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Raster Analysis

Raster cells store data (nominal, ordinal, interval/ratio)

Complex constructs built from raster data

Connected cells can be formed in to networks

Related cells can be grouped into neighborhoods or regions

Examples:

Predict fate of pollutants in the atmosphere

The spread of disease

Animal migrations

Crop yields

EPA - hazard analysis of urban superfund sites

Local to global scale forest growth analysis

Raster

operations

require a

special set

of tools

Raster Analysis

Map algebraConcept introduced and developed by by Dana Tomlin and

Joseph Berry (1970s)

Cell by Cell combination of raster data layers

Each number represents a value at a raster cell

location

Simple operations can be applied to each number

Raster layers may be combined through operations

Addition, subtraction and multiplication

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Scope: Local operations

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Scope: Neighborhood operations

Scope: Global operation

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Many Local

Functions

(page 384 of book)

Logical Operations

ANDNon-zero values are true, zero values are false

N = null values

Pg 385 of book

Logical Operations

ORNon-zero values are true, zero values are false

N = null values

Pg 385 of book

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Logical Operations

NOT

More Local Functions logical comparisons

(pg 386 of book)

Conditional

Function

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Nested

Functions

no yes

Neighborhood

Operations

Moving Windows(Windows can be any size;

often odd to provide a center)

Neighborhood

Operations

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Raster Analysis

Moving windows and kernals can be used with a mean

kernal to reduce the difference between a cell and

surrounding cells. (done by average across a group of cells)

Raster data may also contain noise; values that are large

or small relative to their spatial context.(Noise often requiring correction or smooth(ing))

Know as high-pass filters

The identified spikes or pits can then be corrected or

removed by editing

Raster Analysis

High pass filters

Return:

Small values when smoothly changing values.

Large positive values when centered on a spike

Large negative values when centered on a pit

35.7

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Mean filterapplied

Note edge erosion

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Moving windows: Consider the overlap in cell calculations

Neighborhood operations often

Increase spatial covariance

Overlay in Raster

Union and Clip

Cell by Cell Addition or Multiplication

Attribute combinations corresponding to

unique cell combinations

Raster Clip or Mask(used in Lab 10)

What if you

only want

certain cells?

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Raster Clip or Mask(used in Lab 10)

Note: removed cell output values could be

0 or N depending of the GIS software

used.

Raster zonal function

Issues in Raster Addition

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A Problem with Raster

Analysis

Too many cells Typically, one-to-one relationship between

spatial object and attribute table

Rasters have multiple cells per feature

Attribute tables grow to be unwieldy

Vector Raster

Raster overlay as addition

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Output layer DOES NOT

have unique recordsRaster Overlay

What to do? First multiply Layer A by 10

Cost Surface

The minimum cost of reaching cells in a layer from

one or more sources cells

travel costsTime to school; hospital;

Chance of noxious foreign weed spreading out from an introduction point

Units can be money, time, etc.

Distance measure is combined with a fixed cost per unit

distance to calculate travel cost

If multiple source cells, the lowest cost is typically placed in

the output cell

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Friction Surface (version of a Cost Surface)

The cell values of a friction surface represent the cost per unit

travel distance for crossing each cell varies from cell to cell

Used to represent areas with variable travel cost.

Notes:

Barriers can be added.

Multiple paths are often not allowed

Cost and Friction Surfaces are always related to a source

cell(s); from something

The center of a cell is always used the distance calculations

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Digital Elevation Models &

Terrain Analysis

Terrain determines or influences:

- natural availability and location of surface water,

and hence soil moisture and drainage.

- water quality through control of sediment

entrainment/transport, slope steepness.

- direction which defines flood zones, watershed

boundaries and hydrologic networks.

- location and nature of transportation networks or

the cost(methods) of house(road) construction.

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Digital Elevation Models

Used for: hydrology, conservation, site planning, other

infrastructure development.

Watershed boundaries, flowpaths and direction, erosion

modeling, and viewsheddetermination all use slope and/or

aspect data as input.

Slope is defined as the change is elevation (a rise) with a

change in horizontal position (a run).

Slope is often reported in degrees (0 is flat, 90is vertical)

Formats - Contour Elevation Data

Source Independent

USGS topo maps

Contour shows a

line of constant

elevation

Generally used

more as a

cartographic

representation

From Sean Vaughn, MNDNR

DEMs consist of an array representing

elevation values at regularly spaced intervals

commonly known as cells.

ELEVATION

VALUES (ft)

Formats - Digital Elevation Models

X

Y

Z


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DEM = Raster = Grid


Raster (Format)

DEM = Gridvs. Vector data format

Raster (Format)

DEM = Gridvs. Vector data format


DEM Structure Each cell usually

stores the average

elevation of grid cell.

Typically they store

the value at the

center of the grid cell.

Elevations are

presented graphically

in shades or colors.

67 56 49

53 44 37

58 55 22Digital

Graphical



DEMs are a common way of representing elevation where every

grid cell is given an elevation value. This allows for very rapid

processing and supports a wide-array of analyses.



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Resolution

30 Meter

USGS produced from Quad Hypsography.

DNR published format in MN.

Course resolution

10 Meter

Interpolated

Resampled

52

Previously Published National DEMs


Resolution

1 Meter

3 Meter

Most common published format

in MN.

Storage requirements & faster

drawing speeds.53

Previously Published National DEMs

Resolution Tradeoff

Lower resolution = Faster processing

Higher resolution = Maintain small features

1-meter DEM claims 9-

times more process

resources and storage

than a 3-meter DEM


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Slope

Slope (continued)

Measured in the steepest

direction of elevation

change

Often does not fall parallel

to the raster rows or

columns

Which cells to use?

Several different methods:

Four nearest cells

3rd Order Finite

Difference

Slope (continued)

Elevation is Z

Using a 3 by 3 (or 5 by 5) moving window

Each cell is assigned a subscript and the

elevation value at that location is referred to by

a subscripted Z value

The most common formula:

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Slope (continued)

for ZoZ/x = (49 40)/20 = 0.45

Z/y = (45 48)/20 = -0.15

Slope (continued)

Slope calculation base on cells adjacent to

the center cell

The distance is from cell center to cell

center

for ZoZ/x = (49 40)/20 = 0.45

Z/y = (45 48)/20 = -0.15

Generalized formula for

Z/x and Z/y

Z/x = (Z5 Z4)2*

Z/y = (Z2 Z7)2*

Using the four nearest cells

* = times cell width

Slope (continued)

Z/x = (49 40)/20 = 0.45 Z/y = (45 48)/20 = -0.15

Kernal for Z/x Kernal for Z/y

Multiply (kernal, cell by cell)

Add (results)

Divide by #cells x cell width

Use slope formula

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Multiply (kernal, cell by cell)

Add (results)

Divide by #cells x cell width

Use slope formula

Aspect

Aspect

The orientation (in compass angles) of a slope

Calculation:

Aspect = tan-1[ -(Z/y)/(Z/x)]

As with slope, estimated aspect varies with the

methods used to determine Z/x and Z/y

Aspect calculations also use the four nearest cell or

the 3rd-order finite difference methods

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Curvature

Curvature

Plan Curvature:

measured

perpendicular to the

direction of descent

Describes

converging/diverging

flow

Contour curvature

Profile Curvature:

measured in the

direction of maximum

descent or aspect

direction.

Measure of flow

acceleration,

erosion/deposition

rate

From Joel Nelson, UMN

Curvature

Plan Profile

Convex

Concave


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Curvature Use/Significance

Plan Curvature> Converging/diverging

flow

> Soil water content

> Soil characteristics

Profile Curvature> Flow acceleration

> erosion/depositionrate

> geomorphology


Flow direction

Use in hydrologic analysis

Excess water at a point on the Earth will flow in

a given direction

Flow may be either on or below surface but

always in the direction of steepest descent (oftenthe same as local aspect)

Directions stored as compass angle is raster

data layer

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Watershed

An area that contributes flow to a point on the landscapeWater falling anywhere in the upstream area of a watershed will pass

through that point.

Many be small or large

Identified from a flow direction surface

Drainage network

A set of cells through which surface water flows

Based on the flow direction surface

Elevation

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Pits! Water goes in, and

doesnt come out

D8 Algorithm all flow goes to dominant

direction

Flow Direction

D Infinity Algorithm proportions flow

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D8 Flow Direction Algorithm

D-Infinity Flow Direction Algorithm - the method matters!

Beware of Blindly Filling Sinks!

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Warren County, KY

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Viewshed

The viewshed for a point is the collectionof areas visible from that point.

Views from any non-flat location are blocked by

terrain.

Elevations will hide a point if they are higher than the

viewing point, or higher than the line of site between

the viewing point and target point

not

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Shaded Relief Surfaces

The azimuth is the

angular direction of the

sun.

Measured from north in

clockwise degrees from 0

to 360.

The altitude is the slope or

angle of the illumination

source above the horizon.

Degrees, from 0 (on the

horizon) to 90 (overhead).

Displaying Elevation by Hill Shading


The ESRI default hill shade has an azimuth of

315 and an altitude of 45 degrees.



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By default, shadow and light are shades of

gray associated with integers from 0 to 255

(increasing from black to white).

The Azimuth and Angle change with the season thus the cast

shadows do as well. Should we model that?


92

Default Hillshaded DEM

Hillshade: Azimuth = 315 - Altitude = 45



93


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94



95



96


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Hillshade: Azimuth 360 - Altitude = 45

97


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