1. Introduction
Tropical cyclones (TCs) pose a threat to coastal zones, due to extreme surface winds and intense rainfall (Dare et al. 2012; Brackins and Kalyanapu 2020). TC winds also lead to large and damaging ocean wind-waves (Zieger et al. 2021a,b; Dixon et al. 2022) and storm surges (Freeman et al. 2020; Haigh et al. 2014). It follows therefore that validated estimates of surface mean wind speeds are required to predict wind hazards for risk assessments and to provide inputs to wave and hydrodynamic models. Model simulations are also required to span periods longer than the observed record to make robust probabilistic prediction of rare and catastrophic oceanic events for infrequently occurring TCs (O’Grady et al. 2022).
TC surface wind fields can be predicted effectively using numerical dynamic boundary layer models (Ramsay and Leslie 2008; Chen and Chavas 2020; Powell et al. 2005; Kepert and Wang 2001). However, such models can be expensive in terms of their computational and input data requirements. Due to the infrequency of TC occurrences in the observed record, a common approach to assessing the likelihood of TC hazards is the generation of large numbers of synthetic cyclones (Bloemendaal et al. 2020; McInnes et al. 2014). To achieve this, simplified and computationally efficient nondynamic parametric cyclone vortex models enable rapid approximations of the wind and pressure field surrounding the cyclone from a limited number of input parameters.
The parametric vortex wind profiles capture the basic radial structure of TC winds consisting of an exponential increase inward toward the radius of maximum winds (Rmax) from some outer radius, and then a decrease to calm winds inside the eyewall. They can also represent the asymmetric inflow of a forward moving TC, and can be generated with a near-zero computation cost (Hu et al. 2012). The term parametric is used for the vortex models because they are constructed using analytical solutions to physical mathematical relationships (such as the gradient wind profile), geometric/trigonometric formulas (such as the asymmetric radial wind field) and empirically fitted equations using regression/statistical analysis (such as the inflow angle and surface wind reduction factor).
The parametric tropical cyclone models require, at discrete times along the cyclone track, input that describes the key features of the TC. For example, the TC intensity (as represented by the central pressure Pmin), the distance from the equator (represented by the absolute value of the latitude λ), TC size (as represented by parameters such as Rmax) or profile shape (maximum velocity Vmax and the exponential “peakedness” parameter b). TC location and intensity are generally available from best track databases, but parameters such as TC size and shape are not always available at every time step from observational TC databases such as IBTrACS (Knapp et al. 2010) for input into TC wind and pressure field models. This is particularly true for size parameters such as Rmax or outer wind radii, which have only more recently been incorporated in the best track data. In the Australian region, for instance, historical TC wind radii data are most reliable after about 2003 (Courtney et al. 2021). Moreover, some parameters are difficult to estimate, such as the TC shape parameter b, which directly influences Vmax, particularly for double-vortex profiles (Young 2017). These gaps and inhomogeneities in the shape and size statistics within the best track data necessitate the use of empirical relationships to estimate these input variables (Powell et al. 2005; Arthur 2021; McInnes et al. 2014; Willoughby and Rahn 2004; Vickery and Wadhera 2008; Emanuel et al. 2006; Knaff et al. 2015). In this study, we refer to the parametric vortex model input of Rmax, Vmax, and b as along-track parameters, as they are a single value at each point along the track. These along-track parameters are often defined by statistically fitted formulations to empirical observations.
The availability of along-track parameters influences the choice of parametric vortex model. For example, the Holland 1980 (Holland 1980) vortex model requires the TC size input of Rmax, while the Rankine (Leslie and Holland 1995), Chavas (Chavas et al. 2015), or updated Holland 2010 (Holland et al. 2010) parametric vortex models require the extra size parameter of the outer wind radii, or radius to gales, for which a statistical relationship based on the input of TC intensity, location and/or motion does not exist. Also models such as Kepert (Kepert 2001) require input of the vorticity profile, for which there is an exact analytical solution for the Holland (1980) model, but an exact solution of vorticity was not available for the Holland 2010, Rankine, or Chavas models.
An important process to be resolved in coastal hazard studies is the impact of the terrestrial land surface on TC winds. When a TC makes landfall, strong convection is no longer fed by large surface enthalpy fluxes from warm oceans, and the overall storm intensity decays, a process sometimes referred to as “drying” (Chen and Chavas 2020; Li and Chakraborty 2020; Liu et al. 2021). Second to this, the effect of surface roughness through shear stress can reduce the overall storm intensity of a landfalling TC via changes in the surface drag coefficient (Chen and Chavas 2020, 2023). Third, the wind field of a landfalling TC is generally asymmetric (aside from forward motion asymmetry), with lower wind speeds over land compared to over ocean due to increased terrestrial surface roughness (Bloemendaal et al. 2020; Done et al. 2020; Ramsay and Leslie 2008; Hlywiak and Nolan 2022).
Parametric vortex models are developed to first represent the boundary layer gradient winds, and then a scaling relationship is typically used to reduce these winds to the ocean surface (Kepert 2001; Hubbert et al. 1991; McConochie et al. 2004). Studies have previous compared multiple vortex wind models and wind reduction factors over the ocean for the North Atlantic (Ruiz-Salcines et al. 2019) and Northeast Pacific (Phadke et al. 2003). There is scope to evaluate these reduction factors against observed weather station records in the South Pacific for more recent TC events, and to improve the representation of surface winds over the ocean and land. The reduction of winds in the part of the circulation which is over land is due to increased surface roughness and is represented in dynamical numeric boundary layer modeling (Ramsay and Leslie 2008; Chen and Chavas 2020; Powell et al. 2005; Done et al. 2020; Hlywiak and Nolan 2022), but to the authors knowledge is absent from parametric TC wind field model hazard estimates (Bloemendaal et al. 2020). We note that the recent theoretically based wind field model by Chen and Chavas (2023) does depend on surface roughness, but in their model the effects of land are imposed instantaneously to the entire vortex (i.e., akin to an extremely rapid transition from uniform ocean to uniform land).
Previous studies have used in situ weather station wind observations to validate and calibrate TC wind models (Hu et al. 2012; Gong et al. 2020; Arthur 2021; Nolan et al. 2021; Ruiz-Salcines et al. 2019; Phadke et al. 2003). In situ weather stations provide a ground truth for modeling but can be impacted by local topology/obstacles (trees and buildings), individual device calibration, sampling period (gusts versus mean winds) and can fail in extreme conditions. TC surface winds can also be measured remotely by aircraft and satellites (Bourassa et al. 2019), which are calibrated to in situ weather stations. Satellite remote sensing is essential for capturing TC location and structure such as track position and spatial wind field, because TCs spend most of their existence in the remote oceans. Calibrated remotely sensed surface wind field observations can be considered to provide a homogenous global database compared with individually calibrated weather stations, but remote sensing will always rely on in situ ground truthing for verification. Remotely sensed wind measurements have their challenges too (Bourassa et al. 2019), including rain contamination, temporal gaps, limited calibration to very high wind speeds, and lack of observations near, and over land. The motivation of this study is to find a potentially optimal combination of parameter settings used as input to parametric vortex models for TC hazard assessment of tens of thousands of synthetic TCs. The resulting surface wind field generated by each combination of the parameter space is tested against in situ surface winds from automatic weather stations.
In this study we first list in the methods section the observational datasets, the parametric vortex models and along-track parameters utilized, and the updated surface wind reduction formulation for the land surface. Regression analysis is used to compare modeled historic events and quantile–quantile analysis is used for modeled validation of the TC population in the results section. Finally, discussion is provided on the performance of the parametric models, and how this work fits into current, and future work.
2. Methods
The parameters of the various models used in this study are described in the appendix glossary (Table A1). The model code used in this study to represent TC wind fields is detailed in the open-source R package TCHazaRd (O’Grady 2022). The TCHazaRd code is based on the Tropical Cyclone Risk Model (TCRM) (Geoscience Australia 2022) parametric wind field models (Arthur 2021), which were recoded into the C language (Bosserelle 2016).
a. Observational datasets
The International Best Track Archive for Climate Stewardship (IBTrACS; Knapp et al. 2010) dataset was used for observed Pmin, λ, forward speed (vFm), and position as input into the parametric models. Observed Vmax, Rmax were used for plotting comparison to the predicted along-track statistical relationships. Only recent (post-2005) TC events were selected (Table S1 in the online supplemental material and Fig. 1), noting the quality of the historical TC record is significantly better post-1981 (Schreck et al. 2014; Geiger et al. 2018). Track parameters, provided every 3 h, were linearly interpolated to hourly intervals for model estimates. In situ weather station observations of 10-min mean wind speeds and directions were sourced from the NOAA Integrated Surface Database (ISD) (Smith et al. 2011) accessed by the “worldmet” R package (Carslaw 2021). Stations were considered if they were within a 200 km radius of a TC track but were only included in the analysis if they had at least 16 values in the 24 h centered on a peak surface mean wind speed of at least 10 m s−1 (Table S1). Stations situated offshore (e.g., reefs, islands, and small moorings) were identified as being 2 km off the coastline of mainland Australia (Table S1). The 2 km coastal buffer zone was chosen subjectively and used to ensure offshore locations are unaffected by land and when considering errors in the recorded coastline and station positions.
Tropical cyclones used in this study. Red points are the ISD weather stations, black circles are onshore, and black crosses (with location labels) are the offshore stations. TC track arrows represent the native IBTrACS time step, which is typically 3 h.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
b. Parametric vortex models
Three parametric vortex models which have previously been applied to the Australian region were considered in this study. The parametric vortex models include formulations for a gradient wind profile, inflow angles and gradient wind speed reduction to the surface. Other models, such as the Rankine vortex (Leslie and Holland 1995) and the wind profile model of Chavas et al. (Chavas et al. 2015) were considered, but not included as they require input, such as the radius of gale-force (17.5 m s−1) wind, for which a statistical relationship was not available, or the model required an iterative numerical solution (Chavas et al. 2015). The three model configurations used in this study each comprised of a different surface wind reduction factor (Km) used to bring gradient-level winds down to the surface.
The Kepert model (Kepert 2001) is a linear analytical model of the boundary layer flow in a translating tropical cyclone. The implementation uses the Holland (1980) wind profile with the insertion of a cubic profile inside the radius of maximum winds to avoid the barotropic instability (Kepert and Wang 2001). The surface wind reduction factor varies with a nondimensional parameter χ, from 1 at χ = 0 (i.e., at the vortex center) to 0.5 as χ → ∞. For a stationary vortex with Vmax = 39.3 m s−1, Rmax = 40 km, b = 1.3, and at 15°S latitude, the surface wind reduction factor ranges between ∼1 at the center of the vortex to ∼0.75 at 200 km radius [(Kepert and Wang 2001), see their Fig. 3]. More generally, the wind reduction to the surface varies nonlinearly with gradient wind speed (Vg), and the inertial stability, surface drag and turbulent diffusivity for momentum, which are themselves dependent on Vg.
The Hubbert (Hubbert et al. 1991) model uses a Holland (1980) profile with the insertion of a cubic profile inside the radius of maximum winds and with asymmetric winds based on the forward motion of the TC. Maximum wind speed is 70° to the left (right in Northern Hemisphere) of the TC motion. In addition, the asymmetry is proportional to the forward motion (vFm). The gradient to surface wind reduction factor Km has a constant value of 0.7 following Powell (1980) for 10-min winds over the ocean. Other studies have used a constant Km value ranging from 0.775 to 0.85 depending on the vortex model (Ruiz-Salcines et al. 2019).
c. Along-track parameters
Four different study methods for estimating along-track parameters, Rmax, Vmax, and b were sourced from the cited literature in Tables 1, 2, and 3, respectively. The formulations for these parameters are typically derived empirically from observed statistical relationships and require the input of observed TC central pressure (Pmin) to represent the intensity, latitude (λ) to represent the distance from the equator, and/or forward motion (vFm) for wind field asymmetry. No adjustment (or calibration of the statistically fitted coefficients) was made to the along-track parameters in this study. A comprehensive review of TC parameter estimation is provided in Harper (2002). The Arthur (2021, hereafter AP21) and McInnes et al. (2014, hereafter MK14) parameters have been applied in South Pacific basin studies, whereas Willoughby and Rahn (2004, hereafter WR04) and Vickery and Wadhera (2008, hereafter VW08) are based on North Atlantic basin studies, which provides a data-rich resource of TC observations and associated statistical relationships. The inclusion of the North Atlantic studies assumes that the statistical relationships of observed pressure deficit, forward motion and/or latitude to predict Rmax, Vmax, b over the North Atlantic basin holds for the South Pacific basin, knowing there is some evidence to suggest that those in the South Pacific are typically larger than in the North Atlantic (Chavas et al. 2016). Comparison of TC statistics for each basin are presented in the results section. Other nonstatistical relationships exist (Chavas et al. 2015) which do not require parameter fits for individual basins but do require additional TC size parameters, such as the radius to gales (R17.5ms) for which we had no relationship with the along-track input parameters (Pmin, λ, and vFm), so were not considered in this study.
The radius of maximum wind speeds (Rmax), abbreviated name used in this study and the equation number from reference study.
The maximum wind speeds (Vmax), abbreviated name used in this study and the equation number from reference study.
The profile peakedness shape parameter (b), abbreviated name used in this study, and the equation number from reference study.
The equations for Rmax are formulated based on pressure deficit and latitude, with WR04 differing by including the maximum velocity, which is a function of the square of the pressure deficit and exponential peakedness parameter for radial wind profile. Here, the WR04 Vmax and Rmax equations needed to be refactored to solve for b, to then compute Vmax and finally Rmax. The AP21 includes a second exponential for both pressure deficit (squared) and latitude (squared) and VW08 also uses the pressure deficit exponential (squared), increasing the model sensitivity to these parameters. The MK14 equation can be rearranged to resemble the AP21 and VW08 equations by factoring out a value of 1010 to represent Penv.
The Vmax equations (Table 2) used in this study are almost identical, differing only by assigning a constant b parameter in AP21. In the WR04 study the Holland (1980) relationship was assumed to hold in the absence of geopotential height as input in this study. Here the b parameter is confined to a bounded range between 0.8 and 1.9, where the unbounded pressure differential (dP) can approach an order of two magnitudes larger (say 100 hPa) and, therefore, dP is the main driver of variability in Vmax. However, differences between the models are defined by the formulations of the b parameter (Table 3).
The equations for the peakedness b parameter (Table 3) differ in their formulation compared to the formulations of Rmax and Vmax. Notably, the WR04 equation disagrees with the other models as b increases away from the equator while the other three equations estimate a decrease.
d. Secondary wind reduction factor (KL) calibration
3. Results
To justify the use of parametric equations developed for the North Atlantic basin to be used in the South Pacific, a comparison of TC parameters is first made between the two basins in Fig. 2 using the NOAA/National Hurricane Center plus Joint Typhoon Warning Center (NHC + JTWC) subset of variables in the IBTrACS best track database for the years 1981–2020. A shorter period (2001–20) was used to analyze Rmax and its relationship with Vmax due to the absence of TC size prior to 2001. Notable differences of the North Atlantic TCs when compared to the South Pacific include a wider bimodal distributions of TC latitudes and a larger proportion of TCs with Rmax greater than 100 km (Fig. 2). Yet these basin differences show negligible impact on an apparent universal relationship between Vmax and Rmax in the IBTRACS NHC + JTWC subset as shown by the logarithmic-linear regression plots and equations in Fig. 2. The equations differ within the logarithmic-variance (LV) of Rmax, which is 0.45 for the North Atlantic and 0.3 for the South Pacific. Of the referenced Rmax studies (Table 1), WR04 provide an LV of 0.55 and VW08 provide an LV of 0.441. Here, the differences in LV between basins could be a result of available observations, and the greater span of TC latitudes for the North Atlantic basin. Values for Rmax are estimated by a combination of available observations, including aircraft reconnaissance in the North Atlantic, radar, scatterometry, microwave global satellite data, and supported by infrared and visible imagery, but missing values are potentially derived by applying a climatological relationship of Vmax and latitude (Courtney et al. 2021). We note that, unlike storm location and intensity, Rmax is not subjected to vigorous poststorm review (Knaff et al. 2021).
Statistical comparison of TC parameters for the North Atlantic (NAtl) and South Pacific (SPac) basins using the IBTrACS best tracks database (1981–2020). Histograms are provided for both basins and for the variables Rmax, Vmax, and |λ| and include the mean (μ) and median (Med) statistics. Regression plots for both basins include the equations and R-squared values of a logarithmic-linear regression fit.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
TC Yasi in 2011 was selected from the 10 TC events (Fig. 1) to demonstrate model performance. The other equivalent TC diagnostic plots can be found in the supplemental material. The evolution over time of TC Yasi’s pressure deficit (dP), Rmax, Vmax, and exponential peakedness shape b parameters are provided for the four along-track parameters in Fig. 3. The maximum pressure deficit occurred early on 2 February. Yasi attained category 5 TC winds as it made landfall on 3 February (Australian TC category scale). Of the four along-track parameters, AP21 predicts a higher Rmax, due to its calibration to wind gusts (C. Arthur 2023, personal communication), and the WR04 model predicts a lower Rmax due to its dependence on the largest b shape parameter, otherwise the along-track parameters tend to match the observed Rmax and Vmax. The larger Rmax in the AP21, and smaller Rmax in the WR04 (due to the larger b) would have implications for modeling the location of the peak storm surge and high waves and associated risk to coastal communities.
Along-track parameterization for TC Yasi, which made landfall at 1430:00 UTC 2 Feb 2011.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
The Flinders Reef and Holmes Reef weather stations to the left and right of TC Yasi’s forward motion, respectively, are used as a demonstration of the modeled wind speeds for the different parameterizations (Fig. 4). Noting that at these reef locations terrestrial roughness is assumed negligible and the asymmetric wind field due to the forward translation of the TC is expected to result in higher winds at Flinders Reef (to the left of TC transition in the Southern Hemisphere). MK14, and VW08 tend to agree with the observed time series for all three parametric vortex models, while AP21 predicts the largest and WR04 the smallest wind speeds for all wind field models. This discrepancy is likely because of AP21 Rmax calibration to gusts and possibly because the WR04 calibration is to the North Atlantic basin. The Hubbert parametric vortex model tends to underestimate winds in the time series after the peak, as does the Kepert model to a lesser extent, suggesting the rear quadrant wind field can be underestimated. This does not appear to be an issue for the McConochie double vortex. Both the Hubbert and Kepert models use the 1980 version of the Holland profile to include exact profiles of vorticity, where the 2010 Holland profile study indicates that the 1980 profile underestimates far field winds.
Time series comparison for TC Yasi at (left) Flinders Reef and (right) Holmes Reef with the three parametric vortex model (rows) and four along-track parameters (colored lines see legend). (top) The Kepert parametric vortex model, (middle) Hubbert, and (bottom) McConochie. Blue circles are observations.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
The means of the n model Pearson time series correlation for the 48 h around the peak (rt) are presented in Table 4 and are based on n = 118 instances (listed in Table S1) of a TC impacting a station (where Vobs > 10 m s−1), which reduces to n = 46 for just the offshore stations. The rt quantify the performance of the McConochie double vortex to represent the rise and fall of winds as the TCs pass by. The McConochie model performs better (has a higher rt) than the Kepert and Hubbert models, with the Hubbert model having the lowest rt. Although the McConochie vortex appears to in general outperform these time series profiles (plots in supplemental material), this is not true of all TCs at all stations due to the complex behavior of TCs. The MK14 model was applied in the South Pacific basin and more often results in the highest, or second highest rt of the four along-track parameterizations.
Station instances wind speed summary statistics for n model output VgKm, where r is the Pearson correlation coefficient for the peak, rt is the mean correlation 48 h around the peak, and RMSE is the root-mean-squared error.
The summary calibration statistics for the n instances of weather station peak TC wind speed are also shown in Table 4. The Pearson peak wind correlations (r) for all-station model output sit in a range of 0.57–0.65 for the 12 model combinations. When considering just the offshore stations the r sits between the higher range of 0.69–0.81. Using the unified secondary wind reduction conditional parameterization (KL) increases the range of the all-station correlations to 0.72–0.79 (Table S2) and using the unified exponential decay parameterization (KL) increases the range of the all-station correlations to 0.74–0.81 (Table 5). Here, these correlation ranges indicate that the secondary wind reduction factors can improve the agreement of the modeled winds at all stations to be as good as the unadjusted modeled winds for the offshore stations.
Peak 10-min wind speed calibration summary statistics for the n-corrected model output VgKmKL. Pearson r correlation, RMSE, and bias are for the unified values of the secondary wind reduction factor KL using the exponential decay function. Unified parameters are shown as the 12-model combination median in boldface. Wind reduction parameters of a1, a2, and a3 are the calibrated values for each model parameter combination. Percentage error (PEi) values are for the onshore (KL = a1) and offshore (KL = a2).
The root-mean-square errors (RMSEs) and biases of the unadjusted peak winds are better (closer to zero) when just considering the 46 offshore stations (Table 4) for which the RMSE range is from 5.93 to 9.32 m s−1. The RMSE is lowered overall for winds with secondary wind reduction factors (Table 5) to a range of 4.83 to 7.04 m s−1, likely a result of the calibration and larger sample size (n = 118).
It is difficult to determine if one model combination is statistically significantly better than the rest, because no one equation combination is a special case of another model [i.e., the exact same equations with an extra parameter(s)] to make a hypothesis test (e.g., if latitude was held to a constant 15° south). But when considering the mean 48-h time series correlation around the peak rt and the correlations r, RMSE and bias at the peak, the McConochie parametric vortex model with the MK14 along-track parameterization in general most closely represents the observations. This is not unexpected given both models have been previously applied to the South Pacific basin, as well as the limitations of the other models to represent the rear quadrant winds described above.
Calibrated secondary wind reduction factor (KL) parameters (a1, a2, and a3) and summary statistics using the unified parameters for the exponential decay function are presented in Table 5 and for the conditional function in Table S2. As with the unadjusted statistics (Table 4), the McConochie and MK14 model combination has one of the top-ranked correlations (highest), RMSE (lowest), biases (closest to zero), and PEs (closest to zero).
The peak wind observed and modeled (unadjusted or corrected for KL) at each station and for each TC event is shown in Fig. 5 for the model combination with the one of the top-ranked correlation (highest) and RMSE (lowest) score, which is the McConochie parametric vortex model with the MK14 along-track parameters as input. All other parametric vortex models and along-track parameter combinations are provided in Figs. S1–S7. The unadjusted model output in Fig. 5a shows the bias of the model for onshore stations leading to an overestimation of the observed, which is not as apparent in the offshore stations, as shown in Fig. 5b. The unified secondary reduction factor using the exponential decay function (KL) Fig. 5c for onshore distance brings more instances of a TC passing a onshore station (circle markers) to the one-to-one regression line in Fig. 5d compared to unadjusted in Fig. 5a.
Model validation and correction of peak 10-min surface mean wind speed for the McConochie parametric vortex model with the MK14 along-track parameters. Each point represents the peak wind recorded/modeled at a station for a single TC instance, circles are onshore, and crosses are offshore stations, headings indicate correlation, root-mean-square error, bias, and fitted decay function parameter (a1, a2, and a3) values. (top) Unadjusted secondary reduction factor model validation (a) for all locations and (b) for just offshore stations. (c) Box-and-whisker plot for the ratio of observation to modeled estimates at different onshore distances; red line is the fitted decay function for the secondary reduction factor KL. (d) Corrected model validation using the secondary reduction factor. Outliers on the box-and-whisker plots use R’s default boxplot parameters, which are defined as values being greater than 2.5 times the standard deviation from the mean.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
To further explore the model combinations, we analyze the mean relative error of these combinations for each tropical cyclone (TC) compared to the overall vortex model, encompassing all TCs, as shown in Fig. 6. Here the mean PE is calculated for each model combination and TC and are then relative to the total mean PE calculated for a given vortex model. Figure 6 shows different model combinations can more closely represent an individual TC event while not also representing the top-ranked overall model performance (Table 5). This aligns with previous findings in a study comparing six vortex models for the North Atlantic, which suggested that selecting one model over another does not guarantee superior accuracy (Ruiz-Salcines et al. 2019).
Mean relative error for each TC and model combination. The mean percentage error is calculated for each individual TC and model combination (vortex model and along-track parameterization), then the mean percentage error is calculated for that vortex model and removed to make the TC error relative to the overall vortex model error.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
The spatial footprint of without and with the secondary wind reduction parameterization to reduce wind speeds overland is shown in Fig. 7 for TC Yasi with the McConochie MK14 configuration (Kepert and Hubbert vortex winds are shown in Figs. S8 and S9). This plot, along with Fig. 5c shows that the wind reduction from ocean to land occurs around 1 km of the coast.
Surface wind fields of TC Yasi at 1430:00 UTC 2 Feb 2011 (left) without VgKm and (right) with VgKmKL the secondary reduction factor (KL) for the McConochie parametric vortex model with the MK14 along-track parameters. Black line is the coastline, red line is TC Yasi’s track, heading southwest. Pmin = 929 hPa, λ = −17.85, Rmax = 26.5 km, Vmax = 65.06 m s−1, b = 1.619, vFm = 9.28 m s−1, dP/dt = 0.1 hPa h−1.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
The PE statistic using the fitted exponential decay function parameters (Table 5) indicates that unadjusted modeled winds (VgKm) overestimate observed winds (Vobs) over the ocean by around 13% (median) and over land by around 73.9% (median). The unadjusted Hubbert MK14 model PE indicates the lowest underestimate of observed winds (negative values) over ocean by 2.9% and with an overestimate over land of 51.5%. The rate of change, or how fast the decrease in wind speed in the onshore direction occurs within this transition zone is considered highly uncertain. Importantly, the coastline of Queensland is relatively mountainous and forested, compared to say the Western Australian coast, and ongoing investigations are required to further understand the terrestrial roughness effects on idealized TC winds over land. Stations are predominantly within 40 km of the Queensland coast, and this onshore distance was used as a cutoff for parameter (a1, a2, a3) fitting (Fig. 5c). Therefore, in Figs. 5 and 7, the estimated onshore reduction is assumed to be constant beyond 40 km inland.
The wind profiles of the three parametric vortex models are shown for TC Yasi in Fig. 8. The McConochie double-vortex gradient wind profile has a wider eye than the Kepert and Hubbert, which have the insertion of a cubic profile inside the radius of maximum winds to avoid the barotropic instability (Kepert and Wang 2001). Asymmetry introduced by the forward motion (vFm) of the TC is larger for the Kepert and Hubbert profiles than the McConochie profile. The universal secondary reduction factor increases the winds over ocean (to the left of the forward motion) for all vortex models, which is stronger than an assumed stationary gradient-level winds for the Kepert and McConochie models due to the forward motion asymmetry.
Surface wind speed profiles of TC Yasi at 1430:00 UTC 2 Feb 2011. Profiles are provided for the gradient wind (Vg), assuming a stationary TC (vFm = 0) and with the surface winds (reduced by Km and KL). Profiles for the (a) Kepert, (b) Hubbert, and (c) McConochie vortex models with the MK14 along-track parameters for (d) the radial distance profile [corresponding to the x axis of (a)–(c)]. McConochie surface wind profiles VgKm and VgKmKL in (c) correspond to the left and right panels of Fig. 5, respectively. Vertical back dashed lines are the radial distance Rmax and the horizontal black line is the wind speed Vmax calculated with the MK14 equations.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
The quantile–quantile (Q–Q) method is used to demonstrate that the modeled surface wind speeds can simulate the distribution and range of the observed peak 10-min wind speeds, to evaluate the suitability for synthetic population of thousands of TCs to represent an extended range of winds for hazard assessment (Fig. 9). The plots show the unadjusted observed versus modeled peak winds for all locations (Fig. 9a) and for offshore stations (Fig. 9b), the density distributions of the unadjusted and secondary reduction factor correction (Fig. 9c) and the resulting calibrated distribution for all 118 instances (Fig. 9d). Application of the secondary wind reduction (KL) corrections to the unadjusted modeled peak wind speeds (Fig. 9a) result in a better match to the observations (Fig. 9d). At lower quantiles, the wind cut off (10 m s−1) for observed winds impacts the Q–Q plot because the model can predict winds less than 10 m s−1.
(a),(b),(d)Quantile–quantile (Q–Q) and (c) kernel density estimate plots for the observed peak mean surface wind speed (Vobs) for the McConochie parametric vortex model with MK14 along-track parametric input. The Km unified model parameters used in (c) and (d) were calculated from the median of all 12 individual model combination calibrations.
Citation: Monthly Weather Review 152, 1; 10.1175/MWR-D-23-0063.1
4. Conclusions
A comparison of 12 model formulations for estimating TC surface 10-min winds indicates that the McConochie parametric vortex model with the MK14 along-track parameters as input, both previously applied to the South Pacific basin, presents the top-ranked estimate of wind field 48 h around the peak and at the peak wind speed, based on 118 instances of a set of 10 historical TC events passing a weather station over the eastern Australia region. Figure 6 shows different model combinations can more closely represent an individual TC event while not representing the top-ranked overall model performance (Table 5). This aligns with previous findings in a study comparing six vortex models for the North Atlantic, which suggested that selecting one model over another does not guarantee superior accuracy (Ruiz-Salcines et al. 2019). It is difficult to assess statistical significance based on the limited number of TC events explored here, so we encourage further studies based on an expanded global TC/ISD dataset to evaluate our model rankings.
The peak wind Pearson correlations (r) for all-station model output sit between a range of 0.57 and 0.65. When considering just the offshore stations the r sits between the higher range of 0.69–0.81. Using the unified secondary wind reduction conditional parameterization (KL) improves the all-station correlations to a range of 0.72–0.79 (Table S2) and using the unified exponential decay parameterization (KL) improves the all-station correlations to a range from 0.74 to 0.81 (Table 5). This indicates that the use of the secondary wind reduction factors for the onshore points can improve the modeled winds for all stations modeled winds to the unadjusted model winds for just offshore stations. The Q–Q analysis provided in this study demonstrates that the parametric models can capture the distribution and range of the observed population of peak wind speeds for hazard assessment. Aside from the peak, the rear quadrant wind speeds, observed after the peak has passed, tend to be underestimated by the Kepert, and more so by the Hubbert wind field models. One reason for this could be the larger influence of the modeled wind field asymmetry due to forward motion in these two models compared to the McConochie model. Here the McConochie double-vortex wind field uses the second vortex to better represent far field and rear quadrant, wind speeds. A control on this study was the assumption of the requirement of an exact analytical profile of vorticity for input into the Kepert and Hubbert models. Future studies could relax this control and consider approximate vorticity profiles to investigate other parametric vortex configurations or profile models that also include an extra radial size parameter, such as the Rankine, Chavas (Chavas et al. 2015), or updated Holland 2010 (Holland et al. 2010) studies which use a radius to gales (R17.5ms). There are significant differences in the wind profiles due to forward motion asymmetry and reduction factors. In this study it is difficult to draw definitive conclusions on the correct modeled asymmetry by using the scattered weather station network. The performance of model asymmetry could be better addressed over ocean (however, not land) using satellite derived spatial wind fields (derived from the roughness of the ocean water surface).
The PE statistic using the fitted exponential decay function parameters (Table 5) indicates that unadjusted modeled winds (VgKm) overestimate observed winds (Vobs) over the ocean by 13% (median) and over land by around 73.7% (median). The unadjusted Hubbert MK14 model PE indicates the lowest overestimate of observed winds (negative values) over ocean by 2.9% and over land 51.5%. The rate of change, or how fast, the decrease in wind speed in the onshore direction occurs within a 1 km transition zone is considered highly uncertain. This is indicated by the spread of the tuned exponential parameter values of a3 (Table 5) and the difference between conditional (instant transition between offshore and onshore) and exponential decay (continuous transition) formulation (Table S2) summary statistics. Importantly, the coastline of Queensland is relatively mountainous, compared to say the Western Australian coast, and ongoing investigations are required to further understand how TC winds reduce in the inshore direction. Here, more observed instances of TCs passing weather stations are required to improve the evaluation of the model performance (Table S2).
This study has aimed to provide more robust estimates of the TC hazard which can be used in TC risk studies. The calibration framework presented here could be used to build on and improve existing parametric TC hazard models. For example, when considering the global study by Bloemendaal et al. (2022) vortex wind fields could be improved by
-
resolving wind reduction factors over land for terrestrial roughness asymmetry, which will reduce winds over land, and improve wind category thresholds for baseline and future climates over land.
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represent asymmetric wind fields from the forward motion of TCs, which provide a more plausible 2D wind field than that the symmetric field (Holland 1980) used in the Bloemendaal et al. (2022) global study.
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provide in situ wind hazard validation of the modeled wind field compared to weather stations, where in their preluding study (Bloemendaal et al. 2020) they only show TC characteristics validation against the observational input along-track parameter characteristics (IBTrACS).
Further work is planned to apply the wind and pressure fields to coupled storm tide hydrodynamic and spectral wave models in synthetic climate simulations where tens of thousands of TCs are required to better resolve the distribution of extremes. Future work will also investigate parametric wind model approaches to estimates of waves (Hwang 2016; Young 2017; Tamizi and Young 2020) and storm surge (WMO 2011) for compound and multihazard event analysis for coastal communities.
Acknowledgments.
This work was funded through the Australian Climate Service program.
Data availability statement.
All observational datasets were sourced from openly available data sources. A subset of model data is available at https://github.com/AusClimateService/TCHazaRds/blob/main/OGradyEtAl2023windData.zip, other model data can be provided on request to the lead author.
APPENDIX
Glossary
In Table A1 we show the units and a brief description for each variable and abbreviation used in this document.
Glossary.
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