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AdvancedGIS

UsingESRI 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


from points

Result


from lines


from lines

Result


from polygons


from polygons

Result

Spatial AnalystDistance

Maximum distance

Limits the calculation to values lower than a threshold


Maximum distance

Limits the calculation to values lower than a threshold


Direction

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


Direction

Result


Allocation

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


Allocation

Result


Cost Weighted

Calculates distances in “time”

Requires a “Cost Raster”

Spatial Analyst“Cost 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


Cost Weighted

This calculation is significantly slower


Cost Weighted

Result

Distance


Cost Weighted

Result

Direction


Cost Weighted

Result

Allocation


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)


Cost Weighted

Result

Distance


Cost Weighted

Result

Direction


Cost Weighted

Result

Allocation


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


Shortest Path

Result

Spatial AnalystDensity

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


Result


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


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

Simple

Kernel

Spatial 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


IDWInverse of Distance Weighted

Variable radius


IDW

Variable radius

Result


IDW

Variable radius

Number of Points

12 points20 points


IDW

Fixed radius


IDW

Fixed Radius

Result


IDW

Fixed radius

Radius

15’000 m25’000 m


IDW

Power

1.22


IDW

Variable radius

Maximum distance

Max=10’000 mNo max


IDW

Fixed radius

Minimum points

Max=10’000 mNo max


IDW

Barrier


IDW

Barrier

BarrierNo barrier


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.


Spline

Result


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.

Tension Regularized


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.

Tension Regularized


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.

0.01 0.1


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.

5 0.1


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.

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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. λi = an unknown weight for the measured value at the ith location. s0 = the prediction location. N = the number of measured values.


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.


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 semivariogram cloud), they should become more dissimilar and have a higher squared difference (moving up on the y-axis of the semivariogram cloud).


Kriging

Semivariogram

The distance where the model first flattens is known as the range. Sample locations separated by distances closer than the range are spatially autocorrelated; locations farther apart than the range are not.The value at which the semivariogram model attains the range (the value on the y-axis) is called the sill. Theoretically, at zero separation distance, the semivariogram value is zero. However, at an infinitely small separation distance, the semivariogram often exhibits a nugget effect, which is a value greater than zero. If the semivariogram model intercepts the y-axis at 2, then the nugget is 2. A partial sill is the sill minus the nugget.


Kriging


Kriging

Methods

Ordinary

Universal

Ordinary Kriging is the most general and widely used of the kriging methods and is the default. It assumes the constant mean is unknown. This is a reasonable assumption unless there is a scientific reason to reject it.

Universal Kriging assumes that there is an overriding trend in the data—for example, a prevailing wind—and it can be modeled by a deterministic function, a polynomial. This polynomial is subtracted from the original measured points, and the autocorrelation is modeled from the random errors. Once the model is fit to the random errors and before making a prediction, the polynomial is added back to the predictions to give meaningful results. Universal Kriging should only be used when you know there is a trend in your data, and you can give a scientific justification to describe it.


Kriging

Ordinary Models

Circular

Spherical

Exponential Gaussian Linear

The selected model influences the prediction of the unknown values, particularly when the shape of the curve near the origin differs significantly. The steeper the curve near the origin, the more influence the closest neighbors will have on the prediction. As a result, the output surface will be less smooth.Each model is designed to fit different types of phenomenon more accurately.


Kriging

Models

Spherical

This model shows a progressive decrease of spatial autocorrelation (equivalently, an increase of semivariance) until some distance, beyond which autocorrelation is zero. The spherical model is one of the most commonly used models.


Kriging

Models

Exponential

This model is applied when spatial autocorrelation decreases exponentially with increasing distance. Here the autocorrelation disappears completely only at an infinite distance. The exponential model is also a commonly used model. he choice of which model to use is based on the spatial autocorrelation of the data and on prior knowledge of the phenomenon.


Kriging

Result


Kriging

Variance