- [Instructor] Hi, and welcome to module six
of advanced geographic information systems.
This week we'll cover two primary topics
spread out over four lectures.
The first topic relates to density calculations.
And we'll hear about that here in lecture one.
From there, we'll move on to interpolation
and we'll hear about that in lectures two, three, and four.
Let's get started.
A density calculation is a focal operation,
meaning that it computes the value of a cell of interest
based on the value of the cells
within a neighborhood that surrounds that location.
It's up to you to specify that search region,
that area over which the algorithm looks for other values,
and it's what is considered the neighborhood.
So think about it this way.
You've got a blank slate for your raster dataset,
and you've got a point data set is your input
that you want to use to calculate the density.
For each one of those cells in the new raster
ArcGIS draws a circle and sums the number of points
and writes that information into that cell.
So it's sort of like a buffer
and select by location operation
for identifying the neighbors for a specific cell.
Cells with no neighbors are assigned
a no data value in the output.
Let's walk through an example here.
As (indistinct) has populates the values of the raster
that identifies a cell,
draws a neighborhood around that cell,
then counts or sums the observations
within that neighborhood.
Once that's done,
that value from number two is divided
by the area of the neighborhood.
Again, that's something
that you specify for the calculation.
And then that result from step number three
is assigned to that cell from number one.
From there ArcGIS just continues across the raster
and continues to make those calculations.
So why do this?
Density calculations are nice
to help us identify areas of concentration
and they can create a predicted distribution
of the population.
The total value, or the sum of all values of the neighbors
for each individual cell.
Now we've heard a little bit about the how
in terms of summing those observations
within the neighborhood and dividing by that area
of the neighborhood to produce that density calculation.
You can also use a kernel.
And in this case we're fitting a curve over each cell.
And the kernel supplies the weights.
So closer to the center point
that cell of interest, the weight is highest.
And that weight diminishes with increased distance
from that center point.
If you were to compute the volume under that curve,
and I urge caution here
because now we're getting into the realm of calculus.
That volume would equal the sum
of the population within that search limit.
So within the neighborhood that you specify.
Let's look at a graphical example
to see if that helps.
First, here's a number of different types
of curves for fitting.
And in this case, we're talking about a quartic curve.
So that's the cyan blue that you see
about halfway down in the legend.
If we were to look from above,
imagine that the dark green cell in the center
is our cell of interest, and we fit the curve over that.
The lighter the green color, the lower the weight.
You can see how that weight factor tapers off
as you get further and further out
closer to the edge of the neighborhood.
Now, we'll look at three
different density type calculations.
A kernel density, a line density, and a point density.
The kernel density measures the magnitude per unit area
for point or line inputs using that kernel function
that we just heard about fit to each one of the features.
Line density measures a magnitude per area
from a line feature within some user-specified radius
around each cell.
And then lastly, a point density
measures the magnitude per unit area
from a point feature within a user-specified neighborhood.
Now, when you're working with the density operations
you have the option for not specifying a population field.
So in that case it really is just a hotspot analysis
identifying clusters of the presence
of some specific point feature.
In this case, we'll work with the recreation sites dataset
we've seen before.
We'll use that as our input point features.
For now we'll hold off on specifying a population field.
So we'll leave the default value of none.
And then we'll choose a circular neighborhood
with a radius of 25,000.
Now that 25,000 I should note, is reported in native units
to the input dataset, which is also the coordinate system
of the output raster that will be produced.
Here's the distribution of the input points,
and the resulting raster from that tool parameterization.
Let's take a look at another.
In this case, I've used the same setup
except for I've specified a rectangular neighborhood.
And based on some theory that I have
about a trend in the data
I've decided to create a rectangular neighborhood
7,500 meters wide and 15,000 meters tall.
Let's look at that output
and then compare the two outputs.
So you can see that the definition of the neighborhood,
that size and shape of the neighborhood
can have pretty dramatic impact
on the resulting surface that you estimate.
Of course, if you're going to specify
something other than a circular pattern,
it's better to know about those trends ahead of time
or plan to do some work in data exploration mode
to better understand the potential
for those trends in your data set.
If we zoom in on the same location in each image
we also see that those values are drastically different
even at the local scale.
Now, let's do the same thing
with a circular neighborhood in our 25,000 meter radius.
And this time for our population field
we'll use the acreage.
And if you recall, that's the size
of each one of the recreation sites
that's recorded in that point dataset.
So this leads us to believe that there's more acreage
in the Southern recreation sites
than there are in the Northern recreation sites.
Again, the darker the purple,
the higher the value of that particular cell.
If we compare the two, the result is even more interesting.
Not surprisingly by sheer numbers
there are more recreation opportunities
in the Burlington area,
but by total acreage we see a definite pattern
that emerges along the spine of the Green Mountains.
If we move over to line density we'll start again
with withholding a population factor.
And in this case, we're using the matter
of Valley trails data set that we've looked at before.
We'll specify a search radius of 5,000 for this
and we can see the output here.
The greater number of trails and close proximity,
the higher the density and the darker the purple
value you see displayed here in the image on the left.
Moving onto our last example,
we'll look at the kernel density
using the recreation sites data set again.
Now in this case, we'll once again
withhold the population specification here.
For our neighborhood note that this can only be a circle
and it's up to the user to define the radius.
I'll set that to 25,000
so it matches the same setting
in the point density calculation we did earlier.
Now, ArcGIS will compute a default radius
by looking at that spatial configuration
of the features and the total number of observations
in your input point or line dataset.
Lastly, like the others the area units
assumes the units of the input dataset.
Here's the output from the kernel density calculation.
We see some pretty distinct clusters of locations
in the raster surface that was produced.
And if we compare the two,
the point density and the kernel density,
generally speaking we see some similar patterns
but note the difference here is that the kernel density
because of the weighting scheme that it applies
really drops off to the low end values here.
The darker the color, the higher the value.
And we can see a lot more of the background
of the State of Vermont
and the kernel density output
than we do in the point density output.
Once again, that's due to that weighting scheme
of the kernel that we apply.
This won't be the last time we see kernels
in our investigation this week.
So keep that in mind.
Well, that's it for density calculations.
Join me in a few minutes to learn more
about geostatistics and interpolation.