working with raster
DESCRIPTION
rTRANSCRIPT
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Getting started with surface
analysis
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Learning objectives • Explain what a raster surface is
• Describe surface representation
• Describe how specifying an analysis
environment affects output raster creation
• Control output raster creation by changing
environment settings
– Workspace
– Extent
– Cell size
– Coordinate system
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Surfaces • Considered to be continuous
• For an x,y location, only one z-value
• Can be used to represent
elevation, rainfall, snow depth,
land value, pH
• Surfaces cannot represent
3D objects like buildings
– Not a true 3D model: 2½-dimensional
. ..
.’. ‘.’
‘’ . ..
.’. ‘.’
‘’
. ..
.’. ‘.’
‘’
. ..
.’. ‘.’
‘’
. ..
.’. ‘.’
‘’
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.’. ‘.’
‘’
X,Y
Z1
Z2
Z3
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Representing surfaces • Four ways
• Creating raster surfaces
– Interpolate from points (e.g., elevation, rainfall) Surfaces are created from continuous data
– Derived from another surface (e.g., slope,
aspect, hillshade)
Raster
s
Points
Contour
s TINs /
Terrains
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Sources of topographic data • U.S. federal government
– U.S. Geological Survey (USGS): digital elevation
model (DEM) Several resolutions
– USGS: National Elevation Dataset (NED)
– National Geospatial-Intelligence Agency (NGA):
digital terrain elevation data (DTED)
Spacing Z accuracy
7.5 minutes 30 meters 15 meters
15 minutes 2 arc-seconds
30 minutes 2 arc-seconds ½ of contour interval
1 degree 3 arc-seconds
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Interpolation • Generates surfaces from point measurements
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What is surface analysis? • Find patterns in the data
Elevation
Hillshade
Slope
Aspect
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How does surface analysis work? • Surface analysis is a process
– Input grid(s)
– Parameters
– Output grid
• A new grid can be the input for another process
Operations
Functions
Conditional statements
Analysis environment
Input Output/Input Output
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Before you begin surface analysis...
• Set the working directory
• Set the analysis mask
• Set the analysis
extent
• Set the analysis
cell size
Input 1 Input 2 Output
Maximum of Inputs
Intersection of Inputs Union of Inputs
NoData
D
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Copyright © 2009 ESRI. All rights reserved. Creating and Analyzing Surfaces Using ArcGIS Spatial Analyst
Interpolating surfaces
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Learning objectives • Describe sample points
• Interpolate surfaces
• Assess accuracy
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What is interpolation? • Estimating an unknown value between known
samples
• Based on spatial autocorrelation and dependence
– The degree of relationship between near and far objects
– Things close together are more alike than things far apart Tobler’s first law of geography
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Visual comparison of
interpolators
Natural
neighbors
Spline
Kriging
IDW Topo to Raster
(Covered in lesson 3)
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Linear interpolation • Interpolation of cell values
– A best estimate between samples
Known rainfall values (inches)
Interpolated rainfall values
1.5 1.25 1.75 1.125 1.375 1.875 1.625 2 1
1 Mile
0 1
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The importance of samples • A perfect surface model needs infinite points
– Impossible: Can only record representative locations (samples)
– Other locations are estimated (interpolated) from the samples
• Good samples represent
– Important details
(enough to meet resolution needs)
– Surface extremes
(tops of hills, bottoms of valleys)
– Changes of surface
(breaks in slope)
• Good samples extend beyond the area of interest
(reduce edge effects)
Sampling area
Study
area
+ +
+
+ + + +
+
+
+
+ + +
+ +
+
+
+ +
+
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Controlling sample points • IDW, spline, and kriging control samples
• Two methods control the search radius
– Variable: Expands to find minimum number of
samples
– Fixed: Uses samples found in the specified
radius
Samples = 8
Radius = ?
Variable Fixed
Radius = 1000
Samples = ?
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Barriers to interpolation • Sharp breaks in the surface
– Like cliffs, ridges, fault lines
• IDW, spline, and kriging can use barriers
– Restricts samples to same side of line as cell
– Input as line features With barrier Without barrier
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Inverse distance weighted (IDW) • Averages values of samples near the cell
– Closer points have more influence
– Surface can pass through samples
– Cannot predict hills, valleys
• You set
– Power (how fast influence
drops with distance)
– Search radius
– Barriers
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IDW parameters • Best for dense, evenly spaced samples
• Surface falls between samples
– Averaging
– No hills or valleys
• Can adjust relative
influence of samples
– The Power option
Distance
Z-
va
lue
IDW
Distance
Power 1
Power 2
Sample point
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Natural neighbors • Advanced technique to select samples
– Builds area of influence of samples for each cell
– Uses area-weighted interpolation technique
• Creates a convex hull
around the samples
– Only interpolates
within the hull
• Good for very dense
samples, like lidar
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Spline • The surface passes exactly through the
sample points
– Like a rubber sheet that is bent around the
samples
– Good for smoothly varying surfaces, like
temperature
– Can predict ridges and valleys
Z-v
alu
e
Distance
Spline
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Choosing a spline type • Regularized
– Drapes the surface
– Higher hills, deeper valleys
– Smoother surface
– High {weight} smoothes more
• Tension
– Forces the surface
– Flatter hills and
valleys
– Coarser surface
–High {weight}
coarsens more
2000
3000
4000
Ele
va
tio
n
Distance
Tension
Regularized
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Topo to Raster • The best choice for interpolating terrain
– Creates a hydrologically correct
surface
– No sinks
– Drainage enforcement
• Uses contour lines and
points for samples
• Adjusts surface with
streams and lakes Points
Lakes
Streams
Contours
Boundary
D
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Choosing an interpolation method • If you know nothing about your data…
– Use natural neighbors — It is the most conservative; assumes all
highs and lows are sampled; will not create artifacts
• If your input data is contours…
– Use Topo to Raster — It is optimized for contour input; if not creating
a DEM, turn off the drainage enforcement option
• If you know the highs and lows are not sample…
– Use spline — Be careful of points that are near in space but very
different in value, creating unnatural artifacts
• If your surface is not continuous…
– Use spline with barriers if you know there are faults or other
discontinuities in the surface
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Testing a surface • To test the accuracy of a surface:
– Remove a sample
– Create the surface
– Check the sample against the surface
(Did the interpolator predict the missing sample?)
– Put the sample back; repeat with another sample
– Try a different interpolator and repeat
• Each interpolator gives different results
– None is more accurate than the others for all situations
– Choice is based on the surface type and the samples
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Terrains • Multiresolution surface created from
measurements stored in feature classes
– Large collections of mass point data (e.g., lidar)
– TIN surface generated on the fly for given area of
interest and level of detail
• Typical applications:
– Topographic mapping
– Bathymetric mapping
• Can convert to a raster
D
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Exercise goals • Create surfaces using a variety of
interpolation techniques
• Evaluate interpolation results
• Optionally, interpolate using IDW with
barriers
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Copyright © 2009 ESRI. All rights reserved. Creating and Analyzing Surfaces Using ArcGIS Spatial Analyst
Introduction to kriging
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Kriging • A geostatistical method
– Assumes spatial variation in
data is the same everywhere
– Models variation with
many methods
– You need to know how to use it
• Can create hills and valleys
Ordinary
Universa
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Kriging semivariogram models • ArcGIS Spatial Analyst implements five
semivariogram models
– Spherical
– Circular
– Exponential
– Gaussian
– Linear
• ArcGIS Geostatistical Analyst has more
models and tools
– Interactive variogram modeling
Distance
Actual
variance
0
0
1,500
15,000
Semi-
variance
Predicted
variance
D
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Raster data
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The raster data model
Rows
Columns
X, Y
location
Raster data file
N rows by M columns
X, Y
location
Georeferenced to earth’s
surface
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Raster vs Vector
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Pixels or Cells
• Each pixel contains one numeric value
• Dimension of a pixel varies (resolution)
• Value represents some property of that pixel area, e.g. elevation or rainfall
• Values may be integers or floating point numbers
3 1 4
6 2 1
5 4 3
3 1 4
4
1
3
4
3 1 4 4
1
2
4
1
1
30m
30m
Unlike a polygon, each cell has only ONE attribute: its value.
Storing multiple values means storing multiple rasters.
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Binary data
• Most raster formats use binary storage
• Numbers are stored as a series of 0’s
and 1’s representing numbers in base 2
• Binary values are grouped by eight
10011101
1 bit
one byte
In base 2:
00000000 = 0
11111111 = 255
28 = 256
1111111111111111 = 65,565
216 = 65,566
two bytes
0
1
10
11
100
101
110
111
1000
1001
1010
1011
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Types of raster data
Discrete raster: land use Continuous raster: DEM
Continuous raster: image Discrete raster: roads
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Raster Properties
Scroll down
for more
info
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Bands
• A single raster may include multiple arrays
• Most often used to store color images and
satellite images 7-band Landsat satellite image
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Why use rasters?
• Better at storing certain kinds of data
• Better at analyzing certain kinds of data
• Often faster analysis than vectors
• Imagery desirable for certain maps
• BUT
– Coordinate precision generally lower
– High precision has high storage costs
– Cannot store multiple attributes
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Raster resolution
• Measured by cell size dimensions
• Storage space increases dramatically with
resolution
Vector format 200 m raster 50 m raster
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Cell size units
• Cell x-y resolution units are based on the
raster’s coordinate system definition
– Decimal degrees*
– Meters
– Feet
*Because distances and
areas are fundamental
bases for raster analysis, it
is almost always best to use
projected coordinate
systems for rasters.
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Raster analysis
• Raster analysis uses cell-by-cell functions on one or more input grids.
• Cells must be the same size and line up spatially.
• Older software required the user to ensure that all input rasters had exactly the same size, shape, and aligned cell sizes.
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Resampling
Y2
If input grids do not match, then one
must be resampled to match the
other. Resampling can degrade the
accuracy of a raster even if the
difference in cell size and location is
small.
The new cell grid is determined, and
the old cell values must be fit into the
new structure somehow.
Several methods are used for
resampling.
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Resampling methods Nearest neighbor resampling grabs the value from
the old cell that falls at the center of the new cell. It preserves
the original value and should always be used with categorical
data, or when the original data values need to be preserved. It
is the fastest method.
Bilinear resampling calculates a new value from the
four cells that fall closest to the center of the new cell. It uses
a distance-weighted algorithm based on the old cell centers. It
is best used with continuous data such as elevation.
Cubic convolution resampling calculates a new
value from the sixteen cells that fall closest to the center of the
new cell. It uses a distance-weighted algorithm based on the
old cell centers. It is best used with continuous data such as
elevation. It is the most time-consuming method.
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Raster analysis techniques
Map algebra and Boolean overlay
Other functions
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Map Algebra
( [Inlayer1 + [Inlayer2] ) / 2
Aligns overlying cells and
performs operations on
corresponding cells in input
layers.
Inlayer1
Inlayer2
Output
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Map Algebra
• Rasters are
essentially arrays
of numbers
• Can be added,
subtracted, etc
• Line up matching
cells vertically
5 7
2 4
3 2
1 6
8 9
3 10
Ingrid1
+
Ingrid2
=
Outgrid
Fig. 15.4. Map algebra
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Map Algebra expressions
• Convert precipitation in cm to inches
– [Precip] / 2.54
• Compute earth volume to be moved
– [InitialSurface] – [Finalsurface]
• Enter models based on multiple inputs
[Precip] * 2 + [Slope] * 4 / ( [Erode] – [Vegcover]
• Logical expressions
– [Elevation > 1400]
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Conversions
[Precip_cm] / 2.54
Precip in cm Precip in inches
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Cut and fill on a site
[Initial surface] – [final surface]
Cut
Fill
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Model expressions
Complex expressions with
multiple inputs to calculate
risk or hazard index.
Runoff in cm based on
four input grids: precip,
slope, soil infiltration, and
vegetation cover.
[Precip] * 2 + [Slope] * 4 / ( [Erode] – [Vegcover]
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Logical Operators
[Elevation] > 1200
Logical operators produce either TRUE (1) or FALSE (0)
values in the output grid, based on whether a cell meets
the condition.
[Slope] < 10 [crowncov] < 70 And
[crowncov] > 40
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Boolean rasters
• Boolean rasters represent maps of
True/False states for a particular condition
Slope < 10 degrees?
1 = True
0 = False
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Logical expressions
• Produce a Boolean
grid of 1’s and 0’s
– 1 = True
– 0 = False
[EarthMove] > 0
1
0
Elevation > 1400 1
0
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Boolean operators
A AND B
A XOR B A NOT B
A OR B
A B
Same as intersect! Same as union!
Boolean rasters
can be
evaluated
further using the
Boolean
operators.
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Raster analysis techniques
Map algebra and Boolean overlay
Other functions
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Other raster analysis techniques
• Reclassification
• Surface functions
• Distance functions
• Density functions
• Interpolation
• Neighborhood functions
• Zonal functions
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Reclassify
Convert one set of
grid values to
another
Manual or classify
Slope High slope/low slope
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Local Operations –
Reclassification(single raster)
• Range of values – a new value is given
to a range of values
• in the input raster (integer and floating
point rasters)
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Surface analysis
DEM
Slope
Aspect
Hillshade
Contouring
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Slope function
Calculates slope of the surface
based on surrounding cells. Can be
expressed in degrees or percent.
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Standard Slope Function
a b c
d e f
g h i
cingx_mesh_spa * 8
i) 2f (c - g) 2d (a
dx
dz
acing y_mesh_sp* 8
c) 2b (a -i) 2h (g
dy
dz
22
dy
dz
dx
dz
run
rise
run
riseatandeg
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Aspect function
Calculates direction of steepest
slope, e.g. which way the slope
“faces”. Value represents direction
from 0-360 where 0/360 is North.
Flat areas are assigned a -1 value.
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Aspect – the steepest downslope
direction
dx
dz
dy
dz
dy/dz
dx/dzatan
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Hillshade
Calculates the brightness or
illumination of a surface from a
specified light source.
Applications include terrain display
and modeling satellite reflectance.
Azimuth is direction
of illumination source
(315 by default)
Altitude is the angle
of the source above
the horizon (45 deg)
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Viewshed analysis
• Calculate areas
visible from a set of
observation points
Additional parameters
are available for the tool
version, such as the
horizontal angle included.
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Lecture Materials by
Austin Troy except
where noted © 2008
Viewshed analysis Viewshed analysis can use “offsets” to define the height of
the viewer or of the object being viewed; designated using a new field in the input layer’s attribute table.
offset A
offset B
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Lecture by Austin Troy ©
2005
Viewshed analysis This is done in ArcGIS 8, but can also be done in ArcView.
Red represents areas that can be seen by 1 house, blue by 2
or more
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Lecture by Austin Troy ©
2005
Viewshed analysis In order to compare the viewability of several facilities,
separate viewshed analyses need to be done for each
feature.
In the next example we will look at three candidate sites for a
communications tower.
Each will produce a viewability grid.
This grid can then be superimposed on a layer showing
residential areas.
Since each grid will belong to a different tower, we can tell
which tower will be most viewable from the residential
areas through simple overlay analysis.
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Lecture by Austin Troy ©
2005
Viewshed analysis In this case, red is for tower 1, blue for 2 and green for 3
Introduction to GIS
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Cut and fill on a site
[Initial surface] – [final surface]
Cut
Fill
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Hydrologic functions
Derive streams, watersheds, and other hydrologic features
based on analysis of a DEM.
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67 56 49 46 50
12 11 12
53 44 37 38 48
58 55 22 31 24
61 47 21 16 19
34 53
Digital Elevation Model
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32
16
8
64
4
128
1
2
Eight Direction Pour Point Model
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67 56 49
53 44 37
58 55 22
1
67 56 49
53 44 37
58 55 22
1
26.162
4467
14
1
5367
Slope:
Direction of Steepest Descent
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2 2 4 4 8
1 2 16
1 2 4 8 4
1 1 2 4 8
2 1 4 4 4
1 1
Flow Direction Grid
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Grid Network
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Distance functions
Straight line distance
Cost path distance
Buffers
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Straight line distance
• Starts from a set of features (points, lines, polygons).
• Creates a grid where each cell represents distance to the closest of the features.
• Distance units are given in coordinate system map units
Distance to roads (meters)
The distance
function is the first
step in in creating
raster buffers.
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Lowest cost path 1. Create start/stop
shapefiles
2. Create cost grid
3. Calculate cost
distance grid and
cost direction grid
4. Find lowest cost path
Elevation Slope
Cost distance Cost direction
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What is interpolation?
• Interpolation is the prediction of values in
between measured points.
• Sampling of points may be uniform, random, or
based on a sampling scheme.
• Numerous methods are used which have
different mathematical models and make
different assumptions about the data.
• Best application of interpolation relies on
substantial study of models and assumptions. If
you use it a lot—learn more!
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Sample point features:
climate stations with
annual precipitation values
Interpolated continuous
raster of precipitation
values
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Interpolation is NOT truth!
Actual elevation Elevation interpolated from summits
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Methods
• Interpolation assumes that nearby points
are correlated, e.g. they will have similar
values.
• Four types of interpolation methods are
available in Spatial Analyst
– Inverse Distance Weighted (IDW)
– Spline
– Kriging
– Trend
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Density functions
• Appear similar to interpolation, but are calculated differently
– Interpolation predicts values between points using a variety of mathematical methods
– Density functions count occurrences within a given radius and divide by the area
Occurances may be features
or attributes of features
(number of cities versus city
population).
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Density methods
• Simple density
– Sums attribute (such as population) for points within a specified radius
– Larger radius gives smoother data
• Kernel density
– First spreads value at points out to the search radius using a quadratic formula.
– Then density is calculated again
– Tends to give smoother results for a given radius
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Using simple density
50km radius
100km radius
A larger radius gives smoother
results. The radius is given in
map units.
Units: people/sq km
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Line density
Density of
rivers m/sq km
100 km radius
50 km radius
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Neighborhood statistics Calculates a statistic for the specified window.
3 1 4
6 2 1
5 4 3
3 1 4
4
1
3
4
3 1 4 4
1
2
4
1
1
Window
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Window movement
No overlap. All cells in the block
receive the output value.
Overlap. Only the target cell
receives the value.
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Neighborhood focal functions
Output grid Input grid
3 1 4
6 2 1
5 4 3
3 1 4
4
1
3
4
3 1 4 4
1
2
4
1
1
2.0
2.5
3.4 2.8 3.6
3.8
3.2
2.9 3.0 2.3
3.1
3.3
2.5
Window Target cell
Averaging function
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Neighborhood focal mean
Smooths raster
Effects grow larger
with increasing
window size or
repeated
applications
Good for removing
noise or spurious
values
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Neighborhood focal majority
High slope/low slope areas
Before 5x5 majority filter After two passes of 5x5
majority filter
Useful for simplifying rasters prior to conversion to polygons
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What is a zonal function?
• Examines and manipulates raster values in one within set of zones specified by another layer
• Zones constitute the areas of a discrete raster with the same value
• Requires two inputs
– A layer specifying the zones (raster or feature)
– A raster layer with the values to be evaluated
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What is a zone?
• A zone is the area(s) of a raster or feature
dataset that share the same integer value.
Zones need not be contiguous!
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Zonal statistics
• Zones defined by
the zone layer
(watersheds)
• Generates statistics
for each zone from
the value grid
(slope)
• Output is either a
raster, or a table
Watersheds and slope
Average slope in watershed
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Zonal statistics of lines
Mean slope of
streams in each
watershed
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Zonal statistics of points
• Use name or FID for each point so each is unique zone.
• Calculate stats for each point.
• All statistics are the same—the elevation of the point.
Determine elevation of summits
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Raster analysis example
Siting a landfill
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Landfill raster model
• Problem: Find potential locations for a
new landfill using these criteria
– On flat terrain <= 10 degrees slope
– No more than 1 km from an existing road
– At least 500 meters from a stream
– Meadow or low-density forest
• Develop a Boolean raster for each
condition with 1 = desirable area, 0 = not
desirable area
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Slope condition 1. Use slope function on elevation raster.
2. Use map algebra logical operator to produce Boolean map of slope <= 10
degrees.
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Road distance condition 1. Use distance function to create raster of distance from roads.
2. Use logical operator in map algebra to create Boolean raster of areas within 1000
meters of a road.
[Distance] <= 1000
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Stream distance condition 1. Use distance function to create raster of distance from streams.
2. Use a logical operator in map algebra to create a Boolean map of areas more
than 500 meters from a stream.
[Distance] > 500
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Vegetation condition 1. Select suitable vegetation density and create a layer from the selected polygons.
2. Convert the selected vegetation layer to a raster using the density attribute.
3. Reclassify the three density values all to 1 and the NoData areas to 0.
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Find areas with Boolean AND [Slope] AND [Roads] AND [Streams] AND [Vegetation]
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Additive model [Slope] + [Roads] + [Streams] + [Vegetation]
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Lecture by Austin Troy ©
2005
Raster terrain functions in AV
DEM + Hillshade = Hillshaded DEM
+ =
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Lecture by Austin Troy ©
2005
Viewshed analysis Let’s say we’re local planners who are considering putting in
a new waste treatment facility in valley where the vacation
homes of five rich and powerful Hollywood executives are
located.
We want it in a place that won’t ruin anyone’s views, since
they comprise 95% of the local tax base.
So we geocode the house locations, overlay them on a high-
resolution digital elevation model and run a viewshed
analysis
The lower the resolution, the more likely we’ll be wrong
This generates a grid with three values, representing how
many houses can see a given pixel
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x
x
x
x
A
B