Introduction to Surfaces and Surface Creation

1. Introduction to Surfaces and Surface Creation

2. 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

3. 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

4. What is a Surface? *What data features could be represented with a continuous surface? *What data features could be represented with a discrete surface?

5. Mapping Discrete Surfaces Choropleth Mapping Dot Mapping Dasymetric Mapping

6. Mapping Continuous Surfaces *Surface represented by lines connecting points of equal statistical value (Isorithm’s) *Isorithms differ depending on the data shown: Isolines

7. 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:

8. 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:

9. 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: points of equal barometric pressure *Isorithmic mapping can be used to represent discrete data if you assume the data are continuous

10. Today’s Weather

11. 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

12. 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)

13. Interpolation *Linear Interpolation vs. Spline Interpolation

14. Interpolation *Other non-linear forms of interpolation: -weighted methods -kriging (semivariogram) *Discussed more thoroughly in 4215

15. 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)

16. Elevation, Slope, Aspect, Viewshed *TIN’s are computationally more efficient, yet practically often less accurate and certainly less user-friendly

17. 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 . . .

18. 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

19. 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)

20. Elevation, Slope, Aspect, Viewshed Cell size = 100m What is the average slope?

21. Elevation, Slope, Aspect, Viewshed Ave. slope = 200/2400 = .083 or 8.3% What slope = 100%?

22. 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

23. Elevation, Slope, Aspect, Viewshed Cell size = 100m What is the aspect? OR Which direction has the greatest slope?

24. Elevation, Slope, Aspect, Viewshed Aspect = SW Aspect computed as degrees (1-360) or a simple set of vector values (chain codes) (1-8, anything)

25. 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

26. 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

27. Questions??