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The core of the accessibility model is a cost surface (also called a friction surface) for the region being studied. This is a raster map of the whole region in which the values in the raster cells are equal to the time it takes to cross directly through that cell. If the cell represents part of a fast road, the time will be very short. If it represents steep open land, it may be very large. (If there are barriers in the model, these can be represented by cells with values several magnitudes larger than even the highest non-barrier cells or, in some GIS, they can be defined as barriers to the travel time calculations.) Once the cost surface is created, it can be used for any number of travel time scenarios by defining the location of target features on the surface, and then calculating the cumulative least travel time to the nearest target from every cell on the map. This is process is described under Creating an Accessibility Map below.
In this case study only roads and slope are used as data inputs to the cost surface to keep the process simple and clear. In a real study, barriers to travel such as lakes and borders should be included and some experimental work done to determine genuine travel speeds for people in the study area.
Creating the road and land travel time map
The vector road map from CIAT defines 3 classes of road, (figure 4) major roads, minor roads and tracks.
The road network is clearly very unevenly distributed, which will have significant influence on the general accessibility of different locations. What speed can people travel over a road? Deciding this is very subjective and variable. Someone with a private car can travel rapidly over a metalled highway. Someone walking will not travel at significantly different speeds on any type of road. Someone relying on a bus service will be dependent on bus timetables, reliability and their ability to pay the fare. The speed will also be influenced by the steepness of the road, its straightness and even the prevailing weather. This is an area where values can be varied within to see how sensitive the model is to different speeds.
For this case study the following speeds are assumed, but without any experimental justification.
Experimenting with walking, draught animal, cycling and vehicular speeds can give an indication of the accessibility to services for different affluence levels in the local society. It should be possible to create travel cost surfaces for poor people and affluent people, and these may be very different.
Note that a single speed is used for travelling over non-road surfaces, i.e. all of the spaces between the roads. The model could be further refined by using a landcover map and assigning different speeds for travelling through each type of cover, but this is probably assigning too much detail to the model to be realistic.
The road map is now converted to a raster with a specified cell size. In this case study, cell size is 1km x 1km. The cells are reclassified to show the time to travel across each in minutes (figure 5.)
This basic cost surface assumes that there are no other impediments to travel. To better reflect reality it needs to be modified to allow for the effect of slope on speed of travel.
A slope map at the same resolution as the land travel time map needs to be created. This can be done from a digital elevation model (DEM) or elevation point data set. It is still important not to be too precise and detailed as the model cannot justify this. For this case study, a slope map was derived from a DEM and classified into three categories of slope:
The assumption is then made that below 5%, slope has no influence, between 5 and 10% it doubles travel time and over 10% it increase travel time fivefold. Again, it is worth experimenting with different values to see how sensitive a particular landscape is to these factors. In this case study, very little land is steeper than 10% (figure 6)
The final surface is created by use of simple map algebra. This may be implemented in different ways with different GIS. Put simply, a new raster map is generated in which the value of each cell is the product of the equivalent cells on the land travel time map and the slope factor map. Thus, if the travel time in a cell is 12 minutes and the slope factor is 2, the total travel time will be 24 minutes across that cell. The range of cell travel times will be from 1 (fast road, level ground) to 60 (no road, over 10% slope) (figure 7)
