Analytical/Cost-Estimation Approach

A second approach is to decompose the subway system into major systems (e.g., track, communication systems, power systems, etc.) and estimate the percent damage to the different systems as a result of inundation. This approach is similar to the approach developed in the FLAIR report (N’Jai et al. 1990) and others to develop synthetic depth damage curves. If the linear cost of these systems (cost per kilometer as constructed) is known, the appropriate percentages can be multiplied by replacement cost to yield a total damage per length.

In Neukirchen (1994), the damage estimation makes the assumption that the damages could be estimated using a range of 10% of the construction costs and 15-20% of the electrical costs. According to (Laver and Schneck 1996), as-built costs for for subway systems in the US are as follows:

Table 4.3: Reported Costs of Subway Components (M$) from Laver and Schneck (1996)

Component Median Average Stdev Range

Systems* 1.9 2.4 1.2 1.4 - 5.4

* Systems represent primarily electrical and electronic components

Assuming that stations are located at intervals of approximately 1 km, the total cost of at grade systems average 9M$ per km and range from 8-42 M$ per km, whereas the average total cost of subway systems are 48 M$ per km and range from 25-120 M$ per km. Electrical systems comprise approximately 38% of the total systems and guideway cost for at grade systems but only 9% for subway systems (presumably reflecting the larger component due to excavation costs). Presuming that these ratios can also be used to characterize the ratio of electrical installation/total installation costs of stations, we find that the electrical components are approximately 2.4M$ for subway systems vs 3.1 M$ for at grade systems). One would, a priori, expect these to be similar. By way of comparison, it appears that the Vienna metro is rather expensive. The overall estimated construction cost was given as ranging from 44-145 M€ per km with the estimated construction cost of the U4 between Ober St. Veit and Kettenbruckengasse (roughly speaking, an at-grade system) given as 58 M€ per km⁷. This is above the range reported by Laver and Schneck (1996) for the United States. The reason could be due to inappropriate exchange rates and also to the lack of inclusion of soft-costs and special costs, such as land acquisition, utility relocations, and various engineering design and

7 The rates were originally given in schillings, which were pegged at at 13.7603 öS per euro in 1999.

Because the euro did not exist in 1993, when these estimates were provided, the cost is converted at the official rate adopted when the euro was adopted. The range was given as 600 million to 2 billion schillings per km, with the cost on the U4 between Ober St. Veit and Kettenbruckengasse as 800 M€ per km.

management costs. In addition, labor and tax costs may also vary significantly between Austria and the US.

If we assume that the electrical components comprise approximately 40% of the cost of at-grade systems, and that the damages to electrical systems are approximately 15-20%

of construction costs and damages to constructions are approximately 10% of construction costs, then we obtain a damaged fraction ranging from 11-14% of construction costs for at grade systems and 10-11% for subway systems. Using these ranges, and applying these values to the ranges reported above in Laver and Schneck (1996) for at grade systems, we obtain a range of 0.9-6 M$ per km. Application to subway systems yields 2.8-17 M$ per km. One can perform a similar exercise for costs associated with the Vienna metro.

Table 4.4: Ranges of Damage per Kilometer flooded, Method 2

Damage Percent Total Costs

The data from the empirical studies suggests that the values for alpha could range from 3-20 M€ per km of track flooded, with a most likely value around 5. The results from the engineering estimation yield estimates between 1 and 16, with a most likely value between 5 and 12. Considering the manifold uncertainties, we consider this to be relatively good agreement given that these estimations were developed using independent methods.

In light of these examinations, we have defined the values of alpha and beta according to Table 4.5. It is felt that these represent a reasonable estimate of the uncertainty in the potential damage, as the range is supported by two independent lines of evidence.

Subjectively, it is believed that the use of these values will result in slightly conservative (high) estimates of the damage. The data drawn from case studies may be subject to selection bias (i.e., episodes resulting in extensive damage tend to result in more news coverage than episodes resulting in minimal damage). The analytical estimates may be biased by the potentially high as-built costs of the Vienna subway.

However, this conservatism is not expected to be a major factor and is judged to be well within the bounds of the intervals given. Furthermore, sensitivity studies can be performed to examine the impact of this possible conservatism.

Table 4.5: Adopted values for alpha and beta for use in Equation 4.4

Parameter Value from [21] Value in this study Damage per length of track flooded (α) 7 U(1,20) Damage Multiplier (β) 1* 1-exp(-λQ)

*Implicit: damages were defined at 63 m³/s.

The basic damage equation is therefore largely a function of two stochastic variables, alpha and Q. The distribution of alpha, which has a simple distributional form, was the subject of Chapter 4. The distribution of Q was based upon the hydraulic simulation model, as discussed previously. This is a non standard distribution, thereby suggesting the use of numerical techniques. The way in which this equation is implemented comprises the subject of the next chapter.