Digital Terrain Modeling

Digital Terrain Modeling is the process of simulating or representing the relief and patterns of a surface with numerical and digital methods. It has always been an integral component to geology related fields such as geomorphology, hydrology, tectonics and oceanography but over the past decade has also become a major component to non geophysical applications such as GIS modeling, surveying and land use planning.

Terrain Models are derived from data represented by digital elevation models (DEMs) and can include shaded relief models, slope and aspect models, perspective scene generation, and drainage basin analysis (and other models).

House of Cards Music Video

Always cool to see Geomatics technology used for non traditional geomatics uses!

Making the Music Video:

Geologic Application of RadarSat S2 Mode Data in Northern Nova Scotia

The following image is a photo representation of a larger poster that I made along with Blair Sangster at COGS in March of 1999.

The project also included a detailed paper and presentation that was presented at the Center of Geographic Sciences Auditorium, in Lawrencetown Nova Scotia.

The project used RADARSAT S2 beam mode SAR imagery and ERDAS Imagine together to provide 3D models representing various geological terrain features.

3D Toronto Images

Below are a few 3D Toronto images from a demonstration that I gave comparing Esri Arc Scene with FLY in PCI Geomatica. I generated the digital surface model (DSM) from some demo LIDAR all hits data that we had. The coverage area is for a small portion of downtown Toronto centered around Toronto City Hall.

Slope

The slope or the gradient of a straight line within a Cartesian coordinate system is known as the measure of how steep a line is relative to the horizontal axis.

In calculations; it is generally represented by the letter m, and defined as the change in the Y coordinate divided by the corresponding change in the X coordinate, between two distinct points on the line (X1, Y1 and X2, Y2). Since the Y axis is vertical and the X axis is horizontal by convention, slope is often referred to as the rise over the run or the change in the vertical coordinates, divided by the change in the horizontal coordinates.

Basically, the larger the slope value, the steeper the line is. A horizontal line has a slope of 0, a 45 degree line has a slope of 1, and the slope of a vertical line is typically undefined. In trigonometry two lines are considered to be parallel if and only if their slopes are equal or if they both are vertical and therefore undefined. Two lines are considered to be perpendicular if and only if the product of their slopes is -1 or one has a slope of 0 and the other is vertical and undefined.

There are two common ways to describe slope. One method is to use the angle of the slope in degrees (0 to 90), and the other is to represent the slope as a percentage (0 to 100). Expressing slope as a percent is common but can be confusing because a percent slope can be greater then 100%. A 100% slope is actually only a 45 degree angle due to the fact that the rise and run of a 45 degree angle are equal and when divided always equals 1 and when multiplied by 100 will equal 100%.

In terrain modeling we generally model an entire surface and not just one line so we need to calculate the slope of a best fit surface plane (which is made of lines). Because the terrain model is usually continuous across the entire surface, it is important to be able to calculate how to represent grid cells (or pixels) when going from one elevation to the next. To do this we generally need to know the aspect or the direction that the surface plane is sloped as well. Together the slope combined with the aspect of the surface can virtually define the surface plane completely.

In the example shown to the left, a slope map of Lismore, Nova Scotia was derived from a digital elevation model (DEM) calculated using PCI Geomatica remote sensing software. It is represented with a grey scale color ramp therefore the color white represents a 0 slope and the shades of grey increase through to black which represents an undefined slope. The majority of slopes for this map do not exceed 17 degrees (except for vertical slopes) as this is a relative low lying area of Appalachian terrain.

The image above and to the right is of an actual bedrock cliff with some technical information embedded onto it so it may be used to help better understand slope. The black arrow represents the slope or the measured angle that the rock is dipping towards. The slope in the image would be 45 degrees approximately so the slope would be 1 or 100%. The rise and the run of a slope with a 45 degree angle will always equals 1, thus when multiplied by 100 to calculate percent slope will equal always equal 100%.

Example of a Slope Map

The image below is a Slope Model that I derived from a digital elevation model (DEM) of Lismore, Nova Scotia. The values of the slopes of the DEM are represented by a 0-255 grey scale color ramp, therefore the color white represents a 0 slope and the shades of grey increase through to black which represents an undefined slope. The majority of slopes for this map do not exceed 17 degrees (except for vertical slopes) as this is a relative low lying area of Appalachian terrain.

Click here to learn a little more about Slope Models and how the image below was created.

3D Perspective Views

Most imagery (and/or spatial data) that we view in geomatics is typically viewed vertically downwards from the source toward the map or image. This typical aerial view that we are accustomed to using, allows an abundant amount of information to be represented spatially within a two dimensional cartesian representation. However, occasionally it is useful for us to change our focus from the default traditional view and use a more complex three dimensional visualization view of the data.

This type of terrain model is commonly referred to as a perspective view and often reveals additional information by allowing us to observe the same data obliquely.. In order to do this each location of the image needs to be transformed from the traditional 2-D to a 3-D projection coordinate system.

A perspective view is not really a new tool as it has been around for centuries, but it has become a popular component of most geomatics projects. “A Perspective is a rational demonstration by which experience confirms that the images of all things are transmitted to the eye by pyramidal lines. Those bodies of equal size will make greater or lesser angles in their pyramids according to the different distances between the one and the other. By a pyramid of lines, means those which depart from the superficial edges of bodies and converge over a distance to be drawn together in a single point” (Leonardo da Vinci)¹.

Data integration and overlays are very common with perspective views because it allows traditional flat images to become new products by incorporating an elevation component and providing a new look at the same data. It is also probably used more so for visual appeal then as another method of extracting data.

Sample image on the right is a 3D perspective view of Cape George, Nova Scotia (just north of Antigonish), created with LandSat imagery drapped over a digital elevation model (DEM).

[* quote 1 is from – O’Connor and Robertson (2003) Mathematics and art – perspective www-groups.dcs.st-and.ac.uk/~history/HistTopics/Art.htmlJanuary]

3D Perspective View Samples