GIS Spatial Analysis 3

8/16/2019 GIS Spatial Analysis 3

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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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Documents

GIS Spatial Analysis 3