Logic tree approach for probabilistic typhoon wind hazard assessment

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The wind speeds of the simulated typhoons and the probable maximum wind speeds are estimated using Monte Carlo simulations, and wind hazard curves are derived as a function of the annual exceedance probability or return period. A logic tree decreases the epistemic uncertainty included in the wind intensity models and provides reasonably acceptable wind speeds.

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Nuclear Engineering and Technology 51 (2019) 607e617 Contents lists available at ScienceDirect Nuclear Engineering and Technology journal homepage: www.elsevier.com/locate/net Original Article Logic tree approach for probabilistic typhoon wind hazard assessment Young-Sun Choun*, Min-Kyu Kim Structural and Seismic Safety Research Team, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon, 34057, Republic of Korea a r t i c l e i n f o a b s t r a c t Article history: Global warming and climate change are increasing the intensity of typhoons and hurricanes and thus Received 21 March 2018 increasing the risk effects of typhoon and hurricane hazards on nuclear power plants (NPPs). To reﬂect Received in revised form these changes, a new NPP should be designed to endure design-basis hurricane wind speeds corre- 11 October 2018 sponding to an exceedance frequency of 107/yr. However, the short typhoon and hurricane observation Accepted 12 November 2018 Available online 17 November 2018 records and uncertainties included in the inputs for an estimation cause signiﬁcant uncertainty in the estimated wind speeds for return periods of longer than 100,000 years. A logic-tree framework is introduced to handle the epistemic uncertainty when estimating wind Keywords: Logic tree speeds. Three key parameters of a typhoon wind ﬁeld model, i.e., the central pressure difference, Monte Carlo simulation pressure proﬁle parameter, and radius to maximum wind, are used for constructing logic tree branches. Probabilistic typhoon wind hazard The wind speeds of the simulated typhoons and the probable maximum wind speeds are estimated using assessment Monte Carlo simulations, and wind hazard curves are derived as a function of the annual exceedance Typhoon wind ﬁeld model probability or return period. A logic tree decreases the epistemic uncertainty included in the wind in- Wind hazard curve tensity models and provides reasonably acceptable wind speeds. © 2018 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction of the mean CDF within a range of approximately 1x105 or less per reactor year. At present, however, the risk of core damage by high High winds or severe wind storms from typhoons and hurri- winds may increase because the frequency and intensity of tropical canes are a potential threat to a nuclear power plant (NPP). High cyclones will increase owing to rapid climate changes [3]. The winds can cause dynamic wind loads, large differential pressures, operation experience of NPPs has shown that extreme winds or wind-driven missiles, which can damage the structures, systems, mainly affect offsite power supplies and electrical grids. Large and components (SSCs) of an NPP and result in core damage and the pressure differentials from high winds rarely create false signals in release of radioactive materials into the environment. To ensure the certain instrumentations. For NPPs in coastal areas, heavy salt safety functions of SSCs, which are important to plant safety, sprays have caused shorts in exposed electrical equipment, such as General Design Criteria 2 and 4 of Appendix A to Title 10 of the Code transformer bushings and high-voltage line insulators, leading to a of Federal Regulations Part 50 [1] require design bases against the loss of offsite and onsite power [4]. Under these circumstances, new effects of natural phenomena including hurricanes (Criterion 2) and NPPs should be designed to endure design-basis hurricane wind the dynamic effects of hurricanes and missiles (Criterion 4). speeds corresponding to an annual exceedance frequency of 107 (a Three decades ago, an evaluation study of external hazards to return period of 10 million years), which is also the exceedance NPPs was conducted in the United States [2]. The study estimated frequency used to establish design-basis tornado parameters [5,6]. the plant-speciﬁc core damage frequency (CDF) of high winds A typical technique to estimate typhoon wind speeds is gener- within the range of 9.0x109/yr to 4.3x105/yr through probabi- ally based on the sampling of key parameters of typhoon wind listic risk assessments (PRAs) for eleven U.S. NPPs. The risk of core models (track and intensity models) from distribution functions damage due to high winds is comparable to the evaluation criteria ﬁtting statistical distributions to limited observation data. This procedure results in signiﬁcant uncertainty in the estimated typhoon wind speeds for long return periods, i.e., 1e10 million * Corresponding author. Structural and Seismic Safety Research Team, Korea years. Vickery et al. [7] estimated the uncertainties which arise Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon, when predicting wind speeds by propagating the uncertainties in 34057, Republic of Korea. key model inputs, which in their study were the central pressure, E-mail address: sunchun@kaeri.re.kr (Y.-S. Choun). https://doi.org/10.1016/j.net.2018.11.006 1738-5733/© 2018 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). 608 Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 the pressure proﬁle parameter, the translation speed, the radius to sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃ maximum wind, and the occurrence rate throughout the wind BDp BDp speed prediction stage. The two parameters controlling the overall Vg;max z ¼ 0:61 ; (5) er r uncertainty were the pressure proﬁle parameter and the central pressure, which together are responsible for ~70% of the overall wind speed modeling uncertainty. The uncertainties in the esti- where e is the base of the natural logarithms (e z 2.71828). mated 100-year return period wind speed are approximately 6% The p maximum wind speed in a typhoon is directly proportional ﬃﬃﬃﬃﬃﬃﬃﬃﬃ and 16% along the Gulf of Mexico coastline and the coast of Maine, to BDp . In parametric typhoon wind ﬁeld models, the Holland respectively. parameter B and central pressure difference Dp are important when To apply current wind speed estimation techniques to NPP sites, simulating the maximum wind speeds of a storm. the uncertainty in the estimated wind hazards should be within a Fig. 1 presents pressure proﬁles and gradient balanced wind reasonably acceptable limit. This study introduces a logic-tree velocity proﬁles of a typhoon with pa ¼ 1010 hPa, Dp ¼ 50 hPa, framework which quantiﬁes epistemic uncertainty and applies it and rmw ¼ 20 km for different values of Holland parameter B. When to estimations of the typhoon wind hazards. Logic tree branches are the value of B is enlarged, the eye of the typhoon increases. The created with different models of the three key parameters: the pressure curves intersect at rmw . As the value of B is enlarged, the central pressure difference, the pressure proﬁle parameter, and the wind velocity becomes larger at r rmw but smaller at r > rmw . radius to maximum wind. Wind speeds for the simulated typhoons Because the Holland wind ﬁeld model is axisymmetric, it cannot and the probable maximum winds are predicted using Monte represent the asymmetric structures of a typhoon. Georgiou [9] Carlo simulations. As a result, typhoon wind hazard curves are introduced an advanced model which includes the translation ve- derived. locity of a storm as VT sin q fr 2. Models and methods Vg ðr; qÞ ¼ 2 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2.1. Wind ﬁeld model ðVT sin q frÞ2 BDp rmw B rmw B þ þ exp ; 4 r r r The Holland wind proﬁle [8], which is based on an empirical (6) radial distribution of storm pressures, has been widely used. The sea surface pressure at radial distance r from typhoon center p(r) is where VT is the storm's translation velocity and q denotes the proposed as approach angle of a storm. In the above gradient balance equation, rmw B pðrÞ ¼ pc þ Dp exp ; (1) r where pc is the central minimum sea level pressure, Dp is the dif- ference between the ambient pressure (theoretically at inﬁnite radius), pa , and the central pressure (hereafter referred to as the central pressure difference); rmw is the radius to the maximum wind speed (RMW); and B is Holland's radial pressure proﬁle parameter with values typically between 1 and 2.5. From Eq. (1), the difference between the ambient pressure and the sea surface pressure at radial distance r from storm center, Dpr , can be given by r B mw Dpr ¼ Dp 1 exp : (2) r The gradient wind balance equation becomes V 2g ðrÞ 1 dpðrÞ þ fVg ðrÞ ¼ ; (3) r r dr where Vg ðrÞ is the gradient wind at radius r, f is the Coriolis parameter (f ¼ 2U sin j , where U is the angular velocity of the rotation of the earth, U ¼ 7:292 105 rad=s, and j is the lati- tude), and r is the density of air (r ¼ 1:15 kg=m3 ). Substituting the pressure gradient obtained from the differen- tiation of Eq. (1) into Eq. (3), the gradient balanced velocity for a stationary storm is given by sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ f 2 r 2 BDp rmw B rmw B fr Vg ðrÞ ¼ þ exp : (4) 4 r r r 2 Because the Coriolis force f is relatively small within the region of maximum winds, the terms associated with f can be neglected; Fig. 1. Pressure proﬁles and gradient balanced wind velocity proﬁles for different thus, the maximum wind speed at the RMW is values of Holland parameter B. Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 609 Table 1 Example models of RMW. Source Formula Data set a Vickery et al. (2000) [12] lnðrmw Þ ¼ 2:636 0:00005086Dp2 þ 0:0394899jslnðrmw Þ ¼ 0:3778 Storms North of 30 N Vickery et al. (2000) [12] lnðrmw Þ ¼ 2:713 0:0056748Dp þ 0:0416289jslnðrmw Þ ¼ 0:3394 Storms North of 30 N Willoughby and Rahn (2004) [13] rmw ¼ 51:6expð 0:0223Vmax þ 0:0281jÞ Kawai et al. (2005) [14] rmw ¼ 94:89expððpc 967Þ=61:5Þ Western North Paciﬁc typhoons Powell et al. (2005) [15] lnðrmw Þ ¼ 2:0633 þ 0:0182Dp 0:00019008Dp2 þ 0:0007336j2 slnðrmw Þ ¼ 0:3 Gulf of Mexico and Atlantic coast hurricanes landfalls with latitude 34 N Willoughby et al. (2006) [16] rmw ¼ 46:4expð 0:0155Vmax þ 0:0169jÞ Vickery and Wadhera (2008) [17] lnðrmw Þ ¼ 3:015 0:00006291Dp2 þ 0:0337jslnðrmw Þ ¼ 0:441 All hurricanes, pc < 980 hPa Vickery and Wadhera (2008) [17] lnðrmw Þ ¼ 3:858 0:00007700Dp2 slnðrmw Þ ¼ 0:390 Gulf of Mexico hurricanes, North of 18 N, pc < 980 hPa Vickery and Wadhera (2008) [17] lnðrmw Þ ¼ 3:421 0:00004600Dp2 þ 0:00062j2 slnðrmw Þ ¼ 0:466 Atlantic Ocean hurricanes FEMA (2012) [18] lnðrmw Þ ¼ 2:556 0:000050255Dp2 þ 0:042243032j8 km rrw 150 km Note. pc : central pressure ðhPaÞ. Dp : central pressure difference ðhPaÞ. j : latitude ðdegreeÞ. Vmax : maximum wind speed ðm=sÞ. a Model used in this study. Eq. (6), the maximum wind speed occurs at q ¼ 90+ and near r ¼ still has certain limitations. rmw . In this case, the pressure gradient dominates the second term, Table 1 presents example models to estimate the RMW. and the maximum wind speed can be approximated as sﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2.3. Pressure proﬁle parameter 1 BDp Vg;max z ðVT frmw Þ þ 0:61 : (7) 2 r The Holland B parameter, i.e., the pressure proﬁle parameter, is an important factor that deﬁnes the shape of the radial pressure proﬁle. Theoretically, B can be derived from Eq. (4) for the radius of the maximum wind. When r ¼ rmw and Vg ¼ Vg;max , 2.2. Radius to maximum wind V 2g;max þ Vg;max rmw f re The RMW is a key factor in determining the intensity and size of B¼ (8) a typhoon, and is an important parameter when predicting the Dp maximum typhoon wind speed. Traditionally, the RMW has been If the Coriolis parameter f is neglected, Eq. (8) is simpliﬁed as measured directly by aircraft or by the pressure distribution at the sea surface [10]. This can be determined from infrared satellite V 2g;max re V 2g;max r imagery by measuring the distance between the coldest cloud-top B¼ z2:718 (9) Dp Dp temperature near the eye and the warmest section within the eye of the typhoon. The RMW can also be determined through the use of To estimate parameter B, two methods are mainly used: the ﬁrst empirical models [11]. The approach used to determine the RMW evaluates the gradient velocity from the equilibrium equation of Table 2 Example models of B parameter. Source Formula Data set Hubbert et al. (1991) [20] B ¼ 1:5 þ ð980 pc Þ=120 Empirical formula Harper and Holland (1999) [21] B ¼ 2:0 ðpc 900Þ=160 Empirical formula Vickery et al. (2000) [12] B ¼ 1:34 þ 0:00328Dp 0:00522rmw Dp > 25 hPa, ﬂight levels < 3000 m Vickery et al. (2000) [12] B ¼ 1:38 þ 0:00184Dp 0:00309rmw Dp > 25 hPa, ﬂight levels < 1500 m Willoughby and Rahn (2004) [13] B ¼ 1:0036 þ 0:0173Vmax 0:0313lnðrmw Þ þ 0:0087jsB ¼ 0:25 Powell et al. (2005) [15] a B ¼ 1:881093 0:005567rmw 0:010917jsB ¼ 0:2860:8 33 m/s, ﬂight levels < 700 hPa, Atlantic 15e35N Vickery and Wadhera (2008) [17] B ¼ 1:881 0:00557rmw 0:01295jsB ¼ 0:221 pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Vickery and Wadhera (2008) [17] B ¼ 1:833 0:326 rmw f sB ¼ 0:221, rmw in meters a pﬃﬃﬃ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Vickery et al. (2009) [22] B ¼ 1:732 2:237 AA ¼ rmw f = 2Rd Ts ln½1 þ Dp=ðpc ,eÞsB ¼ 0:225, rmw in meters Note. pc : central pressure ðhPaÞ. Dp : central pressure difference ðhPaÞ. j : latitude ðdegreeÞ. rmw : radius to maximum wind ðkmÞ. Vmax : maximum wind speed ðm=sÞ. f : Coriolis parameter. Rd : gas constant for dry air Nmkg1 K1 . Ts : sea surface temperature ðKÞ. ez2:71828. a Model used in this study. 610 Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 Table 3 Typhoons impacted the site. Distance (km) Number of Name of typhoonsa typhoons 0e50 10 Irving (7910), Khanun (1207), Brendan (9411), Gladys (9112), Ewiniar (0603), Neil (9905), Rammasun (0205), Olga (9907), Ted (9219), Nakri (1412), 50e100 6 Vera (8613), Kit (8508), Judy (8911), Carmen (7811), Rusa (0215), Tembin (1214) 100e150 7 Yanni (9809), Thelma (8705), Seth (9429), Kompasu (1007), Bolaven (1215), Nari (0711), Robyn (9007), 150e200 12 Agnes (5707), Tina (9711), Sanba (1216), Rita (7207), Faye (9503), Doug (9413), Nancy (8605), Maemi (0314), Lee (8509), Saomai (0014), Meari (1105), Prapiroon (0012) 200e250 10 Agnes (8118), Judy (7911), Sarah (5914), Brenda (8520), Kalmaegi (0807), Gilda (7408), Megi (0415), Paul (9908), Muifa (1109), Bolaven (0006) 250e300 8 Holly (8410), Dinah (8712), Fengshen (0209), Danas (1324), Caitlin (9109), Noname (9113), Emma (5612), Soudelor (0306) a The number within the parentheses is the international number ID of the storm. The last two digits of the calendar year are followed by the two-digit serial number ID of the storm. the barometric gradient, and then compares it with the data of the Georgiou [9], Vickery and Twisdale [25], Vickery et al. [12,26,27], wind speed of the upper frictional layer, and the second conducts a Sparks and Huang [28], and Powell et al. [15,29] suggested wind regression analysis of the data of the ground air pressure and then speed reduction factors, which are deﬁned as the ratio of the wind estimates the parameter values [19]. The Holland B parameter can speed at 10 m above the water or ground to the gradient wind be expressed by the function of the central pressure difference and speed. radius to maximum wind. Various models of the B parameter are Vickery and Twisdale [25] proposed a model to estimate the suggested, as shown in Table 2. surface-level (10 m, over water) wind speeds, Vs , from the gradient wind speed, Vg , as follows: 2.4. Surface wind speed 8 < 0:825,Vg r 2rmw Vs ¼ 0:9 0:0375,r=rmw 2rmw < r < 4rmw (10) The mean wind speed at great heights above the ground : 0:750,Vg r 4rmw (gradient wind speed) is constant, but the mean wind speed near the ground decreases owing to the frictional forces caused by the There is inconsistency in the averaging times used for reporting terrain conditions. Thus, for the structure designs, the gradient the sustained winds in tropical cyclones among the various wind speed must be adjusted to the surface level at a height of 10 m agencies; in contrast, the U.S. agencies, such as the Joint Typhoon over the water or ground. To determine the surface-level wind Warning Center (JTWC), use the 1-min mean sustained 10 m wind speed, an atmospheric boundary layer model or a wind speed speeds, and other agencies, such as the Regional Specialized reduction factor is used. Schwerdt et al. [23], Batts et al. [24], Meteorological Center (RSMC), use 10-min averaged values. It is Fig. 2. Location of site and typhoon tracks within a radius of 300 km from the site. Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 611 Fig. 3. Characteristics of typhoons within a radius of 300 km from the site. necessary to adjust the 1-min mean wind speeds to 10-min, or vice site. Their tracks and characteristics (central pressures, radial dis- versa. The maximum 1-min mean wind speed, Vmax;1 , can be tances from the storm center, and heading angles) are shown in roughly converted into the maximum 10-min mean wind speed, Figs. 2 and 3, respectively. Vmax;10 , using the ratio of the maximum gust factor within a 10-min period, G10,inﬁnity, to the maximum gust factor within a 1-min period, G1,inﬁnity, as 2.5.2. Probabilistic distributions of wind ﬁeld parameters The intensity of a storm is characterized by six key parameters: Vmax;10 ¼ Cv ,Vmax;1 ; (11) (1) the central pressure difference Dp, (2) the RMW rmw, (3) the pressure proﬁle shape parameter B, (4) the translation velocity of where Cv is the conversion factor, which is deﬁned as Cv ¼ the typhoon track VT , (5) the minimum distance between the site of G10;inf inity =G1;inf inity . The Cv recommended values are 0.93 for at- sea, 0.90 for off-sea, 0.87 for off-land, and 0.84 for in-land condi- tions [30]. 2.5. Monte Carlo simulation The typhoon wind speed for a return period can be determined using observation records at the location of interest. However, such observation data are clearly not sufﬁcient when attempting to es- timate reliable wind speed for a long return period such as a return period of 1,000,000 to 10,000,000 years. To overcome the lack of data, the Monte Carlo simulation approach is used to predict extreme wind speeds for a long period of time. 2.5.1. Typhoon wind data The site of interest in this study is an NPP site in South Korea. The sources of the typhoon observation data are datasets for severe tropical storms (STS) and typhoons (TY) during the period 1951e2014 from RSMC of the Japan Meteorological Agency. Through simulations, the optimal radius of inﬂuence of typhoons at the site was determined to be 300 km. Table 3 lists 53 typhoons that passed within 300 km from the Fig. 4. Relationship between Vmax;10 and Dp. 612 Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 interest and the typhoon center r, and (6) the heading angle of typhoon track (þfor counter-clockwise) q. The key parameters can be derived from observation data recorded at neighboring stations. 2.5.2.1. Central pressure difference. The central pressure difference Dp is a very important parameter in estimations of typhoon wind speeds. Fig. 4 shows the relationships between the maximum 10- min sustained wind speed Vmax;10 and the Dp value of typhoons that passed the Korean Peninsula from 1977 to 2015. A strong relationship between Vmax;10 and Dp is shown. Thus, the selection of the probabilistic distribution of Dp will signiﬁcantly inﬂuence the estimated wind speeds. To reduce any uncertainty in Dp, both the Weibull distribution and the lognormal distribution ﬁtting the observation data can be used. Fig. 5 shows the observed and ﬁtted probability distribution function (PDF) and cumulative distribution function (CDF) of the central pressure difference. Both the three-parameter Weibull distribution and three-parameter lognormal distribution are adequate to describe Dp, but the Weibull distribution is superior to Fig. 6. Modeled and observed values of rmw . the lognormal distribution because the calculated values of the Chi- Square goodness of ﬁt test for the Weibull and lognormal distri- butions are 8.64 and 10.00, respectively. the U.S. coastal area, the range of 0.5e2.5 [13,17,32] or 0.8e2.2 [15] is more reasonable. For the region where the aircraft data are 2.5.2.2. Radius to maximum wind. When the information of the available, the parameter B is estimated by ﬁtting. On the other RMW of a typhoon is absent in the historical records or a suitable hand, for the region where the aircraft data are not available, B can rmw model does not exist, a combination of available models can be be used by empirical formulae. used to minimize the uncertainty of the estimated values. Infor- Table 4 shows the three B parameter models used in this study. mation on the RMW is not available in the RSMC typhoon database, The proposed models are veriﬁed through a comparison of the although it has been provided in the JTWC best-track database outcomes when they are combined with three observed speeds: since 2001. In this study, the RMW information provided by JTWC is the maximum wind speed at RMW, 25 m/s (50 kt), and 15 m/s used as the RMW value. (30 kt). Fig. 6 shows a comparison of the modeled and observed values Fig. 7 compares the combined wind speed proﬁle with the three of rmw at the latitude of the site, j ¼ 35:415+ . It can be seen that the observed wind speeds for the Typhoon Soudelor (0306). It can be Vickery model [12] (Eq. (12)) can represent rmw well. seen that the combinations of the proposed models can represent the observed values very well. The same combinations of the lnðrmw Þ ¼ 2:636 0:00005086Dp2 þ 0:0394899j; slnðrmw Þ models were applied to eight different typhoons. As shown in Fig. 8, the predicted models can adequately represent the observed ¼ 0:3778 speeds within a radial distance of 300 km, which is the radius of the (12) It is noteworthy that the limits deﬁned by ±2s match the limits Table 4 of the observed data. Therefore, the distribution of the RMW can be B parameter models used in this study. deﬁned using the mean value and the mean ±2s. Equal weights are Model Values Weights used for the three values [31]. Powell [15] Mean 0.05 2.5.2.3. Pressure proﬁle parameter. The range of the pressure proﬁle Vickery [22] Mean 0.30 Holland07 0.7 0.65 parameter B is from 1.0 to 2.5 proposed by Holland [8]; however, for Fig. 5. Observed and ﬁtted distributions of Dp. Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 613 Fig. 7. Veriﬁcation of the proposed wind speed proﬁle models. Fig. 8. Comparison of predicted wind speed proﬁles with observed values. 614 Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 Fig. 9. Observed and ﬁtted distribution of VT . Fig. 10. Observed and ﬁtted distribution of r. inﬂuence of the typhoons at the site. X ∞ Pt ðV > vÞ ¼ 1 PðV < vjnÞ Pt ðnÞ; (13) 2.5.2.4. Translation velocity. The translation velocity of a typhoon n¼0 VT is determined from the 6-hourly position data of the typhoon center at two neighboring locations. In addition, VT is described in which PðV < vjnÞ denotes the probability that the wind speed V is through a lognormal distribution, as shown in Fig. 9. 2.5.2.5. Minimum distance. The minimum distance at the closest approach of a typhoon r is determined using the shortest straight line of the track based on 6-hourly records at two neighboring stations. The value of r is truncated to be less than or equal to 300 km, the radius of the inﬂuence of a typhoon. Here, r is modelled using a uniform distribution, as shown in Fig. 10. 2.5.2.6. Heading angle. The heading angle or approach angle q is determined based on the latitude and longitude of the typhoon center. The angle is taken counter-clockwise positively from the east, and the probability density and cumulative distribution are shown in Fig. 11. Here, q is described using a step function in this analysis. 2.5.3. Return period of extreme wind speeds The occurrence of a typhoon above a speciﬁed threshold in- tensity level is assumed to follow a Poisson distribution [33]. The probability that the typhoon wind speed is exceeded during time period t can be expressed as [12]. Fig. 11. Distribution of q. Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 615 less than v given that n storms occur, and Pt ðnÞ denotes the prob- ability of n storms occurring during a time period of t years. If Pt ðnÞ 1 Tvi ¼ : (16) is deﬁned as a Poisson process and t is set to one year, the annual 1 exp l 1 mþ1 i probability of exceeding a given wind speed is X ∞ 2.5.4. Logic tree ln exp½l Pa ðV > vÞ ¼ 1 F nv ¼ 1 exp½ lð1 Fv Þ; A logic-tree framework is a very useful tool that is widely used n¼0 n! to quantify the epistemic uncertainty associated with the inputs in (14) a hazard evaluation [34]. A logic tree consists of branches with alternative credible models and weights that represent degree-of- where F nv ≡PðV < vjnÞ, and the Poisson parameter l is the annual rate belief values pertaining to the applicability of the corresponding of occurrence of typhoons at the site of interest. In this study, a branch models. The epistemic uncertainty is expressed in a set of threshold storm intensity level of 25 m/s is considered and the branch weights. The weights for various branches are usually annual occurrence rate, l, is 0.828. assigned through subjective judgements by an expert or an expert A set of wind-ﬁeld parameters and wind speeds for a sufﬁciently group because the available data are often too limited for statis- large number of typhoons at the site of interest are obtained tical analyses. For instance, when conducting a probabilistic through a Monte Carlo simulation. The wind speeds are ranked in seismic hazard analysis (PSHA), SSHAC procedures [35] require order, and the probability of occurrence of the i-th ranking wind the broad involvement of experts to identify and quantify un- speed, vi , in a set of m wind speeds can then be written as [24]. certainties. Experts are asked to propose and evaluate different modeling alternatives by assigning different subjective weights (probabilities) to each of the possible alternatives [36]. Never- theless, there are several scientiﬁc challenges involved in both i Fvi ¼ : (15) populating the logic tree branches and in assigning weights to mþ1 these branches [37]. Thus, the mean recurrence interval, Tvi ; is determined by Fig. 12 shows the logic trees used for evaluating the typhoon Fig. 12. Logic tree for evaluating typhoon wind speed. 616 Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 3. Results and discussion A typhoon wind hazard assessment was conducted using a Monte Carlo simulation. To determine the wind speeds for return periods of up to 10,000,000 years, the simulation was run for 10,000,000 iterations. Fig. 13 shows eighteen hazard curves for all branches of logic trees shown in Fig. 12 and the weighted mean hazard curve for the simulated winds, which were generated from a simulation through random sampling of the typhoon parameters. The hazard curves are biased toward þ2s because two of the three wind speed proﬁle models give higher wind speeds than the pre- dicted model as shown in Fig. 8. For the annual exceedance proba- bility (AEP) of 1E-7, eighteen wind speeds are distributed between 48 m/s and 84 m/s, and a mean value of the simulated wind speeds is estimated as 60.6 m/s. The coefﬁcient of variation (COV) is less than 0.20. Fig. 14 shows hazard curves for all branches of logic trees and Fig. 13. Mean wind hazard curves for the simulated wind. the weighted mean hazard curve for the probable maximum winds (PMWs), which occur at r ¼ rmw . The wind speeds for the PMWs, estimated using Eq. (7), always exceed those for the simulated winds. For the AEP of 1E-7, the eighteen wind speeds are distributed between 57 m/s and 92 m/s, and a mean speed of the PMWs is estimated as 69.1 m/s. The COV for the PMWs is less than 0.20. The predicted mean values of 10-min wind speeds at the 10-m level for the simulated winds and the PMWs are presented in Table 5. The simulated wind speeds for return periods of 50, 100, and 200 years are in good agreement with the results of the pre- vious study [38]. 4. Conclusion A probabilistic typhoon hazard assessment was conducted using a logic tree for an NPP site. The logic tree branches were con- structed with three key parameters, i.e., the central pressure dif- ference, the pressure proﬁle parameter, and the radius to maximum wind. The parameter models and their weights were determined Fig. 14. Mean wind hazard curves for the probable maximum wind. using typhoon observation data. Using the logic tree and the Monte Carlo technique, the wind speeds from simulated typhoons and probable maximum wind speeds are estimated, with wind hazard wind speeds in this study. Here, three key parameters of the curves subsequently derived as a function of the annual exceedance typhoon wind ﬁeld model are used: the central pressure difference probability or return periods. A logic tree decreases the epistemic (Dp), the pressure proﬁle parameter (B), and the RMW (rmw ). For uncertainty included in the wind intensity models and gives Dp, two probability distributions, i.e., the Weibull distribution and reasonably acceptable wind speeds. The mean wind hazard curves lognormal distribution, are selected because these two probability for the simulated and probable maximum winds can be used for the models are commonly adopted in predictions of typhoon wind design and risk assessment of an NPP. To minimize the uncertainty speeds. The weights for Dp are set to 0.6 and 0.4, respectively, for included in the wind hazards, uncertainties in the applicable wind the Weibull distribution and the lognormal distribution based on ﬁeld models should be reduced and the scientiﬁc challenges asso- the result of Chi-Square goodness of ﬁt tests. ciated with assigning weights to the branch models of a logic tree should be resolved. Table 5 Predicted 10-min mean wind speeds at 10 m-level. Return period (year) Annual exceedance probability Simulated wind speed (m/s) PMW speed (m/s) Kang et al. [38] 20 5E-2 25.2 31.4 e 50 2E-2 29.0 37.3 30.1 100 1E-2 31.8 40.6 31.9 200 5E-3 34.4 43.6 33.3 500 2E-3 37.4 47.1 e 1000 1E-3 39.7 49.6 e 10,000 1E-4 46.4 56.8 e 100,000 1E-5 52.5 62.2 e 1,000,000 1E-6 57.1 65.9 e 10,000,000 1E-7 60.6 69.1 e Y.-S. Choun, M.-K. Kim / Nuclear Engineering and Technology 51 (2019) 607e617 617 Conﬂicts of interest parameter and radius to maximum winds of hurricanes from ﬂight-level pressure and H*Wind data, J. Appl. Meteor. Climatol. 47 (2008) 2497e2517. [18] Federal Emergency Management Agency, Multi-Hazard Loss Estimation All contributing authors declare no conﬂicts of interest. Methodology: Hurricane Model, HAZUS-MH 2.1 Technical Manual, FEMA, Washington, D.C., USA, 2012. Acknowledgments [19] L. Zhao, A.P. Lu, L.D. Zhu, S.Y. Cao, Y.J. Ge, Radial distribution of typhoon pressure ﬁelds measured by ground multi-point pressure distribution, in: Proceedings of the 7th International Colloquium on Bluff Body Aerodynamics This work was supported by the National Research Foundation and Applications (BBAA7), Shanghai, China, September 2-6, 2012. of Korea (NRF) grant funded by the Korea government (MOE) (NRF- [20] G.D. Hubbert, G.J. Holland, L.M. Leslie, M.J. Manton, A real-time system for forecasting tropical cyclone storm surges, Weather Forecast. 6 (1991) 86e97. 2017M2A8A4015290). [21] B.A. Harper, G.J. 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