Introduction toSurfaces and Surface

Creation

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

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

What is a Surface?

*What data features could be represented with a continuous surface?

*What data features could be represented with a discrete surface?

Mapping Discrete Surfaces

Choropleth Mapping

Dot Mapping

Dasymetric Mapping

Mapping Continuous Surfaces

*Surface represented by lines connecting points of equal statistical value (Isorithm’s)

*Isorithms differ depending on the data shown:

Isolines

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:

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:

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

Today’s Weather

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

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)

Interpolation*Linear Interpolation vs. Spline Interpolation

Interpolation*Other non-linear forms of interpolation:

-weighted methods

-kriging (semivariogram)

*Discussed more thoroughly in 4215

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)

Elevation, Slope, Aspect, Viewshed

*TIN’s are computationally more efficient, yet practically often less accurate and certainly less user-friendly

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 . . .

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

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)

Elevation, Slope, Aspect, Viewshed

90 110 120

80 90 100

70 80 90

Cell size = 100mWhat is the average slope?

Elevation, Slope, Aspect, Viewshed

90 110 120

80 90 100

70 80 90

Ave. slope = 200/2400 = .083 or 8.3%

What slope = 100%?

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

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?

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)

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

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

Questions??