##### AM-18 - Cost surface

- Define “friction surface”
- Apply the principles of friction surfaces in the calculation of least-cost paths
- Explain how friction surfaces are enhanced by the use of impedance and barriers

- Define “friction surface”
- Apply the principles of friction surfaces in the calculation of least-cost paths
- Explain how friction surfaces are enhanced by the use of impedance and barriers

- Define “intervisibility”
- Outline an algorithm to determine the viewshed (area visible) from specific locations on surfaces specified by DEMs
- Perform siting analyses using specified visibility, slope, and other surface related constraints
- Explain the sources and impact of errors that affect intervisibility analyses

- Identify the spatial concepts that are assumed in different interpolation algorithms
- Compare and contrast interpolation by inverse distance weighting, bi-cubic spline fitting, and kriging
- Differentiate between trend surface analysis and deterministic spatial interpolation
- Explain why different interpolation algorithms produce different results and suggest ways by which these can be evaluated in the context of a specific problem
- Design an algorithm that interpolates irregular point elevation data onto a regular grid
- Outline algorithms to produce repeatable contour-type lines from point datasets using proximity polygons, spatial averages, or inverse distance weighting
- Implement a trend surface analysis using either the supplied function in a GIS or a regression function from any standard statistical package
- Describe how surfaces can be interpolated using splines
- Explain how the elevation values in a digital elevation model (DEM) are derived by interpolation from irregular arrays of spot elevations
- Discuss the pitfalls of using secondary data that has been generated using interpolations (e.g., Level 1 USGS DEMs)
- Estimate a value between two known values using linear interpolation (e.g., spot elevations, population between census years)

- List the likely sources of error in slope and aspect maps derived from digital elevation models (DEMs) and state the circumstances under which these can be very severe
- Outline how higher order derivatives of height can be interpreted
- Explain how slope and aspect can be represented as the vector field given by the first derivative of height
- Explain why the properties of spatial continuity are characteristic of spatial surfaces
- Explain why zero slopes are indicative of surface specific points such as peaks, pits, and passes, and list the conditions necessary for each
- Design an algorithm that calculates slope and aspect from a triangulated irregular network (TIN) model
- Outline a number of different methods for calculating slope from a DEM

- List the likely sources of error in slope and aspect maps derived from digital elevation models (DEMs) and state the circumstances under which these can be very severe
- Outline how higher order derivatives of height can be interpreted
- Explain how slope and aspect can be represented as the vector field given by the first derivative of height
- Explain why the properties of spatial continuity are characteristic of spatial surfaces
- Explain why zero slopes are indicative of surface specific points such as peaks, pits, and passes, and list the conditions necessary for each
- Design an algorithm that calculates slope and aspect from a triangulated irregular network (TIN) model
- Outline a number of different methods for calculating slope from a DEM

- Define “friction surface”
- Apply the principles of friction surfaces in the calculation of least-cost paths
- Explain how friction surfaces are enhanced by the use of impedance and barriers

- Identify the spatial concepts that are assumed in different interpolation algorithms
- Compare and contrast interpolation by inverse distance weighting, bi-cubic spline fitting, and kriging
- Differentiate between trend surface analysis and deterministic spatial interpolation
- Explain why different interpolation algorithms produce different results and suggest ways by which these can be evaluated in the context of a specific problem
- Design an algorithm that interpolates irregular point elevation data onto a regular grid
- Outline algorithms to produce repeatable contour-type lines from point datasets using proximity polygons, spatial averages, or inverse distance weighting
- Implement a trend surface analysis using either the supplied function in a GIS or a regression function from any standard statistical package
- Describe how surfaces can be interpolated using splines
- Explain how the elevation values in a digital elevation model (DEM) are derived by interpolation from irregular arrays of spot elevations
- Discuss the pitfalls of using secondary data that has been generated using interpolations (e.g., Level 1 USGS DEMs)
- Estimate a value between two known values using linear interpolation (e.g., spot elevations, population between census years)

- Define “intervisibility”
- Outline an algorithm to determine the viewshed (area visible) from specific locations on surfaces specified by DEMs
- Perform siting analyses using specified visibility, slope, and other surface related constraints
- Explain the sources and impact of errors that affect intervisibility analyses

- Define “friction surface”
- Apply the principles of friction surfaces in the calculation of least-cost paths
- Explain how friction surfaces are enhanced by the use of impedance and barriers

## AM-15 - Calculating surface derivatives