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Density Analysis
takes known quantities of phenomenaand spreads it across the landscape
(area)
analysis based on the
quantity that is measured at eachlocation
spatial relationship of the locations of
the measured quantities
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Why map density?
Density surfaces show where point or linefeatures are concentrated.
Create a surface showing the predicteddistribution throughout the area (spread of thedata)
Population per Km 2
Fish density per Km 2
Population Density surface example
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Point pattern analysis
determine if points (events) are exhibitingspecific pattern or are randomly distributed.
estimate the intensity (density) of how the
point pattern is distributed over the study
area
determine if there is spatial dependence
among points (events)
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A - col lec t ion of point objects B - kernel funct ion for one of the points
The kernel’s shape depends on the distance parameter (radius)
Increasing the radius : results in a broader and lower kernelReducing the radius : in a narrower and sharper kernel.
The result is a density surface whose smoothness depends onthe value of the distance parameter.
A B
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Kernal too small- (radius of 16 km)
each kernal isolated from neighbours
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Kernel radius of 150 km
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Spatial Interpolation
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Deterministic vs. Stochastic
InterpolationA deterministic interpolation method
provides no assessment of errors with
predicted values.
A stochastic interpolation method
offers assessment of prediction errorswith estimated variances.
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What is interpolation?
• Process of creating a surface based on
values at isolated sample points
• Interpolation is used because field data
are sometimes expensive to collect, and
can’t be collected everywhere
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Interpolation
• predict value at un-sampled locations within sampled region
• based on spatial auto-correlation or spatial dependence
– degree of relationship/dependence between near
and distant objects
“everything is related to everything else, but close
things are closely related”
Similarity of objects within an area
Level and strength of interdependence between the variables
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Interpolation types
• Deterministic:
– Surface created from samples based on extent of similarity.
– E.g., IDW, Spline
• Stochastic/Geostatistical
– Spatial variation modeled by random process with spatial
autocorrelation
– Creates error surface —
indicate prediction validity
– E.g., Kriging
Different interpolation methods will produce different results.
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assumes each sample point has influence that diminisheswith distance.
gives greater weight to points closer to the cell than to thosefarther away.
Inverse Distance Weighting (IDW)
POWER ( p) option
Control significance of input points
upon the interpolated values based on
their distance from the output cell.
A larger power results in more distant
points having less influence on theoutput.
Normally, lower power values will
tend to smooth the surface.
/influence
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Spline is intended to fit a minimum-curvaturesurface to the sample points. The surface passesexactly through the sample points.
Spline method is best suited to sample data thatvaries smoothly. It's not appropriate if there are
large changes in value within a short horizontaldistance.
Spline
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Two types of Spline that can be used tointerpolate a surface:
regularised and tension
Regularised Spline offers a looser fit, butmay have overshootsand undershoots
Tension Spline
forces the curve. Makes acoarser surface.
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Kriging is based on statistical models thatinclude autocorrelation.
Weights are based on:
• The distance between the measuredpoints and the predicted location and
• The overall spatial location among thepoints.
Cell value can exceed sample value range
Kriging
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Kriging is implemented using a semi-variogram
Certainty of surface generated can be
determined :
"How good are the predictions?"
Kriging
The goal is to calculate the parameters of the
curve to minimize the deviations from thepoints according to some criterion
Sample locations separated by distances closer than the range are spatially
autocorrelated, whereas locations farther apart than the range are not.
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GIS ANALYSIS MODEL
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*BPI - Bathymetric position index
*
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