working with raster

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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

. ..

.’. ‘.’

‘’ . ..

.’. ‘.’

‘’

. ..

.’. ‘.’

‘’

. ..

.’. ‘.’

‘’

. ..

.’. ‘.’

‘’

. ..

.’. ‘.’

‘’

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

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

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

Return to Outline

Copyright © 2009 by Maribeth H. Price

8-31

Raster data

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8-32

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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8-34

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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8-35

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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8-36

Types of raster data

Discrete raster: land use Continuous raster: DEM

Continuous raster: image Discrete raster: roads

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8-37

Raster Properties

Scroll down

for more

info

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8-38

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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8-39

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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8-40

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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8-41

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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8-42

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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8-43

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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8-44

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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8-45

Raster analysis techniques

Map algebra and Boolean overlay

Other functions

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8-46

Map Algebra

( [Inlayer1 + [Inlayer2] ) / 2

Aligns overlying cells and

performs operations on

corresponding cells in input

layers.

Inlayer1

Inlayer2

Output

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8-47

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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8-48

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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8-49

Conversions

[Precip_cm] / 2.54

Precip in cm Precip in inches

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8-50

Cut and fill on a site

[Initial surface] – [final surface]

Cut

Fill

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8-51

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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8-52

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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8-53

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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8-54

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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8-55

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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8-56

Raster analysis techniques

Map algebra and Boolean overlay

Other functions

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8-57

Other raster analysis techniques

• Reclassification

• Surface functions

• Distance functions

• Density functions

• Interpolation

• Neighborhood functions

• Zonal functions

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8-58

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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8-60

Surface analysis

DEM

Slope

Aspect

Hillshade

Contouring

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8-61

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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8-63

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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8-65

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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8-66

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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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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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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8-71

Cut and fill on a site

[Initial surface] – [final surface]

Cut

Fill

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8-72

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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8-78

Distance functions

Straight line distance

Cost path distance

Buffers

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8-79

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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8-80

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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8-81

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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8-82

Sample point features:

climate stations with

annual precipitation values

Interpolated continuous

raster of precipitation

values

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8-83

Interpolation is NOT truth!

Actual elevation Elevation interpolated from summits

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8-84

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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8-85

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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8-86

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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8-87

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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8-88

Line density

Density of

rivers m/sq km

100 km radius

50 km radius

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8-89

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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8-90

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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8-91

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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8-92

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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8-93

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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8-94

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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8-95

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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8-96

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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8-97

Zonal statistics of lines

Mean slope of

streams in each

watershed

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8-98

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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8-99

Raster analysis example

Siting a landfill

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8-100

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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8-101

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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8-102

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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8-103

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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8-104

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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8-105

Find areas with Boolean AND [Slope] AND [Roads] AND [Streams] AND [Vegetation]

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8-106

Additive model [Slope] + [Roads] + [Streams] + [Vegetation]

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2005

Raster terrain functions in AV

DEM + Hillshade = Hillshaded DEM

+ =

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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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8-109

Return to Outline


8-110

x

x

x

x

A

B

working with raster

Documents

surface analysis return

surfaces return

outline surfaces

outline interpolation

accuracy return

raster surfaces

arcseconds return

rainfall surfaces