Developing an Objective Scheme to Construct Hurricane Bogus Vortices Based on Scatterometer Sea Surface Wind Data

Abstract

This study presents an objective scheme to construct hurricane bogus vortices based on satellite microwave scatterometer observations of sea surface wind vectors. When specifying a bogus vortex using Fujita’s formula, the required parameters include the center position and the radius of the maximum gradient of sea level pressure (R₀). We first propose determining the tropical cyclone (TC) center position as the cyclonic circulation center obtained from sea surface wind observations and then establishing a regression model between R₀ and the radius of 34-kt sea surface wind of scatterometer observations. The radius of 34-kt sea surface wind (R₃₄) is commonly used as a measure of TC size. The center positions determined from HaiYang-2B/2C/2D Scatterometers, MetOp-B/C Advanced Scatterometers, and FengYun-3E Wind Radar compared favorably with the axisymmetric centers of hurricane rain/cloud bands revealed by Advanced Himawari Imager observations of brightness temperature for the western Pacific landfalling typhoons Doksuri, Khanun, and Haikui in 2023. Furthermore, regression equations between R₀ and the scatterometer-determined radius of 34-kt wind are developed for tropical storms and category-1, -2, -3, and higher hurricanes over the Northwest Pacific (2022–2023). The bogus vortices thus constructed are more realistic than those built without satellite sea surface wind observations.

1. Introduction

The accuracy of numerical forecasts of tropical cyclones (TCs) depends on the realism of initial vortices embedded within model initial conditions. Because of scarce conventional observations over the oceans, TC observations rely heavily on infrared instruments [1,2,3] and microwave instruments [4,5]. There is often uncertainty in key structural aspects of global large-scale analysis datasets [6]. The location and size characteristics can vary both among TCs and across a single TC’s life cycle. Vortex initialization incorporates a bogus vortex into model initial conditions to improve forecasts of TCs. Realistic bogus vortices yield better vortex initialization. Traditional methods mainly rely on ships, buoys, and station observations, supplemented by aircraft reconnaissance [7]. However, the United States ended routine Northwest Pacific TC flights after 1987 [8]. Here, an objective scheme is developed to construct bogus vortices utilizing satellite sea surface wind observations.

Microwave scatterometers have become the principal instruments for obtaining global sea surface wind data. Working essentially as radar systems, they measure backscattering coefficients related to sea surface roughness [9]. Due to their low observing frequencies, these scatterometer sea surface wind observations are usable under both clear and cloudy sky conditions. Since the launch of SeaSat by the United States in 1978 [10], multiple scatterometer-equipped satellites have been launched by different agencies, such as the European Space Agency’s ERS series and MetOp satellites, Japan Aerospace Exploration Agency’s ADEOS satellites, NASA’s QuikSCAT, Indian Space Research Organization’s OceanSat series, China’s second-generation National Satellite Ocean Applications Center’s Hai Yang-2 (HY-2) satellites, and Satellite Ocean Application Service Fengyun-3E (FY-3E) [11,12,13].

Constructing a bogus vortex for vortex initialization typically involves specifying an empirical radial profile of sea surface pressure [14] or tangential wind [15]. For example, Bjerknes [16] proposed an axisymmetric model in which the sea level pressure follows a parabolic function in the core region. Takahashi [17] introduced another radial profile that better represents the periphery of a tropical cyclone. By merging both, Fujita [14] developed an empirical function with four parameters: the sea level pressure at the TC center position (P_c), the pressure at infinity of the typhoon (P_∞), the radius of the maximum radial gradient of sea level pressure (R₀), and the radius of the outermost closed isobar (R_out). Thus, Fujita’s formula can represent a bogus vortex with realistic intensity and size. While P_c and R_out are often directly available from the best track data and P_∞ can be approximated from large-scale analysis, R₀ is less certain. Earlier work replaced R₀ with the radius of maximum sustained wind, R_max [18,19,20,21]. Park and Zou [22] instead derived R₀ from the radius of 34-kt wind speed (R_34kt) in the best track data. Specifically, R₀ is regressed on R_34kt using 16 model-based vortices generated via 4D-Var data assimilation [18]. Their approach significantly improved the intensity prediction of Hurricane Bonnie (1998), due to the model capturing larger surface fluxes and latent heat release.

Given the global coverage of microwave scatterometers, it is now possible to use satellite observations to establish a relationship between R₀ and R_34kt directly from observed data rather than from model forecasts. Moreover, scatterometers sea surface wind observations can pinpoint the TC center position [23], complementing brightness temperature-based methods that can suffer from cloud contamination [24]. Furthermore, the assimilation of post-processed scatterometer data significantly improved TC forecasting [25,26,27,28]. Thus, this article employs sea surface wind data observed by multiple satellite microwave scatterometers to (1) extract TC center positions and (2) derive R_34kt. We then build TC category-dependent statistical models of R₀ as functions of R_34kt.

Section 2 describes the data. Section 3 presents the methodology and the TC cases. Section 4 shows results, including (a) center positioning and (b) regression models between R₀ and scatterometer-derived R_34kt for multiple intensity categories (tropical storms, category-1, -2, and 3+). Section 5 summarizes the main findings and discusses further research.

2. Data Description

2.1. Sea Surface Wind Data

A microwave scatterometer operates in the C-band or Ku-band, with different swath widths and resolutions. For example, the AMI-SCAT worked at ~5.3 GHz (C-band) but had a narrow swath (500 km), often not covering entire TCs [29]. NASA’s QuikSCAT SeaWinds (launched in 1999) had a ~1800 km swath, covering approximately 90% of tropical oceans daily [30]. The advanced scatterometer (ASCAT) onboard MetOp satellites has a center frequency near 5.255 GHz (C-band) and ~550 km swath width [31]. China’s first experimental HY-2A satellite (16 August 2011) carried a microwave scatterometer (HSCAT-A) similar to SeaWinds (Ku band, wide 1800/1400 km swath) [32]. HY-2B (2018), HY-2C (2020), and HY-2D (2021) carried improved HSCAT instruments with better signal-to-noise ratio and refined geophysical model functions [33]. Operating in different orbits, HY-2B/2C/2D form a multi-satellite network covering over 80% of global oceans four times daily [34].

FY-3E (launched on 5 July 2021) is China’s second-generation POES equipped with Wind Radar (WindRAD), using dual C- and Ku-band frequencies [35], thus supplementing HY-2B/2C/2D coverage. Altogether, these scatterometers provide 10-m sea surface wind vectors multiple times per day [36].

Our study uses the 10-m sea surface wind vector products from HY-2B/2C/2D HSCAT, MetOp-B/C ASCAT, and FY-3E WindRAD. With different local equator crossing times, these instruments collectively observe TCs several times daily. Figure 1 shows an example of MetOp-B ASCAT vs. HY-2B HSCAT coverage/time on 2 August 2023, illustrating the narrower ASCAT swath (~550 km) compared to HSCAT (~1800/1400 km).

Additionally, we use the MTCSWA dataset from NOAA/NESDIS/STAR [37] to obtain QuickSCAT derived R_34kt. MTCSWA combines multiple POES and GOES data at 3-h intervals [38]. We use the version from 7 September 2022 onward, covering a ~900-km radius around the TC center at 4.5 km and 10° azimuth resolution. We also use the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) [39] to calculate $P_{\infty }$. ICOADS is the most comprehensive global ocean surface dataset, containing multiple variables (SST, SLP, wind speed/direction, etc.) from ships, buoys, and other ocean platforms [39]. We use its near real-time version 3.0.2, which was last updated in February 2022.

2.2. The Best Track, Global Reanalysis, and AHI Data

The International Best Track Archive for Climate Stewardship (IBTrACS) v04r01 is a global TC dataset maintained by NOAA’s National Climate Data Center [40]. It provides TC center position (λ_c, φ_c), 10-m maximum wind speed (V_max), radius of maximum wind speed (R_max), central pressure (P_c), outermost closed isobar radius (R_out) and pressure (P_out), and radii of 34-kt winds in each quadrant.

We employ ERA5 [41] from ECMWF, providing hourly global atmospheric reanalysis on 37 pressure levels (100 hPa–1 hPa) and 0.25° × 0.25° horizontal resolution.

Japan’s Himawari-9, launched in December 2022, replaced Himawari-8 on 13 December 2022 at 140.7°E. The Advanced Himawari Imager (AHI) performs a full disk scan every 10 min with 16 channels. We use Channel 13 (~10.45 μm, ~2-km resolution), which is commonly used to observe cloud-top brightness temperatures. These AHI data can help locate TC centers [24], complementing the scatterometer-based surface wind centers.

3. Methodology and Case Description

3.1. TC Center Positioning Method

We adopt two center-positioning algorithms: (1) scatterometer-based [23] and (2) AHI-based [24].

Scatterometer-based (Figure 2 example):

• Find the max wind speed location (triangle).
• Within a 3° × 3° box, find all minimum wind speeds (circle) that are less than their immediate neighbors.
• Define eight two-component vectors ${\overrightarrow{q}}_i (i=1 ,\dots 8)$ at the eight nearest points around each wind-speed minimum: if the raw wind direction is within 0° ± 22.5°, 45° ± 22.5°, 90° ± 22.5°, 135° ± 22.5°, 180° ± 22.5°, 225° ± 22.5°, 270° ± 22.5°, and 315° ± 22.5°, the discrete vectors ${\overrightarrow{q}}_i$ take the values of (1, 1), (1, 0), (1, −1), (0, −1), (−1, −1), (−1, 0), (−1, 1), and (0, 1), respectively.
• Compute the absolute sum of these eight direction vectors: $Q=|{\displaystyle \sum _{i=1}^8\overrightarrow{q_i}}|$.
• The minimum wind point with the smallest sum $Q$ is the TC center (cross).

AHI-based:

• Use the system-clustering method to identify three points with the lowest brightness temperature in the eyewall. The original channel-13 TB observations are averaged onto a 0.3° × 0.3° grid. The data points where TB observations are less than an empirical value of $T_b^{th}$ = 202 K are determined. Each of the data points is considered as an initial cluster. If there are N data points with TB observations being less than $T_b^{th}$, there are N clusters. The two clusters with the closest minimum distance among the N clusters are merged together to form a new cluster. The new cluster is further merged with one of the remaining clusters whose distance from the new cluster is the smallest. This procedure is repeated until only the newest cluster and one remaining cluster are left. The three points of the minimum TB values in the newest cluster are identified for the next step.
• Fit a circle passing the three points identified by the cluster method; the circle center is the first guess.
• Perform an azimuthal spectral analysis for each grid in a 4° × 4° domain centered at the first guess point with 0.15° × 0.15° resolution, and the grid location leading to the largest wavenumber-0 amplitude is taken as a refined center over the guess point.
• Repeat the spectral analysis for each grid in a 2° × 2° domain centered at a refined center with 0.025° × 0.025° resolution, and the grid corresponding to the largest wavenumber-0 amplitude is taken as the final TC center.

Figure 2. (a) The center of Typhoon Mawar (black cross symbol) determined from HY-2B scatterometer observations of sea surface wind vectors (black arrow) and wind speed (color shading); (b) A schematic illustration of the TC center positioning method applied to data within the 3° × 3° box centered at the maximum wind speed (black dashed box in (a) at 2045 UTC on 25 May 2023. Indicated in (b) are the maximum wind speed position (triangle), all minimum wind speed positions (black circle), eight values around each black circle, and the center of Typhoon Mawar (black cross).

Figure 2. (a) The center of Typhoon Mawar (black cross symbol) determined from HY-2B scatterometer observations of sea surface wind vectors (black arrow) and wind speed (color shading); (b) A schematic illustration of the TC center positioning method applied to data within the 3° × 3° box centered at the maximum wind speed (black dashed box in (a) at 2045 UTC on 25 May 2023. Indicated in (b) are the maximum wind speed position (triangle), all minimum wind speed positions (black circle), eight values around each black circle, and the center of Typhoon Mawar (black cross).

3.2. Bogus Vortex Formula

Fujita’s empirical formula for sea level pressure (SLP) in a bogus vortex [14] is given by:

$$P_{bogus}\left(r\right)=P_{\infty }-{\displaystyle \frac{\left(P_{\infty }-P_c\right)}{{\left[1+{\left(\frac{r}{\sqrt{2}{R}_0}\right)}^2\right]}^{\frac{1}{2}}}},r\le R_{out},$$

(1)

where P_c is the central SLP, R_out is the outermost closed isobar radius, R₀ is the radius of the maximum SLP gradient, and P_∞ is the SLP at large radii.

If we set P_bogus(R_out) = P_out in (1), R₀ can be expressed as:

$$R_0={\displaystyle \frac{R_{out}}{\sqrt{2\left[{\left(\frac{P_{\infty }-P_c}{P_{\infty }-P_{out}(R_{\mathrm{out}})}\right)}^2-1\right]}}},r\le R_{out},$$

(2)

We approximate P_∞ from the ICOADS SLP data in 1.5R_out–2R_out rings.

3.3. Vertical Wind Shear

The vertical wind shear is the difference between 200 hPa and 850 hPa wind vectors averaged in an annular region 200–800 km from the TC center [42,43,44]. Mathematically, it can be written as follows:

$$\overline{\mathrm{VWS}}={\displaystyle \frac{{\displaystyle {\int }_{200}^{800}{\displaystyle {\int }_0^{2\pi }\sqrt{{\left(U_{200}-U_{850}\right)}^2+{\left(V_{200}-V_{850}\right)}^2}\mathrm{d}rd\theta }}}{{\displaystyle {\int }_{200}^{800}{\displaystyle {\int }_0^{2\pi }r\mathrm{d}rd\theta }}}},$$

(3)

where (U₂₀₀, V₂₀₀) and (U₈₅₀, V₈₅₀) are zonal/meridional winds at 200/850 hPa.

3.4. Case Description

We illustrate three 2023 landfalling typhoons: Doksuri, Khanun, and Haikui.

• Doksuri (5th typhoon in 2023 NW Pacific): Formed on 21 July east of the Philippines. Rapidly intensified (RI) before crossing Luzon and reached super typhoon status around 27 July (max wind ~62 m s⁻¹). Made landfall around 28 July near Jinjiang, Fujian (~50 m s⁻¹, 945 hPa), then moved north, with heavy rains. Weakened to depression by 29 July.
• Khanun (6th): Formed on 28 July and reached super typhoon strength around 31 July (935 hPa, 52 m s⁻¹). Initially moved westward, turned northeast around 4 August in the East China Sea, then north. Landfall near Gyeongsangnam, South Korea on 10 August (28 m s⁻¹, 975 hPa), and again near Liaoning, China on 11 August.
• Haikui (11th): Formed on 28 August, reached a severe tropical storm around 29 August, and became a typhoon by around 1 September. Landed in southeastern Taiwan on 3 September (~30 m s⁻¹), and a second landfall on 5 September in Dongshan County, Fujian (~975 hPa).

4. Results

4.1. TC Center Positioning Results

We compare scatterometer-based and AHI-based center positioning results with the IBTrACS best track for Doksuri, Khanun, and Haikui. The best track was determined by integrating different types of data. For example, the Automated Rotational Center Hurricane Eye Retrieval (ARCHER) is an automated TC center-fixing algorithm to determine a TC center position based on the structure and organization of cloud features in visible and infrared imagery from geostationary meteorological satellites and other data sources (e.g., radar data, aerial reconnaissance data, land observations, and ship reports, etc.) [45], and later adding microwave observations from imagers onboard polar-orbiting meteorological satellites [46]. The IBTrACS is one of the most reliable best track datasets that is currently available.

Figure 3 shows the scatterometer-based tracks vs. IBTrACS for each typhoon. The track deviations are usually smaller for stronger typhoons. For Doksuri, 25 scatterometer passes exist (3.65 per day). For Khanun, 67 passes (5.15 per day). For Haikui, 28 passes (4 per day). The joint observations of typhoons by multiple satellites effectively avoid the problem of a single satellite observing a typhoon no more than two times a day. When a typhoon approaches land or islands, the wind field observed by satellite scatterometers cannot cover the center of the typhoon and is excluded from this study. Vortex initialization for TCs located near-shore regions could rely on high-resolution GOES imagers [45,47], as well as radar and aircraft reconnaissance data [8,48].

A systematic northeast deviation of the scatterometer-based track from the best track was noticed during the early period of the lifetime of Typhoon Haikui (Figure 3c). This could result from a displacement of the near-surface circulation center from the upper-level cloud center within Typhoon Haikui during these times. In order to confirm this, we overlap the spatial distribution of scatterometer observations with that of AHI channel-13 infrared observations within and around Typhoon Haikui at 1450 UTC on 29 (Figure 4a, HY-2D) and 1930 UTC 30 on August 2023 (Figure 4b, HY-2C). The typhoon center position (cross symbol) from HY-2C/D scatterometer wind vectors (black arrow) is located to the northeast of the center (black circle symbol) determined from AHI observations of brightness temperature (color shading) at both times. The reasons for the inconsistency of the two data types will be discussed later.

Figure 5 compares all three tracks (best, scatterometer, and AHI). For Doksuri/Khanun (both reached category 3+), the scatterometer and AHI tracks closely match the best track. For Haikui, during the early period, the scatterometer-based centers are northeast of the best track, whereas the AHI-based centers are southwest (Figure 4). Since the determination of the best track was based on multiple sources of satellite observations, radar data, and sounding balloon or dropsonde observations, it is understandable that the best track is located in between the scatterometer-determined and AHI-determined tracks.

In order to confirm the existence of vertical tilt in Typhoon Haikui, we need to know the vertical wind shear, which can be calculated using ERA5 reanalysis. To do so, we must first make sure that the typhoon centers in the ERA5 reanalysis are close to the best track. By applying the same center positioning method as we did with microwave scatterometer observations to the 10-m surface wind field in the ERA5 reanalysis, we can obtain the ERA5-derived track, which is very close to the best track (Figure 6a). We then calculated the vertical wind shear and added it to the scatterometer-determined track (Figure 6b). It was found that the observed center shifts between the near-surface and upper-level data match the vertical tilts of Typhoon Haikui. The phenomenon of tilted TC has been reported and intensively studied over the last few decades [42]. The exact reasons for the inconsistencies between the two data types will be further investigated using numerical simulations of Typhoon Haikui [49].

Quantitative measures of the deviations between the scatterometer sea surface wind observation-determined track and the AHI brightness temperature-determined track from the best track are provided in Figure 7 for typhoons Doksuri, Khanun, and Haikui. For typhoons Doksuri (Figure 7a) and Khanun (Figure 7b), whose intensity exceeded category-3 hurricane, the differences between the scatterometer sea surface wind observation-determined track (color symbol) and the best track were smallest (~20 km) during the periods of strongest intensity. This conclusion is also valid for the differences between the best track and the AHI brightness temperature-determined track. Large differences in the scatterometer sea surface wind observations from the best track are found for Typhoon Doksuri when it passed nearby islands on 26 and 27 July 2023 (Figure 7a). The azimuthal spectral TC positioning algorithm does not work for the center positioning of relatively weak tropical storms when their cloud/rainbands are not axisymmetric. For Typhoon Haikui (Figure 7c), the AHI brightness temperature-determined track deviates more from the best track than the scatterometer sea surface wind observation-determined track, for reasons explained in Figure 6.

4.2. Bogus Vortex Results

Having obtained the TC center positions, we compute the scatterometer-derived 34-kt radius, which will be denoted as $R_{34kt}^{Scat}$. Meanwhile, Fujita’s Formula (1) uses P_c, R_out, R₀, P_out, and P_∞. Because P_c, R_out, and P_out come from IBTrACS, and P_∞ from ICOADS, R₀ remains unknown. Past work approximated R₀ from best track R_34kt or model-based regressions [22]. Here, we derive R₀ from R_34kt for Northwest Pacific TCs in 2022–2023. Figure 8 shows the best tracks during 2022 and 2023, with black symbols marking times missing in the MTCSWA dataset.

Figure 9 plots P_∞ vs. P_out from ICOADS for four intensity categories: tropical storms, category-1, -2, and 3+ hurricanes. As expected, P_∞ > P_out. Next, from Equation (2), we calculate R₀ for each 6-h best track time. Figure 10 shows R₀ vs. R_34kt, grouping the four categories. We find a linear fit: R₀ = aR_34kt + b, with standard deviations ranging from ~55 km for tropical storms to ~22 km for 3+ hurricanes.

As expected, the values of P_∞ are larger than the values of P_out. Once we have P_∞, R₀ can be calculated from the best track data using (2). We can then generate scatter plots of R₀ versus R_34kt for 2022 and 2023 Northwest Pacific tropical storms, category-1 hurricanes, category-2 hurricanes, and hurricanes with intensities stronger than category 2 (Figure 10). There are linear relationships between R₀ and R_34kt. The larger the TC low-pressure system, the larger the wind radius of 34-kt. An empirical linear regression function, R₀ = aR_34kt + b, is thus established for the four TC groups. The regression coefficients (a, b) for the above four groups are (0.389, 71.854 km), (0.371, 34.588 km), (0.349, 9.398 km), and (0.283, −0.904 km), respectively. The standard deviations of the regression function for the four groups are 55.065, 34.644, 25.996, and 21.710 km, respectively.

We also compute the scatterometer-based $R_{34kt}^{Scat}$ and compare it with best-track R_34kt. Figure 11 shows the comparison of R_34kt for the four categories. Again, a linear regression is applied: $R_{34kt}^{Scat}=c{R}_{34kt}+d$. The regression coefficients (c, d) for the above four groups are (0.411, 100.839 km), (0.206, 166.864 km), (0.709, 97.213 km), and (0.521, 149.350 km), respectively. The standard deviations of the regression function for the four groups are 55.927, 39.221, 52.441, and 48.176 km, respectively.

Combining both relationships—R₀ = aR_34kt + b and $R_{34kt}^{Scat}=c{R}_{34kt}+d$— gives a function $R_0=a(R_{34kt}^{Scat}-d)/c+b$. Figure 12 illustrates sample SLP profiles from Typhoons Doksuri, Khanun, and Haikui at different intensities. Stronger storms exhibit faster radial pressure increases. Even within the same category, R₀, and hence the bogus vortex size, can vary significantly, indicating the need for a tailored approach.

The results of this study are finally compared with those without using the newly proposed method. Figure 13 shows the differences in Fujita SLP between using $R_{34kt}^{Scat}$ and R_max for typhoons (a, b) Khanun (Figure 13a,b) and Haikui (Figure 13c,d), indicating the TC intensity and satellite names that provided scatterometer data. It is seen that differences in SLP between the two bogus vortices for tropical storms (left panels) are generally smaller than stronger intensity hurricanes (right panels). For Typhoon Khanun, the largest differences at tropical storm intensity (Figure 13a) can reach 9 hPa around 200-km radial distances, while those at hurricane intensity (Figure 13b) are 14 hPa around 60-km radial distances. For Typhoon Haikui, the SLP differences can also reach 9 hPa at tropical storm intensity (Figure 13c) and 14–15 hPa at hurricane intensity (Figure 13d). A strong case dependence is found for the differences of Fujita SLP between using $R_{34kt}^{Scat}$ and R_max, suggesting the requirement of an instantaneous vortex initiation in TC forecasts.

5. Discussion and Conclusions

We use satellite microwave scatterometers (HY-2B/C/D, MetOp-B/C, FY-3E) and AHI channel-13 (10.45 µm) brightness temperature to determine typhoon center positions of Typhoons Doksuri, Khanun, and Haikui (2023). The scatterometer-based method locates the near-surface circulation center, while the AHI-based method detects upper-level cloud/rainband centers. Their consistency is high for strong storms. In Haikui’s early stage, the centers diverged, reflecting a vertical tilt under vertical wind shear.

After center determination, we derived the scatterometer-based 34-kt wind radius for all Northwest Pacific TCs in 2022–2023 and built linear regressions linking R₀ to it. Our results confirm that a bogus vortex can be specified by using scatterometer data to define R_34kt, and thus R₀ in Fujita’s formula. Different storms, even at the same intensity category, show large variations, underscoring the importance of a tailored or case-dependent bogus vortex in numerical forecasting.

Compared to traditional methods, the advantages of this approach include: (1) reduced empirical data dependency, (2) improved accuracy in TC sizes, and (3) repeatability of the methods for application in other ocean basins. Specifically, the proposed methods for developing the regression models of R₀ and R_34kt are globally applicable, but the regression coefficients should be regenerated for TCs over the Atlantic and other ocean basins, since TC structures differ across different ocean basins. Application of these models is expected to contribute to a reduction in TC intensity forecast error.

In future work, we will assess the impacts of the scatterometer-based vortex initialization on numerical forecasts. We will also explore vortex initialization for tilted storms and evaluate the forecast impacts of these scatterometer-informed bogus vortices.