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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 (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
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