Terrain modelling: the basics

Adding the third dimension In high relief areas variables such as altitude, aspect and slope strongly influence both human and physical environments A 3D data model is therefore essential Use a digital terrain model (DTM) Derive information on: Height (altitude), aspect and slope (gradient) Watersheds (catchments) Solar radiation and hill shading Cut and fill calculations Hillshade VIewshed

Digital Elevation Models are: Data files that contain the elevation of the terrain over a specified area, usually at a fixed grid interval The intervals between each of the grid points will always be referenced to some geographical coordinate system. (e.g. latitude-longitude, UTM, SP). The closer together the grid points are located, the more detailed the information will be in the file. The details of the peaks and valleys in the terrain will be better modeled with a small grid spacing than when the grid intervals are very large.

Digital Elevation Models are: Elevations other than at the specific grid point locations are not contained in the file. As a result peak points and valley points not coincident with the grid will not be recorded in the file. The file also does not contain civil information such as roads or buildings. It is not a scanned image of the paper map (graphic). It is not a bitmap. The does not contain elevation contours, only the specific elevation values at specific grid point locations.

DEMs and DTMs Some definitions… DEM (digital elevation model) Set of regularly or irregularly spaced height values No other information DTM (digital terrain model) But, with other information about terrain surface Ridge lines, spot heights, troughs, coast/shore lines, drainage lines, faults, peaks, pits, passes, etc.

Digital Elevation Model: What it looks like 67 56 49 46 50 12 11 53 44 37 38 48 58 55 22 31 24 61 47 21 16 19 34 Lay a grid over some part of the world and find the average elevation in each cell

Cell Definition cell size (cell value) cell 67 56 49 46 50 12 11 53 44 37 38 48 58 55 22 31 24 61 47 21 16 19 34 cell size cell (cell value) The size of a cell is in either: meters, feet, degrees, or arc seconds

Data Sources Primary Data Sources: Shuttle Radar Topography Mission (SRTM) or other airborne sensors Secondary Sources from existing maps: 30ms from 1:24,000 scale map 1” (arc second ) National Elevation Dataset 3" (100m) s from 1:250,000 scale maps 30" of the earth (GTOPO30)

Data Source Generation: Space Shuttle

Shuttle Radar Topography Mission (SRTM) 1 arc-second elevation data for the United States, 3 arc-second data for the globe Produced by radar measurements from a Shuttle mission, Feb 11-22, 2000 http://srtm.usgs.gov/data/obtaining data.html

Santa Barbara, California http://srtm.usgs.gov/srtmimagegallery/index.html

Interferometry used by SRTM In interferometry, two images are taken from different vantage points of the same area. The slight difference in the two images allows scientists to determine the height of the surface.

Secondary Data Source Generation: Using USGS Topographic Maps

200 Meter Mesh (Universal Transverse Mercator Coordinates) 1km 1km

100 Meter Mesh (UTM Coordinates) 1km 100m 1km

30 Meter Mesh Standard for 1:24,000 Scale Maps

Lattice Points

Cell Stores Elevation at Lattice Point

Elevations Contours 720 700 680 740

Comparison Cell Size 30m 100m

Ordnance Survey Ordnance Survey: Landform Panorama Landform Profile source scale: 1:50,000 resolution: 50m vertical accuracy: ±3m Landform Profile source scale: 1:10,000 resolution: 10m vertical accuracy: ±0.3m

Comparison Landform Panorama Landform Profile

LIDAR data (LIght Detection And Ranging) Horizontal resolution: 2m Vertical accuracy: ± 2cm

Modelling building and topological structures Two main approaches: Digital Elevation Models (s) based on data sampled on a regular grid (lattice) Triangular Irregular Networks (TINs) based on irregular sampled data and Delaunay triangulation

TIN based on same sample points DEMs and TINs with sample points TIN based on same sample points

Advantages/disadvantages DEMs: Accept data direct from digital altitude matrices Must be resampled if irregular data used May miss complex topographic features May include redundant data in low relief areas Less complex and CPU intensive Tins: Accept randomly sampled data without resampling Accept linear features such as contours and breaklines (ridges and troughs) Accept point features (spot heights and peaks) Vary density of sample points according to terrain complexity

Derived variables Primary use of DTMS is calculation of three main terrain variables: Height Altitude above datum Aspect Direction area of terrain is facing Slope Gradient or angle of terrain

Calculating slope Inclination of the land surface measured in degrees or percent 3 x 3 cell filter Find best fit tilted plane that minimises squared difference in height for each cell Determine slope of centre (target) cell z = a + bx + cy Slope = b2 + c2 10 8 9 7 6 5

Calculating aspect Direction the land surface is facing measured in degrees or nominal classes (N, S, E, W, NE, SE, NW, SW, etc.) use 3 x 3 filter and best fit tilted plane determine aspect for target cell Aspect = tan-1 c / b 10 8 9 7 6 5

Other derived variables Many other variables describing terrain features/characteristics Hillshading Profile and plan curvature Feature extraction Etc.

Examples height aspect slope hillshading plan curvature Feature extraction

Problems with DEMs Issues worth considering when creating/using DTMs Quality of data used to generate Interpolation technique Give rise to errors in surface such as: Sloping lakes and rivers flowing uphill Local minima Stepped appearance Etc.

Example applications Visualisation Visibility analysis terrain and other 3D surfaces Visibility analysis intervisibility matrices and viewsheds Hydrological modelling catchment modelling and flow models Engineering cut & fill, profiles, etc.

Terrain visualisation Analytical hillshading Orthographic views any azimuth, altitude, view distance/point surface drapes (point, line and area data) Animated ‘fly-through’

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