Transcript Geographic Information Systems

Advanced
GIS
Using
ESRI ArcGIS 9.3
Spatial Analyst
Spatial Analyst
Activation
Load and relocate
the Spatial Analyst
toolbar.
Be sure to have
activated the
“Spatial Analyst”
extension (Menu –
Tools – Extensions)
Spatial Analyst
Options
Load the “Base 4”
project
In the Options, set
the extent to that of
“Mask” and the cell
size to 5.
Spatial Analyst
Distance
Straight Line
Creates a raster
whose cells
contain the
distance
(calculated basing
upon straight lines)
from given features
Spatial Analyst
Distance
Straight Line
from points
Spatial Analyst
Distance
Straight Line
from points
Result
Spatial Analyst
Distance
Straight Line
from lines
Spatial Analyst
Distance
Straight Line
from lines
Result
Spatial Analyst
Distance
Straight Line
from polygons
Spatial Analyst
Distance
Straight Line
from polygons
Result
Spatial Analyst
Distance
Maximum distance
Limits the
calculation to
values lower than a
threshold
Spatial Analyst
Distance
Maximum distance
Limits the
calculation to
values lower than a
threshold
Spatial Analyst
Distance
Direction
Creates a raster
where each cell
contains the
direction of the
straight line
connecting it to the
closest start
feature
Spatial Analyst
Distance
Direction
Result
Spatial Analyst
Distance
Allocation
Creates a raster
where each cell
contains the name
of the closest start
feature
Spatial Analyst
Distance
Allocation
Result
Spatial Analyst
Distance
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
Spatial Analyst
Distance
Cost Weighted
This calculation is
significantly slower
Spatial Analyst
Distance
Cost Weighted
Result
Distance
Spatial Analyst
Distance
Cost Weighted
Result
Direction
Spatial Analyst
Distance
Cost Weighted
Result
Allocation
Spatial Analyst
Distance
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 Analyst
Distance
Cost Weighted
Result
Distance
Spatial Analyst
Distance
Cost Weighted
Result
Direction
Spatial Analyst
Distance
Cost Weighted
Result
Allocation
Spatial Analyst
Distance
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 Analyst
Distance
Shortest Path
Result
Spatial Analyst
Density
Creates a raster
whose cells will
record the number
of features
contained in one
area unit
Spatial Analyst
Density
Result
Spatial Analyst
Density
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 Analyst
Density
If the field
containing the
value of population
for each feature is
included, the result
will be a map of
population density
Spatial Analyst
Population
Density
Result
Spatial Analyst
Population
Density
Kernel vs. Simple
Simple
Kernel
Spatial Analyst
Density and
Population
Density
Density and
Population Density
can be evaluated
for linear features
too.
Spatial Analyst
Interpolate
There are other
methods besides
TIN to regionalize
sparse data, but
they can produce
rasters only
Spatial Analyst
Interpolate
IDW
Inverse of Distance
Weighted
Variable radius
Spatial Analyst
Interpolate
IDW
Variable radius
Result
Spatial Analyst
Interpolate
IDW
Variable radius
Number of Points
20 points
12 points
Spatial Analyst
Interpolate
IDW
Fixed radius
Spatial Analyst
Interpolate
IDW
Fixed Radius
Result
Spatial Analyst
Interpolate
IDW
Fixed radius
Radius
25’000 m
15’000 m
Spatial Analyst
Interpolate
IDW
Power
2
1.2
Spatial Analyst
Interpolate
IDW
Variable radius
Maximum
distance
No max
Max=10’000 m
Spatial Analyst
Interpolate
IDW
Fixed radius
Minimum points
No max
Max=10’000 m
Spatial Analyst
Interpolate
IDW
Barrier
Spatial Analyst
Interpolate
IDW
Barrier
No barrier
Barrier
Spatial Analyst
Interpolate
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 Analyst
Interpolate
Spline
Result
Interpolate
Spline
Spatial Analyst
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
Tension
to the character of
the modeled
phenomenon.
It creates a less
smooth surface
with values more
closely constrained
by the sample data
range.
Regularized
Interpolate
Spline
Spatial Analyst
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
Tension
to the character of
the modeled
phenomenon.
It creates a less
smooth surface
with values more
closely constrained
by the sample data
range.
Regularized
Interpolate
Spline
Spatial Analyst
Regularized
Weight
Defines the weight
of the third
derivatives of the
surface in the
curvature
minimization
expression.
The higher the
0.01
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.
0.1
Interpolate
Spline
Spatial Analyst
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
Interpolate
Spline
Spatial Analyst
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.
6
12
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
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 yaxis 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).
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Spatial Analyst
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.
Interpolate
Kriging
Result
Spatial Analyst
Interpolate
Kriging
Variance
Spatial Analyst