## 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.

## GIS Mobile Mapping with ArcPad

Included here is a report written for an ArcPad / Trimble mobile mapping project, a presentation that covered all aspects of the project and more general information and links about GIS mobile mapping. The report includes all code used in designing the ArcPad application (visual basic, XML etc). The presentation was presented at COGS in Lawerncetown, Nova Scotia during the fall of 2003. The existing AGRG weather station network now consists of 14 tripods and 1 tower setups (as of Aug 2004).

## GIS Spatial modeling for Kejimkujik National Park

Here is a summer GIS project that I worked on for Parks Canada.

The PDF technical report details the methodologies and issues that were encountered with a Spatial GIS vegetation database and GIS Spatial modeling project at the Applied Geomatics Research Group (AGRG) during the summer of 2004 that involved generating a spatial geographic database for Jeremy’s Bay Campground of Kejimkujik National Park and Historic Site. High resolution aerial photography acquired from a previous AGRG aerial photography mission was used along with extensive data collected during a Rapid Vegetation Assessment survey and a detailed forest stand interpretation.

Kejimkujik National Park and Historic Site is located about 160 km west of Halifax in south western Nova Scotia between Liverpool and Annapolis Royal. The lakes and rivers of the park are habitat for many turtles, frogs and

salamanders; Kejimkujik has more amphibians and reptiles than anywhere else in the Atlantic Provinces. The park is also home to many birds, especially common loons, and fish which include brook trout and white and yellow perch. In Canada, National Parks are considered places where ecosystems and ecological integrity should be maintained and Kejimkujik National Park is no exception.

The project was divided into two main sections that were indirectly related to one other. The first major part of the project was the compilation of digital line work and the creation of a Geographic Information System (GIS) Spatial database of forest stands found within the campground. The second part of the project was focused on generating a GIS spatial database of the vegetation found within each campsite that was collected during a Rapid Vegetation Assessment (RVA) Survey.

Click here for a Poster showing Spatial database forest stands in Kejimkujik National Park and Historic Site.

## Spatial Database Modeling of forest stands in Kejimkujik National Park

Here is a poster generated with ESRI ArcGIS for a summer GIS project that I worked on for Parks Canada. [The PDF technical report details the methodologies and issues that were encountered with a Spatial GIS vegetation database and GIS Spatial modeling project at the Applied Geomatics Research Group (AGRG) during the summer of 2004 that involved generating a spatial geographic database for Jeremy’s Bay Campground of Kejimkujik National Park and Historic Site. High resolution aerial photography acquired from a previous AGRG (COGS) aerial photography mission was used along with extensive data collected during a Rapid Vegetation Assessment survey and a detailed forest stand interpretation.]

## Digital Terrain Modeling – Shaded Relief Models

A shaded relief model uses different color shades according to the varying levels of elevation and azimuth to create an enhanced simulated terrain. The shading is done with the assumption of a defined light source at a fixed location, shone across the surface. The user-specified light source will then determine the positions of shadows and highlighted slopes making ones facing light source appear bright and those facing away appear dark. By default shaded relief models are created with a grey scale ramp that represent the surface reflectance from the light source at any altitude and any azimuth however adding color to it can add an extra chromo stereoscopic component to it.
Assuming that a straight line is drawn connecting the user defined point source to the top left pixel of the image, the azimuth angle is the aspect of this line in degrees clockwise from north; the elevation angle is the elevation of the line in degrees from the horizontal.

The shaded grey level for each cell is the result of a calculation from the cosine of the angle between the normal vector to the surface (i.e. slope andaspect) and the direction of illumination. All surfaces not illuminated by the light source such as a slope of 90 degrees will be set to 0. An elevation exaggeration is sometimes added to help enhance the features of a fairly homogeneous surface.

In the example shown to the right, a raster aspect map of Lismore, Nova Scotia was derived from a digital elevation model (DEM) calculated with an azimuth angle of 315 degrees and an elevation angle of 45 degrees.