Slope and Aspect

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Slope and Aspect

• Calculated from a grid of elevations (a digital
  elevation model)
• Slope and aspect are calculated at each point in
  the grid, by comparing the points elevation to
  that of its neighbors
• usually its eight neighbors
• but the exact method varies
• in a scientific study, it is important to know
  exactly what method is used when calculating
  slope, and exactly how slope is defined

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Slope Definitions

• Slope defined as an angle
• or rise over horizontal run
• or rise over actual run
• various methods
• important to know how your favorite GIS
  calculates slope

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Slope Definitions (cont.)
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Slope and Aspect

• measured from an elevation or bathymetry raster
• compare elevations of points in a 3x3
  neighborhood
• slope and aspect at one point estimated from
  elevations of it and surrounding 8 points
• number points row by row, from top left from 1 to
  9

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Typical Slope Calculation

• tan (slope) sqrt (b2 c2)
• b (z3 2z6 z9 - z1 - 2z4 - z7) / 8D
• c (z1 2z2 z3 - z7 - 2z8 - z9) / 8D
• b denotes slope in the x direction
• c denotes slope in the y direction
• D is the spacing of points (30 m)
• find the slope that fits best to the 9 elevations
  
• minimizes the total of squared differences
  between point elevation and the fitted slope
• weighting four closer neighbors higher

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Aspect

• tan (aspect) b/c
• Angle between vertical and direction of steepest
  slope
• Measured clockwise
• add 180 to aspect if c is positive, 360 to aspect
  if c is negative and b is positive

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Spatial Analysis Transformations

• Longley et al., chs. 13 and 14

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Transformations

• Create new objects and attributes, based on
  simple rules
• involving geometric construction or calculation
• may also create new fields, from existing fields
  or from discrete objects

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Transformations - New Data

• new objects and data sets from existing objects
  anddata sets
• BUFFERING
• POINT IN POLYGON
• POLYGON OVERLAY
• SPATIAL INTERPOLATION
• DENSITY ESTIMATION

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Buffering

• buffering takes points, lines, or areas and
  creates areas
• every location within the resulting area is
  either
• in/on the original object
• within the defined buffer
• width of the original object

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Applications

• find all areas of Siuslaw National Forest beyond
  1 mile from a road
• find all households within 1 mile of a proposed
  new freeway
• and send them notification of proposal
• find all liquor stores within 1 mile of a school
• and notify them of a proposed change in the law

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Variants

• vary the object's buffer width according to an
  attribute value
• e.g. noise buffers depending on road traffic
  volume
• vary the rate of spread according to a friction
  field
• Thiessen polygons
• for point objects

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Point-in-Polygon

• Determine whether a given point lies inside or
  outside a given polygon
• assign a set of points to a set of polygons
• e.g., count numbers of accidents in counties
• e.g., whose property does this phone pole lie in?
• Algorithm
• draw a line from the point to infinity
• count intersections with the polygon boundary
• inside if the count is odd
• outside if the count is even

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Point-in-Poly Algorithm

• inside if the count is odd
• outside if the count is even
• what if the point lies on the boundary?

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Polygon Overlay

• Create polygons by overlaying existing polygons
• how many polygons are created when two polygons
  are overlaid?
• Discrete object
• find overlaps between
• two polygons
• creates a collection
• of polygons

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Overlay Issues

• in raster the values in each cell are combined --
  binary, rating models??
• major computing workload
• Indexing
• swamped by slivers
• tolerance

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Spatial Interpolation GIS

• to calculate some property of a surface at a
  given point
• model all the REAL intricacies of a surface
• to provide contours
• highlight general spatial trend of data for
  decision-making

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Whats A Wildlife Manager to Do?

• 23 animals assumed everywhere?
• pitfalls of applying classical statistics to
  spatial data
• give spatial characterization to the mean (23)
• lets interpolate!

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Spatial Interpolation

• need to estimate values at locations where there
  are no explicit data
• estimates must be determined from surrounding
  values

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Spatial Interpolation - cont.

• We need to be able to model a surface based on
  the sampled points.
• A predictive numerical model of Z values
• Can be conceptually very simple but it requires
  an a priori assumption
• Can the numbers in each successive step be
  determined by a simple mathematical procedure?

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Linear interpolation

• a priori assumption
• Assigning values between known points
• Create an isarithmic (contour map)

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Contouring a TIN
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Nonlinear Interpolation

• When things aren't so simple
• Cant assume linearity of features
• Basic types1. Trend surface analysis
• 2. Minimum Curvature Spline
• 3. Inverse Distance Weighted 4. Kriging