## analysis of surfaces

##### AM-16 - Interpolation methods • 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)
##### AM-15 - Calculating surface derivatives • 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
##### 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
##### AM-17 - Intervisibility • 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
##### AM-16 - Interpolation methods • 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)
##### AM-15 - Calculating surface derivatives • 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
##### 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
##### AM-17 - Intervisibility • 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
##### AM-16 - Interpolation methods • 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)
##### AM-15 - Calculating surface derivatives • 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