Cost Surface

A cost surface can be thought of as a map of the costs of movement from one location to one or more destinations. Cost surfaces are usually generated as the first step in computing least-cost paths between locations. Although cost surfaces are typically represented in raster format, vector-based cost surfaces can be created, though these are more complex and difficult to compute than raster-based models. This entry focuses on cost surfaces represented as rasters. Cost surface maps are also known as cost-of-passage maps, accumulated cost surface maps, and friction surfaces or friction maps.

To create a cost surface within a GIS, it is necessary to consider the following: the mode of transport or movement, the currency used to calculate costs of movement, attributes of the landscape affecting cost of movement, the formulae used to calculate the actual cost of movement, and, finally, the application of the formula to create the cost surface.

The mode of transport is simply the way in which the landscape is traversed. Walking, either on- or off path, as well as vehicular transport, are the most common modes modeled. Note that movement per se is not a strict requirement of cost surface modeling. For instance, a cost surface based upon the projected monetary cost of building a road through different terrain types may be created.

The selection of a cost currency depends on the mode of transport and the problem under study. Most cost surface models are based upon some kind of functional currency, such as energy expenditure or elapsed time between locations for walking, and fuel expenditure, money, or elapsed time, for instance, in a vehicle. Conceptually, nonfunctional currencies, such as attraction to or avoidance of culturally important places, can also be modeled, although in practice these types of currencies are more difficult to implement in a GIS framework.

In cost surface modeling, landscape attributes affecting cost of movement typically include land cover and terrain, water features, possible barriers to travel, and path or road networks. There are two fundamental ways of conceptualizing the costs of movement through a landscape: isotropic and anisotropic costs. Isotropic costs are those that are independent of the direction traveled. Considering land cover, for instance, the costs of traveling through sandy terrain are the same if one enters the raster cell from the north or from the south. Anisotropic costs, however, are those in which both the nature of the landscape and the direction or travel are important. The costs of moving across the landscape in mountainous terrain, for instance, will be different if the raster cell is entered to go upslope as opposed to downslope.

For isotropic cost surfaces, commonly used determinates of cost are surface roughness and land cover. Each cell in a raster is typically assigned a base cost of movement, and then these costs are modified to account for terrain differences. Flat, hard, and smooth surfaces have lower costs than do, for example, loose, sandy soils or mud. Barriers to movement can be modeled by substantially increasing the cost. Crossing wide rivers will incur large costs relative to flat terrain, and absolute barriers can be modeled by increasing costs by orders of magnitude. Conversely, paths or roads can be given lower costs of movement to facilitate their inclusion in the model. It is important to remember, however, that there is little empirical justification for assigning a particular cost to a specific terrain feature, and thus care must be taken in the modeling effort to ensure that cost calculations are reasonable.

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