A simple gradient wind field model for translating tropical cyclones

Transcription

1 Nat Hazards manuscript No. (will be inserted by the editor) 1 2 A simple gradient wind field model for translating tropical cyclones 3 4 Cao Wang 1,2 Hao Zhang 2 Kairui Feng 1 Quanwang Li Received: date / Accepted: date Abstract Understanding the spatial structure of wind speed profile of a tropical cyclone (TC) is of critical importance to assess the TC-related damage and map the risk for afflicted areas. The wind field structure of a TC can be regarded as a horizontal primary circulation superimposed by a vertical-radial secondary convection driven by thermal balance. The gradient wind field model has been widely utilized in literature to describe the radial distribution of wind speed with respect to the TC center. In this paper, a new gradient wind field model is developed for translating TCs, based on the vector summation of the rotational wind speed and the translation speed. The accuracy and efficiency of the proposed model are demonstrated through comparing the wind fields generated from model solution and those recorded historically. Keywords Tropical cyclone wind field model gradient wind translation speed Introduction Severe tropical cyclones (TCs) are continuously posing significant threats to social properties and public safety of coastal areas around the world, especially in this era with a potential influence of climate change and an increasing coastal population (Emanuel 05b; Knutson et al. ). The public and regulatory authorities have, as a result, become increasingly concerned with the TC-related damage loss estimation and mitigation. TC simulation techniques provide a means to assess the TC wind magnitude and duration for regions of interest, taking into account the uncertainties associated with the TC occurrence, track and intensity, where the modeling of TC wind field is a key component. The wind field structure of a TC can be regarded as a horizontal primary circulation superimposed by a verticalradial secondary convection driven by thermal balance (Emanuel 05a). To-date studies have widely considered the gradient wind, under a balance of pressure-gradient, Coriolis Q. Li ( ) li quanwang@tsinghua.edu.cn. 1 Department of Civil Engineering, Tsinghua University, Beijing 084, China. 2 School of Civil Engineering, The University of Sydney, Sydney, NSW 06, Australia.

2 2 C. Wang, et al and centrifugal forces, to approximate the slab wind field of TCs at gradient height ( 0 00 m above the surface) (Georgiou 1986; Lee and Rosowsky 07; Cui and Caracoglia 16; Vickery et al. 00b), which can be further converted to surface-level wind speed (Powell 19). Mathematically, in the natural coordinate system with an origin located at the TC center, the force equilibrium gives 1 p ρ r = V r 2 r + fv r (1) where p = p(r) is the pressure at a distance r from the TC center, ρ is air density, f is the Coriolis parameter, and V r is the tangential (rotational) wind speed. Taking into account the translation speed of the TC, V t, Georgiou (1986) adjusted the radius of curvature as in Eq. (1) with Blaton s formula, and Eq. (1) becomes which yields 1 p ρ r = V g 2 r V g = 1 2 (V t sinα f r) + 1 V t sinα V g + fv g (2) 1 4 (V t sinα f r) 2 + r p ρ r where α is the clock-wise relative angle between heading direction and the radial position of interest, and V g is the gradient wind speed incorporating the translation speed. Eq. (3) has been widely used by the scientific community for modelling the TC wind field and further mapping the TC risk for coastal regions (Lee and Rosowsky 07; Vickery et al. 00b; Cui and Caracoglia 16; Salman and Li 17; Ji and Ellingwood 17). However, it is noticed that the first term at the right-hand side of Eq. (2) represents a pseudo-centripetal acceleration with a direction not passing through the origin, implying that the wind field model generated by Eq. (2) may differ significantly from the realistic case. Some other works have considered a slab boundary layer model to describe the wind field portfolio with an improved accuracy (Thompson and Cardone 1996; Vickery et al. 00a; Li and Hong ). However, these improved models are, for the most part, based on a finite-difference method which involves a set of partial difference equations. Thus it is often computationally expensive to find their solutions, especially when these models are adopted in simulation-based studies requiring a significant amount of replications. Therefore, there is a need to develop a simple yet accurate wind field model for use in hurricane simulations. (3) The proposed model This section develops a new gradient wind field model by considering the gradient wind speed as the vector summation of the rotational wind speed, V r, and the translation speed V t, i.e., V g = V r + V t, which gives where V r is the rotational speed satisfying V g = V g = Vt 2 +Vr 2 + 2V r V t sinα (4) 1 p ρ r = V r 2 r + fv g cosθ (5)

3 A simple gradient wind field model for translating tropical cyclones 3 61 in which θ is the angle between V r and V t. With Eqs. (5) and (4), one has Vr 2 r + fv r + fv t sinα = 1 p ρ r (6) which yields ( V r = 1 ) f r + 2 f r + r p ρ r f rv t sinα (7) Further, the gradient wind speed V g is obtained according to Eq. (4) in an explicit form. Eqs. (4) and (7) present the proposed gradient wind field model, which only involves simple algebras for the sake of simulation efficiency. Gradient wind speed (m/s) Georgiou's model, = Proposed model, = Georgiou's model, = Proposed model, = Radius (RMW) Gradient wind speed (m/s) Georgiou's model, = Proposed model, = Georgiou's model, = Proposed model, = Radius (RMW) (a) V t = 2 m/s (b) V t = 12 m/s Fig. 1 Comparison of the radial wind speed profiles associated with Georgiou s model and the proposed one. The key parameters are: minimum sea-level pressure (MSLP) = 9 millibar, radius to maximum wind (RMW) = km, and maximum sustained wind (MSW) at eye wall = m/s Mathematically, Eqs. (3) and (7) are equivalent for the case of V t = 0. However, the discrepancy between the two models becomes more noticeable as the translation speed increases. Fig. 1 presents the radial wind speed profiles obtained from Eqs. (3) and 7 with different translation speeds. The pressure is assumed to be axisymmetric and its radial distribution is described by Holland s parameter B (Holland 19); it is fitted herein by minimizing the difference between the maximum sustained wind (MSW) obtained from the model and the given one. It is seen that when α =, the wind speed associated with Georgiou s model is smaller than that associated with the proposed one, and this observation is reversed if α =. The difference between the two models increases with the radius (outer the RMW) for the case of α = because the maximum wind speed at the RMW are the same for both cases; however, when α =, the difference is the largest at the RMW. Moreover, the difference between the radial wind speeds given by the two models becomes more significant with a greater translation speed Verification of the proposed model To verify the accuracy of Georgiou s model (1986) and the proposed one, we compare the wind field models obtained from Eqs. (3) and (7) with the historically recorded data. As

4 4 C. Wang, et al. Fig. 2 Wind field of Hurricane Emily 05 at 0929 UTC, 19 July. Figure reproduced from the RMS H* wind legacy archive at Key parameters in relation to the wind field can be determined from the figure and the associated data archive online. The wind speed values are in kts (1 kts = m/s). The center is located at ( E, N), and the MSW is observed at (93. E, N) the practical focus is on the surface-level wind speed, which can be obtained approximately by adjusting the gradient wind filed model with a conversion factor (Powell 19), the historically recorded surface wind fields are considered and compared. First, Hurricane Emily from the 05 season is considered, which formed on July and dissipated 11 days later, with a MSW of 72 m/s and a minimum sea-level pressure (MSLP) of 939 millibar in its entire life. The real-time wind field data (H* data) are available from Risk Management Solutions (RMS) Inc. The radial distribution of wind field at 0929 UTC, 19 July, 05, as shown in Fig. 2, is considered. The key hurricane parameters such as the center location, radius to maximum wind (RMW), MSW, MSLP and heading direction can be read from Fig. 2. Provided these parameters, the wind fields associated with Eqs. (3) and (7) are obtained and presented in Fig. 3. It is seen that the model in Fig. 3(b) agrees better with the realistic one (Fig. 2). For instance, we consider the wind speeds at the locations with a distance of RMW from the TC center and a clock-wise relative angle (α) from the heading direction of 0,, 1 and 2 respectively. Table 1 presents the wind speeds for the four locations from the model solutions and the historically recorded data. The wind speed errors (i.e., (model speed recorded speed)/recorded speed %) are also p- resented for the purpose of comparison. For the case of α =, the speed error is 0 for both models since the considered location is at the MSW. For other values of α, the wind

5 A simple gradient wind field model for translating tropical cyclones speed error associated with the proposed model (Eq. (7)) is significantly reduced compared with that associated with Georgiou s model (Eq. (3)). When α = 2, the overestimation of wind speed associated with Georgiou s model (1986) is consistent with the observation from Fig. 1. Moreover, the wind speed at the outer kidney shape isoline is kts (.9 m/s) according to Fig. 3(b), which is the same as that found in Fig. 2. However, the Georgiou s model (Fig. 3(a)) gives an estimate of kts (36.0m/s), which indeed provides a significant overestimate by 17%. The improved accuracy of Eq. (7) is also demonstrated by considering the wind field of Hurricane Wilma 05 at 07 UTC, 24 October and comparing the wind fields generated by Georgiou s model, the proposed model and the historical data, as shown in Figs. 4 and 5. It is seen that the wind field associated with the proposed method agrees better with the historically recorded one. With Fig. 5(b), the wind speed at the outer kidney shape isoline is kts according to the proposed method (b), which is the same as that found from Fig. 4. However, the Georgiou s model (a) gives an estimate of kts (c.f.fig. 5(a)), which indeed provides a significant overestimate by 28% (a) Georgiou s model (b) The proposed model Fig. 3 Wind field models for Hurricane Emily 05 at 0929 UTC, 19 July generated by (a) Georgiou s model and (b) the proposed one. The wind speed values are in kts consistent with Fig. 2. Table 1 Wind speeds at the four selected locations for Hurricane Emily 05 (Fig. 2) (wind filed unit: kts). Value of α Recorded wind speed Georgiou s Proposed Speed Error.53% 0.00% 2.91% 16.% Speed Error 8.51% 0.00% -3.34% -2.99%

6 6 C. Wang, et al. Fig. 4 Wind field for Hurricane Wilma 05 at 07 UTC, 24 October. Figure reproduced from RMS H* wind legacy archive at Key parameters in relation to the wind field can be read from the figure and the associated data archive online. The wind speed values are in kts (1 kts = m/s). The center is located at ( E,.226 N), and the MSW is observed at ( E, N) Conclusions A new gradient wind filed model, based on the vector summation of the rotational wind speed and the translation speed, has been developed in this paper. The proposed model only involves simple algebra, which is beneficial for practical applications, especially in simulation-based studies of TC wind field modeling. Comparisons with two historical TC wind fields (Hurricane Emily and Hurricane Wilma) demonstrates that the new model can better describe the realistic wind field than the existing Georgiou s model incorporating Blaton s adjusted curvature Acknowledgements This research has been jointly supported by the National Key Research and Development Program of China (Grant No. 16YFC014), the National Natural Science Foundation of China (Grant No. 5783) and the Faculty of Engineering and IT PhD Research Scholarship from the University of Sydney. These supports are gratefully acknowledged. The RMS Inc. is also acknowledged for the open access to the hurricane H* data.

7 0 A simple gradient wind field model for translating tropical cyclones (a) Georgiou s model (b) The proposed model Fig. 5 Wind fields associated with Hurricane Wilma 05 at 07 UTC, 24 October generated by (a) Georgiou s model and (b) the proposed one. The wind speed values are in kts consistent with Fig References Wei Cui and Luca Caracoglia. Exploring hurricane wind speed along us atlantic coast in warming climate and effects on predictions of structural damage and intervention costs. Engineering Structures, 122:9 2, 16. K A Emanuel. Divine wind: the history and science of hurricanes. Oxford University Press. New York, USA, 05a. K A Emanuel. Increasing destructiveness of tropical cyclones over the past years. Nature, 436(51): , 05b. Peter Nicholas Georgiou. Design wind speeds in tropical cyclone-prone regions. PhD thesis, Dept. of Civil Engineering, Univ. of Western Ontario, Cadada, Greg J Holland. An analytic model of the wind and pressure profiles in hurricanes. Monthly Weather Review, 8(8): , 19. Yun Lee Ji and Bruce R. Ellingwood. A decision model for intergenerational life-cycle risk assessment of civil infrastructure exposed to hurricanes under climate change. Reliability Engineering & System Safety, 9: 7, 17. Thomas R Knutson, John L McBride, Johnny Chan, Kerry Emanuel, Greg Holland, Chris Landsea, Isaac Held, James P Kossin, AK Srivastava, and Masato Sugi. Tropical cyclones and climate change. Nature Geoscience, 3(3):7 163,. Kyung Ho Lee and David V Rosowsky. Synthetic hurricane wind speed records: development of a database for hazard analyses and risk studies. Natural Hazards Review, 8(2): 23 34, 07. SH Li and HP Hong. Observations on a hurricane wind hazard model used to map extreme hurricane wind speed. Journal of Structural Engineering, ASCE, 141():014238,. Mark D Powell. Boundary layer structure and dynamics in outer hurricane rainbands. part ii: Downdraft modification and mixed layer recovery. Monthly Weather Review, 118(4): , 19.

8 8 C. Wang, et al Abdullahi M. Salman and Yue Li. Assessing climate change impact on system reliability of power distribution systems subjected to hurricanes. Journal of Infrastructure Systems, 23:0124, 17. Edward F Thompson and Vincent J Cardone. Practical modeling of hurricane surface wind fields. Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, 122(4):1 5, Peter J Vickery, PF Skerlj, AC Steckley, and LA Twisdale. Hurricane wind field model for use in hurricane simulations. Journal of Structural Engineering, ASCE, 126(): , 00a. Peter J Vickery, PF Skerlj, and LA Twisdale. Simulation of hurricane risk in the us using empirical track model. Journal of Structural Engineering, ASCE, 126(): , 00b.