1. Introduction
Tropical cyclones (TCs) pose a global threat to property, infrastructure as well as to human lives and habitat. Understanding the frequency and severity of such events across the world matters for a range of purposes including resilience planning, disaster mitigation, and risk management. To date the best tool to allow quantification of the full probabilistic risk associated with TCs is the catastrophe model, born from the needs of the re/insurance industry (hereafter referred to as Cat model; Mitchell-Wallace et al. 2017).
Cat models rely on very large catalogs of physically realistic but synthetic events called “event sets.” Event sets are designed to expand the small sample of observed historical cases to a full range of plausible, yet so far unseen events based on our physical understanding of physical drivers (e.g., Vickery et al. 2000; Powell et al. 2005; Emanuel et al. 2006; Hall and Jewson 2007; Lee et al. 2018; Bloemendaal et al. 2020; Bongirwar 2020; Jing and Lin 2020; Shen and Wei 2021; Arthur 2021). At any location, these catalogs may include extreme events that go beyond the range of wind intensities observed in recent history. Cat models aim at capturing and quantifying levels of risk never experienced, but plausible, and ensures risk can be consistently quantified across regions as well as for high-return periods (tail risk).
In the case of tropical cyclones, to simulate the millions of physically realistic synthetic events of a catalog, a series of computationally efficient algorithms (e.g., parametric relationships) are needed (Powell et al. 2005; Emanuel et al. 2006; Vickery et al. 2009; Lin and Chavas 2012; Loridan et al. 2015, among others). The common approach to developing such types of algorithms is to rely on historical observations to train parametric relationships. However, consistent TC observations of quality are only available for a limited part of the world (mainly in the North Atlantic), and only for some key parameters of TC risk (maximum wind speeds, trajectories). In the context of global TC risk assessment, this raises important challenges:
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the algorithms at the core of Cat models tend to be overfitted to certain parts of the world, and likely misrepresent regional differences in TC risk in region with little data available (like the Indian Ocean for example),
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using disparate sources of observations to train a catalog of region-specific algorithms leads to inconsistent risk evaluation tools across the globe [e.g., how agencies report maximum wind speeds; Schreck et al. (2014)],
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even in regions blessed with quality observation coverage (e.g., the United States), certain granular aspects of TC risk are not optimally captured (e.g., TC vortex shape characteristics/asymmetry, radial decay, wind field structure).
In this paper we introduce a new global database for TC risk analysis called InCyc. While InCyc is a database of high-resolution numerical simulations rather than an observation dataset, we show that it is a good alternative training data source for the type of algorithms used in Cat models. Importantly, InCyc allows the development of globally consistent algorithms able to capture the variability in TC risk across different basins and regions. It also provides training data for some TC wind risk parameters that can be challenging to measure (e.g., vortex size and shape/horizontal structure).
To illustrate the value of InCyc as a training database, machine learning algorithms are trained and deployed for North Atlantic (NA) hurricanes and western North Pacific (WP) typhoons, with a focus on three aspects of TC wind risk:
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TC inner core size (i.e., radius to the location of maximum winds Rm)
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location of maximum winds relative to the storm motion (i.e., angle of maximum winds Am)
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central pressure to peak wind relationships (P–V relationship).
While there are many more parameters in a TC Cat model (see section a of introduction below), we choose to focus on these three characteristics as (i) they require very granular training data that are rarely available in observation datasets (see section 1b), (ii) they correlate with damage induced by TC winds (Holland et al. 2019), and (iii) they are the key parameters to consistently apply the formulation designed by Loridan et al. (2017). Loridan et al. (2017) proposed an innovative method to emulate spatial wind footprints capturing the whole spectrum of observed wind fields—mainly the shape and asymmetry.
Other storm characteristics could have been investigated; for example, the TC outer size, that plays an important role in TC hazards and risk (Lin et al. 2014; Chavas et al. 2017). However, they were kept out of this study as recent studies (Gori et al. 2022) still randomly draw the outer radius from an empirical lognormal distribution (Chavas and Emanuel 2010) and a similar method could be used here.
a. Cat models and their components
Since the early 1990s the use of Cat models to quantify TC risk has become common practice in the insurance industry (Hall and Jewson 2007) and is now growing in popularity in other sectors (Bloemendaal et al. 2020; Bongirwar 2020; Arthur 2021, among others).
While this study illustrates the value of InCyc to develop elements of a Cat model’s event set, it is important to position these elements in the broader context of a full model. Broadly speaking, the main physical/hazard modules of a TC Cat model are the following:
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a genesis module that assigns a number of events for a given season, as well as their genesis locations,
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a track module that estimates the trajectory of each event,
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an intensity module defining the strength of an event over its lifetime,
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a wind parameter module simulating the main parameters of the wind vortex (size, location of peak winds, shape),
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a wind field module designed to simulate the spatial distribution of wind speeds around the TC center,
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a terrain-correction module to incorporate the impact of terrain interaction (topography-induced speed-ups/slow-downs and impact of changes in surface roughness).
These different modules interplay and are all required to simulate complete, physically realistic synthetic TC events. The end product typically takes the form of wind maps showing the lifetime maximum gust speed for each event (i.e., event “footprints”) or aggregated return-period maps of expected winds. To generate time series of wind footprints to millions of synthetic events, full-physics models are too computationally expensive, and wind field parameterizations are the obvious realistic options. To estimate wind fields, these parameterizations need a range of key characteristics describing the cyclone structure and intensity with the whole range of variability/uncertainty. This is the key focus of the present study (fourth item of the list above): estimating the wind characteristics of a TC from knowledge of its trajectory and intensity. The InCyc database is also of value for the fifth item, wind field module, as detailed in Loridan et al. (2017). Finally, we note that the landfalling and overland wind characteristics (sixth item) are crucial for TC risk assessment and loss estimation, because they provide the most accurate representation of the winds impacting buildings and lives. However, given the underlying complexities of topography and surface roughness impacts (Chen and Chavas 2020), we believe this should be studied separately. Therefore, this paper examines the oversea wind parameters (item 4).
b. Challenges with training datasets
Observation datasets are a logical place to start when attempting to develop algorithms needed by Cat models. In the North Atlantic, sustained efforts have been made to collect and analyze quality hurricane data (Jarvinen et al. 1975; Powell et al. 1998). This includes in situ and remote measurement campaigns as well as aircraft reconnaissance missions. The resulting measurement datasets have allowed significant progress in our understanding of the processes governing hurricanes, as well as the development of a wide range of parametric relationships used in Cat models today. However, such diligent measurement efforts have not been extended to other basins, and while hurricane properties should mostly be generalizable, basin specificities are key to understanding regional TC risk.
The benchmark product for consistent global TC coverage is the International Best Track Archive for Climate Stewardship (IBTrACS, Knapp et al. 2010) providing a centralized view of the location and intensity of historical TCs worldwide, based on agency point estimates. IBTrACS does not provide estimates of the full TC wind field, but mainly metrics quantifying gridpoint maximum winds/minimum pressure along the cyclone path. Information on TC wind structure is, however, scarce (e.g., Rm) or lacking (e.g., Am). While satellite-based products such as the Multiplatform TC Surface Wind Analysis (Knaff et al. 2011a) have made a significant step in this direction, they still face challenges with the heavy precipitation typical of TCs and can suffer from a lack of consistency in coverage (e.g., Mouche et al. 2017; Mouche et al. 2019; Combot et al. 2020; Knaff et al. 2021). In addition, there are still significant uncertainties in measuring and modeling TC tracks, intensity, and outer size metrics (Torn and Snyder 2012; Landsea and Franklin 2013; Heming et al. 2019, for example).
InCyc complements IBTrACS with detailed spatial information on TC structure and associated wind fields on the global scale. InCyc database is made of 1-km spatial resolution simulations of historical TCs obtained using the full-physics Weather Research and Forecasting (WRF) Model (Skamarock et al. 2019). While WRF is a model rather than an observation product, it has been shown to accurately reproduce the key physical mechanisms governing TCs (Nolan et al. 2013). It therefore provides a powerful tool to assemble a high-resolution, globally consistent database of tropical cyclones.
Section 2 describes the InCyc database and introduces a few algorithms widely used to calculate the expected value of TC wind parameters. We also present our approach to modeling TC characteristics based on a machine learning method called quantile regression forest (QRF–Meinshausen 2006; Loridan et al. 2017). Section 3 provides an evaluation of InCyc representativeness and biases, as well as a preliminary look into TC variability for NA and WP basins. Section 4 details the evaluation of the QRF models with Hurricane Florence 2018 and Typhoon Nanmadol 2011 as case studies. Finally, the benefits of our approach in the context of global Cat models are discussed. Our main motivation behind the InCyc initiative is to assemble a globally consistent database from which researchers can 1) study relativities in key TC characteristics across different regions of the world and 2) build/evaluate globally consistent algorithms of the kind used in Cat models. The schematic view presented in Fig. 1 summarizes the whole content of this study and the key steps to select, simulate and evaluate the database and models.
Schematic view of the present study—details can be found in sections 2–4. Data from Ho et al. (1975) and Schwerdt et al. (1979) have been digitized to extend our observational records; they are based on a combination of aircraft observations, radar and surface observations, and aircraft reconnaissance. The term Pc is the central pressure, Vm is the maximum winds, Rm is the radius of maximum winds, and Am is the angle of maximum winds to the direction of cyclone motion.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
2. Data and methods
a. The global InCyc database
The InCyc database is a repository of high-resolution full-physics simulations of an ensemble of historical tropical cyclones, representative of the recent activity. This is aligned with the need of Cat models, that perform assessments over short term horizons, based on the current view of the risk (Mitchell-Wallace et al. 2017). However, the database could be extended in the future with scenarios of TC evolving under a changing climate to capture potential changes in behaviors (Knutson et al. 2020; Chen et al. 2020).
Only a subset of historical TCs is considered for inclusion in InCyc due to the heavy computing requirements. A key challenge is to ensure the selected storms simulated are representative of the activity in each basin, and help generalize findings beyond the individual cases selected. This subset needs to span the range of TC genesis locations, trajectories and intensities observed in each basin. An objective methodology was developed to automatically select representative subsamples from a population of candidates. The methodology consists of three key steps (see appendix A for more details):
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for each basin, a cluster analysis isolates main subgroups of activity based on genesis locations, trajectories and minimum pressure; similar to methods described by Camargo et al. (2007). The clustering is done using historical data from IBTrACS (Knapp et al. 2010) over the satellite-era 1979–2018. As shown by Landsea et al. (2006) or Schreck et al. (2014), some intensity and track position uncertainties can still remain, particularly for the earlier period and regions less scrutinized (like the Indian Ocean for example),
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the historical cluster frequency is calculated and determines the proportion of each cluster to be included in InCyc,
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based on historical cyclones in each cluster, many subpopulations are randomly generated,
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finally, a machine learning algorithm allows identification of the most representative subpopulation for each cluster.
All TCs from the most representative subpopulation (Fig. 2) are then simulated using the WRF Model (Skamarock et al. 2019) at 1-km resolution with initial and boundary conditions from ERA5 reanalysis at 0.25° (Hersbach et al. 2020). WRF is a mesoscale numerical weather prediction system widely used for atmospheric research as well as operational forecasting and has been shown to accurately simulate TC physics (see Table 1 and appendix B for extended details on the configuration).
InCyc database of high-resolution full-physics historical storm simulations. The current content of InCyc (colored lines) is compared to historical occurrences as reported by IBTrACS (gray). Currently InCyc consists of 35 cyclones in the North Atlantic and western North Pacific, while the eastern North Pacific, South Pacific, and south Indian Oceans each contain 25 TCs. The north Indian Ocean is still in progress, aiming for 15 TCs.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
WRF configuration for InCyc runs.
Our intention when using WRF for TC climatology studies is not to exactly recreate historical events, but rather to create physically realistic TCs in a similar environment to those observed; in particular, the ability of the model to reproduce observed variability in TC intensity, size, and wind structures (Wu et al. 2012; Cavallo et al. 2013). For this study, an extensive set of simulations has been carried out to evaluate an optimum combination of physical parameters in WRF to consistently simulate each cyclone (the comparisons mainly focused on capturing the Vm along the TC lifetime). While this study does not look at the variability in these choices, a large number of extra simulations are available within InCyc to investigate the influence of these parameter choices.
Evaluation of the representativeness of the InCyc database in terms of cyclone trajectories and intensity/structures is presented later (see Figs. 5 and 6). The analyses show that the selected cyclones encapsulate the whole range of historical variability while preserving the distribution of each property. This highlights how the algorithm to select a representative subpopulation of cyclones is successful at this task.
To complement IBTrACS data for validation, the data tabulated in Ho et al. (1975) and Schwerdt et al. (1979) are also used to extend our observational records. These measurements were made in Atlantic tropical cyclones near peak intensity and within 150 nautical miles (n mi; 1 n mi = 1.852 km) of the coast based on a combination of aircraft observations, radar, and surface observations and in western North Pacific typhoons via aircraft reconnaissance. These observations were compiled and quality controlled to determine tropical cyclone windborne risks for the U. S. Gulf and East Coasts. Finally, aircraft reconnaissance data of surface radius estimates of Atlantic TCs maximum winds are also used and based on stepped frequency microwave radiometer retrievals (see Klotz and Uhlhorn 2014) and were compiled using inbound and outbound reconnaissance flight legs. They are contained in databases of the Automated Tropical Cyclone Forecast (ATCF; Sampson and Schrader 2000), available from the National Hurricane Center.
b. Extracting TC key properties
Building the training database requires the identification and extraction of key characteristics from the simulated TCs. Nguyen et al. (2014) and Ryglicki and Hart (2015) review the range of techniques designed to identify the tropical cyclone center location. In this work, TCs’ center position and location of maximum winds are extracted for each simulated snapshot (Fig. 3), and four key parameters are derived:
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Central pressure (Pc, in hPa): for a given time step, the 1-km WRF grid cell where the minimum (overwater) pressure is simulated within the cyclone eye (also named storm center).
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Maximum wind (Vm, in m s−1): the 1-km cell where the maximum (overwater) 10-m wind speed are recorded (i.e., the peak wind location). We note that although WRF simulates an instantaneous wind value, it can be interpreted as a good estimate of 1-min sustained winds (Davis et al. 2010).
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Radius of maximum winds (Rm, in km): the distance between the location of maximum winds and the cell with the minimum winds within a 2-km radius of the storm center.
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Angle of maximum winds (Am, in radians): the angle between the location of maximum winds and the storm heading direction. We measure Am clockwise from the storm heading, meaning that Am = π/2 for instance represents maximum winds at right angle of motion, to the right (as is typical for the Northern Hemisphere—hereafter noted RHS). Locations left of motion are recorded as negative angles −π < Am < 0 and denoted LHS.
The 10-m winds from InCyc simulation of Hurricane Wilma 2005 as it approaches the coast of Mexico. The dark arrow shows the heading direction, while the white star indicates the location of minimum winds around the storm center. The white line points to the location of maximum winds.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
c. TC wind parameter reference models
The models proposed in this study are compared to a range of well-established relationships. These relationships have been developed over the past decades, and are routinely used operationally to estimate key aspects of TC wind risk including measures of expected TC inner core size and intensity (Atkinson and Holliday 1977; Willoughby and Rahn 2004; Holland 2008; Vickery and Wadhera 2008; Knaff et al. 2016, among others). These relationships are commonly used to estimate spatial wind fields via parametric wind formulations (MacAfee and Pearson 2006). These formulations either focus on simulating winds from the specification of the pressure gradient field and gradient wind assumptions (e.g., Holland 1980; Georgiou 1985), or on directly simulating the wind field (e.g., DeMaria et al. 1992; Phadke et al. 2003; MacAfee and Pearson 2006; Willoughby et al. 2006). These wind fields are idealized and aimed at capturing the axisymmetric characteristics associated with a cyclone.
Pressure–wind (P–V) models are traditionally of the form Vm = αΔpβ (Harper 2002), where Δp is the pressure deficit (in hPa) between the cyclone center and the environmental pressure. This relationship is the form of the widely used formulation of Atkinson and Holliday (1977) or the Dvorak pressure–wind model (Dvorak 1975, 1984), for example. While they have shown skills to capture the maximum wind of a tropical cyclone, they are not designed to represent the broad range of variability occurring in nature, as the empirical parameters are assumed constant. To overcome this gap, new formulations were derived and developed (Willoughby and Rahn 2004; Knaff and Zehr 2007; Holland 2008; Vickery and Wadhera 2008; Courtney and Knaff 2009, for example) and are driven by additional processes affecting TC winds. The model proposed by Knaff and Zehr (2007) depends on pressure deficit, latitude, size, storm motion and intensification rates while other models (Willoughby and Rahn 2004; Knaff and Zehr 2007; Holland 2008; Vickery and Wadhera 2008) aim at capturing the variability of the Holland B parameter (Holland 1980) based on similar physics, and following the relationship
In risk assessment studies, the key parameters of a tropical cyclone are necessary to build a complete hazard wind footprint based on parametric profile models (Mitchell-Wallace et al. 2017; Done et al. 2020; Yang et al. 2022). While a new generation of event set models based on weather and climate information are emerging (Lee et al. 2018; Bongirwar 2020; Jing and Lin 2020), it still strongly contrasts with an operational modeling framework. Indeed, in the deployment phase of a stochastic event set model, weather/climate information will not be available to estimate the cyclone characteristics following more complex relationships used operationally (such as air density or tangential winds at 400–600 km of the cyclone eye for example).
The reference models are therefore chosen with this consideration in mind. Equations and variable requirements are fully described in appendix C. The selected models are the following:
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for the estimation of Vm: the models of Atkinson and Holliday (1977), Holland (2008), and Vickery and Wadhera (2008) are used,
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while Rm estimates are computed according to Knaff et al. (2015), Vickery and Wadhera (2008), Gross et al. (2004), and Willoughby and Rahn (2004).
These parametric relationships serve two purposes: (i) Assessing the variability between the various formulations, and (ii) providing a reference basis for the mean prediction of TC parameters. We acknowledge the fact that these formulations were developed from sparse and/or lower-resolution data and were not aimed to be directly compared to gridpoint maxima from high-resolution model output. For these reasons, InCyc WRF parameters are averaged over a 6-h window to be more comparable to parametric wind formulations. Finally, we also note the very recent studies from Chavas and Knaff (2022) and Fischer et al. (2022); this Rm model and dataset are not included here as they were not available at the time this study was performed.
d. Decision trees, forests, and prediction intervals
The aim of this study is to estimate the whole distribution of outcomes instead of relying on a single mean estimate. In the set of reference models presented in the previous section, parameter estimations are performed by fitting methods such as relying on ordinary least squares approach theory (Hastie et al. 2009). Here we choose a nonparametric approach and examine supervised machine learning techniques to predict key components of a TC (Rm, Vm, and Am). The concept behind supervised learning is that, given a large amount of relevant data covering a realistic spectrum (feature), the model is trained to predict an outcome (called target) without explicit rule formulation (no functional form is imposed, therefore reducing the bias). Subsequently, we are not directly providing the model with specific assumptions, but rather feeding it with a broad range of associated available TC characteristics (latitude, transitional speed, bearing, for example). Providing this learning database (relevant features and associated target) is a key part of the process.
Decision trees (sequences/layers of if… else… rules) constitute an intuitive and easily interpretable supervised learning techniques (Larose and Larose 2014). However, they lack stability and small changes in the input data can lead to radically different tree architectures (Aluja-Banet and Nafria 2003). To overcome these issues, Breiman (2001) proposed an ensemble algorithm (random forest) based on a large number of decision trees. In this approach, each tree is trained using 1) a random subset of the data (sampled with replacement) and 2) a random subset of the available features at each tree node. The final prediction from the forest is then obtained by averaging the predictions from each tree. Random forests have shown good accuracy (Fawagreh et al. 2014) and provide both model stability and performance compared to a unique decision tree (Biau et al. 2008). They can learn complex relationships between predictors and a large number of targets, while keeping a limited number of parameters. On the theoretical side, Scornet et al. (2015) have brought significant mathematical guarantees to explain this success, and the risk of overfitting to the training data is then reduced. However, the interpretation of the model is not as straightforward due to enhanced complexity (Haddouchi and Berrado 2019; Aria et al. 2021).
Random forests estimate the expected mean value of the predicted target. Risk assessment studies require information about the variability around this mean prediction, and therefore it is crucial to model the full distribution of potential outcomes. Prediction intervals are a natural way to assess this variability. Quantile regression forest method (Meinshausen 2006) extends random forest algorithm to provide the estimation of the quantiles of the full distribution (in this study, simulating the complete distribution of TC parameters). They are particularly useful because they allow modeling of conditional distributions without requiring a functional shape to be prescribed. In other words, the distribution comes from data rather than a human imposed relationship. This then allows us to account for uncertainty in the modeled parameter when deploying the models. This contrasts with the standard random forest, which only provides the mean outcome. Details of the algorithms are also discussed in Loridan et al. (2017) and Lockwood et al. (2023).
e. Prediction of TC key properties
In the present study, quantile random forests are trained to estimate the distributions of Vm and Rm. The Vm is modeled indirectly through the estimation of the coefficient α in Vm = αΔp1/2. This α parameter can be related to the Holland B parameter as B = ρeα2 (Knaff et al. 2011b). The power 1/2 in the equation represents cyclostrophic balance (Knaff and Zehr 2007). The impact of this parameter is shown in Fig. S3 in the online supplemental material for an upper-range value of 0.8; it highlights more extreme mean values and higher variability.
Traditional random forest algorithms are not designed to capture periodic properties of the outcomes (in this case the angle Am) as no direct rules about periodicity is part of the algorithm. Instead, we use the circular regression forest algorithm (Lang et al. 2020) to estimate the parameters of a von Mises distribution (also called circular normal distribution).
For the three models (Vm, Rm, and Am), the features consist of the transitional speed, bearing, central pressure and associated rate of changes (including the rate of longitude and latitude change but not directly the longitude and latitude); they are provided every hour along the TC lifetime. Finally, Rm model is also conditioned to the maximum wind speed Vm (i.e., Vm is an input feature of the Rm model). We excluded the direct geographical information of the TC center to obtain predictions that are not location specific; we want a model generalizing behaviors and not learning a specific pattern at each latitude/longitude. As the latitude has been shown to have importance in the cyclone size, four latitude categories are defined as an input feature (lat ≤ 20°N, 20°N < lat < 30°N, 30°N < lat < 40°N and lat > 40°N). However, Chavas and Knaff (2022) show that the Rm growth with latitude is primarily the result of R34 (radius of gale force wind, 34 kt; 1 kt ≈ 0.51 m s−1) becoming larger during poleward motion and the storm ages. Therefore, latitude might just be a proxy for more complex processes. As an example, one could use the sea surface temperature as a feature to improve the predictions of cyclone structure and intensity; the model would remain generalized (i.e., not location-specific).
For the purpose of this study, the models are only trained with InCyc data and no observations are included. To avoid overfitting (i.e., evaluating models based on data already used to train them) we employ a leave-one-out evaluation at the storms level (Hastie et al. 2009): each of the storm simulated is iteratively left out of the training data and used for evaluation only. The evaluation data has therefore never been used for the training phase by any of the models involved.
3. Capturing regional characteristics with InCyc
a. InCyc data processing for evaluation
WRF provides raw hourly wind output. As in Loridan et al. (2017) and Lockwood et al. (2023), hourly outputs are filtered to keep only the wind fields with no land interference (overwater winds) and to discard the first 48 h of a storm (spin-up period). Additionally, cyclones too weak to represent a vortex structure were also discarded from the analysis. This was done by manual screening of the data. Although the InCyc database simulates around 5% of the satellite-era activity, it aims at capturing regional-scale characteristics and realistic physical systems that encompasses the range of historical variability (to be shown after).
For representativeness analysis (section 3b), data are analyzed as distributions. For point-wise analysis (section 3c), we consider a 6-h window (±6 h around IBTrACS timestamp due to its 6-h time step) and the nearest InCyc location to observation is compared to allow for small potential temporal lags. In the following sections, 58 storms located in the North Atlantic and western North Pacific are used (see in Table 2 for the range of values simulated).
Characteristics of NA and WP cases in the InCyc database.
b. InCyc variability, evaluation, and representativeness
Oversea trajectory characteristics between InCyc storms and their associated observations from IBTrACS are shown in Figs. 4 and 5. While trajectories vary from observations, WRF is able to simulate a reasonable path for every cyclone (Fig. 4). The longitude, latitude, transitional speed, and bearing of the selected subpopulation closely correlate with the whole IBTrACS data covering the period 1980–2020 (Fig. 5). This proves the selection of cyclones included in InCyc is representative of the overall population preserving the distributions of each key track parameter. In addition, InCyc WRF simulations also show the same track parameter distributions corroborating the WRF capability to simulate cyclone trajectories in line with observations.
Trajectories comparisons between observed tracks (colored) and oversea simulated InCyc tracks used in the study (white) for the (a) NA and (b) northern WP basins. InCyc consists of a representative subsample of the historical TC database that has been simulated with WRF. Land-contaminated snapshots or snapshots with poorly defined structures, mainly at the start and end of the cyclone lifetime are not displayed here for InCyc.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
Distribution of key track characteristics extracted from the InCyc database for (left) the 30 cyclones simulated in NA and (right) the 28 cyclones simulated in WP for Cat1+ snapshots. The percentage of data for the (first row) longitude, (second row) latitude, (third row) transitional speed, and (fourth row) bearing in the whole 1980–2020 IBTrACS observations (black), the selected IBTrACS observations for the InCyc cyclones (blue), the InCyc WRF database (red), and the observations collected by Ho et al. (1975) and Schwerdt et al. (1979) (dashed white). Fifty bins are used to discretize the data, and a smoothing over 10 bins is used on each set to prevent discontinuity with dataset with data scarcity.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
When looking at track characteristics (Fig. 6), the distributions show the InCyc WRF simulations lead to a higher proportion of stronger systems (deeper central pressure and stronger winds). These differences result from the rejection of poorly defined systems as well as the 48-h spin-up of the simulations. The shift in Vm distributions toward more intense systems in the WP (Figs. S1 and S2) is particularly true for low latitude systems. The InCyc database generally stands between IBTrACS data and the observations of Ho et al. (1975) and Schwerdt et al. (1979); this confirms the good representativeness of the database. As shown in Fig. 6 (bottom panels), the distribution of Rm captured by the InCyc database closely reflects the IBTrACS data both for the overall tracks and for the selected tracks.
Distribution of key wind characteristics extracted from the InCyc database. As in Fig. 5, but for (top) center pressure Pc, (middle) maximum wind speed Vm, and (bottom) radius of maximum winds Rm.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
To go beyond a qualitative analysis, appendix D (and particularly Table D1) provides a range of statistics for each parameter to quantify differences between datasets as well as goodness-of-fit tests between distributions. For the four trajectory parameters, InCyc compares very well with IBTrACS as a whole and with the selected cyclones. More importantly, InCyc covers an extended range of the observations while overall maintaining the distributions which is the key goal of this database. Ho et al. (1975) and Schwerdt et al. (1979) data shows a narrower spectrum of variability due to the conditions in which they were collected. Generally, IBTrACS and InCyc data pass the goodness-of-fit tests on trajectory properties (p values in Table D1). However, the tests fail most of the time for the track characteristics (Vm, Pc, and Rm), and while the distribution have similar ranges and patterns, statistically the distributions differ.
c. InCyc point-wise evaluation and patterns
After evaluating the database in term of range and distribution across both NA and WP, a point-wise evaluation is carried out. Figure 7 illustrates the oversea comparisons between InCyc storms and their associated observations from IBTrACS for central pressure, maximum wind and P–V relationship for the North Atlantic (NA) and western North Pacific (WP), and displacement errors:
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The P–V wind relationship is in very close agreement with the one observed in both NA and WP regions (Figs. 7a,d, respectively).
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Correlation of 0.7 for central pressure between simulations and observations without biases (mean bias of about −2 hPa; Fig. 7e); however, a range of variability is highlighted [root-mean-square error (rmse) = 21 hPa].
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Correlation of 0.65 for maximum winds (with a bias of 2.6 m s−1 and rmse = 13 m s−1; Fig. 7b).
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Errors in zonal and meridional displacements (Figs. 7c,f) are mostly small, generally lower than 100 km though some points can be apart (about 23% are over 100 km and 7% over 200 km); this is due to the choice of associating InCyc data with IBTrACS based on timestamps and not the nearest spatial observations.
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Table 3 summarizes the statistics of track properties for both NA and WP.
Central pressure and wind speed comparisons. (a),(d) The P–V relationship between InCyc and observed for both basins. (b) Wind speed and (e) central pressure P–P plots of observations vs simulations. Finally, (c) track errors and (f) displacement errors are shown. For the northern WP, the U.S. agencies were used to provide 1-min sustained winds to prevent discrepancies in the way agencies report sustained winds (Lander 2008). A 6-h moving averaged was applied to the InCyc data. The color bar shows the percentage of samples per bin.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
Comparisons between observations and InCyc. Pearson correlation between observations and InCyc, bias between InCyc and observations, and the root-mean-square errors are provided. In addition, the 95% confidence intervals on the mean errors and the interquantile range (IQR) are also calculated.
Finally, InCyc simulated wind fields for Typhoon Mawar 2012 is compared to two ASCAT (Advanced Scatterometer) satellites passes (Ricciardulli and Wentz 2016) for the same system (Figs. 8a–d). Figures 8e and 8f illustrate a similar comparison for Hurricane Joaquin (2015) where the InCyc WRF simulation is compared to a snapshot of ocean surface winds from the Soil Moisture Active Passive (SMAP) NASA mission (Meissner et al. 2017). These comparisons show the ability of WRF to reproduce the structure of the system during its evolution from a pure tropical system (Fig. 8b) to a transition system (Fig. 8d). This shows that the model is capable of simulating subtle complex TC physics such as extratropical transition.
Comparison to satellite products of ocean winds at 10 m above the sea surface (particular examples). Typhoon Mawar as captured by an ASCAT descending pass from (a) 4 Jun 2012 and (c) 6 Jun 2012 and (b),(d) simulated by WRF in InCyc; Hurricane Joaquin as captured by (e) SMAP and (f) WRF at 0945:00 UTC 7 Oct 2015.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
Previous studies have highlighted sources of biases in WRF simulations due to the choices of parameterizations or other numerical parameters. These could significantly affect the training of new algorithms or relationships, resulting in biased parametric models. For example, biases in TC intensity or structure can be driven by the boundary layer parameterizations (Nolan et al. 2009b,a), the microphysics parameterizations and cloud-radiative feedbacks (Fovell et al. 2016), the drag coefficient parameterizations (Li et al. 2016; Jiang et al. 2021), or simply by the choice in resolution (Rotunno et al. 2009). Overall, these known biases do not strongly impact the studied parameters as suggested by the results shown above.
d. North Atlantic versus West Pacific intensity and structure
1) Maximum winds (
Wind parameters extracted from the InCyc database are compared with independent data (white distributions in Fig. 6) and red triangles in Figs. 7a and 7d digitized from Ho et al. (1975) and Schwerdt et al. (1979), for both NA and WP basins. The InCyc relationships between center pressure and maximum velocity (Figs. 7a–d) mirror the well-documented P–V relationships, however, they also exhibit a large range of uncertainty (for a given wind speed, the central pressure can be ±10 hPa from the average value in both IBTrACS and InCyc).
2) Radius of maximum winds (
As expected, the storm size shows a clear dependency on intensity, with smaller Rm values to be expected from intense systems than from weak ones (Fig. 9); this agrees with the restricted amount of observations from Ho et al. (1975) and Schwerdt et al. (1979) as well as the aircraft reconnaissance data for the North Atlantic.
Relationship between Rm and Vm considering (a) the InCyc database (both NA and WP), (b) the observations collected by Ho et al. (1975) and Schwerdt et al. (1979), and (c) the aircraft reconnaissance data for the North Atlantic. The color bar shows the percentage of samples per bin.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
Perhaps more surprisingly, in InCyc WRF simulations, the dependence on latitude (while secondary to intensity) is not as obvious as commonly accepted (e.g., Knaff et al. 2015). Although the Rm distributions do shift toward higher values for higher latitudes (Fig. 10), we also note a significant proportion of small systems in the higher-latitude bins, primarily in InCyc database and in the western North Pacific. The InCyc inner core size generally matches aircraft reconnaissance measurements as well as the IBTrACS database (Figs. S1 and S2). We notice that large systems are less present in the InCyc database though; this could be driven by the method to identify the maximum winds in the study (pixel and not a region of maximum wind–see section 2b) and by the disregarded snapshots mentioned in the method section; it could also be linked to the extent of aircraft reconnaissance data as Fig. 6 shows good match between IBTrACS and the simulated distributions.
Distributions of Rm from InCyc for NA (30 TCs) and WP (28 TCs) for different latitude regions. Surface wind estimates of Rm from aircraft reconnaissance data for the North Atlantic are also provided for comparison. Number of samples available, the mean of the distribution, and 10th and 90th percentiles are provided in the legend. To note, the goodness-of-fit tests would fail between these distributions.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
3) Location of maximum winds relative to the storm motion (
Similarly, while the distribution of Am shows the right-hand side of the storm (RHS) as the more likely location of peak winds, it also reveals occurrences of left-hand-side (LHS) peak winds (Fig. 11—about 15%–20%). This suggests assuming that peak winds are to be expected to the right for the Northern Hemisphere systems is not always appropriate.
Distributions of Am from InCyc for NA (30 TCs) and WP (28 TCs).
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
We note that the Am values sometimes oscillate quickly over time (see Fig. 3). This may be explained by the high horizontal (1 km) and temporal (hourly) resolutions of the InCyc data. However, we also believe that short convective bursts and rapid track direction changes can quickly switch the location of peak winds from one side of the storm to the other [consistent with Stern et al. (2016)]. From a risk assessment point of view this is a reminder that important wind risk exists on both sides of a TC track.
4. Predicting the distributions of TC wind parameters for two case studies
Figures 12 and 13 present the time series of TC characteristics for major Hurricane Florence 2018 and Supertyphoon Nanmadol 2011. These two cyclones have been chosen as they have long temporal series of parameters, strong winds and show significant intensification. Red dots indicate the InCyc WRF parameters averaged over a 6-h window to be comparable to parametric wind formulations. All reference models (section 2c) approximate the mean parameters (dark symbols on Figs. 12 and 13). Since the QRF models are designed to capture any quantile in the response distribution, we choose to present quantiles ranging from the 5th to 95th (by step of 10th). As a result, the different color shaded regions (Figs. 12 and 13) provide information on prediction intervals (e.g., 10%, 30%, 50%, 70%, and 90% confidence) along with the single best guess (median) prediction.
NA TC Florence 2018 leave-one-storm-out comparisons of the Rm, Vm, and Am TC characteristics between the new models (with prediction intervals 90%, 70%, 50%, 30%, and 10%) superimposed with the InCyc data (red circles) and for a range of established models: Knaff et al. (2015) is KN15, Vickery and Wadhera (2008) is VW08, Gross et al. (2004) is GR04, Willoughby and Rahn (2004) is WR04 for Rm and Atkinson and Holliday (1977) is AH77 and Holland (2008) is HO08 for Vm. The input parameters for each formulation come from the InCyc database to compare each model in a similar manner.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
As in Fig. 12, but for WP TC Nanmadol 2011.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
a. Hurricane Florence—2018
In the case of Hurricane Florence (2018; Fig. 12) the InCyc time series of Rm values varies significantly during the first half of the simulation, and then drops to around 25–30 km at the later more intense stage of the storm. The reference models are very stable in comparison, with only Knaff et al. (2015) showing some level of variability over the life of the storm matching the oscillations seen in the WRF simulations; however, it overestimates the small Rm after 200 h when the TC reaches its peak wind speed. The QRF predicted distributions also show a level of variability with a dip and shrinkage of the whole predicted range from time step 200 h that matches the InCyc pattern. This translates to an increased level of certainty from the QRF estimates of Rm at higher intensity. More importantly the predicted QRF distributions contain most of the InCyc data (except for a few time steps around 175 h) as well as the reference models throughout the storm life. This suggests the uncertainty of the Rm parameter can be effectively estimated. Training the model with the raw InCyc data (i.e., no 6-h smoothing) leads to higher variability highlighting how less certain the model is in its prediction (not shown).
The Vm predictions (given knowledge of Pc) show a close agreement between the reference models with a consistent underestimation of the InCyc Vm values. In comparison the median of the QRF-predicted distributions is closer to the InCyc records (especially for strong Vm). We note that the QRF distribution covers most of the variability in Vm (similar to the one of Rm), with only Atkinson and Holliday (1977) consistently outside of the modeled range during the early stages of the storm agreeing with Knaff and Zehr (2007) conclusions. The QRF, as the parametric models, fails to capture the variability in maximum wind between time step 100 and 150 h present in the InCyc simulated data, with each model predicting a smooth evolution of Vm.
As previously discussed, the evolution of Am is by far the hardest to simulate. In the absence of any other model of reference we only provide the QRF predictions. This is consistent with the InCyc data. The predicted Am distribution shows a large range of uncertainty. Apart from occasional occurrences of near-left maxima, it predicts maximum winds to be mostly located to the right of the track (RHS–most common for the Northern Hemisphere). After iteration 260 h, the model also captures the shift toward maximum winds located to the front that are well captured.
b. Typhoon Nanmadol—2011
Figure 13 presents the WP Typhoon Nanmadol (2011) with peak winds reaching nearly 80 m s−1. For most of the storm’s life the reference models agree with its expected size where mean simulated Rm values are about 20–40 km—a good approximation of the InCyc range—though variability between the models could reach 10 km. As for Hurricane Florence (2018), the predicted distributions do capture the InCyc data as well as the estimates from all reference models. In the case of the Vm predictions, all models are in close agreement and provide good estimates of most of the InCyc records. This high level of confidence is also visible from the narrower predicted range in our method for the second half of the cyclone’s lifetime. The evolution of Am shows mostly a right-hand-side location of the maximum winds, but also highlights the type of oscillations between right and left sides of motion previously discussed and clearly visible after 250 h (illustrated by Fig. 3); the model is able to capture well this variability. While the predicted Am distributions are still expecting the front RHS as the most probable location for peak winds, it also accounts for a higher probability of LHS occurrences than in the case of Hurricane Florence (2018; Fig. 12).
Figures S4–S8 illustrate other historical storms from the database to highlight different outcomes from the QRF and extend the evaluation. For example, a systematic overestimation of the Rm for WP cyclone Jebi (2018; Fig. S7) while the different parametric models perform well, or an underestimation of the Vm for NA cyclone Gustav (1990; Fig. S8) as all other parametric models.
c. Statistical validations of the 58 storms
Figure 14 shows the QRF correlations, biases, and root-mean-square errors for each of the 58 cyclones simulated with the leave-one-storm-out method described previously. This highlights that generally the QRF median predictions are capturing well the dataset for unseen data (particularly high level of correlations for Vm). The few cases with negative correlations are cases with short time series and very little variability. QRF median predictions are largely unbiased, while errors are in the range of 10–20 km for Rm and 5 m s−1 for Vm. Compared to the range of reference models, the QRF performs very well with lower errors. We note that the reference models are generally negatively biased in wind speed (and therefore positively biased in Rm); this is probably due to them being established from data with less variability. Nonetheless, this shows the QRF is able to predict median behaviors with similar (if not better) accuracy to existing models, while providing information on the uncertainty and the whole distribution of parameters instead of only an average estimate. Table D2 summarizes 95% confidence levels for each of these mean parameters.
Performance of the QRF across the 58 events. Distribution of (top) correlations, (middle) biases, and (bottom) root-mean-square errors for (left) Rm and (right) Vm for the median prediction of the 58 events simulated in NA and WP (blue histogram), the 48 events with more than 2 days of values (red histogram), and the spread of reference models used in the study. The statistics of the two cyclones used previously are displayed by the vertical plain (NA TC Florence 2018) and dashed (WP TC Nanmadol 2011) lines.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
While there is no reason to expect the observations and the median predictions (or the estimates from the reference models) to match at every time steps, a well calibrated model would ensure that the data falls within the 50% (resp. 70%, 90%) intervals for roughly 50% (resp. 70%, 90%) of the time steps. This is verified by the leave-one-storm-out evaluation of the 58 TCs selected for each modeled parameter. Figure 15 shows the results of this evaluation and reveals that the Vm model is the best calibrated one, and this holds for all size bins. The Rm model is well calibrated as a whole but tends to underestimate observed Rm variability for both the smallest and biggest storms (tail of the distribution); i.e., the expected outcomes fall too often outside the range of predictions for these two categories. Finally, the Am model is on the conservative side; i.e., the distribution is wider, highlighting more uncertainty in the outcomes. The proportion of cases falling within the 50% prediction interval is consistently larger than 50% for all size bins. This is due to larger uncertainty in the data, and this highlights the model’s difficulty predicting well on new data. Overall, the three models cover most of the observed variability with appropriate levels of prediction therefore providing a way to better account for parameter variability within TC risk assessment systems.
Leave-one-storm-out estimation of the QRF models performance (top) Rm, (middle) Vm, and (bottom) Am for all 58 cyclones. Bars represent the percentage of prediction falling with the 90% (dark blue), 70% (cyan), and 50% (green) prediction intervals. Each bar is therefore expected by construction to fall near the respective red 90%, 70%, and 50% lines. (left) All data together are shown. (center) Data are split per Rm bins. (right) Percentage of data where the Rm between two consecutive time steps is over 10 km as well as an Am shift of over 45°. As an example of interpretation, the green bars represent the proportion of time steps falling within the predicted 50% prediction interval; a well-calibrated model would show all green bars lined up at the 50% level (lowest horizontal red line).
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
5. Application to catastrophe models and risk distributions
The main role of a TC risk assessment system (or “catastrophe model,” e.g., Vickery and Wadhera 2008) is to quantify the full distribution of TC risk, providing users with a way to conceptualize risk beyond the range of historical observed outcomes. These systems usually rely on Monte Carlo types of simulations to sample distributions of TC parameters. In this context it is critical to employ modeling methods that do not simply provide estimates of the mean response, but rather quantify the full variability in simulated parameters. The quantile regression forest approach was designed with this application in mind, and here we describe how it can be efficiently deployed within a catastrophe model.
We assume that a method to generate stochastic TC events is in place, such as the ones described by Hall and Jewson (2007) and Rumpf et al. (2007), or more recently in Bloemendaal et al. (2020) or Bongirwar (2020) among others. For each TC event the evolution of TC center location as well as its center pressure is therefore known and can be used to estimate the key parameters discussed in this paper: Vm, Rm, and Am. Thanks to the ability of our approach, one can iteratively sample from the full simulated distributions rather than systematically using mean predictions (i.e., the reference models). The method captures a much broader range of risk variability, while maintaining consistency between key simulated parameters. This in turn ensures a better approximation of the full risk profile.
In this study, the QRF were trained and conditioned to other properties of the TC; in future investigations, information about the local or regional climate state such as sea surface temperature or wind shear for example, could be added to the QRF to condition the model and predictions to these properties, and potentially enhanced the predictive skills. This is, however, left out of the present study.
6. Conclusions
We have assembled a global database of high-resolution TC simulations (InCyc) to facilitate the analysis of TC structures across basins in a consistent way.
First, high-level analysis of key wind characteristics is presented (peak wind location and intensity), using data from North Atlantic and western North Pacific basins. While most documented properties between latitude, TC size, intensity and maximum wind location are present in our database we also note a very high level of variability around these mean relationships. To model the full distribution of the TC wind parameters (Vm, Rm, and Am), we introduce the quantile random forest (QRF) algorithm to explicitly capture uncertainty.
Our innovative approach allows quantification of prediction intervals. In a leave-one-storm-out evaluation exercise, we show that this algorithm performs well and provides a good representation of the expected range of values. We then discuss how such an approach can be implemented in risk assessment systems to allow sampling of uncertainty.
Beyond this analysis we believe the InCyc database offers outstanding value as a training set for machine learning models trying to capture TC spatial patterns such as their wind and precipitation fields distributions. TC surface wind and precipitation fields are often estimated via simplified parametric profiles Holland (1980), Willoughby et al. (2006), Grieser and Jewson (2012). While these parametric profiles do not match the level of physical complexity achieved by WRF, they offer very fast runtimes, and therefore have flourished as the tool of choice for the type of large TC ensembles at the core of risk assessment systems.
Recent advances in the field of machine learning offer a powerful alternative to build TC wind and precipitation field models directly from data, and without the need for human engineered rules. The pilot study by Loridan et al. (2017) shows the potential of these techniques with a coarser resolution TC database focused on the western North Pacific. The global and high-resolution catalog of storms of InCyc enables machine learning algorithms to learn from a much broader range of TC features.
It is our hope that the data will serve to help academic groups around the world, and we welcome applications for use of the data.
Acknowledgments.
This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian government and the government of Western Australia. J. Knaff thanks NOAA/Center for Satellite Applications and Research for providing the time to contribute to this work. The views, opinions, and findings contained in this report are those of the authors and should not be construed as an official National Oceanic and Atmospheric Administration or U.S. government position, policy, or decision. C-2015 ASCAT data are produced by Remote Sensing Systems and sponsored by the NASA Ocean Vector Winds Science Team. Data are available at www.remss.com. SMAP sea surface wind data are produced by Remote Sensing Systems and sponsored by NASA Earth Science funding. Data are available at www.remss.com/missions/SMAP/winds/.
Data availability statement.
Due to its proprietary nature and competitive interest, the InCyc database cannot be made openly available. However, InCyc has been designed to facilitate analysis of TC wind risk across basins and would be made available to research institutions on demand to the authors.
APPENDIX A
Identifying the InCyc Population
In seeking a statistically representative subsample of the population, a novel machine learning algorithm was designed to identify such a set of records. The method rests on the idea that a statistically representative set is one that is statistically indistinguishable from the main population. To that end, machine learning was used to build classification models, and thus measure the distinguishability of samples and remaining data (using resampling to measure the distinguishability of thousands of sample sets, and selecting the one with the least distinguishability from the main sample). Area under the (receiver operating characteristic) curve (AUC) was used as the key measure. The best estimate produced an AUC closest to 50%, which represents complete randomness i.e., indistinguishability.
a. Cluster analysis by basin
Following Kossin et al. (2010), each track trajectory is approximated with a set of six parameters using a quadratic fit for the time dependent longitude and latitude coordinates and storm peak intensity is characterized by the minimum pressure recorded over the lifetime of each event. Similar to previous analysis (Camargo et al. 2007; Kossin et al. 2010; Ramsay et al. 2012, among others), a cluster analysis is carried out for each basin according to their track trajectories. Based on experimentation, an optimum number of four clusters are selected for each basin as it provides more stable and robust clusters. While this number might differ from previous studies [e.g., Camargo et al. (2007) had seven clusters for the western North Pacific], it only aims at identifying key groups of the historical cyclone population for the next selective step. This ensures that each population is proportionally represented in the final selection; however, this step is not necessary considering the algorithm below and has been inherited from an early stage of the study.
b. Identifying the most representative subpopulation
Due to obvious computing performance limitations, only a subselection of the historical cyclones has been simulated dynamically using the full-physics Weather Research and Forecasting modeling system. To identify a/the most representative selection of cyclonic activity within a basin, the following algorithm has been applied to each basin/cluster combination:
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Candidate sampling and training the algorithm:
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For each basin/cluster draw a random subsample from the ensemble of events.
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Train a random forest to distinguish this subsample from the remaining events based on knowledge of track trajectory parameters and peak intensity (seven input parameters: six for the trajectory via the quadratic fit to the longitude and latitude and one for the minimum pressure of a TC over its lifetime).
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Compute the area under the curve (AUC) score for this sample.
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Cycle through candidates: Repeat first step 5000 times to examine 5000 potential candidates and store the AUC score for each candidate sample.
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Identify a/the most representative candidate: the candidate sample with the AUC score closer to 0.5 (i.e., the most random/the less distinguishable from the complete set of observations) is the most representative.
This selective algorithm works in a reverse way to what is usually expected. Many random subpopulations are created (here 5000), and a random forest algorithm to dissociate this subpopulation from the whole population is trained. If the random forest has skills to dissociate it, this subpopulation is not representative. In this application, the subpopulation that scores the worst (the closest from randomness i.e., AUC around 0.5) meaning the algorithm cannot dissociate it from the overall population is considered as the most representative.
There are two considerations here to keep in mind: 1) the subgroup should be large enough so that each potential subgroup is not scoring a 0.5 AUC (meaning any random draw could be the subset); 2) in this context (restrictive historical tracks combined to medium size subsample) the method leads to a range of subgroups that are as representative as each other. For this reason, other groups could have been selected. The key point of this step is to prevent the subgroup from only consisting of similar tracks as well as to prevent a biased human selection.
Figures 5 and 6 illustrate how the subpopulation generated by the algorithm represents very well the overall IBTrACS database (1980–2020) in terms of trajectories: longitude and latitude spreads and translational speeds and bearing. The distribution of storm intensity and shape parameters (Pc, Vm, and Rm) of the subpopulation are also in very good agreement with the whole IBTrACS database.
APPENDIX B
WRF Model Configuration
WRF version 4.0 is used with three nested domains. The outer domain (d01) is static with 9-km horizontal resolution and covers the whole track of the TC. Within this are two vortex-following domains (d02 and d03) with 3- and 1-km horizontal resolution, respectively. Here d02 is 1000 km × 1000 km in size and d03 is 600 km × 600 km. All domains use 60 levels up to a height of 20 hPa. The two-way feedback between domains is turned on.
The ERA5 reanalysis from ECMWF is used to provide initial and boundary conditions for all TC simulations. ERA5 provides hourly estimates of a large number of historical atmospheric fields on a 0.25° horizontal grid to a height of 80 km. Importantly, it spans the 1980–present period.
Analysis nudging on velocity, temperature and moisture variables is used in d01 to maintain rough similarity with the historical weather conditions for a particular storm. The inner domains, d02 and d03, evolve freely without any nudging. Track paths are not provided to WRF either.
The principle physical schemes used are as follows (summarized in Table B1). The cumulus parameterization scheme (CPS) is the new simplified Arakawa–Schubert scheme (Han and Pan 2011). The inner domains, d02 and d03 do not use a CPS. The planetary boundary layer (PBL) scheme used is the Yonsei University Scheme (Hong et al. 2006). The microphysics scheme is the WRF single-moment 6-class scheme (WSM6) (Hong and Lim 2006). Shortwave and longwave radiation physics use the RRTMG schemes (Iacono et al. 2008). Also, the air-sea surface flux parameterization for momentum and moist enthalpy is activated as it is more adapted to cyclone dynamics as recent research has shown; the constant version is used here via isftcflx = 1 (Green and Zhang 2013). The five-layer thermal diffusion scheme (Dudhia 1996) and revised MM5 scheme (Jiménez et al. 2012) are used for the land and surface layer, respectively.
WRF parameters tested.
To optimize the best set of parameters/options, over 150 combinations have been simulated for few cyclones:
In addition, the impact of the nudging time scale, the nested options (vortex-following or not), and the sea surface temperature inputs have also been examined.
APPENDIX C
Reference Models for Vm and Rm
To assess the performance of the model designed in this study, and based on quantile random forest (QRF; Meinshausen 2006), a set of reference models to predict the maximum winds Vm and the radius of maximum winds Rm are used and describes below.
a. Estimating the maximum winds Vm
Given the latitude φ and the central pressure Pc, the following models are used to estimate Vm:
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Atkinson and Holliday (1977): Vm = 3.4(1010 − Pc)0.644; the original coefficient is scaled to provide wind in meters per second (m s−1)
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Holland (2008):
with Vt the transitional speed and -
Vickery and Wadhera (2008): B = 1.881 − 0.005 57Rm − 0.012 95φ
The Knaff and Zehr (2007) formulation allowing broader variability due to the impact of storm motion and latitude is not used in this study as it also requires the knowledge of a normalized size parameter that we cannot estimate in a risk assessment framework (Courtney and Knaff 2009). For Vickery and Wadhera (2008) formulation, Rm is taken from the WRF simulations. The air density ρ is set to 1.15 kg m−3 though in reality it would vary.
b. Estimating the radius of maximum winds Rm
The Rm calculations are done using the formulations of
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Vickery and Wadhera (2008): ln(Rm) = 3.015 − 6.291 × 10−5 Δp2 + 0.0337φ
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Gross et al. (2004): Rm = 35.37 − 0.111Vm + 0.57(φ − 25)
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Willoughby and Rahn (2004): Rm = 51.6 exp(0.0223Vm + 0.0281φ)
For Knaff et al. (2015) and Gross et al. (2004), the Vm is in knots and Rm is in nautical miles. The maximum wind speed is taken from the WRF simulations directly.
APPENDIX D
Statistical Evaluation
Figures 5 and 6 highlight how the subsample of historical cyclones selected to derive the InCyc WRF database are capturing the ranges and distributions of key characteristics of tropical cyclones. Here we propose to do a more robust and quantitative evaluation of the InCyc database. For each of the parameters used in the study, and for the different sources of data (whole IBTrACS, IBTrACS selection, InCyc and the data of Ho et al. (1975) and Schwerdt et al. (1979), a range of metrics have been computed (Table D1):
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the mean and standard deviation are used as standard metrics,
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the cumulative ranked probability score is computed to quantify the divergence between the two distributions,
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the mean p value of the Kolmogorov–Smirnov test (goodness-of-fit test) are also provided.
Comparison of cyclone properties for NA and WP. For each parameter, the mean and standard deviation are provided for the whole IBTrACS data, the selection of IBTrACS, the InCyc database, and, if available, the data from Ho et al. (1975) and Schwerdt et al. (1979). The cumulative ranked probability score (CRPS) is also given to compare IBTrACS vs IBTrACS selection, IBTrACS selection vs InCyc and InCyc vs Ho et al. (1975) and Schwerdt et al. (1979) (if available). Finally, the mean p value of the goodness-of-fit test is also provided.
a. Cumulative ranked probability score
The cumulative ranked probability score (CRPS; Zamo and Naveau 2018) is commonly used to evaluate a forecast to an observation. As an example, Fig. D1a shows the distributions of longitude in the NA for the selection of IBTrACS, the InCyc database and the data of Ho et al. (1975) and Schwerdt et al. (1979). The squared area between the CDFs represents the CRPS (Fig. D1b) and can be seen as an absolute mean error. The CDFs of the IBTrACS selection to the InCyc WRF database largely follow the same patterns and the area in-between remains very small (0.4°). On the other side, the CDF derived from the data of Ho et al. (1975) and Schwerdt et al. (1979) is very different, leading to a very large area (8.9°) between the CDFs; this illustrates the large differences between the two distributions (to be expected considering this data have been collected in U.S. coastal regions).
Examples of statistical testing applied to the longitude for the 30 cyclones simulated in NA. (a) Probability density function (PDF) of longitudes (from Fig. 5) for the selected IBTrACS observations for the InCyc cyclones, the InCyc WRF database, and the observations collected by Ho et al. (1975) and Schwerdt et al. (1979). (b) The cumulative density function (CDF) derived from the PDF with the area between curves shaded and (c) distribution of the p values for the Kolmogorov–Smirnov test applied over 1000 random subsamples.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-22-0317.1
b. Goodness-of-fit test
To test the goodness-of-fit between two distributions, 1000 random values are sampled with replacement and the Kolmogorov–Smirnov test (Kolmogorov 1933; Smirnov 1939) is carried out to obtain a p value. This step is repeated 1000 times and the average p value is computed. Figure D1c shows the distribution of the p values. Comparing Ho et al. (1975) and Schwerdt et al. (1979) to InCyc leads to a mean p value of about 0 (well below the defined cut p < 0.05); this means we reject the null hypothesis, i.e., the data were not drawn from the same distribution. The opposite happens when looking at the IBTrACS selection versus the InCyc WRF database; the mean p value is about 0.15 (p > 0.05), i.e., we cannot reject the null hypothesis.
c. Bootstrapping for confidence levels
To assess the variability in parameters, confidence intervals around key metrics have been computed by randomly resampling (1000 times) the distribution with replacement. The summary of the variability in RMSE, bias, and correlation for Fig. 14 are shown in Table D2.
Uncertainty in the different mean parameters computed by bootstrapping.
REFERENCES
Aluja-Banet, T., and E. Nafria, 2003: Stability and scalability in decision trees. Comput. Stat., 18, 505–520, https://doi.org/10.1007/BF03354613.
Aria, M., C. Cuccurullo, and A. Gnasso, 2021: A comparison among interpretative proposals for random forests. Mach. Learn. Appl., 6, 100094, https://doi.org/10.1016/j.mlwa.2021.100094.
Arthur, W. C., 2021: A statistical–parametric model of tropical cyclones for hazard assessment. Nat. Hazards Earth Syst. Sci., 21, 893–916, https://doi.org/10.5194/nhess-21-893-2021.
Atkinson, G. D., and C. R. Holliday, 1977: Tropical cyclone minimum sea level pressure/maximum sustained wind relationship for the western North Pacific. Mon. Wea. Rev., 105, 421–427, https://doi.org/10.1175/1520-0493(1977)105<0421:TCMSLP>2.0.CO;2.
Biau, G., L. Devroye, and G. Lugosi, 2008: Consistency of random forests and other averaging classifiers. J. Mach. Learn. Res., 9, 2015–2033.
Bloemendaal, N., I. D. Haigh, H. de Moel, S. Muis, R. J. Haarsma, and J. C. J. H. Aerts, 2020: Generation of a global synthetic tropical cyclone hazard dataset using STORM. Sci. Data, 7, 40, https://doi.org/10.1038/s41597-020-0381-2.
Bongirwar, V., 2020: Stochastic event set generation for tropical cyclone using machine-learning approach guided by environmental data. Int. J. Climatol., 40, 6265–6281, https://doi.org/10.1002/joc.6579.
Breiman, L., 2001: Random forests. Mach. Learn., 45, 5–32, https://doi.org/10.1023/A:1010933404324.
Camargo, S. J., A. W. Robertson, S. J. Gaffney, P. Smyth, and M. Ghil, 2007: Cluster analysis of typhoon tracks. Part I: General properties. J. Climate, 20, 3635–3653, https://doi.org/10.1175/JCLI4188.1.
Cavallo, S. M., R. D. Torn, C. Snyder, C. Davis, W. Wang, and J. Done, 2013: Evaluation of the advanced hurricane WRF data assimilation system for the 2009 Atlantic hurricane season. Mon. Wea. Rev., 141, 523–541, https://doi.org/10.1175/MWR-D-12-00139.1.
Chavas, D. R., and K. A. Emanuel, 2010: A QuikSCAT climatology of tropical cyclone size. Geophys. Res. Lett., 37, L18816, https://doi.org/10.1029/2010GL044558.
Chavas, D. R., and J. A. Knaff, 2022: A simple model for predicting the tropical cyclone radius of maximum wind from outer size. Wea. Forecasting, 37, 563–579, https://doi.org/10.1175/WAF-D-21-0103.1.
Chavas, D. R., K. A. Reed, and J. A. Knaff, 2017: Physical understanding of the tropical cyclone wind-pressure relationship. Nat. Commun., 8, 1360, https://doi.org/10.1038/s41467-017-01546-9.
Chen, J., and D. R. Chavas, 2020: The transient responses of an axisymmetric tropical cyclone to instantaneous surface roughening and drying. J. Atmos. Sci., 77, 2807–2834, https://doi.org/10.1175/JAS-D-19-0320.1.
Chen, J., Z. Wang, C.-Y. Tam, N.-C. Lau, D.-S. D. Lau, and H.-Y. Mok, 2020: Impacts of climate change on tropical cyclones and induced storm surges in the Pearl River delta region using pseudo-global-warming method. Sci. Rep., 10, 1965, https://doi.org/10.1038/s41598-020-58824-8.
Combot, C., A. Mouche, J. Knaff, Y. Zhao, Y. Zhao, L. Vinour, Y. Quilfen, and B. Chapron, 2020: Extensive high-resolution Synthetic Aperture Radar (SAR) data analysis of tropical cyclones: Comparisons with SFMR flights and best track. Mon. Wea. Rev., 148, 4545–4563, https://doi.org/10.1175/MWR-D-20-0005.1.
Courtney, J., and J. Knaff, 2009: Adapting the Knaff and Zehr wind-pressure relationship for operational use in tropical cyclone warning centres. Aust. Meteor. Oceanogr. J., 58, 167–179, https://doi.org/10.22499/2.5803.002.
Davis, C., W. Wang, J. Dudhia, and R. Torn, 2010: Does increased horizontal resolution improve hurricane wind forecasts? Wea. Forecasting, 25, 1826–1841, https://doi.org/10.1175/2010WAF2222423.1.
DeMaria, M., S. D. Aberson, K. V. Ooyama, and S. J. Lord, 1992: A nested spectral model for hurricane track forecasting. Mon. Wea. Rev., 120, 1628–1643, https://doi.org/10.1175/1520-0493(1992)120<1628:ANSMFH>2.0.CO;2.
Done, J. M., M. Ge, G. J. Holland, I. Dima-West, S. Phibbs, G. R. Saville, and Y. Wang, 2020: Modelling global tropical cyclone wind footprints. Nat. Hazards Earth Syst. Sci., 20, 567–580, https://doi.org/10.5194/nhess-20-567-2020.
Dudhia, J., 1996: A multi-layer soil temperature model for MM5. Preprints, Sixth PSU/NCAR Mesoscale Model Users’ Workshop, Boulder, CO, PSU–NCAR, 49–50.
Dvorak, V. F., 1975: Tropical cyclone intensity analysis and forecasting from satellite imagery. Mon. Wea. Rev., 103, 420–430, https://doi.org/10.1175/1520-0493(1975)103<0420:TCIAAF>2.0.CO;2.
Dvorak, V. F., 1984: Tropical cyclone intensity analysis using satellite data. NOAA Tech. Rep. NESDIS 11, 47 pp., http://satepsanone.nesdis.noaa.gov/pub/Publications/Tropical/Dvorak_1984.pdf.
Emanuel, K., S. Ravela, E. Vivant, and C. Risi, 2006: A statistical deterministic approach to hurricane risk assessment. Bull. Amer. Meteor. Soc., 87, 299–314, https://doi.org/10.1175/BAMS-87-3-299.
Fawagreh, K., M. M. Gaber, and E. Elyan, 2014: Random forests: From early developments to recent advancements. Syst. Sci. Control Eng., 2, 602–609, https://doi.org/10.1080/21642583.2014.956265.
Fischer, M. S., P. D. Reasor, R. F. Rogers, and J. F. Gamache, 2022: An analysis of tropical cyclone vortex and convective characteristics in relation to storm intensity using a novel airborne Doppler radar database. Mon. Wea. Rev., 150, 2255–2278, https://doi.org/10.1175/MWR-D-21-0223.1.
Fovell, R. G., Y. P. Bu, K. L. Corbosiero, W.-W. Tung, Y. Cao, H.-C. Kuo, L.-H. Hsu, and H. Su, 2016: Influence of cloud microphysics and radiation on tropical cyclone structure and motion. Multiscale Convection-Coupled Systems in the Tropics: A Tribute to Dr. Michio Yanai, Meteor. Monogr., No. 56, Amer. Meteor. Soc., https://doi.org/10.1175/AMSMONOGRAPHS-D-15-0006.1.
Georgiou, P. N., 1985: Design windspeeds in tropical cyclone-prone regions. Ph.D. thesis, University of Western Ontario, 316 pp.
Gori, A., N. Lin, D. Xi, and K. Emanuel, 2022: Tropical cyclone climatology change greatly exacerbates U.S. extreme rainfall–surge hazard. Nat. Climate Change, 12, 171–178, https://doi.org/10.1038/s41558-021-01272-7.
Green, B. W., and F. Zhang, 2013: Impacts of air–sea flux parameterizations on the intensity and structure of tropical cyclones. Mon. Wea. Rev., 141, 2308–2324, https://doi.org/10.1175/MWR-D-12-00274.1.
Grieser, J., and S. Jewson, 2012: The RMS TC-rain model. Meteor. Z., 21, 79–88, https://doi.org/10.1127/0941-2948/2012/0265.
Gross, J., M. DeMaria, J. A. Knaff, and C. R. Sampson, 2004: A new method for determining tropical cyclone wind forecast probabilities. 26th Conf. on Hurricanes and Tropical Meteorology, Miami, FL, Amer. Meteor. Soc., 11A.4, https://ams.confex.com/ams/26HURR/webprogram/Paper75000.html.
Haddouchi, M., and A. Berrado, 2019: A survey of methods and tools used for interpreting random forest. 2019 First Int. Conf. on Smart Systems and Data Science (ICSSD), Rabat, Morocco, Institute of Electrical and Electronics Engineers, 1–6, https://doi.org/10.1109/ICSSD47982.2019.9002770.
Hall, T. M., and S. Jewson, 2007: Statistical modeling of North Atlantic tropical cyclone tracks. Tellus, 59A, 486–498, https://doi.org/10.1111/j.1600-0870.2007.00240.x.
Han, J., and H.-L. Pan, 2011: Revision of convection and vertical diffusion schemes in the NCEP global forecast system. Wea. Forecasting, 26, 520–533, https://doi.org/10.1175/WAF-D-10-05038.1.
Harper, B. A., 2002: Tropical cyclone parameter estimation in the Australian region: Wind-pressure relationships and related issues for engineering planning and design—A discussion paper. SEA Rep. J0106-PR003E, 83 pp., https://doi.org/10.13140/RG.2.2.13057.04961.
Hastie, T., R. Tibshirani, and J. H. Friedman, 2009: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. 2nd ed. Springer, 745 pp.
Heming, J. T., and Coauthors, 2019: Review of recent progress in tropical cyclone track forecasting and expression of uncertainties. Trop. Cyclone Res. Rev., 8, 181–218, https://doi.org/10.1016/j.tcrr.2020.01.001.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Ho, F. P., R. W. Schwerdt, and H. V. Goodyear, 1975: Some climatological characteristics of hurricanes and tropical storms, Gulf and East Coasts of the United States. NOAA Tech. Rep. NWS15, 87 pp.
Holland, G. J., 1980: An analytic model of the wind and pressure profiles in hurricanes. Mon. Wea. Rev., 108, 1212–1218, https://doi.org/10.1175/1520-0493(1980)108<1212:AAMOTW>2.0.CO;2.
Holland, G. J., 2008: A revised hurricane pressure–wind model. Mon. Wea. Rev., 136, 3432–3445, https://doi.org/10.1175/2008MWR2395.1.
Holland, G. J., J. M. Done, R. Douglas, G. R. Saville, and M. Ge, 2019: Global tropical cyclone damage potential. Hurricane Risk, J. Collins and K. Walsh, Eds., Hurricane Risk Book Series, Vol. 1, Springer, 23–42.
Hong, S.-Y., and J. Lim, 2006: The WRF Single-Moment 6-Class microphysics scheme (WSM6). Asia-Pac. J. Atmos. Sci., 42, 129–151.
Hong, S.-Y., Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341, https://doi.org/10.1175/MWR3199.1.
Iacono, M. J., J. S. Delamere, E. J. Mlawer, M. W. Shephard, S. A. Clough, and W. D. Collins, 2008: Radiative forcing by long-lived greenhouse gases: Calculations with the AER radiative transfer models. J. Geophys. Res., 113, D13103, https://doi.org/10.1029/2008JD009944.
Jarvinen, B. R., C. J. Neumann, and M. A. S. Davis, 1975: A tropical cyclone data tape for the North Atlantic Basin, 1886-1983: Contents, limitations, and uses. NOAA Tech. Memo. NWS NHC 22, 24 pp., https://repository.library.noaa.gov/view/noaa/7069.
Jiang, W., L. Wu, and Q. Liu, 2021: High-wind drag coefficient based on the tropical cyclone simulated with the WRF-LES framework. Front. Earth Sci., 9, 694314, https://doi.org/10.3389/feart.2021.694314.
Jiménez, P. A., J. Dudhia, J. F. González-Rouco, J. Navarro, J. P. Montávez, and E. García-Bustamante, 2012: A revised scheme for the WRF surface layer formulation. Mon. Wea. Rev., 140, 898–918, https://doi.org/10.1175/MWR-D-11-00056.1.
Jing, R., and N. Lin, 2020: An environment-dependent probabilistic tropical cyclone model. J. Adv. Model. Earth Syst., 12, e2019MS001975, https://doi.org/10.1029/2019MS001975.
Klotz, B. W., and E. W. Uhlhorn, 2014: Improved Stepped Frequency Microwave Radiometer tropical cyclone surface winds in heavy precipitation. J. Atmos. Oceanic Technol., 31, 2392–2408, https://doi.org/10.1175/JTECH-D-14-00028.1.
Knaff, J. A., and R. M. Zehr, 2007: Reexamination of tropical cyclone wind–pressure relationships. Wea. Forecasting, 22, 71–88, https://doi.org/10.1175/WAF965.1.
Knaff, J. A., M. DeMaria, D. A. Molenar, C. R. Sampson, and M. G. Seybold, 2011a: An automated, objective, multiple-satellite-platform tropical cyclone surface wind analysis. J. Appl. Meteor. Climatol., 50, 2149–2166, https://doi.org/10.1175/2011JAMC2673.1.
Knaff, J. A., C. R. Sampson, P. J. Fitzpatrick, Y. Jin, and C. M. Hill, 2011b: Simple diagnosis of tropical cyclone structure via pressure gradients. Wea. Forecasting, 26, 1020–1031, https://doi.org/10.1175/WAF-D-11-00013.1.
Knaff, J. A., S. P. Longmore, R. T. DeMaria, and D. A. Molenar, 2015: Improved tropical-cyclone flight-level wind estimates using routine infrared satellite reconnaissance. J. Appl. Meteor. Climatol., 54, 463–478, https://doi.org/10.1175/JAMC-D-14-0112.1.
Knaff, J. A., C. J. Slocum, K. D. Musgrave, C. R. Sampson, and B. R. Strahl, 2016: Using routinely available information to estimate tropical cyclone wind structure. Mon. Wea. Rev., 144, 1233–1247, https://doi.org/10.1175/MWR-D-15-0267.1.
Knaff, J. A., and Coauthors, 2021: Estimating tropical cyclone surface winds: Current status, emerging technologies, historical evolution, and a look to the future. Trop. Cyclone Res. Rev., 10, 125–150, https://doi.org/10.1016/j.tcrr.2021.09.002.
Knapp, K. R., M. C. Kruk, D. H. Levinson, H. J. Diamond, and C. J. Neumann, 2010: The International Best Track Archive for Climate Stewardship (IBTrACS): Unifying tropical cyclone data. Bull. Amer. Meteor. Soc., 91, 363–376, https://doi.org/10.1175/2009BAMS2755.1.
Knutson, T., and Coauthors, 2020: Tropical cyclones and climate change assessment: Part II: Projected response to anthropogenic warming. Bull. Amer. Meteor. Soc., 101, E303–E322, https://doi.org/10.1175/BAMS-D-18-0194.1.
Kolmogorov, A. N., 1933: Sulla determinazione empirica di una legge didistribuzione. Giorn Dell’Inst Ital Degli Att, 4, 89–91.
Kossin, J. P., S. J. Camargo, and M. Sitkowski, 2010: Climate modulation of North Atlantic hurricane tracks. J. Climate, 23, 3057–3076, https://doi.org/10.1175/2010JCLI3497.1.
Lander, M. A., 2008: A comparison of typhoon best-track data in the western North Pacific: Irreconcilable differences. 28th Conf. on Hurricanes and Tropical Meteorology, Orlando, FL, Amer. Meteor. Soc., 4B.2, https://ams.confex.com/ams/28Hurricanes/techprogram/paper_137395.htm.
Landsea, C. W., and J. L. Franklin, 2013: Atlantic hurricane database uncertainty and presentation of a new database format. Mon. Wea. Rev., 141, 3576–3592, https://doi.org/10.1175/MWR-D-12-00254.1.
Landsea, C. W., B. A. Harper, K. Hoarau, and J. A. Knaff, 2006: Can we detect trends in extreme tropical cyclones? Science, 313, 452–454, https://doi.org/10.1126/science.1128448.
Lang, M. N., L. Schlosser, T. Hothorn, G. J. Mayr, R. Stauffer, and A. Zeileis, 2020: Circular regression trees and forests with an application to probabilistic wind direction forecasting. J. Roy. Stat. Soc., 69C, 1357–1374, https://doi.org/10.1111/rssc.12437.
Larose, D. T., and C. D. Larose, 2014: Discovering Knowledge in Data: An Introduction to Data Mining. 2nd ed. Wiley, 336 pp.
Lee, C.-Y., M. K. Tippett, A. H. Sobel, and S. J. Camargo, 2018: An environmentally forced tropical cyclone hazard model. J. Adv. Model. Earth Syst., 10, 223–241, https://doi.org/10.1002/2017MS001186.
Li, F.-N., J.-B. Song, H.-L. He, S. Li, X. Li, and S.-D. Guan, 2016: Assessment of surface drag coefficient parametrizations based on observations and simulations using the weather research and forecasting model. Atmos. Oceanic Sci. Lett., 9, 327–336, https://doi.org/10.1080/16742834.2016.1196105.
Lin, N., and D. Chavas, 2012: On hurricane parametric wind and applications in storm surge modeling. J. Geophys. Res., 117, D09120, https://doi.org/10.1029/2011JD017126.
Lin, N., P. Lane, K. A. Emanuel, R. M. Sullivan, and J. P. Donnelly, 2014: Heightened hurricane surge risk in northwest Florida revealed from climatological-hydrodynamic modeling and paleorecord reconstruction. J. Geophys. Res. Atmos., 119, 8606–8623, https://doi.org/10.1002/2014JD021584.
Lockwood, J. W., T. Loridan, N. Lin, M. Oppenheimer, and N. Hannah, 2023: A machine learning approach to model over ocean tropical cyclone precipitation. J. Hydrometeor., https://doi.org/10.1175/JHM-D-23-0065.1, in press.
Loridan, T., S. Khare, E. Scherer, M. Dixon, and E. Bellone, 2015: Parametric modeling of transitioning cyclone wind fields for risk assessment studies in the western North Pacific. J. Appl. Meteor. Climatol., 54, 624–642, https://doi.org/10.1175/JAMC-D-14-0095.1.
Loridan, T., R. P. Crompton, and E. Dubossarsky, 2017: A machine learning approach to modeling tropical cyclone wind field uncertainty. Mon. Wea. Rev., 145, 3203–3221, https://doi.org/10.1175/MWR-D-16-0429.1.
MacAfee, A. W., and G. M. Pearson, 2006: Development and testing of tropical cyclone parametric wind models tailored for midlatitude application—Preliminary results. J. Appl. Meteor. Climatol., 45, 1244–1260, https://doi.org/10.1175/JAM2407.1.
Meinshausen, N., 2006: Quantile regression forests. J. Mach. Learn. Res., 7, 983–999.
Meissner, T., L. Ricciardulli, and F. J. Wentz, 2017: Capability of the SMAP mission to measure ocean surface winds in storms. Bull. Amer. Meteor. Soc., 98, 1660–1677, https://doi.org/10.1175/BAMS-D-16-0052.1.
Mitchell-Wallace, K., M. Jones, J. Hillier, and M. Foote, 2017: Natural Catastrophe Risk Management and Modelling: A Practitioner’s Guide. 1st ed. Wiley-Blackwell, 544 pp., https://doi.org/10.1002/9781118906057.
Mouche, A., B. Chapron, B. Zhang, and R. Husson, 2017: Combined co- and cross-polarized SAR measurements under extreme wind conditions. IEEE Trans. Geosci. Remote Sens., 55, 6746–6755, https://doi.org/10.1109/TGRS.2017.2732508.
Mouche, A., B. Chapron, J. Knaff, Y. Zhao, B. Zhang, and C. Combot, 2019: Copolarized and cross-polarized SAR measurements for high-resolution description of major hurricane wind structures: Application to Irma category 5 hurricane. J. Geophys. Res. Oceans, 124, 3905–3922, https://doi.org/10.1029/2019JC015056.
Nguyen, L. T., J. Molinari, and D. Thomas, 2014: Evaluation of tropical cyclone center identification methods in numerical models. Mon. Wea. Rev., 142, 4326–4339, https://doi.org/10.1175/MWR-D-14-00044.1.
Nolan, D. S., J. A. Zhang, and D. P. Stern, 2009a: Evaluation of planetary boundary layer parameterizations in tropical cyclones by comparison of in situ observations and high-resolution simulations of Hurricane Isabel (2003). Part I: Initialization, maximum winds, and the outer-core boundary layer. Mon. Wea. Rev., 137, 3651–3674, https://doi.org/10.1175/2009MWR2785.1.
Nolan, D. S., D. P. Stern, and J. A. Zhang, 2009b: Evaluation of planetary boundary layer parameterizations in tropical cyclones by comparison of in situ observations and high-resolution simulations of Hurricane Isabel (2003). Part II: Inner-core boundary layer and eyewall structure. Mon. Wea. Rev., 137, 3675–3698, https://doi.org/10.1175/2009MWR2786.1.
Nolan, D. S., R. Atlas, K. T. Bhatia, and L. R. Bucci, 2013: Development and validation of a hurricane nature run using the joint OSSE nature run and the WRF model. J. Adv. Model. Earth Syst., 5, 382–405, https://doi.org/10.1002/jame.20031.
Phadke, A. C., C. D. Martino, K. F. Cheung, and S. H. Houston, 2003: Modeling of tropical cyclone winds and waves for emergency management. Ocean Eng., 30, 553–578, https://doi.org/10.1016/S0029-8018(02)00033-1.
Powell, M. D., S. H. Houston, L. R. Amat, and N. Morisseau-Leroy, 1998: The HRD real-time hurricane wind analysis system. J. Wind Eng. Ind. Aerodyn., 77–78, 53–64, https://doi.org/10.1016/S0167-6105(98)00131-7.
Powell, M. D., G. Soukup, S. Cocke, S. Gulati, N. Morisseau-Leroy, S. Hamid, N. Dorst, and L. Axe, 2005: State of Florida hurricane loss projection model: Atmospheric science component. J. Wind Eng. Ind. Aerodyn., 93, 651–674, https://doi.org/10.1016/j.jweia.2005.05.008.
Ramsay, H. A., S. J. Camargo, and D. Kim, 2012: Cluster analysis of tropical cyclone tracks in the Southern Hemisphere. Climate Dyn., 39, 897–917, https://doi.org/10.1007/s00382-011-1225-8.
Ricciardulli, L., and F. Wentz, 2016: Remote sensing systems ASCAT C-2015 daily ocean vector winds on 0.25 deg grid, version 02.1. Accessed 15 July 2019, https://www.remss.com/missions/ascat/.
Rotunno, R., Y. Chen, W. Wang, C. Davis, J. Dudhia, and G. J. Holland, 2009: Large-eddy simulation of an idealized tropical cyclone. Bull. Amer. Meteor. Soc., 90, 1783–1788, https://doi.org/10.1175/2009BAMS2884.1.
Rumpf, J., H. Weindl, P. Höppe, E. Rauch, and V. Schmidt, 2007: Stochastic modelling of tropical cyclone tracks. Math. Methods Oper. Res., 66, 475–490, https://doi.org/10.1007/s00186-007-0168-7.
Ryglicki, D. R., and R. E. Hart, 2015: An investigation of center-finding techniques for tropical cyclones in mesoscale models. J. Appl. Meteor. Climatol., 54, 825–846, https://doi.org/10.1175/JAMC-D-14-0106.1.
Sampson, C. R., and A. J. Schrader, 2000: The Automated Tropical Cyclone Forecasting System (version 3.2). Bull. Amer. Meteor. Soc., 81, 1231–1240, https://doi.org/10.1175/1520-0477(2000)081<1231:TATCFS>2.3.CO;2.
Schreck, C. J., III, K. R. Knapp, and J. P. Kossin, 2014: The impact of best track discrepancies on global tropical cyclone climatologies using IBTrACS. Mon. Wea. Rev., 142, 3881–3899, https://doi.org/10.1175/MWR-D-14-00021.1.
Schwerdt, R. W., F. P. Ho, and R. W. Watkins, 1979: Meteorological criteria for standard project hurricane and probable maximum hurricane windfields, Gulf and East Coasts of the United States. NOAA Tech. Rep. NWS 23, 356 pp., https://repository.library.noaa.gov/view/noaa/6948.
Scornet, E., G. Biau, and J.-P. Vert, 2015: Consistency of random forests. Ann. Stat., 43, 1716–1741, https://doi.org/10.1214/15-AOS1321.
Shen, Z., and K. Wei, 2021: Stochastic model of tropical cyclones along China coast including the effects of spatial heterogeneity and ocean feedback. Reliab. Eng. Syst. Saf., 216, 108000, https://doi.org/10.1016/j.ress.2021.108000.
Skamarock, W. C., and Coauthors, 2019: A description of the Advanced Research WRF Model version 4. NCAR Tech. Note NCAR/TN-556+STR, 145 pp., https://doi.org/10.5065/1dfh-6p97.
Smirnov, N. V., 1939: On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bull. Math. Univ. Moscou, 2, 3–14.
Stern, D. P., G. H. Bryan, and S. D. Aberson, 2016: Extreme low-level updrafts and wind speeds measured by dropsondes in tropical cyclones. Mon. Wea. Rev., 144, 2177–2204, https://doi.org/10.1175/MWR-D-15-0313.1.
Torn, R. D., and C. Snyder, 2012: Uncertainty of tropical cyclone best-track information. Wea. Forecasting, 27, 715–729, https://doi.org/10.1175/WAF-D-11-00085.1.
Vickery, P. J., and D. Wadhera, 2008: Statistical models of Holland pressure profile parameter and radius to maximum winds of hurricanes from flight-level pressure and H*Wind data. J. Appl. Meteor. Climatol., 47, 2497–2517, https://doi.org/10.1175/2008JAMC1837.1.
Vickery, P. J., P. F. Skerlj, and L. A. Twisdale, 2000: Simulation of hurricane risk in the U.S. using empirical track model. J. Struct. Eng., 126, 1222–1237, https://doi.org/10.1061/(ASCE)0733-9445(2000)126:10(1222).
Vickery, P. J., F. J. Masters, M. D. Powell, and D. Wadhera, 2009: Hurricane hazard modeling: The past, present, and future. J. Wind Eng. Ind. Aerodyn., 97, 392–405, https://doi.org/10.1016/j.jweia.2009.05.005.
Willoughby, H. E., and M. E. Rahn, 2004: Parametric representation of the primary hurricane vortex. Part I: Observations and evaluation of the Holland (1980) model. Mon. Wea. Rev., 132, 3033–3048, https://doi.org/10.1175/MWR2831.1.
Willoughby, H. E., R. W. R. Darling, and M. E. Rahn, 2006: Parametric representation of the primary hurricane vortex. Part II: A new family of sectionally continuous profiles. Mon. Wea. Rev., 134, 1102–1120, https://doi.org/10.1175/MWR3106.1.
Wu, C.-C., Y.-H. Huang, and G.-Y. Lien, 2012: Concentric eyewall formation in Typhoon Sinlaku (2008). Part I: Assimilation of T-PARC data based on the ensemble Kalman filter (ENKF). Mon. Wea. Rev., 140, 506–527, https://doi.org/10.1175/MWR-D-11-00057.1.
Yang, Q., C.-Y. Lee, M. K. Tippett, D. R. Chavas, and T. R. Knutson, 2022: Machine learning–based hurricane wind reconstruction. Wea. Forecasting, 37, 477–493, https://doi.org/10.1175/WAF-D-21-0077.1.
Zamo, M., and P. Naveau, 2018: Estimation of the continuous ranked probability score with limited information and applications to ensemble weather forecasts. Math. Geosci., 50, 209–234, https://doi.org/10.1007/s11004-017-9709-7.
