Have you recently used RARS Table 9.3, or simply omitted transport system users in your PAR calculations? It turns out that you might have underestimated the exposed population at risk.
Ever since the Interim Guide was published in 2004, dam engineers undertaking failure inundation mapping typically tend to calculate the Population At Risk adopting the approach that has been included in the Risk Assessment for Reservoir Safety Management (RARS) Tier 2 methodology. This uses a combination of the number of vehicles a day, the occupancy rate of those vehicles, and the average speed to, broadly speaking, determine a notional PAR per distance of network. Table 9.3 of this document is often referenced in order to determine the population at risk on transport networks. It includes 4 types of network: A Road, Country Lane, Footpath, and Railway.
I would like to stress that, at the time of first publication, Table 9.3 (which was first included in the Interim Guide and its supplementary publications) was the best guidance available. It is only in recent years that adoption of this table has been questionably inappropriate due to advances in simulation techniques and improved data availability.
The underlying data supporting this table has not been updated in a number of years. And furthermore because of the populations assessed for each of these transport networks (i.e. 'A Road' only considers cars) the full PAR value hasn't been calculated. Truth be told, I know of a number of consultants who have, in recent years, dropped assessing transport networks altogether. When asking why they did this, usually the answer that comes back is 'it never seems to make much of a difference'.
As I was embarking on a recent dam failure simulation project, this approach bothered me. 'It never seems to make a difference'. Does this honestly stand up to any form of rigorous scrutiny? I personally doubt it. This is like saying 'we chose not to adopt a method because it gives negligible results' rather than saying 'hmm. This method seems to give very low numbers which might not be realistic, I wonder whether I should investigate further'.
The real reason why I started to question this was because, behind the scenes, I've been developing a coupled, stochastic damage and life loss model for inundation zones (further publications in due course) - and it needs a realistic disaggregated set of PAR values. I noticed on reviewing many shocking survivor videos from a number of tsunamis that, unless a shelter fails, it really is predominantly the exposed populations (i.e. pedestrians, cyclists, car and other vehicle occupants) who are the most at risk from sudden hydraulic loading. To simply adopt a PAR(transport) of 0 doesn't make sense, and it is not what is observed in storm surges, tsunamis, and other very intense flooding events. Further to this survivor videos are often taken from the safety of a rooftop or elevated position (i.e. sheltering populations), and normally the footage focuses on pedestrians or vehicles fleeing the active inundation zone (i.e. exposed populations). You do not need to search websites like YouTube for long to see this demonstrated.
So, with some justification to challenge Table 9.3 in RARS, I considered producing an update. Rather than focus on an arbitrary 500 m inundation zone (as is done in said table), I instead focused on developing generalised PAR values, in the units of people per kilometre. Quickly I discovered a huge wealth of statistical data that is freely available from the Department for Transport. Not only does it give regional and national survey values for annualised average daily flow (AADF) disaggregated by transport mode, but it also has documentation covering average speeds for different classes of vehicles. This is perfect, and off the back of this I very quickly determined the PAR/km for various road classifications on a national level using the following equation
Where PAR(R,C) is the PAR per km for road class R and vehicle class C, n is the annual average daily flow (vehicles per day), o is the average occupancy of the vehicle (people per vehicle) and v is the velocity (m/s). Using the Department for Transport values, you can work this out for each road class, and for different classes of powered vehicles.
It will not, however, tell you how to determine the number of pedestrians on a roadway. This is a much more complicated task, and whilst I give a summary of how I did this in my recent paper 'Calculating the population at risk for transport system users' (Dams and Reservoirs, due for inclusion in Volume 27 Issue 2), it is a method which does not produce values which are easily summarised into a PAR(R,C) format. Whilst I give some notional values, I also detail the method I used to get baseline numbers for various urban and rural areas (I used an area of Yorkshire as a sample since it have a good variety of urban and rural spaces). Generally I found that, as you might expect, pedestrians are more commonly encountered in urban spaces.
This is a different approach, and it uses census data and some assumptions about how (or more specifically, where) walks start and end. If this is something that interests you, I suggest looking into the paper. It allowed me to produce a map like this (for Leeds/Bradford and York):
So what was the major finding? It turns out the Table 9.3 has inadvertently (and through republishing without updates) given values which, in some cases, might be an order of magnitude too small. The paper presents a new table, which brings Table 9.3 back in line with calculated values, but it also includes a more detailed disaggregated (by vehicle class and road type) table for anyone doing more detailed inundation mapping. Additionally, if you are working in a specific region, you can follow the documented method to calculate bespoke PAR values.
The use of Table 9.3 is an example of one of a few bits of guidance that, during initial production, was conceived under the notion that they would be updated once better information became available. Just like Figure 9.1 (fatality rates from RARS) which I am also currently updating, it has instead been adopted as 'the last word' or 'guidance', even though it was never intended for use in extremely detailed studies and is based on little or no validation data. Furthermore, neither of these were designed with point application in mind (2D modelling was not regularly undertaken for inundation models in the late 1990s and early 2000s) - so applying them without at least questioning them would be inappropriate at best, and non-conservative at worst (bear in mind the usual applications for this type of study).
So the next time you find yourself saying 'I can leave this out because it never makes a difference', I urge you to question that way of thinking - and to challenge the source data and assumptions that led you there in the first place.