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 (1970’s)

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

Scope: Local operations

Scope: Neighborhood operations

Scope: Global operation

Many Local

Functions

(page412 of book)

Logical Operations

ANDNon-zero values are “true”, zero values are “false”

N = null values

Pg 412 of book

Logical Operations

ORNon-zero values are “true”, zero values are “false”

N = null values

Pg 412 of book

Logical Operations

NOT

More Local Functions – logical comparisons

(pg 414 of book)

Conditional

Function

Nested

Functions

no yes

Output= Con(ISNULL(LayerA), LayerC, LayerB)

Neighborhood

Operations

Moving Windows(Windows can be any size;

often odd to provide a center)

Neighborhood

Operations

Neighborhood Operations: Mean Function

What about the edges?

Neighborhood Operations:Separate edge kernals can be used

Example:Identifying

spatial differences in

a raster layer

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

Mean filter

applied

Note edge erosion

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?

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

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

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 costs”Time 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

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

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.

Digital Elevation Models

•Used for: hydrology, conservation, site planning, other

infrastructure development.

•Watershed boundaries, flowpaths and direction, erosion

modeling, and viewshed determination 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, 90° is 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

DEM’s 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

From Sean Vaughn, MNDNR

DEM = Raster = Grid

Digital Elevation Models

Raster (Format)

DEM = Gridvs. Vector data format

From Sean Vaughn, MNDNR

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 22

Dig

ital

Gra

phic

al

Digital Elevation Models

From Sean Vaughn, MNDNR

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.

Digital Elevation Models

From Sean Vaughn, MNDNR

Resolution

30 Meter

USGS produced from Quad Hypsography.

DNR published format in MN.

Course resolution

10 Meter

Interpolated

Resampled

52

Previously Published National DEMs

From Sean Vaughn, MNDNR

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

From Sean Vaughn, MNDNR

Viewshed

The viewshed for a point is the collection

of 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

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

From Sean Vaughn, MNDNR

The ESRI default hill shade has an azimuth of

315 and an altitude of 45 degrees.

Displaying Elevation by Hill Shading

From Sean Vaughn, MNDNR

Displaying Elevation by Hill Shading

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?

From Sean Vaughn, MNDNR

64

Default Hillshaded DEM

Hillshade: Azimuth = 315 - Altitude = 45

From Sean Vaughn, MNDNR

Hillshade: Azimuth = 315 - Altitude = 70

65

From Sean Vaughn, MNDNR

Hillshade: Azimuth = 315 - Altitude = 80

66

From Sean Vaughn, MNDNR

Hillshade: Azimuth = 90 - Altitude = 45

67

From Sean Vaughn, MNDNR

Hillshade: Azimuth = 180 - Altitude = 45

68

From Sean Vaughn, MNDNR

Hillshade: Azimuth 360 - Altitude = 45

69

From Sean Vaughn, MNDNR

Slope

• Describes overland

and subsurface

flow velocity and

runoff rate.

• Slope quantifies

the maximum rate

of change in value

from each cell to its

neighbors.

Slope

Blue Earth

County

Minnesota

Beauford

Sub-Watershed

High

Low

Slope

•Overland and

subsurface flow

•Velocity and runoff rate

•Precipitation

•Vegetation

•Geomorphology

•Soil water content

•Land capability class

Use/Significance

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:

Slope (continued)

for Zo

ΔZ/Δx = (49 – 40)/20 = 0.45

ΔZ/Δy = (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 Zo

ΔZ/Δx = (49 – 40)/20 = 0.45

ΔZ/Δy = (45 – 48)/20 = -0.15

Generalized formula for

ΔZ/Δx and ΔZ/Δy

ΔZ/Δx = (Z5 – Z4)2*

ΔZ/Δy = (Z2 – Z7)2*

Using the four nearest cells

* = times cell width

Slope (continued)

ΔZ/Δx = (49 – 40)/20 = 0.45 ΔZ/Δy = (45 – 48)/20 = -0.15

Kernal for ΔZ/Δx Kernal for ΔZ/Δy

Multiply (kernal, cell by cell)

Add (results)

Divide by #cells x cell width

Use slope formula

Multiply (kernal, cell by cell)

Add (results)

Divide by #cells x cell width

Use slope formula

Aspect

• Defines the cardinal direction (0 – 360 degrees) a surface is facing

• Uses - Fire management, soil moisture, evapotranspiration, flora and fauna distribution and abundance

From Joel Nelson, UMN

Aspect

Aspect

The orientation (in compass angles) of a slope

Calculation:

Aspect = tan-1[ -(ΔZ/Δy)/(ΔZ/Δx)]

As with slope, estimated aspect varies with the

methods used to determine ΔZ/Δx and ΔZ/Δy

Aspect calculations also use the four nearest cell or

the 3rd-order finite difference methods

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

From Joel Nelson, UMN

Curvature• Use/Significance

– Plan Curvature> Converging/diverging

flow

> Soil water content

> Soil characteristics

– Profile Curvature> Flow acceleration

> erosion/deposition rate

> geomorphology

From Joel Nelson, UMN

Plan

Curvature

http://www.et-st.com/ET_Surface/UserGuide/Raster/ETG_RasterCurvature.htm

Profile Curvature

http://www.et-st.com/ET_Surface/UserGuide/Raster/ETG_RasterCurvature.htm

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 (often

the same as local aspect)

Directions stored as compass angle is raster

data layer

Catchment Area

• Measure of surface or shallow subsurface runoff at a given point on the landscape

• Combines the effects of upslope surface drainage area and convergence of runoff

• Also called flow accumulation

From Joel Nelson, UMN

Terrain Attributes: Catchment Area or

Flow Accumulation

• Primary attribute representing the drainage area of any given cell

• Indicates overland flow paths

• Also known as catchment area, upslope contributing area

Elevation

300 m

308 m

30

10,000

Flow

Accumulation

From Joel Nelson, UMN

Catchment

Area

Blue Earth

County

Minnesota

Beauford

Sub-Watershed

High

Low

From Joel Nelson, UMN

Flow Accumulation

•Runoff volume

•steady-state runoff rate

•soil characteristics

•soil-water content

•geomorphology

Use/Significance

From Joel Nelson, UMN

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

Flow Direction

Flow Accumulation

Why a Disconnected Network?

Pits! – Water goes in, and

doesn’t come out

D8 Algorithm – all flow goes to dominant

direction

Flow Direction

D – Infinity Algorithm – proportions flow

D8 Flow Direction Algorithm

D-Infinity Flow Direction Algorithm - the method matters!

Pit Filling• Pit filling artificially draws base

elevation levels in “sinks” or “peaks” to bank-height or surrounding elevation values

• Usefulness/appropriateness depends on landscape and data

From Joel Nelson, UMN

Pit Filling• Useful for:

> Removing anomalies and erroneous values

> Closed depression landscapes

> Flood drainage scenarios – fill up water over depressions to force flow

• Caveats:• Data and drainage is being

altered, made artificial

• Depicts accurate flow at flood stages or higher

From Joel Nelson, UMN

Pit Filling

From Joel Nelson, UMN

Beware of Blindly Filling Sinks!

SimplifiedSteps to derive a Watershed

Fill in “sinks”

establish Flow Directionestablish & classify Flow Accumulation (2 steps)

create and locate Snap Pour Pointderive Watershed