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Geographic Information Systems

AdvancedGISUsingESRI ArcGIS 9.3Spatial Analyst

Spatial AnalystActivation

Load and relocate the Spatial Analysttoolbar.

Be sure to have activated the Spatial Analyst extension (Menu Tools Extensions)

Spatial AnalystOptions

Load the Base 4 project

In the Options, set the extent to that of Mask and the cell size to 5.

Spatial AnalystDistanceStraight Line

Creates a raster whose cells contain the distance (calculated basing upon straight lines) from given features

Spatial AnalystDistance Straight Line

from points

Spatial AnalystDistance Straight Line

from points

Result

Spatial AnalystDistance Straight Line

from lines

Spatial AnalystDistance Straight Line

from lines

Result

Spatial AnalystDistance Straight Line

from polygons

Spatial AnalystDistance Straight Line

from polygons

Result

Spatial AnalystDistance

Maximum distance

Limits the calculation to values lower than a threshold

Spatial AnalystDistance

Maximum distance

Limits the calculation to values lower than a threshold

Spatial AnalystDistance

Direction

Creates a raster where each cell contains the direction of the straight line connecting it to the closest start feature

Spatial AnalystDistance

Direction

Result

Spatial AnalystDistance

Allocation

Creates a raster where each cell contains the name of the closest start feature

Spatial AnalystDistance

Allocation

Result

Spatial AnalystDistance

Cost Weighted

Calculates distances in time

Requires a Cost Raster

Spatial AnalystCost Raster

In a Cost Raster each cell contains a value indicating the cost (time) needed to cross it.

It may be calculated in different ways, depending on the final aim of the Cost Weighted calculation.

The simplest one may be a slope map

Spatial AnalystDistance

Cost Weighted

This calculation is significantly slower

Spatial AnalystDistance

Cost Weighted

Result

Distance

Spatial AnalystDistance

Cost Weighted

Result

Direction

Spatial AnalystDistance

Cost Weighted

Result

Allocation

Spatial AnalystDistance

Cost Weighted

More complex Cost Raster may give better results.

For example, rivers and buildings can be associated to extremely high cost

Complex cost rasters will severely slow down the calculation(s)

Spatial AnalystDistance

Cost Weighted

Result

Distance

Spatial AnalystDistance

Cost Weighted

Result

Direction

Spatial AnalystDistance

Cost Weighted

Result

Allocation

Spatial AnalystDistance

Shortest Path

Once created the Cost Raster and calculated the Direction Raster, the shortest path connecting the start features to other features (shapefiles) can be calculated creating polylines

Spatial AnalystDistance

Shortest Path

Result

Spatial AnalystDensity

Creates a raster whose cells will record the number of features contained in one area unit

Spatial AnalystDensity

Result

Spatial AnalystDensity

Kernel vs. Simple

Kernel will calculate the density of features in a search radius centered on the feature;Simple will center the analysis on the center of each raster cell

Simple

Kernel

Spatial AnalystDensity

If the field containing the value of population for each feature is included, the result will be a map of population density

Spatial AnalystPopulation Density

Result

Spatial AnalystPopulation Density

Kernel vs. Simple

SimpleKernelSpatial AnalystDensity and Population Density

Density and Population Density can be evaluated for linear features too.

Spatial AnalystInterpolate

There are other methods besides TIN to regionalize sparse data, but they can produce rasters only

Spatial AnalystInterpolate

IDWInverse of Distance Weighted

Variable radius

Spatial AnalystInterpolate

IDW

Variable radius

Result

Spatial AnalystInterpolate

IDW

Variable radius

Number of Points

12 points

20 points

Spatial AnalystInterpolate

IDW

Fixed radius

Spatial AnalystInterpolate

IDW

Fixed Radius

Result

Spatial AnalystInterpolate

IDW

Fixed radius

Radius

15000 m25000 m

Spatial AnalystInterpolate

IDW

Power

1.22

Spatial AnalystInterpolate

IDW

Variable radius

Maximum distance

Max=10000 mNo max

Spatial AnalystInterpolate

IDW

Fixed radius

Minimum points

Max=10000 mNo max

Spatial AnalystInterpolate

IDW

Barrier

Spatial AnalystInterpolate

IDW

Barrier

BarrierNo barrier

Spatial AnalystInterpolate

Spline

The Spline method is an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.

Spatial AnalystInterpolate

Spline

Result

Spatial AnalystInterpolate

Spline

The Regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range.

The Tension method controls the stiffness of the surface according to the character of the modeled phenomenon. It creates a less smooth surface with values more closely constrained by the sample data range.

TensionRegularized

Spatial AnalystInterpolate

Spline

The Regularized method creates a smooth, gradually changing surface with values that may lie outside the sample data range.

The Tension method controls the stiffness of the surface according to the character of the modeled phenomenon. It creates a less smooth surface with values more closely constrained by the sample data range.

TensionRegularized

Spatial AnalystInterpolate

Spline

Regularized

Weight

Defines the weight of the third derivatives of the surface in the curvature minimization expression. The higher the weight, the smoother the output surface. It must be equal to or greater than zero: typical values are 0, 0.001, 0.01, 0.1, and 0.5.0.010.1

Spatial AnalystInterpolate

Spline

Tension

Weight

For the Tension method, the weight parameter defines the weight of tension. The higher the weight, the coarser the output surface. The values entered must be equal to or greater than zero. The typical values are 0, 1, 5, and 10.50.1

Spatial AnalystInterpolate

Spline

N. of points

Identifies the number of points used in the calculation of each interpolated cell.

The more input points you specify, the more each cell is influenced by distant points and the smoother the output surface. The larger the number of points, the longer it will take to process the output raster.612Spatial AnalystInterpolate

Kriging

Geostatistical methods, such as kriging, are based on statistical models that include autocorrelation. Because of this, not only do geostatistical techniques have the capability of producing a prediction surface, they also provide some measure of the certainty or accuracy of the predictions.

Kriging is similar to IDW in that it weights the surrounding measured values to derive a prediction for an unmeasured location. The general formula for both interpolators is formed as a weighted sum of the data:

where: Z(si) = the measured value at the ith location. i = an unknown weight for the measured value at the ith location. s0 = the prediction location. N = the number of measured values.

Spatial AnalystInterpolate

Kriging

Fitting a model, or spatial modeling, is also known as structural analysis, or variography. In spatial modeling of the structure of the measured points, you begin with a graph of the empirical semivariogram, computed as: Semivariogram(distance h) = 0.5 * average[ (value at location i value at location j)2 ]

for all pairs of locations separated by distance h. The formula involves calculating the difference squared between the values of the paired locations. The image below shows the pairing of one point (the red point) with all other measured locations. This process continues for each measured point.

Spatial AnalystInterpolate

Kriging

Often each pair of locations has a unique distance, and there are often many pairs of points. To plot all pairs quickly becomes unmanageable. Instead of plotting each pair, the pairs are grouped into lag bins. For example, compute the average semivariance for all pairs of points that are greater than 40 meters apart but less than 50 meters. The empirical semivariogram is a graph of the averaged semivariogram values on the y-axis and the distance (or lag) on the x-axis (see diagram below).

Spatial autocorrelation quantifies a basic principle of geography: things that are closer are more alike than things farther apart. Thus, pairs of locations that are closer (far left on the x-axis of the semivariogram cloud) should have more similar values (low on the y-axis of the semivariogram cloud). As pairs of locations become farther apart (moving to the right on the x-axis of the semivari