For comparison, the wind model described in (referred to in ) is implemented. The model relies on the gradient wind formula from , which assumes that the pressure gradient force, given by 's formulation, is balanced by the centrifugal and Coriolis forces. The gradient wind is then extrapolated to the altitude of interest using a power law . considered a shear exponent of 0.1 for offshore applications. The shear exponent depends on the roughness length through an empirical formula in . For wind over terrain, the Global Land Cover dataset from Copernicus gives a 100 m resolution discrete classification of the type of soil. Each class is assigned a roughness length. The roughness length over sea is set to 1.6×10-4 m to match a shear exponent of 0.1 using the empirical formulation from . The averaging time of the wind speed from this parametric model applied to the best-track dataset is assumed to be a 3 h average . In the present study, time series and surface wind fields at specific time steps are compared. For time series, the 3 h wind speed can be converted to 10 min average following the method described in , which is based on random realisations of a normal distribution. However, this method can not be applied to assess a wind field at a given instant. Therefore, for consistency in the averaging period for surface wind field comparisons and to obtain a consistent order of magnitude, the maximum 10 min wind speed is derived from the 3 h wind field by using the time conversion model described in . The maximum M minute average wind speed UMmax to 10 min average U10minmax is computed from 8UMmaxU10minmax=1-0.0810M-10600.5457, with M the number of minutes.

The surface and gradient wind models were derived assuming open-ocean conditions. However, upstream orography may disturb the wind flow in coastal regions. A standard practice for accounting for these effects is to compute a speed-up ratio that corrects the wind from the parametric model . The speed-up ratio is defined as the ratio between the wind computed over the actual orography and the wind speed over a flat surface of uniform roughness. The MASCOT software is used to derive the variation in the speed-up ratio with wind direction.

In , the wind direction is given by an empirical formulation, while the surface wind model of provides no information on the actual wind direction. The wind direction is thus defined as the tangential direction corrected by an inflow angle. The inflow angle corresponds to the difference between the tangential direction relative to the TC centre and the actual surface wind direction. In this study, the inflow angle is fixed to -22.5° in the OROWSHI model for the application of the speed-up ratio.

To assess the limitations of the parametric models in coastal regions, their results are compared with those obtained from a mesoscale model and a reanalysis, which incorporate detailed physics, in particular, the effects of terrain and surface obstacles.

For comparison with the parametric models, a mesoscale model and a global reanalysis dataset accounting for more physics are presented. Below is a brief description of the available data.

The maximum wind speed from IBTrACS is local (two-dimensional) while the axisymmetric wind profile from requires an azimuthally averaged Vm. In this study, the correction proposed by is implemented to obtain an azimuthally averaged maximum wind, consistent with the parametric model. The relationship follows: 12Vm=0.8066VIBTrACS+2.985, with VIBTRrACS corresponding to the parameter USA_WIND in the best-track dataset.

An important parameter in the description of TCs is the radius of maximum wind Rm, which represents the distance from the TC centre to the location of the strongest winds. It is therefore a key parameter for accurately estimating wind speeds, especially when the TC is close to the site of interest. In most studies, Rm is used as provided in the best-track data. However, it is derived from the local (two-dimensional) maximum wind rather than azimuthally averaged quantities, which may introduce significant uncertainty in its use within parametric models.

highlighted that Rm is difficult to measure and is badly resolved in models and reanalyses. Here, Rm is estimated from Vm, ϕ, and R34 following the methodology of . The angular momentum is given by 13Ma=rV+12fr2, with r the radius, V the tangential wind speed, and f the Coriolis parameter.

Knowing the ratio Ma(r=Rmax)/Ma(r=R34), Rm can be computed as follows: 14Rm=Vmf1+2fMa(r=Rmax)Vm2-1.

computed the ratio Ma(r=Rmax)/Ma(r=R34) from an SAR–radiometer collocation dataset and derived the following parameterisation, adopted here: Ma(r=Rmax)/Ma(r=R34)=0.531×exp⁡[-0.00214(Vm-17.5)15-0.00314(Vm-17.5)12fR34].

In the IBTrACS dataset, R34 is available for the TC four quadrants. The mean value of R34 is used to consistently obtain an axisymmetric Rm. The parameterisation (Eq. ) was obtained with a 1 min azimuthally average wind speed. The intensity Vm from IBTrACS corrected by Eq. () is used to estimate Rm in Eqs. () and ().

In , Rm is fitted from measured sea surface pressure, but no pressure measurements are available on the site of this study. Since the equation of is an axisymmetric pressure model which requires an azimuthal average Rm, Rm obtained from the abovementioned methodology is used. Note that the current implementation differs from the original study from as parameters from the Japan Meteorological Agency (JMA) were used, restricting the application to the Western Pacific basin. In particular, Rm is not provided by the JMA. In this study, the TC parameters from the US agency are used. Since they are provided for almost every TC, the current implementation is applicable anywhere.

The I&Y15 model also requires the ambient pressure to apply the equation of , taken to 1013 hPa here . The USA_PRES parameter from the IBTrACS dataset gives the central pressure, which is used to quantify the central pressure depth.

A lidar located on Tairajima Island (33.70° N, 129.62° E) recorded winds from Typhoon Hinnamnor and Nanmadol (2022) on 20 vertical levels from 50 to 285 m. Only measurements at 95 and 205 m are considered for comparison with wind models. The locations of the TCs provided by IBTrACS are represented in Fig. . The wind intensity Vm from the US agency is presented for each location. The minimum distance from the TC centre to the site is 2.8 Rm and 1.0 Rm for Typhoon Hinnamnor and Nanmadol, respectively.

The site is relatively close to Iki Island (≈5 km). Thus, local orographic effects may affect the wind. The variation in the speed-up ratio with wind direction (true north convention) is presented in Fig. . MASCOT software predicts a decrease in wind direction between 0–90°, due to Iki Island, while Kyushu Island affects the wind speed from 90 to 225°.

A floating lidar located at 39.55° N, 73.43° W recorded the winds of Hurricane Isaias (2020). Figure  displays the TC track and wind intensity. The TC passed about 2.0 Rm from the site. During the event, two of the four quadrants of the TC are overland, with values of R34 very low compared to those over sea. Since the present study aims at evaluating the performance of the parametric models over the sea, only the mean R34 of the eastern quadrants is used for this case. The vertical discretisation of the measurements is 20 m from 18 to 198 m. The altitudes 98 and 198 m are used as reference for the comparison of the wind speed.

The site is over 60 km from the coast. In this case, orographic effects are neglected.

Taiwan is hit by numerous typhoons every year. With mountains over 3 km high, this island is of particular interest for studying the interactions of tropical cyclones with mesoscale orography e.g..

The surface wind speed and the drag coefficient are derived from a least-squares linear fitting as in for each sample. u*/κ is given by the slope and z0 by the intercept on a log height scale. The surface wind U10 is derived from Eq. () and the drag coefficient from Eq. (). Figure  displays the drag coefficient computed for each sample from the 10 min mean wind speed. The observations are highly scattered and site-dependent. The dispersion of the results could in part be due to the difference in measurement heights across the various sites but also to upstream terrain affecting the vertical wind profiles. The drag coefficient derived from TC Megi (2016) is significantly different depending on the site, with a ratio of 2 between the two sites for U10>30 ms-1. This discrepancy may be attributed either to upstream topographic effects or to differences in wave conditions within the Taiwan Strait. The WASP and formulations are presented for comparison. The two parameterisations are consistent with the mean value, which does not vary substantially for this wind speed range. Table  presents the mean bias error (MBE) and root mean square error (RMSE) of wind speed computed at 200 m (corresponding to hub height of 25 MW OWT ) using WASP drag coefficient and DNV's recommendations. The reference value is computed from the fitted log law since level 200 m is not available in the data. The lowest errors are obtained with WASP for the analysed data. Extreme wind speeds at hub height are thus better estimated on average using the WASP drag coefficient than the DNV recommendation for this dataset.

The power law (Eq. ) is also widely used in the industry to extrapolate wind speed. suggests using an exponent α=0.12 for open-ocean conditions with waves. In , α is set to 0.10. Recommendations from suggest extrapolating the 50-year extreme wind speeds using α=0.11. The shear exponent is derived from the measurement using all available vertical levels to assess the reliability of the various proposed values.

A power law is fitted to the vertical profiles with U10 and shear exponent α as free parameters. Figure  presents the variation in the shear exponent with the surface wind. There is no significant variation in the mean value of α as a function of U10, which is equal to 0.106. The median is 0.107, slightly higher than the value reported in . Table  presents the MBE and RMSE of wind speed computed at 200 m using shear exponents from 0.10 to 0.12. IEC's recommendations give the best results for this dataset. Although the power law with a shear exponent α=0.11 performs slightly better, the logarithmic law based on the WASP drag coefficient is retained for its stronger physical basis and interpretability.

Wind time series from TC Hinnamnor are presented in Fig. . All the methods presented here align well with the observations. The scores of the wind speed predicted by the parametric models are similar to those obtained with ERA5 and HWRF and remain low (MBE<3 ms-1 and RMSE<5 ms-1; see Table ). In this configuration, the parametric models are able to accurately capture the peak wind speed (PDmax<2 %), while HWRF slightly underestimates it due to its coarse temporal output sampling (PDmax<-5 %). The surface wind field estimated by the four models on 5 September at 18:00 GMT is presented in Fig. . This time instant corresponds to the HWRF time step closest to the instant of the maximum wind speed measured at the site. Parametric models predict an eyewall spot similar to that of HWRF (Fig. a). ERA5 (Fig. b) shows lower wind speeds in the inner core compared to HWRF. This is due to its coarse horizontal resolution but also to inadequate physics parameterisations for cyclonic conditions . The apparent good agreement of the weak winds between ERA5 and HWRF in the outer area may be coincidental. HWRF is expected to perform better in representing the inner-core structure, but a comparison with measurements would be necessary to evaluate the accuracy of both models.

The formulation used in always predicts the location of the azimuth of maximum wind at 90° on the right-hand side of the direction of TC propagation (41° here) (Fig. d), which is reasonable at this specific instant. However, the area of high wind is larger than that predicted by HWRF and by the OROWSHI model, which could lead to different sea states in this area when the wind field forces a wave model.

The two parametric models satisfactorily predict the peak winds. Although both models are based on IBTrACS parameters, they differ in their primary inputs: the OROWSHI model is driven by Vm (Eq. ), whereas I&Y15 depends on the central pressure depth. The maximum wind speeds predicted by the two models at a given instant are not necessarily the same.

Figure  presents the comparison of the wind speeds induced by TC Nanmadol. The parametric models underestimate the wind speed during the TC approaching phase by a factor of 2, which is a source of large errors in terms of RMSE (RMSE>5 ms-1; see Table ). Nevertheless, the peak wind speed and the wind during the leaving phase are quite well predicted, with a PDmax lower than 6 % from the measurements at the two altitudes. The surface wind fields on 18 September at 09:00 GMT are presented in Fig. . The TC begins to make landfall on Kyu¯shu¯ Island at this instant. HWRF results (Fig. a) show that the high-wind spot is located opposite to the direction of TC direction (357° at this instant). The observed asymmetry is certainly due to the island perturbing the flow, which can not be represented by the OROWSHI model as it relies on SAR images over open-ocean conditions. Note that the radius of the eyewall predicted by the present implementation of the I&Y15 model is also much larger in this case, leading to a more extensive area of high wind speeds (>30 ms-1) than those predicted by HWRF and the OROWSHI model.

The surface wind fields during landfall on 18 September at 18:00 GMT are presented in Fig. . The OROWSHI model (Fig. c) is not designed to predict such a configuration when the TC is mainly over land. The area of high winds predicted by HWRF and by the OROWSHI model is located just around Kyushu Island's northern part, while the surface wind from the I&Y15 model is rather axisymmetric.

The wind time series of TC Isaias is displayed in Fig. . The OROWSHI model shows a reasonable agreement with the measurements with low MBE and RMSE (less than 5 ms-1; see Table ), but all models underestimate the main wind peak by at least 4 %. Note that HWRF accurately reproduces the measured wind speeds at the available output times. However, the 3 h output interval is too coarse to capture the maximum wind speed for this event. The winds from I&Y15 largely underestimate the measurements during the whole event with MBE and RMSE larger than 8 ms-1.

Figure  shows the surface wind field of Isaias on 8 August at 15:00 GMT, at the HWRF time step closest to the maximum observed wind speed, when part of the TC is over open-ocean. The TC made landfall at the shown time step. The high-wind area is above the ocean according to HWRF. The faster decay of the wind speed profile with increasing distance to the TC centre using the I&Y15 model causes the TC to have reduced coverage, that is, smaller area of high wind speeds larger than 20 ms-1, than the other methods, which explains the wind speed underestimation at the measurement site, being ≈220 km to the north-west of the cyclone centre at the shown time. Note that the I&Y15 model takes into account the ambient pressure, set to 1013 hPa here. A more accurate estimate of this pressure would lead to different results.

Wind speeds in Taiwan are presented in Figs. –. The parametric models can reproduce the increase in the wind until the main peak but deviate from the measurement during the leaving phase, with large discrepancies during low-wind conditions.

The wind direction measured by the wind vanes during TC Megi is presented in Fig. . The crosses correspond to the instant of maximum wind speed measured at sites 1 and 2. The wind blows from the sea during the main peak (wind direction lower than 30° for site 1 and 70° for site 2). Therefore, neglecting orographic effects has no impact on the maximum speed estimate in this specific case. Thus, the parametric models captured the main peak fairly well with a relatively low PDmax (less than 13 %); see Tables –) compared to the results from HWRF and ERA5. Indeed, HWRF and ERA5 highly underestimate the maximum wind speeds in these cases with PDmax larger than 20 %, although both models account for the presence of the island. The wind decreases significantly after the main peak as the TC moves to the Taiwan Strait, and the blockage effect due to the island highly affects the wind prediction.

As HWRF results are not available for Typhoon Dujuan, the surface wind assessment focuses on Typhoon Megi, which was also studied in among two similar configurations. The surface wind field of TC Megi on 27 September at 06:00 GMT is shown in Fig. . This time step corresponds to the time instant of maximum speed measured at site 2 and is also selected to illustrate the complexity of the interaction with Taiwan. The wind field predicted by HWRF (Fig. a) is highly unstructured, while ERA5 (Fig. b) largely underestimates the surface wind around the island. Also, at site 1, the wind speed at the second altitude (222 m) predicted by HWRF is slightly lower than the surface wind, leading to a negative shear exponent at this instant (-2.8×10-3). The vertical extrapolation using a power law is thus invalid between the first two levels, while the wind speed increases for the vertical levels above several hundred metres. ERA5, on the other hand, predicts a shear exponent of 0.173 at the same instant but highly underestimates the observed wind speeds.

Due to the presence of the mountains, the eyewalls predicted by both the OROWSHI model (Fig. c) and I&Y15 (Fig. d) are unrealistic as the parametric models do not account for the asymmetry caused by the orography here. An eyewall positioned on the opposite side of the obstacle (i.e. in the south-eastern quadrant) would be more consistent with HWRF results. Nevertheless, the wind speed in the outer core is fairly predicted and the magnitude of wind speed is reasonably estimated at this instant (see Figs.  and ). HWRF predicts the highest intensity among the models. However, the highest wind in Fig. a might be due to orographic acceleration over the island (south part of Taiwan).

When the TC passes through the Taiwan Strait, the wind direction increases as the TC propagates westward, with the sites located to the north of the cyclone track (Fig. ), and the wind speed decreases significantly (Figs.  and ). The measurement zone becomes very calm with low wind speeds due to the mountain blockage. This is also reported in , where wind shear and veer vary highly in this area. Large variations in wind direction occur at low wind speeds (see Figs. –). Parametric models largely overestimate wind at these instants by neglecting orography effects. Thus, the RMSE for the two parametric models are much higher than in the other configurations (RMSE>12 ms-1; see Tables –). HWRF and ERA5 can predict this phenomenon better as they incorporate the influence of the terrain. This is illustrated in Fig. , where the wind field of the four models is displayed for TC Megi on 27 August at 18:00 GMT. At this time, the TC is located in the Taiwan Strait, and complex interactions occur with the island. HWRF can capture fine features due to its high resolution, including orographic acceleration and deceleration, both on the continent and on Taiwan. However, the most interesting pattern is the wake effect north-west of the island at the site locations, caused by the upstream mountainous terrain that strongly disturbs the wind flow. This is also predicted by ERA5 despite its coarse resolution (Fig. b). Also, both ERA5 and HWRF predict an area of strong winds located over the sea at this instant, located in the direction opposite to the TC translation (299° at this time). The region of highest wind speeds is confined between the two obstacles, Taiwan and the continental shelf. This illustrates the complexity of wind forecasting using simplified parametric models that do not account for large-scale disturbances generated by an island like Taiwan.

The mean absolute bias error (MABE), the mean root mean square error (MRMSE) on the wind time series, and the mean absolute percentage deviation from the maximum measured wind (MAPDmax) are presented in Table .The whole time series is better predicted by the reanalysis and the mesoscale model (MABE<2ms-1 and MRMSE<4ms-1) than by the parametric models, which show larger errors (MABE≫5ms-1 and MRMSE>9ms-1). These deviations are essentially caused by the overestimation of the wind speeds during the passage of the TCs through the Taiwan Strait and the significantly underestimation of wind speeds of Isaias by the I&Y15 model. On the other hand, the parametric models better estimate the highest wind at the sites, an essential parameter for extreme wind statistics. In particular, the OROWSHI model shows only a 5.1 % mean absolute percent deviation from the peak observed wind speed, which is less than half the error of the other methods. ERA5 largely underestimates the peak winds, and should therefore be used with caution for tropical cyclone wind assessment. The parametric models are highly effective in their field of application, i.e. on the open-ocean without large-scale disturbances. The source of errors in parametric models is mainly due to land interactions that affect the TC asymmetry and orographic effects that strongly decrease wind speed downstream of Taiwan's mountains. In complex environments where tropical cyclones are perturbed at the mesoscale, advanced numerical models are required to capture complex flows. Coupling the ERA5 wind field with a TC parametric model also appears to be a viable approach for improving wind speed predictions under such conditions, as demonstrated by .