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Introduction toSurfaces and Surface
Creation
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What is a Surface?
*any measurable values (ordinal, interval or ratio scale) which can be thought of as occurring throughout a definable area could be represented as a surface, known as a Statistical Surface
*surface features always contain Z-values (i.e., X and Y represent the location, and Z represents the amount (value) associated with the surface feature at that location
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What is a Surface?
*surfaces can be divided into “continuous” or “discrete”
*a continuous surface is used to represent data which occur at some degree for every location within the area of interest
*a discrete surface represents data with equal values within a given unit area
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What is a Surface?
*What data features could be represented with a continuous surface?
*What data features could be represented with a discrete surface?
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Mapping Discrete Surfaces
Choropleth Mapping
Dot Mapping
Dasymetric Mapping
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Mapping Continuous Surfaces
*Surface represented by lines connecting points of equal statistical value (Isorithm’s)
*Isorithms differ depending on the data shown:
Isolines
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Mapping Continuous Surfaces
*Surface represented by lines connecting points of equal statistical value (Isorithm’s)
*Isorithms differ depending on the data shown:
Isolines: points of equal elevation
Isotherms:
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Mapping Continuous Surfaces
*Surface represented by lines connecting points of equal statistical value (Isorithm’s)
*Isorithms differ depending on the data shown:
Isolines: points of equal elevation
Isotherms: points of equal temperature
Isobars:
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Mapping Continuous Surfaces
*Surface represented by lines connecting points of equal statistical value (Isorithm’s)
*Isorithms differ depending on the data shown:Isolines: points of equal elevationIsotherms: points of equal temperatureIsobars: points of equal barometric pressure
*Isorithmic mapping can be used to represent discrete data if you assume the data are continuous
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Today’s Weather
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Mapping Continuous Surfaces
*A continuous surface is derived from a set of data sampling points
*If the data points are systematically spaced in a consistent fashion throughout the area of interest, they are considered a “grid”
*More often, the data sampling points are irregularly spaces
*Deriving continuous data completed through Interpolation
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Interpolation*The task is to calculate the most likely value of
the new point based on available observations.*The user can determine different calculation
protocol:-closest point (new value the same as
closest known value-linear (new value calculated from a
straight line between the closest two observations)
-spline (new value calculated from a curve between the three closest points)
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Interpolation*Linear Interpolation vs. Spline Interpolation
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Interpolation*Other non-linear forms of interpolation:
-weighted methods
-kriging (semivariogram)
*Discussed more thoroughly in 4215
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Elevation, Slope, Aspect, Viewshed
*A continuous layer of elevation is known as a Digital Elevation Model (DEM) or Digital Terrain Model (DTM)
*A DEM can be used in both vector format and raster format
*In vector format, slope, aspect, and viewshed can be derived from a Triangular Irregular Network (TIN)
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Elevation, Slope, Aspect, Viewshed
*TIN’s are computationally more efficient, yet practically often less accurate and certainly less user-friendly
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Elevation, Slope, Aspect, Viewshed
*For ease of understanding, we will discuss slope, aspect and viewshed in the context of raster (grid) data
*So, why would we want to know slope??
-lets hear some examples . . .
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Elevation, Slope, Aspect, Viewshed
*For ease of understanding, we will discuss slope, aspect and viewshed in the context of raster (grid) data
*So, why would we want to know slope??
-building your mountain cabin on a flat spot
-finding a large flat area to build an airport
-locating places to clear beginner, intermediate, and advanced ski runs
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Elevation, Slope, Aspect, Viewshed
*Slope, like all “roving window” functions, is derived from analyzing the target pixel elevation value relative to its neighbours, and writing an output to the center pixel
*Different algorithms are used to compute different slope-derived features:
-average slope (most common)
-greatest slope (where water would flow)
-least slope (where the hiker would walk)
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Elevation, Slope, Aspect, Viewshed
90 110 120
80 90 100
70 80 90
Cell size = 100mWhat is the average slope?
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Elevation, Slope, Aspect, Viewshed
90 110 120
80 90 100
70 80 90
Ave. slope = 200/2400 = .083 or 8.3%
What slope = 100%?
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Elevation, Slope, Aspect, Viewshed
*So, why would we want to know aspect/azimuth/orientation?
-vegetation on north vs. south slopes
-where to build wind generators
-prevailing slopes of fault blocks or exposed folds
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Elevation, Slope, Aspect, Viewshed
90 110 120
80 90 100
70 80 90
Cell size = 100mWhat is the aspect? OR Which direction has the greatest slope?
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Elevation, Slope, Aspect, Viewshed
90 110 120
80 90 100
70 80 90
Aspect = SWAspect computed as degrees (1-360) or a simple set of vector values (chain codes) (1-8, anything)
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Elevation, Slope, Aspect, Viewshed
*Viewshed (intervisibility) defines the regions visible from a given point
*So, why would we want to know viewshed?
-locating the optimal location for telephone, radio, and cell phone transmitters/receivers
-optimal location for fire towers
-routing highways not visible to nearby residents
-no harvesting areas seen from a waterway
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Elevation, Slope, Aspect, Viewshed
*In vector, viewshed is completed with ray tracing-the user defines the origin and viewer position-the calculation determines which areas along that vector can be seen and which cannot
*In raster, viewshed is completed by area growing-the user defines the origin cell-computation works outward from the origin in all directions to define what can and cannot be seen
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Questions??