Density Estimation Concepts and Applications (MOD 8)

DENSITY ESTIMATION
• Spatial Interpolation’s Cousin
• Spatial Interpolation creates interpolated points from known samples.
• Density Estimation does this also.
• How do they differ?
• Spatial 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

(a)  

Density Estimation:
A __________ field
measured at _____
irregularly spaced
sample points
OR...
Eight ________
objects with nothing
but _____ space
between them?


(a)  

DENSITY ESTIMATION
• Appropriate Application
• Spatial Interpolation techniques should not be applied to ________ objects.
• Similarly, Density Estimation techniques should not be applied to __________ fields.
• Consider the techniques you have learned in the past for mapping density (Population, for example)
• 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!

(a)  

DENSITY ESTIMATION
• Removal of _________ is the last thing that we would want when searching for a geographic ________!
• Fortunately, 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 a more localized scale.
• We are no longer forced to describe density upon an arbitrary (national/state/county) scale!

(a)  

DENSITY ESTIMATION
• Thus, rather than discussing Population Density in the traditional sense, we should discuss the Population density of varying _______ ___________
• Consider Palm Beach County:
• Land Area – 1,969.76 mi2
• Population – 1,471,150 people
• Population Density = 670.2 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 _______ __________

(a)  

DENSITY ESTIMATION
• These reduced spatial resolutions are computed as a ______ ________ about the discrete point.
• The shape of the kernel is dependent upon a parameter.
• Increasing the distance produces a broader, flatter shape
• These kernels are then ______ to produce a composite _______

(a)  

Density Estimation:
The __________ of the resulting field depends on the width of the kernel
The kernels should _____ together to produce a continuous surface (right)
If the distance parameter is too low, the kernels will remain discrete objects (below)

(a)  

Calculating Density with Spatial Analyst:
(a)   density - Points or
lines that fall within the search area are summed, then divided by the search area size to get each cell's density value.

Calculating Density with Spatial Analyst:
__________ density - The values associated with each point are spread out, starting from the point location, to the specified radius.
The density is ________ at the point location and diminishes to ____ when reaching the specified radius.

(a)  

MEASUREMENTS
• Many tasks require measurement from maps
• Measurement of distance, area
• Such measurements are tedious and inaccurate if made by hand
• Measurement using GIS tools and digital databases is
____, ________, and ________
• It was this ability that led the Canadian government to fund the development of the world’s first GIS, CGIS, in mid-1960s

(a)