Elevation, Slope and Aspect

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Elevation, Slope and Aspect
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Overview

• Questions on Exercise 3?
• Elevation as DEM
• Slope and Aspect as Derivative Mapping
• How it works in IDRISI

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DEMs

• DEM Digital Elevation Model
• DTM Digital Terrain Model
• Each cell has a value or attribute of height
  above some reference
  
• arbitrary zero
• MSL or Mean Sea Level
• You made a crude one in Ex2 and 3

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DEM

• Digital Elevation Model
• Each cell contains an elevation value

Notice that the ortho view is NOT in perspective
that is the definition of orthographic
Orothograpic view of Nifkins DEM
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So?

• DEMs are pretty simple (x,y,z) values!
• BUT we typically do a lot with them
• Calculate slope and aspect!
• shape of country analysis,
• solar insolation,
• Hydrologic modeling base
• Flow direction, flow accumulation watersheds,
• viewsheds,
• construction (roads/harvest operations),
• soil erosion,
• lots of other stuff
• DEMs and Soils are the most common layers in the
  environmental and natural resources fields
  

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So?

• DEMs are pretty simple (x,y,z) values!
• BUT we typically do a lot with them
• Calculate slope and aspect!
• shape of country analysis,
• solar insolation,
• watersheds,
• viewsheds,
• construction (roads/harvest operations),
• soil erosion,
• lots of stuff

Note The correct term for elevation maps and
images
is Hypsography NOT Topography!
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Topographic Map

• The configuration of a surface and the relations
  among its man-made and natural feature
  
• A map that represents the vertical and horizontal
  positions of features, showing relief in some
  measurable form, such as contour lines,
  hypsometric tints, and relief shading.

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Planimetric map

• A map that displays only the locations of
  features and represents only horizontal
  distances. (ESRI)

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Where do DEMs come from

• Interpolation of
• Contour maps ( may not be very good)
• Elevation points (Works well but complicated)
• Gestault photo mapper makes DEMs as a byproduct
• Airborne Lidar Local areas, very fine, 1
  pixels and inches in vertical accuracy
  
• Airborne Radar larger areas

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DEM Scales/Resolution

• DEMs come in different scales/resolutions
• 30m, 1/24,000 scale 7.5 minute Quad sheets
• Can be nominal LANDSAT actually 29.someting m
• 90m, 1/500,000 scale
• 10m, for New York, by Quad, from Quad Sheet
  contours (Not Gestault photo mapper)
  
• 2m, Parts of NY, All of CT soon.
• Lidar,the newest tool, can be less than a foot

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Availability

• Downloadable from a number of sites
• Cornell U. CUGIR site
• NY State GIS Clearing House
• PA, VT, CT,
• Links on my home page
• Downloading easy (but large files)
• But converting to IDRISI may not be!
• The DEMIDRIS module can be used

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Continuous Surfaces

• Any Continuous Surface can be represented like a
  DEM
  
• Elevation
• Slope and Aspect - Derived from elevation
• Water table
• Pollution levels in air or soil
• Noise levels
• Any Field phenomenon
• All generally have a high spatial autocorrelation
  

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Spatial Autocorrelation?

• Each cells value is like values in surrounding
  cells --gradually changing values (continuous
  data)
  
• If all cells have the same values then Morans I
  1
  
• If all cells are not the same (dissimilar) as the
  surrounding cells Morans I-1
  
• For ELEV.

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Spatial Autocorrelation?
Moran I 0.9743

• Each cells value is like values in surrounding
  cells --gradually changing values (continuous
  data)
  
• If all cells the same Morans I 1
• If all cells dissimilar than surrounding cells
  Morans I-1
  
• For ELEV

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What to do with a DEM

• Probably the most important layer for most
  environmental, planning, and forestry uses
  
• If a DEM is used the most common derivative
  layers are slope and aspect!
  
• Raster based hydrologic models are based on DEMs.
  Slope and aspect allow the calculation of flow
  direction and flow accumulation
  
• Planning of ski areas
• Transportation design, Cut and Fill

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So?
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Slope

• Slope is the average rate of change of elevation
  over a 9 cell kernel which passes over the DEM
  

• Slope rise/run averaged over the kernel

Run 100 units Rise 33 uits slope (33/100
)100 33
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two ways to calculate Slope
As an Angle from horizontal - degrees
Engineering, solar
Planning, Natural Resources, etc.
As a percent 100(Rise/Run) gradient
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Slope

• Most GISs will calculate slope in either or
  degrees
  
• used most commonly in environmental and natural
  resources work
  
• Degrees used in scientific work

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Aspect

• Aspect is the direction in which that slope
  faces. This is determined as the direction you
  would be facing if you were looking downhill on
  the line of steepest descent (Maximum slope)
• 0 to 360 degrees azimuth (N,S,E, W)
• Flat areas are given value 1 NO aspect!
• Points of the compass are
• N, NE, E, SE, S, SW, W, NW, and flat

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Root Mean Square
N
W
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Calculation of slope aspect

• Heres the rub!
• Only way to calculate these is to do it over a
  kernel of some size, usually 3x3 (In IDRISI)
  
• A kernel is a square, small or sub array
• There is NO slope to a single cell!
• Slope can be over 3x3,5x5,7x7,
• The value calculated is then assigned to the
  central cell of the kernel
  
• So the resolution and accuracy of slope and
  aspect is NOT the same as that of the original
  data!!!!
  
• It is worse!
• 30 m pixel DEM yields 90 m slope and aspect

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Kernel passes over image
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Determining Slope always Smooths (Filters)

• Since these values are for a 3x3 kernel the image
  is effectively smoothed, and simplified
  
• Like you ran sandpaper over a model of the surface

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Determining Slope always Smooths (Filters)

• Since these values are for a 3x3 kernel the image
  is effectively smoothed, and simplified
  
• Like you ran sandpaper over a model of the surface

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Two basic ways to calculate SA
Uses all data. BUT processing time greater!
Only uses 4 or 5 data points
Uses 8 or 9 data points
IDRISI (4)
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Queen vs. Rook

• Queen can move in any direction one cell
• therefore queens case uses all 8 cells all
  data. Use center cell then 9
  
• Rook can move one cell N-S or E-W, NOT NE or SW
• therefore rooks case uses only 4 of the 8
  surrounding cells. Center cell 5
  
• Some systems do use the central cell
• IDRISI uses Rooks case and does not use the
  central cell -- unless you program it to do
  something different

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The Math
Based on two slopes, either queens case or
rooks case
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Slope calculation possibilities

• Statistically fitting a flat surface to elevation
  points
  
• Statistically fitting a curved surface to
  elevation points
  
• Flat is faster than curved!

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On a flat surface..

• Slope is toward the SE (aspect) at 45 degrees or
  100
  
• However, there are slopes in the N-S direction
  facing S and in the E-W direction facing E.
  
• And there is NO slope NE to SW!

N
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OR, you can fit a curved surface

• A curved surface is fit to the elevation points
• A complex operation (See appendix)
• Aspect of slope is toward the SE
• Planform slope is at 90 degrees to slope or
  toward the NE.

N
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For both flat and curved

• Programming/settings required
• Mathematical algorithms required
• Processing Time!
• But, it could be more applicable to what you
  want, like a change in the rate of slope

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Back to what we need to know

• IDRISI SURFACE
• Rooks case, 9-cell kernel, uses EW / NS vectors,
  no inclusion of central cell.
  
• Very simple/takes very little processing time
• for gradient of slope..
• 100Sqrt(EW/res2)2(NS/res2)2
• Thats it

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The Edge Problem

• In the text it is pointed out that because slope
  and aspect calculations use at least a 3x3 kernel
  the edge pixels will never be correct!

? ? ?
kernel
20 15 10 0
15 10 5 0
10 5 0 0
10 5 0 0
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The Edge Problem

• In IDRISI it sets the edge cell value equal to
  the same value as its neighbor

20 20 20
kernel
20 15 10 0
15 10 5 0
10 5 0 0
10 5 0 0
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Question?

• What is the direction of 0 (zero) slope?
• If a flat plane is being fit to the surface then
  the direction of zero slope MUST be at 90 degrees
  from the maximum slope!
  
• So what?
• Sometimes you want to find the direction of zero
  slope so you can find a minimum slope pathway
  over terrain.

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SO!

• There are a lot of different ways to compute
  slope!
  
• None are wrong, they are just different measures
  of the same thing
  
• Important point is that slope and aspect are
  representative of 9 cells, NOT 1 cell

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