Road Density as a Proxy for Population Density

Landslide susceptibility, hazard and risk assessment are particular interests of mine. Risk, in the jargon of formal risk assessment, is a combination of hazard and consequence, where the hazard is a measure of the probability of some potentially damaging event occurring, and consequence is a measure of the severity of impact, given the hazard affects some element at risk, or potentially affected receptor.

When we think of consequence, we can speak of dollar cost, or we might try to quantify it in terms of loss of life.

In order to determine the potential for loss of life, it is necessary to understand the probable spatial and temporal location(s) of people. This can be modelled in many different ways, but when attempting to do this on a small scale (meaning large area, so regional scale, or national scale), one can work with population density within some sort of spatial model (e.g. in a geographic information system, or GIS).

Population density data are not very easy to obtain, particularly on a larger scale (i.e. zoomed in closer, smaller area). Nearly two years ago, after a landslide in Quebec killed a family in their basement watching the NHL playoffs, I did a bit of work to try to compare road density with population density, to see if I could convert an existing landslide susceptibility map into something closer to a landslide risk map. The landslide susceptibility map follows:

From that map, one can estimate the (very low) likelihood of a large landslide occurring in different parts of the study area, which i much higher in selected areas than most of the map.

The risk to human life is a function of presence of residents. Available population density data at the time were quite coarse, as shown here:

That degree of resolution in population density is not very useful, as one of the largest subdivisions in the centre of that map is a major urban centre, with much higher density in its core, for example, than in its outer suburbs or industrial lands, but the whole block is averaged over a very large area.

The next map shows roads within that area, and you can imagine a higher density in areas with more roads:

At the time I felt it might be possible to come up with a better model for population density by making inferences from road density. The following two images show population density inferred from available county population data, followed by that inferred from a best fit comparison between county population density and county road density, to estimate population density locally from the presence of roads:

The latter image gives an approximation of population density that is a much better fit to intuition, looking very much like a satellite image at night, where population density could be inferred from light intensity.

From the latter interpretation, I made a comparison with landslide susceptibility to come up with a VERY PRELIMINARY landslide risk map for the region, as follows:

I’ve been wanting to take this further to put it onto a firm analytical footing, but until now didn’t have data to support the investigation. This year Statistics Canada has released all their 2006 Canadian census data for free. My firm has also obtained high quality topographic data from a Caribbean island and permission to use it for research. Therefore I am working on trying to establish defensible relationships between road density and population density. Here is a first result:

This graph shows population density versus road density for data drawn from two different sets of spatial boundaries: Census Tracts in Quebec (these are smaller subdivisions within larger metropolitan areas) and Census Subdivisions in Ontario (these are larger areas, and some of them include Census Tracts within their boundaries, for example Montreal and Ottawa each contain dozens of Census Tracts within their Census Subdivisions).

One can see that while there is considerable scatter, particularly as road density increases, there is a strong trend. Further, one can take a fairly confident “probable lower bound” from the data, and expect that given a certain road density, the population density is very likely to be AT LEAST some predicted value.

The following graph shows the data in a log-log plot with some sense of the variability, namely the “best fit” relationship, and then 1 standard deviation above and below the best fit:

This is just the first push on this topic. More to follow… πŸ™‚


About petequinn

I'm a Canadian geotechnical engineer specializing in the study of landslides. I started this page to discuss some mathematical topics that interest me, initially this involved mostly prime numbers, but more recently I've diverted focus back to a number of topics of interest in geotechnique, geographic information systems and risk. I completed undergraduate training in engineering physics at Royal Military College (Kingston, Ontario), did a masters degree in civil (geotechnical) engineering at University of British Columbia (Vancouver), and doctorate in geological engineering at Queen's University (Kingston). I was a military engineer for several years at the beginning of my career, and did design and construction work across Canada and abroad. I've worked a few years for the federal government managing large environmental clean up projects in Canada's arctic, and I've worked across Canada, on both coasts and in the middle, as a consulting geotechnical engineer. My work has taken me everywhere in Canada's north, to most major Canadian cities and many small Canadian towns, and to Alaska, Chile, Bermuda, the Caribbean, Germany, Norway, Sweden, Bosnia, and Croatia. My main "hobby" is competitive distance running, which I may write about in future.
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