Estimating the Risk of Extreme Wind Gusts in Tropical Cyclones Using Idealized Large-Eddy Simulations and a Statistical–Dynamical Model

Daniel P. Stern aUniversity Corporation for Atmospheric Research, Monterey, California

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George H. Bryan bNational Center for Atmospheric Research, Boulder, Colorado

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Chia-Ying Lee cLamont-Doherty Earth Observatory, Columbia University, Palisades, New York

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James D. Doyle dU.S. Naval Research Laboratory, Monterey, California

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Abstract

Recent studies have shown that extreme wind gusts are ubiquitous within the eyewall of intense tropical cyclones (TCs). These gusts pose a substantial hazard to human life and property, but both the short-term (i.e., during the passage of a single TC) and long-term (over many years) risk of encountering such a gust at a given location is poorly understood. Here, simulated tower data from large-eddy simulations of idealized TCs in a quiescent (i.e., no mean flow or vertical wind shear) environment are used to estimate these risks for the offshore region of the United States. For both a category 5 TC and a category 3 TC, there is a radial region where nearly all simulated towers experience near-surface (the lowest 200 m) 3-s gusts exceeding 70 m s−1 within a 10-min period; on average, these towers respectively sample peak 3-s gusts of 110 and 80 m s−1. Analysis of an observational dropsonde database supports the idealized simulations, and indicates that offshore structures (such as wind turbines) in the eyewall of a major hurricane are likely to encounter damaging wind speeds. This result is then incorporated into an estimate of the long-term risk, using analyses of the return period for major hurricanes from both a best-track database and a statistical–dynamical model forced by reanalysis. For much of the nearshore region of the Gulf of Mexico and southeastern U.S. coasts, this analysis yields an estimate of a 30%–60% probability of any given point experiencing at least one 70 m s−1 gust within a 30-yr period.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Daniel P. Stern, dstern@ucar.edu

Abstract

Recent studies have shown that extreme wind gusts are ubiquitous within the eyewall of intense tropical cyclones (TCs). These gusts pose a substantial hazard to human life and property, but both the short-term (i.e., during the passage of a single TC) and long-term (over many years) risk of encountering such a gust at a given location is poorly understood. Here, simulated tower data from large-eddy simulations of idealized TCs in a quiescent (i.e., no mean flow or vertical wind shear) environment are used to estimate these risks for the offshore region of the United States. For both a category 5 TC and a category 3 TC, there is a radial region where nearly all simulated towers experience near-surface (the lowest 200 m) 3-s gusts exceeding 70 m s−1 within a 10-min period; on average, these towers respectively sample peak 3-s gusts of 110 and 80 m s−1. Analysis of an observational dropsonde database supports the idealized simulations, and indicates that offshore structures (such as wind turbines) in the eyewall of a major hurricane are likely to encounter damaging wind speeds. This result is then incorporated into an estimate of the long-term risk, using analyses of the return period for major hurricanes from both a best-track database and a statistical–dynamical model forced by reanalysis. For much of the nearshore region of the Gulf of Mexico and southeastern U.S. coasts, this analysis yields an estimate of a 30%–60% probability of any given point experiencing at least one 70 m s−1 gust within a 30-yr period.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Daniel P. Stern, dstern@ucar.edu

1. Introduction

The lowest kilometer within the eyewall of intense (categories 4 and 5) tropical cyclones (TCs) is characterized by some of the strongest wind speeds found anywhere on Earth. A recent analysis of dropsonde observations indicates that gusts in excess of 90 m s−1 are common within such TCs (Stern et al. 2016), as nearly every category 5 hurricane that has been sampled by aircraft has at least one such sonde measurement (Stern and Bryan 2018, hereafter SB18). In situ observations within the boundary layer of TCs are generally quite sparse, and even in the most intensively sampled storms, there are only 10–20 sondes released within the region of maximum wind speed for a given flight. Therefore, it is quite challenging to quantitatively estimate the frequency of extreme wind gusts. We can make progress in this respect through the use of emerging technologies such as fine-resolution radars (Guimond et al. 2018) and drones (Cione et al. 2020), but also with very high-resolution numerical simulations. For example, SB18 analyzed a large-eddy simulation (LES) of a category 5 hurricane, and from simulated dropsonde profiles, found that for four randomly located eyewall sondes (a typical observational strategy for a single NOAA P3 or Air Force C-130 flight), the peak sampled wind speed was most likely to range from 95 to 105 m s−1. They also found that for a single random sonde dropped near the radius of maximum winds (RMW), there was a greater than 90% chance of the peak sampled wind speed exceeding 90 m s−1. Notably, the true peak instantaneous wind speeds in the simulation examined in SB18 substantially exceeded that which would be sampled by a realistic number of simulated dropsondes, and gusts exceeding 120 m s−1 were present somewhere within the simulated TC at nearly all times.

In addition to SB18, several other studies (e.g., Wu et al. 2018, 2019; Ito et al. 2017; Ren et al. 2020; Cécé et al. 2021) have begun to investigate extreme wind gusts in TCs using the LES framework. Wu et al. (2018) and Wu et al. (2019) used a 37-m grid spacing WRF-LES run to examine “tornado-scale vortices” in the eyewall. Their simulation was semi-idealized, embedding a vortex within the large-scale environment derived from Typhoon Matsa (2005). These studies found vortices of 1–2-km horizontal scale (somewhat larger than seen in SB18) along the inner edge of the TC eyewall, associated with both extreme updrafts and relatively strong surface wind speeds. Notably, nearly all of the diagnosed tornado-scale vortices (based on a threshold of vertical velocity and vorticity) in their simulated category 3 TC occurred in the left-of-shear semicircle, consistent with the dropsonde analyses of Stern et al. (2016).1

Ren et al. (2020) used WRF-LES to conduct idealized simulations at varying grid spacings (as fine as 62 m) with different SSTs, using a similar setup to the study of Rotunno et al. (2009), who were the first to present TC simulations at such high resolution. Ren et al. (2020) found that small-scale turbulent features could occur at coarser grid spacings for higher SSTs. However, as the TC mean intensity generally increases with increasing SST, it is difficult to separate any direct effects of SST from that of intensity itself. They also found that the RMW was larger at high SST, and argued that this would therefore result in greater damage from extreme wind gusts for such TCs. It is unclear if this result is robust, as these differences tended to emerge as a response to the initialization of the high-resolution nests, and also because there are several different factors that have been shown to modulate TC size (e.g., Hill and Lackmann 2009; Xu and Wang 2010), and which factor is dominant in reality remains poorly understood.

Recently, Cécé et al. (2021) used WRF-LES to simulate category 5 Hurricane Irma [2017; best track intensity: 155 knots (kt) or ∼80 m s−1] at 31-m grid spacing, focusing on extreme wind gusts during passage over islands in the Lesser Antilles. Over a 6-h period, they found that locations over the ocean at 10 m above sea level (ASL) experienced peak 3-s wind gusts of ∼100 m s−1 for a ∼70 m s−1 peak 1-min mean wind speed. Both 3-s gusts and 1-min mean surface wind speeds could be greatly enhanced over island terrain in their simulation, exceeding 180 and 140 m s−1 respectively (their Figs. 8 and 9). Although they did not analyze the environmental vertical wind shear and its relationship to storm structure, it can be seen that one half of the simulated Irma experienced substantially higher gusts than the other, consistent with Wu et al. (2018) and Stern et al. (2016), and with the known effects of shear in inducing wavenumber-1 asymmetries in TCs (e.g., Uhlhorn et al. 2014; Klotz and Jiang 2017). Similar to SB18, Cécé et al. (2021) found that the extreme wind gusts were associated with vortices and updrafts on a scale of approximately 500 m.

Wurman and Kosiba (2018) documented tornado-scale vortices in the eyewall of Hurricane Harvey (2017) as it made landfall in Texas, using Doppler on Wheels (DOW) and a collocated anemometer (at 8 m AGL), and were able to relate individual vortices to localized enhanced wind damage. Such vortices were trackable for a few minutes as they translated at ∼50 m s−1 over distances of ∼10 km, and locally enhanced the wind speed at the DOW by 10–20 m s−1 for a period of less than 10 s. All of these characteristics (including the implied spatial scale of ∼500 m) are similar to what was seen in the simulation of SB18, except the translation speed of the vortices was greater (∼75 m s−1) in the idealized simulation, consistent with Harvey being less intense overall (115 kt ≈ 59 m s−1) than the simulated TC (150 kt ≈ 77 m s−1). Accordingly, the peak 3-s wind gust adjusted to 10 m reported in Wurman and Kosiba (2018) for Harvey was only 63 m s−1, although this was also likely influenced by both local flow over land and the fact that Harvey started to rapidly weaken at landfall.

From a societal perspective, it is important to understand the risk of encountering such near-surface extreme wind gusts, which pose a threat to both human life and property. For a direct hit by a given storm, the risk of gusts exceeding a given threshold depends on the frequency of the gusts, the areal extent of the region which contains these gusts, and the translation speed of the storm. The long-term climatological risk further depends on the statistical return period of TCs of sufficient intensity to produce extreme wind gusts. These two types of risk are both important to understand, and they are both difficult to estimate. For many years, the National Hurricane Center (NHC) has used a Monte Carlo technique (known as HURISK) to estimate the climatological return periods of TCs of various intensity thresholds for points within the North Atlantic basin (Neumann 1987). NHC has used HURISK to produce maps of the return period of (for example) major hurricanes (peak surface wind speed ≥ 96 kt ≈ 49 m s−1) for locations along the U.S. coastline (Fig. 1). It can be seen that the regions from southeast Texas to the Florida Panhandle, southern Florida, and South and North Carolina have return periods for a major hurricane (passing within 50 n mi of a given point) of 30 years or less. Therefore, these regions are relatively susceptible to encountering extreme wind speeds, but it is not straightforward to use the return periods of major hurricanes to quantitatively estimate the long-term risk of short-period (e.g., 3-s) gusts at a given point. The reason is that the region of strong winds in a hurricane is relatively compact (varying between approximately 25- and 100-km diameter) and so may not pass over a given point, and because the most extreme gusts occur on even smaller scales (500–1000 m). The likelihood of a given location experiencing these gusts during storm passage is unclear, and is the primary focus of this study.

Fig. 1.
Fig. 1.

The return period of major hurricanes for locations along the U.S. Atlantic and Gulf coasts, from an analysis by NHC. The analysis uses the HURISK program (Neumann 1987) with data through 2010, and the return period is for the passage of a major hurricane within 50 n mi (∼93 km) of a given location. The blue circles highlight regions where the return period is less than 30 years. This image is adapted from a figure produced by NHC, available at https://www.nhc.noaa.gov/climo/images/return_mjrhurr.jpg.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Numerous studies have attempted to statistically estimate the return periods of TCs of varying intensities for different locations, either semiempirically (e.g., Darling 1991; Keim et al. 2007; Emanuel and Jagger 2010), by fitting a probability distribution to the historical record of estimated TC tracks and intensities (e.g., Rupp and Lander 1996; Jagger et al. 2001; Malmstadt et al. 2010), or through statistical–dynamical downscaling (e.g., Emanuel et al. 2006; Lee et al. 2018, 2020). Tropical cyclone “intensity” is usually defined as some measure of the maximum “sustained” surface [generally taken to be 10 m above sea level (ASL)] wind speed anywhere within the storm. For example, in the United States, the maximum 1-min average wind speed at 10 m ASL is used to define intensity. On the other hand, wind damage might be more related to shorter-period gusts; in the wind engineering community, the peak 3-s average wind speed (within some defined longer period) is generally used for determining construction standards (e.g., ASCE 2013; API 2007). Note, however, that the most relevant timescale for damage-producing winds is uncertain (Doswell et al. 2009; Blanchard 2013; Wurman et al. 2013; Dahl et al. 2017), and the 3-s standard is based on the measurement interval of historical anemometers (Harper et al. 2010; Dahl et al. 2017). The aforementioned TC climatology studies typically estimate return periods for 1-min (Rupp and Lander 1996; Jagger et al. 2001; Keim et al. 2007; Emanuel and Jagger 2010; Malmstadt et al. 2010) or 10-min (Darling 1991) wind speeds. However, some studies (Rupp and Lander 1996) also rely on 3-s gust measurements as the data source for their estimates, using an assumed gust factor to convert between 3-s and 1-min wind speeds. Indeed, this procedure is consistent with the current NHC method for analyzing/forecasting gust strength, where a factor of 1.20 is used (J. Cangialosi 2016, personal communication). The guidance produced by the American Petroleum Institute (API 2007) for risk to offshore oil platforms in the Gulf of Mexico provides estimates of expected peak 3-s gusts for various return periods, but these are also calculated through the use of an assumed gust factor, in this case from 1-h wind speeds. Due to the difficulty in obtaining high-frequency wind speed data in the inner core of intense hurricanes, the reliability of these techniques are uncertain [see Harper et al. (2010) for an overview and discussion of gust factors and the challenges in converting wind speeds among different averaging periods]. SB18 found in their simulation that the peak 3-s wind speed at 10 m ASL was on average 1.30 times the peak 1-min wind speed, and so it is possible that near-surface wind gusts in intense TCs are stronger than is often assumed—for example, Table 1 of Harper et al. (2010) recommends a gust factor of 1.11 for open-ocean conditions, and the 3-s to 1-min gust factor used by API (2007) varies from ∼1.12 to 1.19 as 1-min wind speed increases from ∼25 to 80 m s−1.

The purpose of this study is to use simulations, such as the one analyzed by SB18, to gain insight into the risk posed to offshore structures by extreme wind gusts in tropical cyclones. This work is largely inspired and motivated by the recent studies of Worsnop et al. (2017) and Kapoor et al. (2020), who used the same simulation as SB18 to demonstrate that gusts within a category 5 hurricane can exceed the design criterion of offshore wind turbines. As discussed in Worsnop et al. (2017), there are plans to develop offshore wind farms near the U.S. coastline, including within regions that are vulnerable to tropical cyclones. Current design standards are for survival of turbines in mean wind speeds of up to 50 m s−1 and 3-s gusts of up to 70 m s−1, both of which were shown by Worsnop et al. (2017) to be exceeded in their simulated hurricane. Indeed, coastal (onshore) wind turbines have been damaged or destroyed by typhoons in the west Pacific (Ishihara et al. 2005; Chen and Xu 2016). Note that although the specific motivating analysis of our study is the risk to offshore wind turbines, our methodology and analysis is equally applicable to any offshore structures.2 For example, numerous offshore oil and natural gas platforms in the Gulf of Mexico were damaged or destroyed (Cruz and Krausmann 2008) by Hurricanes Katrina (2005) and Rita (2005), and so our study is also relevant for understanding the risk to these structures.

Offshore structures are generally engineered to withstand wind speeds based on the maximum value that is expected, on average, to be exceeded once within a chosen time period; for example, a 50-yr return period is often used (IEC 2009; Rose et al. 2012). Due to the difficulties in measuring wind speed in TCs and the limited historical record of TC tracks and estimated intensities, there remains a great deal of uncertainty in the estimation of the expected maximum wind gust that will be encountered by a given structure over its lifetime. In this study, we extend the analyses of Worsnop et al. (2017) and Kapoor et al. (2020), in order to provide an estimate of the probability that a given structure in the offshore U.S. Gulf and Atlantic coasts will experience extreme (defined here as ≥70 m s−1) near-surface (0–200 m ASL) wind gusts over a long period of time. In section 2, we provide an overview of the LES technique and of the simulations that we analyze. In section 3, we assess the peak wind gusts as a function of radius, height, and storm intensity, and determine the probability of given locations within a single TC sampling extreme wind gusts over a short period (10 min) of time. In section 4, we combine our analysis of wind gusts with analyses of the return period of major hurricanes [using both the best track data and the statistical–dynamical model of Lee et al. (2018)] in order to provide an estimate of the long-term (30 yr) probability of a given location within the Gulf of Mexico or the Atlantic coast of encountering an extreme wind gust. We present a summary and conclusions in section 5.

2. Simulation methodology and overview

a. The LES framework

We use Cloud Model 1 (CM1; Bryan and Fritsch 2002; Bryan and Rotunno 2009; Bryan and Morrison 2012) to simulate idealized TCs at turbulence-resolving resolutions, following the technique described in detail in Bryan et al. (2017a). A brief description is as follows. An axisymmetric simulation is run for a period of 12 days, and a time average from this precursor simulation is used to define the initial conditions for the large-eddy simulation, with the time period chosen based on the desired intensity. For example, the simulation analyzed in both Worsnop et al. (2017) and SB18 used a precursor axisymmetric simulation from t = 11 days (averaged over a 48-h period), in order to simulate a small and very intense TC in the LES. We will analyze that same simulation in this study and hereinafter refer to it as the Cat5 simulation. The Cat5 simulation was run on a 3000 km × 3000 km domain, which is large enough to contain the entire tropical cyclone. An 80 km × 80 km LES subdomain in the domain center has uniform horizontal grid spacing of 31.25 m. This fine-mesh region covers the inner core (eye and eyewall and nearby rainbands) of the TC, and the grid spacing stretches outside this region, increasing to 15 km at the domain boundary. The vertical grid spacing (throughout the domain) is 15.125 m within the lowest 3 km ASL, increasing gradually to 500 m at 8 km ASL, where it remains until the model top at 25 km ASL.

Inside of the fine-mesh region, no parameterization of the boundary layer is used, only an LES subgrid turbulence parameterization that is based on Deardorff (1980) plus a “two-part” eddy viscosity model near the surface following Bryan et al. (2017b). Resolved turbulent kinetic energy (TKE) is much greater than parameterized TKE except at the lowest two model levels (not shown), indicating that the simulation explicitly simulates the most energetic turbulent eddies using the model’s governing equations of motion. Outside of the fine-mesh region, the model is configured for traditional mesoscale simulations, using a Louis-type PBL parameterization (Louis 1979; Kepert 2012), with an asymptotic vertical mixing length l = 100 m. At the edge of the fine-mesh region, the “eddy-injection” technique of Bryan et al. (2017a) is used to stimulate turbulence, which otherwise can be slow to develop when transitioning from low to high resolution. This technique nudges three-dimensional velocity fields into a narrow transition zone using perturbations from a precursor small-domain LES (Bryan et al. 2017b).

Further details on model settings for the Cat5 simulation are given in SB18. In addition to the Cat5 simulation, in this study we present results from two additional simulations, which we refer to as Cat3 and Cat1, based on their approximate intensities.3 The Cat3 and Cat1 simulations are initialized from the same axisymmetric precursor simulation as the Cat5 simulation, but at earlier time periods (t = 60 and 49 h, respectively), corresponding to weaker mean intensities. Due to the computational expense, only the Cat5 simulation was run at the highest resolution, and so the Cat3 and Cat1 simulations were run with a horizontal grid spacing of 62.5 m within the fine-mesh region, and a vertical grid spacing of 31.25 m below 3 km ASL (i.e., twice the respective grid spacings of the Cat5 simulation).

Figure 2 shows time series of the instantaneous and 1-min averaged maximum 10-m wind speed for all three simulations. Consistent with SB18, starting from an axisymmetric initial condition, boundary layer turbulence rapidly develops in all simulations, and the peak instantaneous wind speed becomes essentially statistically steady after 20 min of model integration (other features of the simulated TC, such as the magnitude, width, and location of the mean eyewall updraft, take ∼1 h to reach approximate steady state).4 Peak instantaneous surface wind speed is typically 110–120, 80–90, and 50–60 m s−1 for the Cat5, Cat3, and Cat1 storms, respectively. These values may seem large, but recall that such local maxima occur at small scales (∼100–500 m), and that “intensity” is generally defined by the maximum of a longer-period time-averaged wind speed. The peak 1-min mean surface wind speed averaged over the final hour of each simulation is respectively 77, 59, and 43 m s−1 for the Cat5, Cat3, and Cat1 storms, and these mean intensities remain fairly steady.5

Fig. 2.
Fig. 2.

Time series of (a) the maximum instantaneous wind speed (over the previous minute) at 10 m ASL and (b) the maximum 1-min averaged wind speed at 10 m ASL, for the Cat1, Cat3, and Cat5 simulations. The x-axis and y-axis ranges are both different between (a) and (b). Note that (a) shows the full 4 h of each simulation, whereas only the final hour of each simulation is shown in (b).

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

All three idealized simulations examined here have relatively small eyewalls/RMWs; the Cat5 storm was inspired by Hurricane Felix (2007), a storm that was documented by Aberson et al. (2017) to be characterized by both extreme wind speeds (100 m s−1 measured by a dropsonde within the lowest 150 m ASL) and extreme updrafts (31 m s−1 measured in situ by the NOAA P3 aircraft at ∼3 km ASL). As discussed below with respect to simulated tower data and as demonstrated in SB18 using simulated dropsonde data, these simulations are realistic in that TCs have been observed with similar characteristics (e.g., size, peak wind gusts), but it should be kept in mind that with only three simulations, we have yet to fully explore with LES the parameter space of TCs in terms of both size (in particular) and intensity. We discuss additional caveats, such as the representativeness of the assumed drag coefficient, and the lack of storm motion and environmental vertical wind shear, in section 5.

b. Simulated tower data

As described in Worsnop et al. (2017), simulated tower data are obtained for the Cat5 simulation by saving velocities at every time step (0.1875 s) for a 10-min period at the end of the simulation, on all 33 model levels between 7.81 and 507.81 m, every 1 km horizontally (every 32nd grid point) within the innermost 60 km × 60 km region of the domain [3721 towers; see Fig. 1 of Worsnop et al. (2017)]. Figure 3a shows the 10-min time series of wind speed at model level 7 (∼100 m) for a simulated tower located within the eyewall, indicating the instantaneous values, as well as the 3-s, 1-min, and 10-min means. This tower has the highest instantaneous and 3-s wind speeds sampled at this level, and so although it is not representative of the typical maximum for a given tower in our dataset, it is illustrative of what is possible in terms of wind speed fluctuations in LES. Also note that, because of limited sampling, the gusts experienced by this tower still underestimate the true maximum within the simulated TC (SB18). At this fixed point, the 10-min mean wind speed is 88 m s−1, while the 1-min mean fluctuates between 83 and 95 m s−1. Within this period, there about 15–20 distinct gusts (depending on how they are defined) evident in the 3-s wind speed, typically with peak magnitudes of 95–105 m s−1, but with one gust exceeding 120 m s−1. For reference and comparison, Fig. 3b shows time series for the same tower, but for the 10-m wind speed. The 1-min mean surface winds fluctuate between 63 and 74 m s−1, and so this simulated tower is experiencing category 5 surface winds. The 3-s wind speeds vary between 50 and 93 m s−1, indicative of the tremendous horizontal gradients that are present within the eyewall of this simulated TC (cf. Figs. 9 and 10 of SB18).

Fig. 3.
Fig. 3.

For the Cat5 simulation, time series of the wind speed at (a) model level 7 (∼100 m ASL) and (b) at 10 m for the simulated tower that sampled the strongest instantaneous wind speed over a 10-min period. The instantaneous (blue), 3-s (red), 1-min (magenta), and 10-min (black) mean wind speeds are shown. Note that the y-axis values differ between (a) and (b), but the range is the same.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Figure 4a shows the time–height cross section of instantaneous wind speed for the same tower discussed above, in the lowest 500 m ASL for t = 5–10 min (of the sampled period). It can be seen that although there is variability on multiple time scales, there are approximately 1–2 prominent gusts per minute (as indicated by the 100 m s−1 contours highlighted in Fig. 4), each lasting for 5–15 s. The gusts are also vertically coherent, often extending over depths of 200–400 m, including down to the lowest model level. Figure 4b shows the same data as Fig. 4a, but is zoomed in on a 1-min period that includes the peak wind gust, and it is evident that this gust is experienced for 5–10 s, nearly throughout the lowest 500 m. SB18 found that the features responsible for the extreme wind gusts in this simulation translated azimuthally within the eyewall at ∼75 m s−1 (implying a time scale at a fixed point of ∼7 s) and are associated with coherent eddies with a spatial scale on the order of 500 m (see Fig. 10 of SB18). This scale is roughly consistent with the 1-km estimated horizontal scale of the eyewall vorticity maximum encountered by the NOAA P3 aircraft in Hurricane Hugo (1989) (Marks et al. 2008), which was associated with a wind speed maximum of 82 m s−1 at 450 m ASL, and similar to (although somewhat smaller than) the 1–3-km scale features with 70–85 m s−1 wind speeds observed by Guimond et al. (2018) with the Imaging Wind and Rain Airborne Profiler (IWRAP) radar in Hurricane Rita (2005). It is also consistent with the ∼500-m scale documented by Wurman and Kosiba (2018) for such vortices observed by the DOW in Hurricane Harvey (2017), and qualitatively similar to the dropsonde and flight-level observations of Aberson et al. (2006) in Hurricane Isabel (2003) and Aberson et al. (2017) in Hurricane Felix (2007). Also note that the translation speed of the vortices in the Cat5 simulation is comparable to that inferred from radar reflectivity features in Isabel (Aberson et al. 2006).

Fig. 4.
Fig. 4.

For the Cat5 simulation, time–height plots of the instantaneous wind speed over the lowest 500 m ASL for the simulated tower that sampled the strongest instantaneous wind speed over a 10-min period. (a) A 5-min period (t = 300–600 s from the start of the tower data) and (b) a 60-s subset of this period (t = 500–560 s), with both (a) and (b) including data from every model time step. The feature corresponding to the peak wind speed passes this simulated tower at approximately t = 530–540 s. The black contour indicates 100 m s−1.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

It is evident that in this Cat5 simulation, the peak 3-s wind speeds that occur throughout the lowest 500 m greatly exceed the design criterion (70 m s−1) for offshore wind turbines (Worsnop et al. 2017). Although the simulated TC here is particularly intense, it is realistically so, with maximum 1-min surface wind speeds (∼150 kt ≈ 77m s−1) that are similar to those in Hurricanes Mitch (1998), Katrina (2005), Rita (2005), Dean (2006), Felix (2007), Irma (2017), and Maria (2017), and weaker than in Wilma (2005) and Dorian (2019).6 The peak tower-sampled 3-s gusts of 102 m s−1 at 10 m ASL and of 124 m s−1 at any height in the Cat5 simulation7 are also comparable to the strongest dropsonde sampled wind speed (111 m s−1 at ∼150 m ASL; Stern et al. 2016) and the strongest 10 m AGL 3-s gust (113 m s−1; Courtney et al. 2012) observed in real tropical cyclones. So it is clearly possible for a wind turbine (or other offshore structure) to experience wind gusts that are capable of resulting in its destruction, consistent with Worsnop et al. (2017). The more practical question is: what is the likelihood of such gusts occurring at any given location? We will address this question in the following sections.

3. The frequency of extreme wind gusts within a tropical cyclone

a. Assessing the simulations and sensitivity to TC intensity

Figure 5 shows horizontal cross sections (at 10 and 100 m ASL) of the 3-s average wind speed, for each of the simulations. It can be seen that, as expected, the 3-s wind speeds increase with the mean intensity. A close examination reveals some effects of model grid spacing, as some smaller-scale features are evident in the Cat5 simulation (Δx = 31.25 m) as compared to the Cat3 and Cat1 simulations (Δx = 62.5 m). Nevertheless, similar small-scale (∼500 m) local wind maxima are present in all simulations. As all three simulations are initialized (at different times) from the same precursor axisymmetric simulation, they share a similar vortex structure and all have similarly small RMWs. Although TCs tend to contract as they intensify, contraction is often completed well before the end of intensification (Stern et al. 2015), and so it is not actually unusual for a category 3 TC to be slightly smaller than a category 5 TC (as seen in our simulations), despite the climatological relationship for a stronger storm to be on average smaller (which we document later in this study).

Fig. 5.
Fig. 5.

Example horizontal cross sections of the 3-s mean wind speed, at (left) 10- and (right) 100-m height, for the (top) Cat1, (middle) Cat3, and (bottom) Cat5 simulations. Only the northeast quadrant (20 km × 20 km) is shown, and the respective maximum value shown is indicated in the upper right of each panel. For the right panels, the radius of peak azimuthal-mean 3-s wind gust (within a 10-min period) is indicated by the dashed quarter-circle, and the inner and outer extents of the 70 m s−1 azimuthal-mean 3-s wind gust are indicated by the solid quarter-circles. Note that these radii are obtained from the simulated tower data shown in Fig. 6, and the respective time periods are not exactly the same as for the cross-sectional data.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Figure 6 shows the peak 3-s gust over a 10-min period for each of the simulations, as a function of radius (0–25 km) and height (0–200 m). Similar to Worsnop et al. (2017), we produce these analyses on a radius-height grid with 1-km-wide radial bins, and extract the peak 3-s wind speed from each tower. For the left panels (Figs. 6a–c), we then take the maximum over all towers within each radial bin, and at each model level. This analysis shows the absolute maximum (sampled) 3-s wind speed as a function of radius and height. For the right panels (Figs. 6d–f), we take an average of the peak gusts over all of the towers within each bin, and so this analysis shows the expected peak 3-s wind speed that would, on average, be encountered over a 10-min period. Not surprisingly, the peak 3-s gust increases with TC intensity, and the absolute maximum gust is (by definition) stronger than the azimuthal-mean peak gust. More interesting is that for the Cat3 and Cat5 storms, the azimuthal-mean peak 3-s gust greatly exceeds 70 m s−1 (Figs. 6e,f). In other words, if a wind turbine (or other structure) were in the eyewall of these simulated TCs for 10 min, on average, it would encounter a peak 3-s wind speed of about 80 and 110 m s−1, respectively. Also note that the magnitude of these peak wind speeds does not vary much between 50 and 200 m ASL, which is the layer where the hub height of most offshore wind turbines is found.

Fig. 6.
Fig. 6.

For the (top) Cat1, (middle) Cat3, and (bottom) Cat5 simulations, the (left) maximum and (right) azimuthal-mean peak 3-s wind speed over the radially binned towers as a function of radius (0–25 km) and height (0–200 m ASL). For each individual simulated tower, the peak 3-s wind speed over a 10-min period is taken. The 70 m s−1 contour is thickened, and the maximum value shown for each panel is indicated at the top right.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

To gain insight into the risk of structures encountering extreme wind gusts, we compute the probability that a given tower will sample 3-s winds in excess of 70, 80, and 90 m s−1, as shown in Fig. 7, for the Cat3 and Cat5 simulations (for Cat1, the probabilities are everywhere zero). For Cat5 (Figs. 7d–f), there is an annular region where every simulated tower samples gusts exceeding each of these thresholds (corresponding to 100% frequency). This region is about 10 km wide for 70 m s−1, narrowing to about 5 km for 90 m s−1, and extending down to or very near to the lowest model level for all thresholds. This simulation strongly suggests that any point in the lowest 200 m experiencing the eyewall for at least 10 min would encounter at least one 3-s gust of 70 m s−1 or greater. For the Cat3 simulation, the chances of a given location encountering a 90 m s−1 wind gust are very small (Fig. 7c), although nonzero over a narrow region. However, the probabilities of exceeding 80 m s−1 are substantial (Fig. 7b), and for 70 m s−1 (Fig. 7a) the probabilities are greater than 90% over a several kilometer wide region.

Fig. 7.
Fig. 7.

For the (left) Cat3 and (right) Cat5 simulations, the percentage of towers in each radial bin and at each model level that have at least one 3-s gust within a 10-min period exceeding (top) 70, (middle) 80, and (bottom) 90 m s−1. The maximum value shown for each panel is indicated at the bottom right. Note that the contoured range in (c) differs from the other panels.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

The above frequencies of encountering an extreme wind gust are calculated over a 10-min period. As the probability of such an encounter will generally depend on the length of time that a given location experiences sufficiently strong mean wind speeds, it is worth examining whether or not 10 min is representative of the actual time expected for the period of strong winds in a real TC. Unlike most real TCs, our simulated TCs do not translate because, for simplicity, we do not impose any environmental mean flow. Therefore, we cannot directly evaluate this question using the simulations alone. However, we can gain insight by using the simulations in conjunction with an assessment of the translation rate of observed TCs. Figure 8 shows the translation speed of TCs observed in the Gulf of Mexico and near-coastal western Atlantic (from the HURDAT2 best track dataset), as a function of intensity. There is a tendency for stronger TCs to move slightly faster, though the median translation speed is near 5 m s−1 for all intensities above 100 kt (≈51 m s−1), and the middle 50% of the distribution falls between about 3.5 and 7 m s−1.

Fig. 8.
Fig. 8.

The median (blue) and 25th and 75th percentiles (black) of the storm translation speed (m s−1) for TCs within the Gulf of Mexico and near-coastal western Atlantic (west of 75°W and north of 20°N) from 1944 to 2019, binned by best track intensity (kt). Each intensity bin includes the plotted intensity and the value 5 kt lower, except the first and last bins, which also include all remaining weaker and stronger intensities, respectively.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

It can be seen from Fig. 7 that there is a sharp radial gradient in the frequencies of extreme wind gusts in the simulations, and the regions exceeding 90% for the 70 m s−1 threshold are approximately 3 and 10 km wide for the Cat3 (Fig. 7a) and Cat5 (Fig. 7d) TCs, respectively. The passage of such regions would therefore be expected to take about 10 and 30 min, given a translation speed of about 5 m s−1. This time is for only one side of the eyewall; assuming an equally strong eyewall on the other side of the TC, the total expected time of sufficiently strong mean winds would be 20 and 60 min, respectively. Real TC wind fields are often somewhat asymmetric (e.g., Kepert 2006; Uhlhorn et al. 2014; Klotz and Jiang 2017), even for intense hurricanes (e.g., Stern et al. 2016; Didlake et al. 2017; Guimond et al. 2018), and so this latter estimate is likely an upper bound (for the assumed translation speed). As noted above, however, our simulated TCs are on the smaller end of the observed distribution (particularly for the Cat1 and Cat3 simulations; see later analysis in section 4b), and this may lead to an underestimate of the typical width of the region of strong wind speeds, as it can be shown that for a Rankine vortex (a widely used model for TC structure), the radial extent of any wind speed threshold (e.g., 70 m s−1) increases proportionally with the RMW. Given these complicating factors, the length of time for which a given location is exposed to extreme wind gusts in real TCs is uncertain and merits further investigation. However, for a direct hit by a major hurricane, the period in which near-surface gusts exceeding 70 m s−1 could potentially occur is likely in general to be longer than 10 min, and so our estimated exceedance frequencies from Fig. 7 may be underestimates (where less than 100%) because of the limited period of sampling within the simulation.

b. Comparison to observations

It is difficult to compare the above analyses of simulated tower data to observations from real TCs, because such tower data within the inner core of major hurricanes are extremely rare. Although the advent of airborne and satellite remote sensing platforms such as SFMR and SAR has proved invaluable for estimating tropical cyclone mean intensity, such measurements require calibration against an external source, and as they are calibrated to correspond to the 1-min average wind speed at 10-m ASL over a spatial scale of a few kilometers (Uhlhorn et al. 2007; Uhlhorn and Nolan 2012; Combot et al. 2020), they cannot be used for examining 3-s gusts produced by subkilometer-scale vortices. Here, we present a qualitative comparison using GPS dropsondes (Hock and Franklin 1999), which provide an in situ wind speed measurement two to four times per second as they fall from the aircraft to the ocean surface at ∼10 m s−1. Figure 9a shows the peak wind speed (in kt) measured by dropsondes within the lowest 200 m ASL versus the analyzed best track intensity (also in kt, linearly interpolated to the time of each sonde). This analysis uses approximately 6000 dropsondes released from NOAA P3 aircraft, based on the dataset of Wang et al. (2015).8 Note that the raw dropsonde wind speeds are nearly instantaneous (Franklin et al. 2003; SB18). Time filtering is typically applied during quality control, and this dataset uses a filter time scale of 5 s, which given the fall speed implies a vertical scale of ∼50 m [see discussion in Franklin et al. (2003)]. However, this filtering does not make the sonde observations equivalent to Eulerian averages over such a period, because the sondes drift with the wind and so the observations are semi-Lagrangian.9 Therefore, the precise time scale of the sonde data is unclear, although it is likely on the order of a few seconds or less. Note that Franklin et al. (2003) estimate the horizontal wind speed accuracy for dropsondes to be 0.5–2.0 m s−1 and so any measurement error is likely small relative to sampling errors (discussed below) or to uncertainties in the representative time scale.

Fig. 9.
Fig. 9.

(a) Maximum wind speed below 200 m ASL for each dropsonde (blue dots) within the dataset of Wang et al. (2015) as a function of best track intensity, and the peak for all sondes within each 5-kt intensity bin (black dots; the dashed portion of the connecting line indicates a discontinuity in the data, as there are no cases at 155-kt intensity). Note that the sonde wind speeds are in knots to be consistent with the best track data. (b) The fraction of eyewall dropsondes (see text for definition) in each flight (blue dots) that sampled maximum wind speeds exceeding 70 m s−1 below 200 m ASL, and the mean fraction over all flights within each 5-kt intensity bin (black dots). The red and magenta dots show similar respective calculations, but for randomly located (within the eyewall) simulated dropsondes in the Cat5 simulation.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Each blue dot in Fig. 9a represents the peak wind speed (within 0–200 m ASL) from a single dropsonde. At any given best track intensity, there is a wide range of peak sampled wind speeds. This scatter occurs because we are not restricting the data to the eyewall region, and many of the dropsondes were released far away from the radius of maximum winds. By binning the best track intensity in 5-kt increments, we can take the maximum sonde wind speed within each bin as the peak observed eyewall wind gust, which is plotted in black. An approximately linear relationship is evident between the peak wind gust and the best track intensity, and above the hurricane intensity threshold (≥64 kt ≈ 33 m s−1), the resulting “gust factor” ratio is roughly constant at ∼1.3–1.4. Note that peak wind gusts (in the lowest 200 m ASL) begin to exceed 70 m s−1 for best track intensities of 105 kt (≈54 m s−1). This result is very likely an overestimate of the mean intensity necessary to produce such gusts, because of systematic undersampling by dropsondes, as discussed in SB18 (see their Fig. 16). To further illustrate this problem, the magenta and red dots respectively show the maximum sampled wind speed from 10 and 100 randomly located (within the eyewall) simulated dropsondes from the Cat5 simulation [see SB18 for details on methodology]. For 10 random simulated sondes, the maximum sampled wind speed (98 m s−1) is similar to that from the observed sonde dataset, but for 100 simulated sondes, the maximum (107 m s−1) becomes substantially larger than observed (at the corresponding “intensity”). Therefore, as a conservative estimate, dropsonde observations do indicate that nearly all major hurricanes (categories 3, 4, and 5) are capable of producing near-surface wind gusts exceeding 70 m s−1, consistent with the simulations. Also note that the dropsonde observations are qualitatively consistent with the IWRAP radar analyses of Guimond et al. (2018) in Hurricane Rita (2005), where 70–85 m s−1 wind speed maxima of 1–3-km horizontal extent were found at 500 m ASL, when Rita had a best track intensity of 110 to 125 kt (≈57–64 m s−1).

Quantifying the observed dropsonde gust frequency is challenging because there is no specific indication within the Wang et al. (2015) dataset of whether a sonde was released within the eyewall, and although the distance from the TC center can be computed, the RMW is also unknown from this dataset. We attempt to roughly classify sondes as being within the eyewall in the following manner. It is assumed that at least one sonde for each flight was dropped within the eyewall10 [because as discussed in SB18, this is the standard observational sampling strategy (OFCM 2020)], and so we find the sonde with the maximum wind speed and take its release location to be at the RMW. Then we find all other sondes from the same flight that were released within 10 km inside or outside of this estimated RMW, and take these to also be within the eyewall. Although this method is imperfect, it appears to work reasonably well in identifying eyewall sondes. We can now estimate the observed frequency of gusts exceeding 70 m s−1 within the lowest 200 m, by dividing the number of sondes with at least one such gust by the total number of eyewall sondes for each flight. Figure 9b shows this frequency as a function of best track intensity, for each flight, and binned every 5 kt in mean intensity (as in Fig. 9a). Starting from zero frequency of 70 m s−1 gusts for TCs weaker than 105 kt (≈54 m s−1), the frequency rapidly increases with intensity, and approaches 80%–100% for category 5 TCs. At any given intensity, the probability of gusts exceeding 70 m s−1 is likely an underestimate, both because of undersampling by dropsondes, and because of the broad definition used to estimate the radial extent of the eyewall. We can, however, say with some confidence that for weak TCs (categories 1 and 2), near-surface wind gusts are unlikely to exceed 70 m s−1, whereas for very strong TCs (categories 4 and 5) such gusts are likely. We can also conclude that our simulations (note red and magenta dots on Fig. 9) compare at least qualitatively well with the observations (cf. Figs. 6, 7, and 9).

At this point, it is worth considering how environmental vertical wind shear may affect the spatial distribution of extreme wind gusts, and therefore affect our estimates of the likelihood of a given location encountering these gusts from simulations that do not include such environmental shear. As discussed above, the wind field can be asymmetric even in intense TCs (e.g., Uhlhorn et al. 2014; Klotz and Jiang 2017), and a primary cause of this asymmetry is vertical wind shear. Stern et al. (2016) showed that the distribution of +90 m s−1 dropsonde-sampled wind speeds is strongly influenced by shear, with approximately 80% of such sondes found in the left-of-shear semicircle. We can extend this estimate to the 70 m s−1 threshold of the current study, using the Wang et al. (2015) dataset.11 Figure 10a shows the radius–azimuth distribution of the location of all sondes that sampled 70 m s−1 wind speeds in the lowest 200 m ASL, rotated such that each sonde (at its final location) is shown relative to the respective vertical wind shear vector from the Statistical Hurricane Intensity Prediction Scheme (SHIPS) dataset. In addition to the fact that all such sondes are found inside of a 60-km radius, the peak frequency is clearly in the left-of-shear semicircle, consistent with Stern et al. (2016). Figure 10b shows a histogram of the shear-relative azimuth of these sondes; about 70% are left of shear. Note that Stern et al. (2016) also found that there is a shear-relative asymmetry in overall sampling within the Wang et al. (2015) dataset (more NOAA sondes are dropped left of shear than right of shear), and so 70% may represent an upper bound on the actual asymmetry in the frequency of +70 m s−1 near-surface wind speeds.

Fig. 10.
Fig. 10.

(a) Shear-relative location of each of the 178 dropsondes in the Wang et al. (2015) dataset that measured wind speeds of at least 70 m s−1 within the lowest 200 m ASL. Range rings are shown every 10 km, and the azimuths are labeled in degrees clockwise (positive) or counterclockwise (negative) of the respective vertical wind shear vector for each sonde (0° is directly downshear), obtained from the SHIPS dataset. (b) Histogram of the shear-relative azimuth for the same sondes shown in (a). Note that the location of each sonde is taken at its respective final valid data point before hitting the ocean surface.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

An asymmetric distribution in the frequency of extreme wind gusts will affect the probability of a given location encountering such gusts, by altering the length of time that the location is potentially exposed to these features as the TC moves past it. In the extreme case where the +70 m s−1 gusts are entirely suppressed in half the TC, then the time of exposure is also cut in half if the direction of motion is orthogonal to the vertical wind shear vector. If, on the other hand, the wind shear and motion vectors are aligned (or counteraligned), then the time of exposure would go to zero for locations traversed by one half of the TC while being unaltered for locations traversed by the other half (again assuming that all +70 m s−1 gusts are confined to one half of the eyewall). Although about half of TCs have a motion vector between 90° and 180° to the left of the shear vector (Corbosiero and Molinari 2003; Stern et al. 2016), TCs of any orientation are possible. It is therefore difficult to generalize the effect of vertical wind shear on the likelihood of a given location encountering an extreme wind gust during the passage of a TC, other than to conclude that an upper bound on the magnitude of the effect is a reduction in probability by a factor of 2 (although it is unlikely to be nearly this large). Note again, however, that this potential overestimate in probability from neglecting the effects of shear is counteracted by underestimates induced by the narrow eyewall width in our small simulated TCs and the limited (10-min) period of sampling by our simulated towers.

4. Estimating the long-term climatological frequency of extreme wind gusts

a. The climatology of major hurricanes

From the analysis in section 3, we have estimates of the probability of encountering an extreme near-surface wind gust, given a location that is directly affected by the eyewall of a sufficiently strong hurricane. Although this is useful information on its own, it is the long-term risk over the lifetime of a structure that is more relevant to stakeholders (e.g., government agencies, electric utilities, wind turbine manufacturers, and insurance and reinsurance companies). This risk depends critically on the expected return period of sufficiently strong TCs, which as alluded to in section 1, is difficult to reliably estimate due to sampling and observational limitations. In this study, we use the HURDAT2 dataset from 1944 to 2019 to calculate return periods for TCs within the Atlantic basin.12 In choosing the period to examine, there is an inherent trade-off between the increased sample size allowed by a longer record, and the increasing uncertainty and likely biases for the earlier portions of the full HURDAT2 dataset, which extends from 1851 to the present. The dataset is believed to be much more reliable following the advent of aircraft reconnaissance in 1944 (Landsea and Franklin 2013), and so our analyses use data beginning from this time. Nevertheless, substantial underestimates of intensity for most major hurricanes are likely for the 1940s and early 1950s, because aircraft at that time did not penetrate the eyewall of such strong TCs, and so were unable to measure the central pressure (Hagen and Landsea 2012). Therefore, it is possible that our return period estimates will be somewhat conservative, and this would result in an underestimate of the long-term risk of encountering extreme wind gusts.

In addition to the estimate from HURDAT2, we provide an alternative estimate of long-term risk using the Columbia Hazard model (CHAZ). CHAZ is a statistical–dynamical model, which uses downscaling of global model data to predict the track and intensity of synthetic TCs that are randomly seeded with a distribution given by the Tropical Cyclone Genesis Index (TCGI) of Tippett et al. (2011). Here, we use the CHAZ simulations of Lee et al. (2018), which are downscaled from the ERA-Interim (herein ERA-I) dataset. For these simulations, monthly averaged ERA-I data from 1981 to 2012 are used to calculate the genesis frequency with TCGI. Following genesis, the track of each synthetic TC is advanced in time with a beta and advection model (Li and Wang 1994), using monthly-averaged environmental winds from ERA-I, and a statistical parameterization of the submonthly variability (Emanuel et al. 2006). Finally, the intensity of each synthetic TC is predicted using an autoregressive linear statistical model (Lee et al. 2016), with the monthly-averaged potential intensity, vertical wind shear, and midlevel relative humidity as environmental predictors, and with an additional variable to account for stochasticity. In Lee et al. (2018) (and as used in this study), 100 different 32-yr realizations of the genesis component of CHAZ are used as input to the track model; for each resulting set of tracks, 40 ensemble members of the intensity model are run.

Figure 11a shows the observed track density of major hurricanes in the western Atlantic and Gulf of Mexico. For this analysis, we use a 1° × 1° grid, linearly interpolate the original 6-h data to hourly intervals to avoid missing fast-moving TCs, and count each TC at most once within each grid box. The choice of grid size can have a substantial effect on the calculated return period (Fig. 12) and its interpretation, as the larger the grid size, the shorter the return period, and so it is important to keep this in mind whenever comparing such analyses. There is also an inherent trade-off between grid size and sampling error. Ideally, we would like the grid size to be as small as possible, but with a limited observational record, unphysical spatial variations and noise will occur for small grid sizes. To mitigate such sampling errors, we apply a Gaussian smoother with a length scale of three grid points to the HURDAT2 analysis of track density, and this smoothed track density is shown in Fig. 11b.13 In the raw data (Fig. 11a), most grid boxes south of 35°N have encountered at least one major hurricane from 1944 to 2019, excepting the Bay of Campeche and the extreme southern Caribbean Sea. The smoothing reduces the maximum observed track density from 10 major hurricanes to 7, and also adds storms to isolated grid boxes that had zero such encounters. Both of these characteristics make the smoothed analysis arguably a more realistic representation of the true mean, and so all subsequent observational analyses use the smoothed track density.

Fig. 11.
Fig. 11.

Track density for major hurricanes (a) without and (b) with spatial smoothing (described in text). HURDAT2 data (Atlantic basin only) from 1944 to 2019 are used, and calculations are performed on a 1° × 1° grid. Individual grid boxes are shown (without contouring) for both the raw and smoothed fields to emphasize the discrete nature of track density. Grid boxes with a track density of zero are unfilled, and the smoothed data are also rounded (only for this analysis).

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Fig. 12.
Fig. 12.

Return period for major hurricanes from (a) spatially smoothed HURDAT2 observations and (b) the ensemble mean of CHAZ simulations. Both (a) and (b) use data calculated on a 1° × 1° grid. The 25-yr return period is contoured in black for reference.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

The return period for these analyses can be calculated as the record length divided by the track density, and this is shown in Fig. 12a for the smoothed observations. It can be seen that for a large portion of the Gulf of Mexico and the region offshore of the southeast U.S. coastline (Florida to North Carolina), the return period for major hurricanes is 20–50 years. The return period rapidly becomes large north of approximately 35°N, and is either 76 years (the length of the observational record) or undefined (no major hurricanes in the period examined) for much of the offshore region of the northeastern United States. Note that the limited length of the observational record precludes a reliable determination of these longer return periods, and that (as discussed above) the lack of inner-core aircraft reconnaissance in the early part of the record will tend to result in a return period estimate that is biased high (i.e., the track density is biased low).

Figure 12b shows the return period of major hurricanes in CHAZ (on the same 1° × 1° grid as with HURDAT2), using the mean over the 40 intensity ensembles. A key advantage of CHAZ is that sampling error is essentially eliminated, as the effective length of the dataset is approximately 28 000 years.14 Consistent with the observational record, CHAZ yields a return period of 20–50 years over much of the Gulf of Mexico and southeastern U.S. coastal region. An important caveat is that CHAZ is not independent of HURDAT2, as bias corrections have been applied both to bring the basinwide frequency into agreement with HURDAT2 and to adjust the relative proportions of landfalling hurricanes in different subbasins to agree with HURDAT2. Therefore, it is perhaps best to consider CHAZ here to be a type of “reanalysis” that is complementary to the raw observational record. That being said, there are a few notable differences between the HURDAT2 and CHAZ return periods. CHAZ has a shorter return period of major hurricanes than HURDAT2 in most locations, in particular in the western Gulf of Mexico and portions of the Atlantic offshore of the northeastern United States. In contrast, CHAZ has a longer return period than HURDAT2 at most locations along the immediate U.S. coastline. This latter difference might be related to the landfall component of the CHAZ model, which tends to weaken the synthetic TCs when they approach within 300 km of land (Lee et al. 2016).

An alternative perspective of the same data can be seen by computing the expected value for the number of major hurricanes within a given time period, and this is shown for a period of 30 years in HURDAT2 and CHAZ in Figs. 13a and 13b. The expected value is simply the inverse of the return period multiplied by the number of years considered, and so for example, where the return period is 30 years, the expected number of major hurricanes in a 30-yr period is equal to one. In much of the Gulf of Mexico and offshore of the southeast Atlantic coast, the expected number of major hurricanes in a given 1° × 1° box within a 30-yr period in HURDAT2 is 0.5–1.5, and in some regions (e.g., south Florida) approaches 2.0. In CHAZ, the distribution of the expected value is spatially smoother and in most locations (away from the immediate coastline) somewhat higher than observed, and in general, 1.0–2.0 major hurricanes per 30 years is typical.

Fig. 13.
Fig. 13.

Expected number of major hurricanes within a 30-yr period for (a) HURDAT2 and (b) CHAZ on a 1° × 1° grid and for (c) HURDAT2 and (d) CHAZ at a given point location (see text for details). The black contour indicates 1 major hurricane expected within a 30-yr period.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

b. What is the probability of a gust exceeding 70 m s−1 over 30 years?

Given that we have shown in section 3 that a direct hit by a major hurricane is likely to result in a gust exceeding 70 m s−1, an average of 1 major hurricane per 30 years would seem to suggest a substantial risk of encountering damaging wind gusts. However, using the expected number of major hurricanes within a 1° × 1° box overestimates the risk of such gusts, because not all locations within a box of this size will suffer a direct hit by the eyewall. To illustrate this issue, Fig. 14 shows a horizontal cross section of the 3-s wind speed at 100 m ASL for the Cat3 simulation, highlighting 70 m s−1 values with the magenta contour. For this relatively small TC, the region where gusts exceeding 70 m s−1 are found is much smaller than the 100 km × 100 km box that is shown (which approximates 1° × 1°). Most real TCs have a substantial translation speed, and so a swath of strong winds will be carved out within a box, although this will still generally encompass a region substantially smaller than 1° × 1°. What we would like to know is the expected number of (or return period for) major hurricanes at a given point location. By making our box smaller we could mitigate this overestimate, but at the cost of increased noise and sampling error (at least for the observations). Alternatively, we can use information on climatological eyewall size in order to estimate the probability of encountering the eyewall of a given storm, and thereby determine a factor by which we can convert the expected number of storms within a box to the expected number passing over a given point.

Fig. 14.
Fig. 14.

Example horizontal cross section of the 3-s mean wind speed at 100 m ASL for the Cat3 simulation with the 70 m s−1 contour highlighted in magenta. A 100 km × 100 km box is shown, which is comparable in area to the 1° × 1° grid cells used in Fig. 11.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

To illustrate our method of converting areal estimates of return period to point estimates, Fig. 15a shows a 100 km × 100 km box, within which we draw 100 random lines that represent hypothetical TC tracks. We can then count the tracks that pass within a given distance of the center of the box, and use this information to estimate the frequency of an eyewall passing over a given point. Note that this analysis is purely a geometric calculation, not relying on any actual properties of TCs. We are, however, implicitly assuming that the tracks are linear within the dimensions of the box, that the true climatological probability is constant within the box, and that a typical TC does not evolve during the time it takes to transit the box (the translation speed itself does not otherwise matter for this estimate). For a box size of 100 km × 100 km, these assumptions seem reasonable. Figure 15b shows the frequency of tracks crossing within a given distance of a point (for 10 000 random tracks). We can also interpret this distance to represent the size of the eyewall (distance from center); for example, if the eyewall radius is 20 km, then all tracks passing within 20 km of a point would result in eyewall encounters. As the eyewall becomes very small, the probability that a random track through the box would pass over a given point becomes negligible. Alternatively, as the eyewall becomes very large, the probability of an encounter approaches 100%, as the eyewall would encompass the entire box, necessarily traversing every location within the box. As expected, the frequency of an eyewall passing over a given point depends strongly on the size of the eyewall, and so we need to estimate and account for eyewall size in order to avoid overestimating risk.

Fig. 15.
Fig. 15.

(a) Example of 100 random straight-line tracks across a 100 km × 100 km box. The center of the box is indicated by the black plus sign, and the black circle is drawn at r = 20 km. (b) The frequency of a hypothetical eyewall passing over a given point within a 100 km × 100 km box as a function of the outer radius of the eyewall. See text for further description.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

Figure 16 shows the RMW as a function of maximum wind speed, for the Enhanced Vortex Data Message (VDM+) dataset of Vigh (2015). The VDM+ dataset uses the observed flight-level RMW from 5989 aircraft penetrations into 246 TCs within the Atlantic basin from 1989 to 2015.15 The median RMW tends to decrease with increasing intensity, although as discussed in Stern et al. (2015) this sensitivity becomes relatively small for major hurricanes, with the median lying between 20 and 30 km for intensities between 100 and 140 kt (≈51 and 72 m s−1). Recall that in our simulations (and presumably in real TCs), the width of the region containing gusts that exceed 70 m s−1 increases with increasing intensity. Therefore, although the overall size of the eyewall tends to become smaller with increasing intensity, the width of the annulus of strong winds becomes larger, and so these two effects counteract in determining the outer radius of sufficiently strong winds. It is this outer radius that is most relevant for determining whether extreme wind gusts are possible at a given point. Based on Figs. 7 and 16, a simple but reasonable approximation is that the outer radius is (on average) approximately constant at 30 km for category 3 through category 5 hurricanes. This estimate follows from the width of the +70 m s−1 gust region approaching zero at the threshold of category 3 intensity (Fig. 7a) where the observed median RMW is ∼30 km, and being about 10 km wide for category 5 intensity (Fig. 7d) where the observed median RMW is ∼20 km (Fig. 16). Applying this value (30 km) as the eyewall radius in Fig. 15b, we arrive at a factor of 0.64 to convert the expected number of TCs passing within a 1° × 1° box to the expected number of TCs passing over a given point location. Note that a considerable amount of uncertainty is introduced through this step of our analysis as, for example, varying the assumed outer radius of strong winds from 20 to 40 km will nearly double the estimated frequency of direct hits by a major hurricane.

Fig. 16.
Fig. 16.

Observed RMW (km) as a function of surface-adjusted maximum flight-level wind speed (kt) for all aircraft-observed Atlantic TCs from 1989 to 2015 from the VDM+ dataset of Vigh (2015). The median is shown by the solid blue line and the 25th and 75th percentiles are indicated by the dashed black lines below and above, respectively.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

An estimate of the expected number of major hurricanes passing over any given point within a 30-yr period is shown for HURDAT2 and CHAZ in Figs. 13c and 13d. For this analysis, we simply take the respective values for the 1° × 1° box (Figs. 12a,b) and multiply by the reduction factor of 0.64. The ultimate quantity that we are seeking is the probability that a given point will experience a 3-s wind speed exceeding 70 m s−1 within a 30-yr period. To obtain this probability from the expected number of major hurricanes, we make two final approximations. First, we assume that the number of storms can be modeled as a Poisson process, which means that at any given location, storms are considered to occur randomly at a constant average rate, and that each storm is independent. This is a reasonable assumption (Emanuel 2013), which is widely made in tropical cyclone risk analyses (e.g., Emanuel and Jagger 2010; Malmstadt et al. 2010; Villarini et al. 2010; Tippett et al. 2011). The second assumption that we make here is that for every major hurricane that passes over a given point, there is a 100% probability of experiencing a 3-s wind speed greater than 70 m s−1 in the lowest 200 m ASL. The validity of this assumption is less certain, although it is supported by the analyses of simulations in Fig. 7 and of observations in Fig. 9. Figure 9 indicates that the frequency of 3-s wind speeds exceeding 70 m s−1 sampled by eyewall dropsondes increases sharply from 0% to nearly 100% between category 3 (100 kt ≈ 51 m s−1) and category 5 (140 kt ≈ 72 m s−1) intensity thresholds. Note that assuming a binary transition from 0% to 100% probability could potentially result in either an underestimate or an overestimate of the true long-term probability of encountering an extreme wind gust, depending on whether the 0% threshold is in reality below or above where we are assuming it occurs (100 kt). Although Fig. 9 implies that the 0% threshold is near 100 kt, systematic undersampling by dropsondes (see Fig. 16 of SB18) means that the true threshold intensity is at least somewhat lower.

For a Poisson process (Wilks 1995), the probability of exactly k storms occurring within a given period is
P(k)=eλλkk!,
where in our case λ is the expected number of storms per 30 years (as shown in Figs. 13c,d). The probability of at least one storm passing over a given point within this period is therefore one minus the probability of zero storms:
P(k1)=1eλλ00!=1eλ.
Figures 17a and 17b show the spatial distribution of this probability for HURDAT2 and CHAZ, which we approximate as being equivalent to the probability of at least one encounter with a 3-s gust exceeding 70 m s−1 within the same period. It can be seen that for much of the Gulf of Mexico and southeast Atlantic coastal region, the long-term probability derived from HURDAT2 of a given location experiencing a 3-s wind speed greater than 70 m s−1 is estimated to be 30%–60%, with the greatest nearshore risks from New Orleans to the Florida Panhandle, as well as southern Florida and North Carolina. The estimated probability derived from the CHAZ model is generally somewhat higher (particularly in portions of the western Gulf of Mexico and offshore of New England), though it is also 30%–60% for most points within a few hundred kilometers of the coast. Based on these analyses, the risk posed to offshore wind turbines in this region is substantial, particularly if they are only designed to withstand 3-s wind speeds up to 70 m s−1.
Fig. 17.
Fig. 17.

(a) Probability of at least one major hurricane (which we equate to the probability of a 3-s gust exceeding 70 m s−1) experienced within 30 years at a given point location for (a) HURDAT2 and (b) CHAZ. The 50% contour is in black.

Citation: Monthly Weather Review 149, 12; 10.1175/MWR-D-21-0059.1

5. Discussion and conclusions

a. Summary

It is important to improve our understanding of the risk posed by localized extreme wind gusts within tropical cyclones. In this study, we used large-eddy simulations, along with dropsonde observations, climatological storm information from the best track and VDM+ datasets, and the statistical–dynamical TC hazard model of Lee et al. (2018), in order to estimate both the short-term and long-term probability that a given point location offshore of the United States would encounter a near-surface (0–200 m ASL) 3-s wind gust exceeding 70 m s−1. As demonstrated from observations by Stern et al. (2016) and in a simulation by SB18, such gusts are ubiquitous in strong tropical cyclones.

Here, we calculated the frequency of extreme wind gusts in the simulation of SB18, as sampled at simulated towers, following the work of Worsnop et al. (2017). Over a 10-min period of sampling, there is a 10-km-wide region in the simulated category 5 TC where every simulated tower encounters at least one ≥70 m s−1 wind gust. We performed the same analysis for two new simulations of weaker TCs, and the category 3 TC exhibited a 3-km-wide region where 90% of simulated towers sampled ≥70 m s−1 wind gusts over a 10-min period, while the category 1 TC had no such sampled wind gusts.

From a dataset of over 6000 observed dropsondes (Wang et al. 2015), we showed that the peak wind gust in TCs increases linearly with the estimated best track intensity, and begins to exceed 70 m s−1 (within the lowest 200 m ASL) at an intensity of about 105 kt (≈54 m s−1). Although this is likely an overestimate (because of undersampling) of the true minimum intensity necessary to produce such wind gusts, it is generally consistent with our simulations, and strongly suggests that nearly all major hurricanes possess near-surface wind gusts in excess of 70 m s−1. In support of this conclusion, we note that for observed category 5 TCs, the large majority (>80%) of eyewall dropsondes have sampled ≥70 m s−1 near-surface wind speeds.

To estimate the long-term climatological frequency of extreme wind gusts, we combined what we learned from the large-eddy simulations and dropsondes with estimates of the return period of major hurricanes. We used two different datasets to calculate the return period: the HURDAT2 official best track data of observed Atlantic basin TCs from 1944 to 2019, and the CHAZ model of Lee et al. (2018) as forced by 4000 different realizations of 32 years (1981–2012) of ERA-Interim fields. On a 1° × 1° grid, the return period of major hurricanes over much of the region within a few hundred kilometers of the U.S. coastline south of 35°N is 20–50 years. Using observed climatological RMW data, we calculated a factor to convert this value to a point estimate, and the result corresponds to an approximate return period of 30–80 years for a given location experiencing the eyewall of a major hurricane. Although this period may seem long, it equates to a relatively large probability (30%–60%) of such a direct hit within a 30-yr period, assuming a Poisson distribution. Finally, by assuming that all encounters with major hurricane eyewalls result in a near-surface (z < 200 m) wind gust exceeding 70 m s−1, the probability of a location experiencing at least one such gust over a 30-yr period is also approximately 30%–60%.

b. Sources of uncertainty and future work

We have made a number of simplifications and assumptions in our analyses, and so it should be emphasized that what we are calculating is only an estimate of the risk of extreme near-surface wind gusts. Perhaps the greatest uncertainty comes from a lack of precise knowledge of the return period of major hurricanes and its spatial variation, which largely reflects the limited length of the period during which observations are sufficiently reliable for estimation of TC intensity. These sampling errors can be mitigated to a certain extent through spatial smoothing, and via comparison to the CHAZ model, but ultimately, a more precise estimate of risk will likely await either future decades of additional observations or the development of reliable convective-permitting global dynamical models. However, we do have enough precision and confidence from existing data to state that the return period of a direct hit (passage of the eyewall) by a major hurricane at a given location in most of the nearshore region of the Gulf and southeastern U.S. coasts is generally 30–80 years.

Another major source of uncertainty in this work is in relating the return period of major hurricanes to the probability of encountering a gust exceeding 70 m s−1. Observations of wind speed in intense hurricanes from fixed offshore platforms are rare, and so determining the relationship between mean TC intensity and the strength and frequency of wind gusts is difficult. Dropsonde observations are more common, but an individual dropsonde observes the lowest 200 m for only ∼20 s and is subject to large (effectively) random variability; even when aggregating over many dropsondes, substantial systematic undersampling remains (SB18). Our main tool for analyzing the gust magnitudes and frequencies is the large-eddy simulations, and although these simulations produce reasonable results that compare well with observations, there are several caveats that are important to note. First, although most turbulence is resolved in LES, the smallest scales remain parameterized, and the unresolved turbulence is most important at the lowest few model levels. The real ocean surface is also wavy and covered in varying amounts of foam and sea spray (which may affect the character of the wind field), whereas our simulated ocean is a flat rigid boundary, with an estimated drag coefficient that is valid for deep ocean waters. Another issue is that our simulations do not incorporate storm motion or environmental vertical wind shear, both of which are important in producing asymmetries in the low-level wind field (Uhlhorn et al. 2014; Klotz and Jiang 2017), and which influence the distribution of extreme wind gusts (Stern et al. 2016). Finally, we only have simulations corresponding to three different intensities, all of which correspond to small TCs, and so much of the observed parameter space remains unexplored so far with LES.

The final major source of uncertainty in our analysis is the simplifying assumptions we have made in applying the LES results toward converting return period estimates to wind gust exceedance probabilities. An important assumption is that we have treated the probability of encountering an extreme wind gust as a step function, being 100% for all major hurricanes and 0% for all weaker TCs. Although this is an oversimplification, both the simulations and dropsonde analyses indicate that the probability of such wind gusts does increase sharply near this threshold, and we currently lack the data necessary to specify a more realistic functional form. Note also that with increasing intensity, the climatologically decreasing RMW counteracts the increasing width of the high-wind region, and so it is plausible that the probability of a given location experiencing a wind gust exceeding 70 m s−1 in the lowest 200 m is approximately constant above some intensity threshold. However, this remains a key unknown factor that could substantially affect our results.

A more sophisticated way of assessing the long-term risk of extreme wind gusts would be to use a Monte Carlo technique to randomly sample from the respective observed statistical distributions of TC intensity, size, and translation speed, which in principle could yield a more reliable estimate. This is essentially what is currently done for NHC’s HURISK system (Neumann 1987) to estimate climatological return periods of landfalling TCs of varying intensities. Alternatively, we could draw from the respective distributions within CHAZ, or implement a direct calculation of wind gust probabilities into each individual synthetic TC within CHAZ. Both of these latter techniques would benefit from incorporating into CHAZ a parameterization of storm size and/or the mean wind field structure, which is the subject of ongoing work. We also plan to add realistic environmental flow (including vertical wind shear) to future large-eddy simulations, which along with analysis of a broader spectrum of simulated TC sizes, will help to refine our understanding of the risk of encountering extreme near-surface wind gusts.

As the global mean temperature continues to warm in association with anthropogenic climate change, the frequency, distribution, and intensity of tropical cyclones will likely change as well. There is widespread agreement that the average lifetime maximum intensity of TCs will increase by 1%–10% by the middle of the twenty-first century (Knutson et al. 2020), and so for an encounter with a given TC, the probability of experiencing an extreme local wind gust should increase as well. However, the long-term risk of such a gust is dependent on the frequency and spatial distribution of TCs as well. Although the large majority of earlier modeling studies found an overall decrease in global TC frequency [see Fig. 1 of Knutson et al. (2020)], a few more recent analyses of downscaled (Emanuel 2013) or higher-resolution global climate models (Bhatia et al. 2018) instead project an increase in this frequency. As there is no existing theory for TC frequency, it is challenging to reconcile these disparate predictions. Very recently, Lee et al. (2020) used CHAZ downscaled from CMIP5 models to show that the sign of TC frequency change is dependent on the choice of moisture variable used in the genesis index, which provides the prediction of the number of seeds within the downscaling framework. As dynamical climate model resolution remains inadequate to represent intense TCs, statistical–dynamical downscaling is still necessary in order to improve our understanding of how the hazards posed by TCs will evolve in a changing climate. We hope to build on the framework developed in this study so as to better understand the long-term risk of extreme local wind gusts in TCs, and how this risk is changing.

Acknowledgments

Daniel Stern and James Doyle were supported by the Chief of Naval Research through the NRL Base Program (PE 61153N) and the Office of Naval Research TC Rapid Intensification DRI (PE 0601153N). George Bryan was supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Chia-Ying Lee was supported by the Climate and Life Fellowship and NVSERDA.

Data availability statement.

VDM+ data can be obtained at https://verif.rap.ucar.edu/tcdata/vortex/, and IBTrACS data can be downloaded from https://www.ncdc.noaa.gov/ibtracs/. Simulation data are available from the authors upon request.

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1

Although Wu et al. (2019) do not explicitly note the maximum 1-min wind speed at 10 m ASL, the peak azimuthal mean surface wind speed of ∼45 m s−1 and peak instantaneous surface wind speed of ∼60–75 m s−1 likely indicates a category 3 TC.

2

We do not address the risk of extreme wind gusts on land in this study, because this is greatly influenced by land surface and terrain effects, which are not accounted for in our simulations.

3

For reference, category 1, 3, and 5 hurricanes correspond to maximum 1-min surface wind speeds of 33–42, 50–58, and ≥70 m s−1, respectively.

4

Note that this adjustment to steady state is a short-term response to initializing the LES from the axisymmetric precursor simulation, and this does not represent the true long-term steady state, as expected from potential intensity theory. All three simulations have the same potential intensity, and given enough time (much longer than the 4-h length of the simulations), the Cat1 and Cat3 simulations would be expected to achieve a similar peak intensity as the Cat5 simulation.

5

For the Cat1 and Cat3 TCs, there is an increase in 1-min wind speed from the initial axisymmetric maximum, such that the quasi-steady intensity is on the border of category 2 and category 4, respectively. Nevertheless, for the purposes of this study, we name the simulations based on their initial axisymmetric intensity.

6

For the interested reader, detailed information on each of these hurricanes can be found in the respective NHC Tropical Cyclone Report at https://www.nhc.noaa.gov/data/tcr/.

7

Note that these values are higher than indicated in Fig. 3, as the peak gust at 10 m ASL is sampled by a different simulated tower than the peak gust at 100 m ASL, and the peak gust at any height occurs at model level 14 (∼210 m).

8

We applied additional quality control to the Wang et al. (2015) dataset to remove some sondes with erroneous wind speeds (and all sondes that were dropped at greater than 100 km from the storm center), and for Fig. 9a (but not Fig. 9b), we also include the 210 sondes from Stern et al. (2016).

9

Note that because dropsondes are always falling relative to the vertical wind speed, they are not true Lagrangian observations.

10

Although tropical depressions and weak tropical storms are unlikely to have an eyewall, this does not affect our analysis, because such TCs also have no extreme wind gusts.

11

As Stern et al. (2016) created their dataset by specifically searching the raw dropsonde data for all sondes satisfying the 90 m s−1 threshold and performing quality control on each individual sonde, it is not possible to directly use this dataset to examine other lower wind speed thresholds.

12

The HURDAT2 data are acquired from IBTrACS v4.0, but we take only the original 6-hourly data, and so we essentially start with HURDAT2 in our analysis.

13

Smoothing is only applied over the set of grid boxes that are entirely over the ocean, in order to avoid a large artificial increase in return period for coastal ocean locations.

14

There are a total of 128 000 years (32 × 40 × 100) in the raw CHAZ output, but bias corrections reduce the effective length by a factor of ∼5.

15

The VDM+ dataset also includes data for the east Pacific and central Pacific basins, but we only use the Atlantic basin data in our analysis.