked at before.

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We'll specify a search
radius of 5,000 for this

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and we can see the output here.

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The greater number of
trails and close proximity,

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the higher the density
and the darker the purple

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value you see displayed here
in the image on the left.

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Moving onto our last example,

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we'll look at the kernel density

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using the recreation sites data set again.

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Now in this case, we'll once again

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withhold the population
specification here.

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For our neighborhood note
that this can only be a circle

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and it's up to the user
to define the radius.

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I'll set that to 25,000

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so it matches the same setting

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in the point density
calculation we did earlier.

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Now, ArcGIS will compute a default radius

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by looking at that spatial configuration

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of the features and the
total number of observations

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in your input point or line dataset.

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Lastly, like the others the area units

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assumes the units of the input dataset.

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Here's the output from the
kernel density calculation.

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We see some pretty distinct
clusters of locations

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in the raster surface that was produced.

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And if we compare the two,

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the point density and the kernel density,

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generally speaking we
see some similar patterns

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but note the difference here
is that the kernel density

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because of the weighting
scheme that it applies

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really drops off to the
low end values here.

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The darker the color,
the higher the value.

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And we can see a lot
more of the background

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of the State of Vermont

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and the kernel density output

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than we do in the point density output.

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Once again, that's due
to that weighting scheme

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of the kernel that we apply.

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This won't be the last time we see kernels

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in our investigation this week.

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So keep that in mind.

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Well, that's it for density calculations.

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Join me in a few minutes to learn more

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about geostatistics and interpolation.