This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Spatial Analysis III
Spatial Analysis III
Density Estimation
Measurements
Descriptive Summaries Density Estimation
Densit
Spatial Interpolation’s Cousin
Spatial Interpolation creates interpolated
points from known samples.
Density Estimation does this also.
Estimation does this also How do they differ?
Spatial Interpolation strives to fill in the
Interpolation strives to fill in the
_______ of a continuous field
• e.g. a point upon a hillside that has not been directly observed Density estimation, on the other hand,
creates a _______ from _______ objects.
• The field’s value at any point is an _______ of the _______
of discrete objects at that point. Density Estimation
Densit
A continuous
field measured
at eight
irregularly
spaced sample
points 75
75 54
72
69 OR…
73 Eight discrete
objects with
nothing but
nothing but
empty space
between them. 68
57
66 Density Estimation
Densit
Appropriate Application Spatial Interpolation techniques should not
Interpolation techniques should not
be applied to _______ objects.
Similarly, Density Estimation techniques
should not be applied to
should not be applied to _______ fields.
fields Consider the techniques you have
learned in the past for mapping density
(Population, for example)
(P
Dot Density Mapping • Effective, but your objects remain _______ Choropleth Mapping • Though your mapping units may be _______, they remain
_______.
• Internal _______ within your (arbitrary) mapping unit is
_______ by the areal averaging process! Density Estimation
Densit
Removal of _______ is the last thing
that we would want when searching for
a geographic _______!
Fortunately, thanks to GIS, we are not
thanks to GIS we are not
confined to these parameters.
While Choropleth maps have always been
popular due to their relative ease of
preparation, GIS has permitted us to map
density upon more localized scale
density upon a more localized scale.
• We are no longer forced to describe density upon a
arbitrary (national/state/county) scale! Density Estimation
Densit
Thus, rather than discussing
Population Density in the
th
traditional sense, we should
discuss the Population density of
discuss the Population density of
varying
varying _______ __________
Consider Palm Beach County:
Palm Beach County:
• Land Area – 2,023 mi2
• Population – 1,287,987 people
• Population Density = 637 people/mi2
– Does this adequately describe the distribution of
people within our county?
– It would be far superior to analyze density at a
greatly reduced _______ __________ Density Estimation
Densit
These reduced spatial resolutions
are computed as a ______ ______
about the discrete point.
The shape of the
th
kernel is dependant
upon a _______
parameter.
• Increasing the distance
produces a broader,
broader,
flatter shape These kernels are
A typical kernel function
then
then _______ to produce
to produce
a composite _______ Density Estimation
Densit
The __________ of the resulting
field depends on the width of the
field depends on the width of the
kernel
kernel
The kernels should _______
together to produce a continuous
surface (right)
If the distance parameter is too
low, the kernels will remain
di
discrete objects (below)
(b Density Estimation
Densit
In ArcMap, Spatial Analyst,
Density
Density Density Estimation
Densit
Calculating Density with Spatial
Analyst
As you can see, Spatial Analyst
permits either Simple or Kernel
permits either ‘Simple’ or ‘Kernel’
density calculations Density Estimation
Densit
Calculating Density with Spatial
Analyst
__________ density
• Points or lines that
li
th
fall within the
search area are
summed, then
th
divided by the
search area size to
get each cell's
density value. Density Estimation
Densit
Calculating Density with Spatial
Analyst
Analyst
_______ density
• The values associated with
each point are spread out,
starting from the point
location, to the specified
radius.
• The density is greatest
at the point location and
diminishes to zero when
reaching the specified radius. Measurements
Many tasks require measurement from
maps
maps
Measurement of distance, area
Such measurements are tedious and
measurements are tedious and
inaccurate if made by hand Measurement using GIS tools and
Measurement using GIS tools and
digital
digital databases is _______, _______,
and _______
It was this ability that led the Canadian
government to fund the development of the
world first GIS CGIS in mid
world’s first GIS, CGIS, in mid1960s Measurements
Measurement of Length
_______
• A rule for determining distance between points
in space. Pythagorean/Straightline Metric:
• Simplest Metric
• The shortest distance between two points
(x1, y1) and (x2,y2) on flat plane is the
(x1, y1) and (x2,y2) on a flat plane is the
hypotenuse of a rightangled triangle:
D=
– (The square of the hypotenuse is equal to the sum of the squares of the other two sides) Measurements
Measurement of Length (Cont.)
Pythagorean/Straightline Metric:
• This is only suitable when working with a _______
projection
projection.
– i.e. the surface of the Earth is NOT accounted for. Network distance:
• Most trips do not occur upon a straight line basis.
• Thus, the _______ distance of network segments along
a travel route must be calculated
travel route must be calculated
• Each segment is calculated using the Pythagorean
metric. Measurements
Measurement of Length (Cont.)
The Great Circle metric:
• Gives the _________ ___________ (the Great Circle
distance) between two points on spherical globe
distance) between two points on a spherical globe.
Decimal Degrees:
r * acos[sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(lon2  lon1)]
r=6378.7 (kilometers); r=3963.0 (normal miles)
(http://www.meridianworlddata.com/Distance(http://www.meridianworlddata.com/DistanceCalculation.asp) Measurements
Issues with Length Measurement
The abstracted Polyline is never a perfect
representation of the real world equivalent.
It will always tend to cut _______
will always tend to cut The length of a Polyline tends to be ______
than the length of the object it represents
• The exception to this rule are those cases where the object
truly is _______ : Surveyed Features (Buildings, roads, parcel
boundaries) Measurements
Issues with Length Measurement
Measurements in GIS will usually be
based upon 2D features.
• In these cases, an _________ surface will NOT
be accounted for. • Thus the measurement reported may be
substantially _______ than reality Measurements
Measurement of Area
Measuring area is superficially
obvious but difficult in practice
In GIS, it is based on coordinates of
polygon vertices
• Breaks _______ shapes
into a series of trapezia
• The area of these is
area of these is
then calculated and
summed. Measurements
Measurement of Shape
Shape is a property of many objects
of interest in geography
• CBD, electorate district, habitat patch, etc. The description
of which may
be verbal… Measurements
Shape & Gerrymandering The 12th Congressional District of NC was drawn in
1992 using a GIS,
Designed to be majority
Designed to be a majorityminority district: with a
district: with
majority of African American voters, expected to
return an African American to Congress. This
objective was achieved at the cost of a very
contorted shape
contorted shape.
The U.S. Supreme Court eventually rejected the
design. Measurements
Measurement of Shape
A common measurement is:
S = P/ 3.54 x SQRT(A)
where, P perimeter, A area
• Normalized, the
compactness of a
circle is _____
• The more contorted
more contorted
the area, the ______
the shape measure Descriptive Summaries
Descri
Attempt to summarize useful
properties of data sets in one or
properties of data sets in one or
two
two statistics Descriptive summaries can borrow
summaries can borrow
many concepts and techniques from
nonspatial statistics • especially when they are used for nonspatial attributes
when they are used for non
attributes However, caution should be applied
when using them for spatial
attributes
attributes • For example, many statistical techniques are designed to
make inferences about a larger population based upon
the assumption that you are working with a _______
and _______ sample.
• However, most geographic data sets are neither of these Descriptive Summaries
Descri
The Centroid or Mean Center
The point at which an imaginary, flat,
weightless, and rigid map would
_______ perfectly if weights of
if weights of
identical value were placed on it so
that each weight represented the
location of a single entity within a
population. Descriptive Summaries
Descri
The Centroid or Mean Center
Found for a point set by
taking the weighted
______ of coordinates
coordinates
• Each enumeration unit has a
Centroid with an x,y coordinate
• Each of these is weighted by
of these is weighted by
the population in question
• The mean of these weights is then achieved by dividing
by the sum of the weights. While a single centroid may seem
boring, a set of centroids may provide
useful insights.
i ht Florida’s Hispanic
Population Centroid Florida’s Total
Population Centroid Descriptive Summaries
Descri
The Point of Minimum Aggregate Travel
(MAT)
(MAT)
MAT point minimizes the sum of _______
from each point to the center (MAT point)
from each point to the center (MAT point)
MAT point may be a good candidate point to
_______ any _______ service,
• e.g. schools, hospitals, stores, fire stations, government
centers No simple mathematical expression for MAT
• It must be found by a trialanderror process of iteration:
• An initial guess is successively improved using a suitable
algorithm Descriptive Summaries
Descri
Dispersion
Used to measure the _______ of
points around a center.
• i.e. The antithesis to clustering. Mean distance from the centroid is a
simple measure of dispersion in 2D
di Descriptive Summaries
Descri
Measures of Pattern
The distribution of points may be
either:
• _______
– Points are located independently, and all locations
are equally likely. • _______
– Some locations are more likely than others, and the
presence of one point may _______ others to its
vicinity
vicinity.
– Identification of clustering is the necessary first step
prior to the isolation of a _______ for clustering.
– e.g. The spread of some disease,
The spread of some disease
Symbiotic organisms Descriptive Summaries
Descri
Measures of Pattern
Distribution of points may be either
(Cont.):
• _______
– The presence of one point may make others
_______ likely in its vicinity.
– Such patterns are commonly the result of
patterns are commonly the result of
_________ for space.
– i.e. The presence of one population inhibits the
presence of another.
presence of another.
– Organisms, retail outlets, etc. These patterns can be identified
th
through various statistical methods
statistical methods Descriptive Summaries
Descri
Fragmentation Statistics
Measure the degree of fragmentation
of spatial data sets
Useful in landscape ecology, forestry
in landscape ecology forestry
etc.
• Habitat fragmentation affects the success of certain
species (particularly major predators)
• Plant/animal populations are less likely to _______ in
highly fragmented landscapes that have potentially
_________ regions in between habitable _______
in between habitable Various Indices of Fragmentation:
• Number of patches
• Size distribution
• Average shape of patches (for each class) Descriptive Summaries
Descri
Fragmentation
Statistics
Three images of part of
the state of Rondonia in
the state of Rondonia in
Brazil, for 1975, 1986,
and 1992.
Note the increasing
fragmentation of the
natural habitat as
natural habitat as a
result of settlement. ...
View
Full
Document
 Spring '11
 roberts

Click to edit the document details