*2.4. Quantifying Impacts from Tra*ffi*c Model*

The impacts of flooding on traffic flows can be quantified in a number of ways including but not limited to, lost time, fuel consumption and pollution levels. Based on the Multi-Coloured Manual (MCM) [24], we estimated the costs accrued to a vehicle (in GBP) over time and distance in relation to its speed. Table 6 shows a breakdown of costs in pence per unit of speed for five vehicle classes.



For simplicity in our analysis, we assumed all the vehicles to be of generic petrol driven cars. Figure 11 shows the derived relationship between the estimated costs incurred per car per hour in relation to its speed whereby the line of best fit is described by the function in Equation (3).

$$\text{Cost} = 9.6275 \times \text{Speed}^{-0.925} \tag{3}$$

For the TransCAD® model the accumulated costs were derived from analysing the model outputs at a link level where the total accumulated cost is derived using Equation (4).

$$Total\ Cost = \sum\_{\text{Links}} \left(Traffic\ Volume\_{\text{Link}} \times Length\_{\text{Link}} \times SFn\_{\text{Link}}\right) \tag{4}$$

where

*Tra*ffi*c VolumeLink* = Number of Vehicles per km per hour per link. *LengthLink* = Length of link in km. *SFnLink* = Calculated cost value with respect to average speed derived via Equation (3).

An estimate of monetary impacts of a flood event with respect to changes in vehicular speed is thus derived via comparing the costs under flooded conditions to the costs under dry weather conditions (Equation (5)).

$$\text{Monetary Impact} = \text{Costs}\_{\text{Followed}\\_\text{Conditions}} - \text{Costs}\_{\text{Dry}\\_\text{Conditions}} \tag{5}$$

As the Barcelona model has no temporal information applied to traffic flows, the associated costs were derived with respect to incurred costs per hour of disruption. For the Bristol case study, as we adopted a micro-scale traffic model with a temporal component, the incurred costs were assessed during the period of time the network was deemed to be impacted.

**Figure 11.** Derived Cost to Speed relationship Cars based on MCM data.

For the Bristol model, data at the link level were also exported but in contrast to the Barcelona model, these outputs vary over time, therefore, Equations (3)–(5) were applied accordingly during the identified period of traffic disruption.
