# An Integrated Wind Risk Warning Model for Urban Rail Transport in Shanghai, China

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## Abstract

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## 1. Introduction

^{−1}(at 10 m) on 28 February 2007 in Xinjiang (China), 11 train carriages derailed, causing three deaths [13]. Studies of aerodynamic effects have largely used wind tunnel observations [14,15,16] and computational fluid dynamics (CFD) modelling [17,18]. Examples include: A scale model of a high speed passenger train at zero yaw in a wind tunnel was used to study the dependence of train skin friction drag and total aerodynamic drag on Reynolds number [14]; wind tunnel tests consider three types of rail vehicles in different configurations to identify the most critical wind conditions for running safety and the principal parameters influencing aerodynamic behavior [16]; and the stability, aerodynamic performance of a train, and the surrounding flow field in detail with numerical simulation [17]. Research on strong winds [19,20,21] and the effects of wind load on rail vehicle performance [22] have expanded considerably in the last decade, but much less attention has been given to the development of integrated systems of monitoring, forecasting, warning, and decision-making.

## 2. Meteorological Background

## 3. Methodology

- Background wind determined from numerical weather prediction (NWP) or observations (used here) to create a high-resolution wind field.
- Vulnerability model to calculate the influence of the wind load on rail carriages.
- Risk model to develop a warning.

#### 3.1. Wind Field

_{0_local}) and zero plane displacement (z

_{d_local}) influence the wind load on a rail vehicle. To calculate these the mean roughness, the element height (H

_{av}) is obtained from the ASTER (advanced space borne thermal emission and reflection radiometer) global digital elevation model (GDEM V1, resolution = 30 m) [26]. The “rule of thumb” morphometric method [27,28,29,30]:

_{0}= 0.2 and ƒ

_{d}=1.4. Rougher surfaces decrease the velocity (U) near the ground, as expressed in the logarithmic wind profile assuming neutral stability [32]:

_{*}is the friction velocity, k = 0.4 is von Karman’s constant, and z is the height above ground level (agl). Thus, given background wind data and the roughness parameters for the fetch over which the wind has blown as it approached the rail carriage, a local wind velocity can be estimated for any heights for which the log-law (Equation (3)) is applicable [31].

^{2}based on SRTM3 (Shuttle Radar Topography Mission) data (90 m resolution) [33]) and 2009 (30.09 km

^{2}based on ASTER GDEM V1) means the surroundings of many AWS have changed. As these are not ‘traditional’ WMO sites [34] (e.g., influenced by a tall building in one direction and/or by trees in another), measurements may be unrepresentative of the regional, or background, wind field. Accounting for variations by direction may lead to more appropriate wind interpolation. To reduce the probability of physically unreasonable spatial inhomogeneity being generated during the interpolation, 10 m wind speeds (U

_{10}) were logarithmically raised to 300 m (U

_{300}):

_{0_eff,300}is the effective roughness length for winds at 300 m and z

_{d,300}is the zero-plane displacement for winds at 300 m (Figure 4). These data are spatially interpolated using inverse weighting [35] and then logarithmically reduced to 70 m (U

_{70}):

_{car}):

_{0_eff,70}is the effective roughness length for winds at 70 m, and z

_{d,70}is the zero-plane displacement for winds at 70 m (Figure 4). The effective surface roughness length at a blending height, z

_{r}, is determined from [36]:

_{d_mean}(z

_{r}) is the mean value of drag coefficients, C

_{d}(z

_{r}), obtained by averaging the drag coefficient of an area:

_{r}is a reference height (i.e., 70, 300 m) to allow calculations for winds at 70 m (effective roughness length, z

_{0_eff,70}) and 300 m (z

_{0_eff,300}). Linear spatial averages are calculated for a height-fetch ratio of 1:50, i.e., 3480 and 15000 m squares (Figure 4), respectively, given the 30 m resolution.

_{0_eff,70}was calculated for 16 sectors (i.e., 22.5°, 1740 m extent) around each of the 119 AWS in Shanghai (Figure 5). The background wind field is interpolated from selected AWS across the whole area using the individual sectors for each AWS with z

_{0_eff,70}≤ 0.3 m. In the suburbs (beyond the pink area, Figure 4a), most stations meet the requirement in all 16 sectors; whereas within the urban area (pink, Figure 4a), frequently only a few sectors are usable (Figure 5). When the wind is from the north, 63 stations are used to interpolate the background wind field across the Shanghai province; whereas from the east 70, south 61, and west only 57 stations are used. The wind is interpolated every 10 min to provide a 30-m resolution gridded data set. Using the log-law with both the local and effective aerodynamic parameters, the wind speed is determined along the Metro line at z

_{car}(train track ground level + centre height H

_{c}of the vehicle). If this height is lower than where the log-law is applicable, then the within canopy exponential decrease [37] is applied.

#### 3.2. Vulnerability Model

#### 3.2.1. Wind load Modeling

_{T}) but are mirror images of each other. This enables the train to be driven in both directions. The front of each has an oblique angle of 25°, whereas the end that attaches to the M carriage is vertical (Figure 6). The M carriage has two vertical sides and length L

_{M}. The complete train is characterized by its length (L = 2L

_{T}+ L

_{M}), width (W), height (H), and the carriage bottom to the rail track surface (H

_{b}) distance (Figure 6).

_{0}= 0.2 m). For the rear planes, the pressure outlet condition is set to a gauge value. For the train surface planes, the standard wall function is used to permit separated flow around a bluff body while the ground plane is a user defined fixed wall function to ensure the accuracy of numerical simulation [39]. The other planes are considered as symmetrical.

_{relative}) and its yaw angle (β) relative to the vehicle travel direction. This is the resultant of the vehicle and wind velocity vectors. In this paper, β is defined as the angle of attack. Figure 6 shows the relation between the vehicle velocity, U

_{vehicle}, the wind velocity, U

_{wind}, the relative wind velocity, U

_{relative}, and their yaw angles, β

_{0}, β. However, in the CFD simulation, the train model is stationary, so U

_{relative}= U

_{wind}and thus β = β

_{0}. As the train is symmetric, only seven wind attack angles between 0° and 90° are simulated (interval = 15°).

_{pi}(= p

_{i}(0.5ρU

_{wind,Hc}

^{2})

^{−1}) is defined as the ratio of actual wind pressure to incoming flow pressure at a reference height (H

_{c}), where p

_{i}is wind pressure of point i, ρ is air density, and U

_{wind,Hc}is wind velocity at H

_{c}(i.e. the centre height of the vehicle used here).

#### 3.2.2. Effect of Angle of Attack

_{L}, lateral (or side) aerodynamic force, F

_{S}, and overturning moment force, F

_{M}, which can directly influence the lateral stability of rail vehicles (Figure 6). The three aerodynamic forces are associated with wind and vehicle velocities, which are changing all the time. For the convenience of wind load calculation, the nondimensionalized coefficients of the three forces are defined:

^{2}, middle [M] = 69.7 m

^{2}), ρ is the air density, and H is the height of the vehicle.

_{S}) and the overturning moment coefficients (C

_{M}) decrease from the front (T1) to the middle (M) to the back (T2) carriages. The largest C

_{S}and C

_{M}of the whole train are found between the T1 and M carriage. The aerodynamic lift force coefficient (C

_{L},) of the M vehicle is slightly larger than the others.

#### 3.2.3. Effect of Wind Direction, Wind Velocity, and Vehicle Velocity

^{−1}. A wind velocity of 18 m·s

^{−1}is used with the aerodynamic forces with respect to wind direction (Figure 9) obtained from Equations (9) to (12). This wind speed is chosen as the Shanghai Metro Operation Management Center sets a maximum vehicle velocity when the Beaufort Scale wind is eight (assumed here to be equivalent to 18 m·s

^{−1}).

_{L}), lateral aerodynamic force (F

_{S}), and overturning moment (F

_{M}) change in a similar manner with the wind direction. For the situation considered, all three aerodynamic forces have minimum values (0) at both 135° (southeast wind) and 315° (northwest wind), i.e., when the vehicle runs parallel to the wind direction and the wind angle of approach is 0°. However, the three aerodynamic forces maxima occur at different wind directions: For F

_{L}, at 56.25° and 213.75°; for F

_{S}, at 67.5° and 202.5°; and F

_{M}, at 78.75° and 191.25°. This analysis shows that wind direction has a considerable influence on the aerodynamic forces on rail vehicles. Thus, under conditions of known wind velocity and vehicle velocity, judgments can be made if the vehicle velocity should be reduced with respect to the prevailing wind direction. This approach has considerable potential to improve network operation efficiency.

_{L}, F

_{S}, and F

_{M}increase gradually with wind velocity, with increasing rates with greater wind velocities (Figure 10). With a wind velocity of 18 m·s

^{−1}, the three forces are 13.3 kN, 15.8 kN, and 16.9 kN·m, respectively. However, if the wind velocity is doubled (i.e., 36 m·s

^{−1}), the three forces more than double: Increases of 2.39 (45.1 kN), 2.25 (51.3 kN), and 2.15 (53.2 kN·m) times, respectively.

_{L}having the slowest rate. When the vehicle velocity is 40 km·h

^{−1}(80 km·h

^{−1}), the three forces are 13.3 (17.0) kN, 15.8 (22.1) kN, and 16.9 (24.3) kN·m, respectively. Thus, if the vehicle velocity is doubled, the aerodynamic forces increase by 0.28, 0.40, and 0.44 times, respectively. As the vehicle aerodynamic forces are more sensitive to wind velocity than vehicle velocity, when wind velocity doubles, the vehicle velocity needs to be reduced by a greater factor to ensure stability.

#### 3.3. Risk Model

_{S}, F

_{L}, and F

_{M}are the lateral aerodynamic force, aerodynamic lift force, and overturning moment, respectively, and Δ

_{S}, Δ

_{L}, Δ

_{M}are their thresholds, respectively. From a mechanics perspective, both F

_{L}and F

_{S}can affect the lateral force balance (F

_{M}is a resultant moment of F

_{L}and F

_{S}). Thus, there are complex cross effects between F

_{L}, F

_{S}, and F

_{M}. Given the Shanghai Metro Operation Management Center stipulate a maximum vehicle velocity at Beaufort Scale eight (~18 m·s

^{−1}) based on consideration of the comprehensive effects of all aerodynamic forces, the maximum aerodynamic forces when the vehicle runs at this maximum velocity are taken as the thresholds. Using Equations (9) to (12), Δ

_{S}is 1.7·10

^{4}N, Δ

_{L}is1.8·10

^{4}N, and Δ

_{M}is 1.9·10

^{4}N·m.

## 4. Application

^{−1}) in Shanghai, reaching 9 to 11 (20.8–30.3 m·s

^{−1}) along coastal areas with a maximum wind velocity of 30.3 m·s

^{−1}(AWS #12, Figure 1). The mean bias errors of the wind velocities (observed –simulated) at 10 m for the Wild Animal Park and Lingang Avenue metro stations (Figure 1) on 11 July 2015 (when Chan-hom made landfall) are 1.34 and 1.31 m·s

^{−1}, respectively (Figure 12); i.e., the model under-estimates. Figure 13 shows the risk distribution at 7:50 LST on 11 July 2015 based on the five rail transport risks classes (Table 2) associated with minimum wind velocities.

_{c}. Although WR2 has been available to the Shanghai Shentong Metro Group Co. since July 2016, with no typhoons in this area since then, it is not possible to assess the impact of it use on operations.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of both the Shanghai Metro Line 16 (blue line) with station names (red dots) and 12 AWS (Automatic Weather Stations) around it, within Shanghai (inset), China.

**Figure 3.**Steps to evaluate rail transport safety within the wind risk warning model for rail transport (WR2).

**Figure 4.**Spatial variation in Shanghai based on ASTER GDEM V1 (NASA/METI 2009) data (resolution = 30 m) of: (

**a**) local roughness length (z

_{0_local}) (Equation (1)); and effective roughness length (Equation (7)) for (

**b**) 70 m agl (z

_{0_eff,70}) averaged over 3480 m; (

**c**) for 300 m agl (z

_{0_eff,300}) for 15,000 m.

**Figure 5.**All 119 AWS locations in Shanghai (●) and the wind directions the data were used to assess background wind based on criteria in Section 3.1: all directions (triangle), north (green), east (blue), south (grey), and west (red).

**Figure 6.**(

**a**) Model and mesh details in CFD (Computational Fluid Dynamics) simulation. The whole model domain is a 24-sided prism, with an externally tangent circle diameter of 30 L. The train model with two oblique faces of 25° lies in the center of the model domain, and its horizontal, longitudinal, and vertical lines are meshed with 30, 30, and 350 grids, respectively. (

**b**) Relation between vehicle velocity (U

_{vehicle}), wind velocity (U

_{wind}), and resultant relative wind velocity (U

_{relative}) for a train subjected to crosswinds. β is the yaw angle of the relative wind velocity, β

_{0}the yaw angle of wind velocity. (

**c**) Aerodynamic forces reference system: the aerodynamic lift force, F

_{L}, lateral (or side) aerodynamic force, F

_{S}, and overturning moment, F

_{M}. The dimensions refer to X and Y.

**Figure 7.**Wind pressure distribution coefficients of the rail train at angles of attack (

**a**) 0°, (

**b**) 45°, (

**c**) 90° calculated with realizable k–ε turbulence model.

**Figure 8.**Aerodynamic force coefficients of rail vehicles versus angle of attack derived from Equation (9). (

**a**) Aerodynamic lift force coefficient C

_{L}, (

**b**) lateral (or side) aerodynamic force coefficient C

_{S}, (

**c**) overturning moment coefficient C

_{M}; for front (T1), middle (M), and back (T2) carriages, plus for the whole train (WHOLE).

**Figure 9.**Impact of wind direction when a vehicle is travelling southeast at 40 km·h

^{−1}with a wind velocity of 18 m·s

^{−1}on aerodynamic forces: aerodynamic lift force (F

_{L}, kN), lateral (or side) aerodynamic force (F

_{S}, kN), and overturning moment (F

_{M}, kN·m). Note that the meteorological convention for wind direction is used (i.e., northerly is 0°, increasing clockwise).

**Figure 10.**As in Figure 9 but the impact of wind velocity variations assuming an easterly wind (90°).

**Figure 11.**As in Figure 9 but the impact of vehicle velocity.

**Figure 12.**Observed and simulated 10 min average wind velocities at Wild Animal Park and Lingang Avenue metro stations (Figure 1) on LST 11 July 2015 during Typhoon Chan-hom landfall.

**Figure 14.**Spatial variation of local roughness length (z

_{0_local}) (Equation (1)) within 2 km along Shanghai Metro Line 16 based on ASTER GDEM V1 [26] data (resolution = 30 m).

**Table 1.**Typhoons that have affected Shanghai for longer than 3 h between 2005 and 2013. N is the number of hours Shanghai was impacted. A total of 311 h of data were analyzed. TC: Tropical cyclone [25].

Year | TC Code | Name | Time affected Shanghai (LST) | N |
---|---|---|---|---|

2005 | 0509 | Matsa | 5 Aug, 05:00–7 Aug, 23:00 | 67 |

2005 | 0515 | Khanun | 9 Sep, 11:00–16:00 | 8 |

2006 | 0601 | Chanchu | 18 May, 08:00–17:00 | 10 |

2006 | 0604 | Bilis | 14 Jul, 06:00–15 Jul, 16:00 | 35 |

2007 | 0713 | Wipha | 19 Sep, 00:00–20:00 | 21 |

2007 | 0716 | Krosa | 6 Oct, 12:00–21:00 7 Oct, 20:00–8 Oct, 22:00 | 37 |

2011 | 1109 | Muifa | 6 Aug, 10:00–7 Aug, 16:00 | 31 |

2012 | 1209 | Saola | 3 Aug, 05:00–12:00 | 8 |

2012 | 1211 | Haikui | 6 Aug, 08:00–9 Aug, 05:00 | 70 |

2012 | 1215 | Bolaven | 27 Aug, 03:00–28 Aug,02:00 | 24 |

**Table 2.**Wind risk scale (R, Equation (13) for rail transport and the minimum wind velocity at vehicle center height associated with each class.

Range | 0 < R ≤ 0.25 | 0.25 < R ≤ 0.5 | 0.5 < R ≤ 0.75 | 0.75 < R ≤ 1 | R > 1 |
---|---|---|---|---|---|

Risk Level | Very low | Low | Medium | High | Very high |

Minimum Wind Velocity (m·s^{−1}) | - | 7.0 | 11.9 | 15.7 | 18.0 |

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**MDPI and ACS Style**

Han, Z.; Tan, J.; Grimmond, C.S.B.; Ma, B.; Yang, T.; Weng, C.
An Integrated Wind Risk Warning Model for Urban Rail Transport in Shanghai, China. *Atmosphere* **2020**, *11*, 53.
https://doi.org/10.3390/atmos11010053

**AMA Style**

Han Z, Tan J, Grimmond CSB, Ma B, Yang T, Weng C.
An Integrated Wind Risk Warning Model for Urban Rail Transport in Shanghai, China. *Atmosphere*. 2020; 11(1):53.
https://doi.org/10.3390/atmos11010053

**Chicago/Turabian Style**

Han, Zhihui, Jianguo Tan, C. S. B. Grimmond, Bingxin Ma, Tongxiao Yang, and Chunhui Weng.
2020. "An Integrated Wind Risk Warning Model for Urban Rail Transport in Shanghai, China" *Atmosphere* 11, no. 1: 53.
https://doi.org/10.3390/atmos11010053