How to use empirical data to improve transportation infrastructure 1 risk assessment 2

11 Rainfall-induced hazards, such as landslides, debris flows, and floods cause significant 12 damage to transportation infrastructure. However, an accurate assessment of rainfall-induced 13 hazard risk to transportation infrastructure is limited by the lack of regional and asset-tailored 14 vulnerability curves. This study aims to use multi-source empirical damage data to generate 15 vulnerability curves and assess the risk of transportation infrastructure to rainfall-induced 16 hazards. The methodology is exemplified through a case study for the Chinese national railway 17 infrastructure. In doing so, regional and national-level vulnerability curves are derived based 18 on historical railway damage records. This is combined with daily precipitation data and the 19 railway infrastructure market value to estimate regionaland national-level risk. The results 20 show large variations in the shape of the vulnerability curves across the different regions. The 21 railway infrastructure in Northeast and Northwest China is more vulnerable to rainfall-induced 22 hazards due to low protection standards. The expected annual damage (EAD) ranges from 1.88 23 https://doi.org/10.5194/nhess-2021-277 Preprint. Discussion started: 19 October 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
For the available 236 railway damage records, 84% occurred in the summer (June, July, and 4 August). Most of the disasters occurred in July, accounting for 40% of the 236 railway damage 5 records; 30% and 14% occurred in June and August, respectively. These numbers correspond 6 to most parts of China's rainy seasons in which precipitation is a crucial trigger of rainfall-7 induced hazards.  They provide the range of average unit costs for the 200 km/h double-track railway (AUC-land acquisition and resettlement, and four first-level structures: (2) civil works (embankment, 1 bridge or trunk), (3) track, (4) signalling, and (5) communications and electrifications. We use 2 the mean value to present the unit cost of the element (e.g. the mean value is 6 million/per km 3 of track element). The average railway market value used in this work is 56 million RMB, 4 which does not consider land acquisition and resettlement costs since those parts were paid 5 before construction. 6

Methods
8 Figure 3 presents an overview of the methodological framework used in this study. The 9 methods in this study are divided into two parts: (1) vulnerability assessment and (2) risk 10 estimation. In the first part, national and regional vulnerability curves that characterize the 11 railway susceptibility by relating the damage degree to precipitation intensity are generated. In 12 the second part of the research, we estimate the risk to the Chinese railway system. The railway 1 market value is combined with the vulnerability curve developed in the first part of the research 2 and spatial data on the precipitation intensity to calculate the risk represented by expected 3 annual damage (EAD).   10 The 88 damage records that are provided with additional local precipitation information from 11 the news are shown in Fig. 4a with red lines. For each remaining damage record, we use the 12 maximum 1-day precipitation amount along the damaged segment in the five consecutive days 13 (M1-5d) before the damage occurred to present the precipitation intensity, shown in Fig. 4a  14 with black lines. To keep the consistency of the precipitation, we use the extracted precipitation 1 information from the news to correct the M1-5d. The relationship between precipitation from 2 news and M1-5d is given in Eq. (1) and derived using a least-squares fitting method, as 3 presented in Fig  respectively. For bridges and tunnels, the total cost ratios are shown in Appendix Table  5 A2.  Table 4. 11

Precipitation intensity estimated for damage records
3. Calculate the numerical damage ratio range for a combination of a railway structure 12 and a damaged state, and determine associated damage descriptive information based 13 on news sources for each combination. The final damage ratio table is presented in 14  1 We choose the log-normal distribution to fit the vulnerability curve. The cumulative 2 distribution function of log-normal distribution is shown in Eq. 2, 3

Fitting the vulnerability curves
(2) 4 which has two parameters, the location parameter φ and the scale parameter , namely, the 5 median and standard values, respectively (Porter et al., 2007). We use the precipitation intensity 6 as the value and the damage ratio as the ( ) value. A log-normal vulnerability function is 7 chosen because it is a parsimonious two-parameter distribution with positive support (ensuring 8 that unrealistic negative loads cannot occur) and has many precedents for its use in fragility 9 analysis (Porter et al., 2007). 10 In this study, we generate a total of seven vulnerability curves for the railway system: one 11 for each of the six sub-regions (we combine North China into Central China since the damage 12 records are less in North China), and one at the national level. To eliminate the noise and 13 significant changes in the damage ratio, a moving average method is used to smooth the damage 14 ratio in each precipitation intensity range. We use the criteria for classifying the precipitation 15 intensity issued by the China Meteorological Administrator (2008), which is presented in Table  16 https://doi.org/10.5194/nhess-2021-277 Preprint. Discussion started: 19 October 2021 c Author(s) 2021. CC BY 4.0 License. 5, to apply the moving average method. 1 Table 5 Classification of the precipitation intensity 2

Risk assessment
is the ℎ return period, is associated with damage to the railway 9 infrastructure, which is defined in Eqs. (4)  where is the precipitation intensity amount of raster cell with a return period of 13 T-year, is the vulnerability curve, is the railway market value of raster cell , is the 14 number of raster cells that intersect the railway line, and DL is a damage length factor for 15 calibration. In Eq. 5, is the average damage length (753 m) per damage place in an event, 16 and is the average railway length for all raster cells that intersect with railway lines. This 17 study and previous studies assume that assets exposed in one raster cell are exposed to the same 18 damage degree for a certain hazard intensity. Based on the yearly railway damage data (sec 2.3), 19 the average damage length in one damage place per event is 753 m. This is much shorter 20 compared to the precipitation resolution (ca. 28 km) used in this work and is also shorter than 21 the average railway length in each cell (ca. 14.6 km for double-track lines). We, therefore,  The national-and regional-level vulnerability curves are presented in Fig. 5. The upper 5 boundary is the maximum vulnerability curve, the lower boundary is the minimum vulnerability 6 curve, and the middle black line is the average vulnerability curve, fitted by maximum, 7 minimum, and average ratios, respectively. Vulnerability curves have noticeable regional 8 differences across the country. When considering relatively low precipitation intensities, 9 railway lines in Northwest China are vulnerable to rainfall-induced hazards. Damage ratios in 10 Northwest China are higher than other regional-and national-level damage ratios with the same 11 precipitation intensity. For example, when the precipitation is 100 mm (torrential rain), the 12 national railway damage ratio is 0.124, whereas the railway damage ratio in Northwest  ratio. The maximum 2 is the square for the maximum vulnerability curve, the average 6 2 is the square for the average vulnerability curve, the minimum 2 is the square for 7 the minimum vulnerability curve. 8 9 To incorporate the regional characteristics of the vulnerability for the Chinese railway system, 10 we use the regional vulnerability curves to assess the risk of the Chinese railway system. We China. 12

Risk analysis
The regional and national EAD to railway infrastructure due to rainfall-induced hazards are 13 presented in Fig. 7 using regional vulnerability curves. The national railway EAD is 14 The risk per province calculated using the regional average vulnerability curves of the 2 railway infrastructure to the rainfall-induced hazards are presented in Fig. 8 Sichuan, Shanxi and Guangdong provinces. From the provincial perspective, these two 12 provinces need to allocate more resources to reduce the risk of rainfall-induced hazards. spatiotemporal damage and hazard intensity information, regional and national vulnerability 12 curves to link hazard characteristics and exposures are rare in many regions. This work tries to 13 overcome the universal problem of the lack of detailed vulnerability data. The fitted 14 vulnerability curves are used as the descriptive damage state in the information on damage and 15 precipitation derived from the news and exited precipitation dataset; these data are more easily 16 collected. Combining the fitted vulnerability curve, precipitation product, and railway 17 infrastructure exposure, the estimated risk of the national railway infrastructure, after 18 calibration with a damage length factor, is approximately 3.91 billion RMB. The overall railway 19 infrastructure risk results are broadly correlated with the yearbook average direct economic 20 damage from 2000 to 2017, which is 3.29 billion RMB. The results reveal that vulnerability and risk can be estimated accurately using multi-source empirical data. 1 Several assumptions and limitations are acknowledged in this study. First, for damage 2 records without local precipitation information, we use the maximum daily precipitation 5 days 3 before damage occurrence (M1-5d) along the damaged segment to present the precipitation 4 intensity. However, there exists deviation for the local damage places along with the damaged 5 segments. In addition, the resolution of the CN05.1 precipitation data is too coarse to accurately 6 capture local extreme precipitation events. We hence use the extracted precipitation information 7 from the news to correct the M1-5d. In a certain way, it would decrease the uncertainty and 8 keep the consistency of the precipitation. Second, due to a lack of different railway market 9 values and detailed information on each railway infrastructure, this work uses the railway 10 market value for 200 km/h railways of double tracks as the value for all types of railway 11 infrastructure. This leads to an overestimation of risk because most conventional railway speeds 12 are lower than 200 km/h, and the relative price has a high probability of being lower than 56 13 million RMB. Post-disaster reconstruction using higher design standards to improve railways ' 14 ability to defend against disasters can reduce the risk for future hazards. 15 From approximate and common news information to national datasets (e.g. railway damage 16 data), the method used in this work can be a new direction to assess vulnerability and risk by 17 combining multiple sources of empirical data. In addition, the low resolution of the 18

1
In this study, we use multi-source empirical data to assess the vulnerability and risk to railway 2 infrastructure in China associated with rainfall-induced hazards. Regional-and national-level 3 precipitation vulnerability curves are derived based on news information and a custom damage 4 ratio table. Based on precipitation data, fitted vulnerability curves, the market value of railway 5 infrastructure, and a damage length factor, we assess and calibrate the annual direct damage 6 from 2000 to 2017 caused by rainfall-induced hazards to Chinese railway infrastructure. 7 Due to the spatial unevenness of protection standards, the regional vulnerability curves of 8 railway infrastructure to rainfall-induced hazards show high spatial inconsistency. Railways in 9 South, Southwest, North, East, and Central China are robust to rainfall-induced hazards since 10 higher protection standards have been used to defend the heaviest rainfall. Railways in 11 Northwest and Northwest China are relatively vulnerable to rainfall-induced hazards. In 12 addition, the regional curves generated in this study can be applied in other works after 13 adjusting the length factor based on the methodology illustrated in sec 3.2. 14 The national railway infrastructure risk is approximately 3.91 billion RMB, and we find that 15 the estimated annual direct damage of railway infrastructure to rainfall-induced hazards 16 increases due to increasing extreme precipitation and railway exposure. Due to the spatially 17 uneven precipitation intensity, exposure distribution and vulnerability curves, the risk in China 18 show high spatial differences. The heaviest rainfall and high exposure density lead to a high 19 absolute risk to railway infrastructure in South, East and Southwest China, even though they 20 are robust to rainfall-induced hazards. Provinces such as Sichuan and Guangdong have high 21 absolute and relative risks. For railway infrastructure risk reduction and sustainable 1 development of railway transportation in China, more attention and high protection standards 2 need to be allocated to these high-risk areas. This work provides regional and national 3 vulnerability and risk information for decision-makers. 4 Code/Data availability 5 Supporting data are accessible through the associated reference, and the historical railway 6 damage data used is in supplement material. The data in this study were analysed with Python 7 package, and the figures were created with ArcViewTM GIS and Python packages. All codes 8 used in this work are available upon request. 9 Declaration of Competing Interest 16 The authors declare that they have no known competing financial interests or personal 17 relationships that could have appeared to influence the work reported in this paper.