slope and aspect ( panta si orientarea versantilor) harta pantelor si orientarii versantilor
TRANSCRIPT
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 point’s 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
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
Slope Definitions (cont.)
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
1 2 3
4 5 6
7 8 9
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 1 2 3
4 5 6
7 8 9
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
1 2 3
4 5 6
7 8 9
Spatial Analysis:
“Transformations” Longley et al., chs. 13 and 14
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
“ Transformations” - New Data
• new objects and data sets from existing
objects anddata sets
• BUFFERING
• POINT IN POLYGON
• POLYGON OVERLAY
• SPATIAL INTERPOLATION
• DENSITY ESTIMATION
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
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
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
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
Point-in-Poly Algorithm
• inside if the count is odd
• outside if the count is even
• what if the point lies on the boundary?
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
Overlay Issues
• in raster the values in each cell are
combined -- binary, rating models??
• major computing workload
– Indexing
• swamped by slivers
– tolerance
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
What’s A Wildlife Manager to Do?
• 23 animals assumed everywhere?
• pitfalls of applying classical statistics to spatial data
• give “spatial” characterization to the mean (23)
• let’s interpolate!
X
X
Spatial Interpolation
• need to estimate values at locations where there are no explicit data
• estimates must be determined from surrounding values
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?
Linear interpolation
• a priori assumption
• Assigning values between known points
• Create an isarithmic (contour map)
Contouring a TIN
Nonlinear Interpolation
• When things aren't so simple
• Can’t assume linearity of features
• Basic types: 1. Trend surface analysis
2. Minimum Curvature Spline
3. Inverse Distance Weighted 4. Kriging