Unformatted text preview: Spatial Analysis II
Sp
Transformations (2 of 2) Overlay Maps Represented As Raster
Raster overlay can implement the equivalent
operation of polygon overlay
But raster overlay brings a lot of flexibility due
to its capacity to represent a continuous
surface.
It can deal with overlays between nominal/
categorical data, and numerical data
(ordinal, interval, ratio)
Categorical data is represented by index, (e.g. use 1
to represent forest, 2 to represent grass) Raster overlay is relatively easy to implement
through Map Algebra Map Algebra
Map algebra is a data manipulation
language designed specifically for
raster based GIS.
Map
Map algebra is similar to arithmetic
algebra but in map algebra
algebra, but in map algebra
expressions:
expressions:
The objects are grids or values;
Use not only arithmetic but also other
statistical operators, such as maximum;
• Include many special functions working on an individual
cell, or a set of a cell’s neighbors, or the whole grid
• Other more complex operations Map
Map Algebra
Operators can be placed between two input raster
two
layers (grids), or one raster layer and a number:
Addition: [inlayer1] + [inlayer2] OR [inlayer1] + 2
operation: adding the values on a cellbycell basis and
result written to a new grid. 1 23
1 32
1 11 + 222
222
222 = 345
354
333 Other arithmetic operator (, *, /, ) has similar operation
process Many
Many functions (Abs, Int/Float, Sin, Exp, Sqr …) can
Int/Float,
be applied to ONE grid on a cellbycell basis
ONE
cellby ArcMap, Spatial Analyst, Raster Calculator
Arithmetic operators:
Two grids, cellbycell The functions all apply to a
raster layer, cellbycell Weighted Overlay ArcMap, Spatial Analyst,
Raster Calculator Weighted overlay is possible by using Map
Algebra: simply multiply each input grid layer with
a weight number before addition Complex
Complex Statistics Of Two Or More Grids The cell value for output grid can be the statistics
of the values of the same cell in all the input grids Complex Statistics Of Two Or More Grids
ArcMap, Spatial Analyst,
Cell Statistics Supported
statistics
For categorical
data Spatial Interpolation
Values of a field are often measured at sample points;
always need to estimate values at other points
Spatial interpolation is based on Tobler’s first law of
geography:
Everything is related to everything else, but near things are
more related than distant things.
If such an assumption doesn’t hold, spatial interpolation
will fail Local interpolation
The value of a predicted point
is estimated based on sample
points within a chosen
neighborhood
Many local interpolation
methods. They differ in:
• The sample points used
• The relative importance of
sample points to interpolation Spatial
Spatial Interpolation
The sample points can be specified in
several ways
Number of nearest points
• But points may be too far away
to be of use Points within a neighborwithin neighbor
hood search shape
• A circle with a fixed radius r.
– r should be determined by
the phenomena • An ellipse may be used if directional difference is known
• To avoid bias in a particular
direction, the circle or ellipse
can be divided into sectors
from which an equal number
of points are selected. Thiessen Polygons
(Proximity Polygons, For Coverage)
Assign unsampled point with the value at its nearest
unsample point
Each proximity polygon contains only one sample
point, and any location within a polygon is closer to
its control point than to the other control points
All points within the proximity polygon are assumed to share
the same value as the sample point.
A
B Thiessen Polygons Thiessen
Thiessen Polygons
Result in a blocky discontinuous surface
with abrupt jumps across the
boundaries of polygons.
Applicability depending on underlying
phenomena and the assumption of
phenomena, and the assumption of
abrupt
abrupt change
For nominal data, e.g.
soil, vegetation types,
this approach is often
reasonable and useful,
although not usually
called interpolation Inverse Distance Weighting (IDW)
The unknown value of a field at a point is estimated
by taking an average over the known values
But weighing each known value by its distance from
the point, giving greatest weight to the nearest
points
Point si
known value Z(si)
distance di0 The estimate is a weighted average unknown value
(to be interpolated)
At location s0 Weights decline with distance, Issues
Issues With IDW
The range of interpolated values cannot
exceed the range of observed values:
Not bigger than the max,
Nor smaller than the min in the data It is important to position sample points to
It
include the extremes of the field
This can be very difficult
This set of six data points may
interpolate into a surface (solid
line) different than the real hill
profile (dashed line). ...
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Full Document
 Spring '11
 roberts
 operation, Spatial Analyst, map algebra

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