To directly observe the evolution of meteorological factors and the EDH during Typhoon Koinu, three wave gliders were deployed southeast of Taiwan Island for continuous monitoring. For easy identification, they were designated WG1, WG2, and WG3. Typical meteorological elements that included Air Pressure (AP), AT, RH, SST and WS were recorded by these wave gliders, with data output at approximately every1 hour. Table 1 shows the data description of wave glider sensors height.

Figure 1a shows the track of Typhoon Koinu and the positions of the three wave gliders (WG1: cyan line, WG2: green line, WG3: purple line), with the start and end times of the observations by each glider indicated. Figure 1b presents a photograph of a wave glider. Typhoon Koinu originated over the Northwest Pacific Ocean on the morning of September 30, 2023. Following a northwestward trajectory, the typhoon underwent steady intensification and attained super typhoon status on October 4. Particularly noteworthy is that during the evening of October 4, an extreme WS of 95.2 m/s was recorded on Lanyu Island, confirming Koinu’s status as the most intense typhoon to make landfall in China in 2023. WG2 traversed the eye area during the first half of October 4, while WG1 and WG3 simultaneously navigated the high-WS region of the typhoon. All times presented herein are converted to Beijing time.

Reanalysis data offer large-area, long-term, and high-resolution meteorological parameters to support typhoon research. Data from the ERA5 dataset from the European Centre for Medium-Range Weather Forecasts (ECMWF) (Hersbach et al., 2020) were used to compute the evaporation duct distributions during Typhoon Koinu. As the ECMWF’s fifth-generation reanalysis product tailored for global climate and weather studies, ERA5 provides data with horizontal resolution of 0.25° × 0.25°for the atmosphere and 1-h temporal resolution. ERA5 data have been used in many earlier studies for investigating evaporation duct properties (Huang et al., 2022; Qiu et al., 2023; Qiang et al., 2024; Feng et al., 2025). For example, Wang et al. (2022) studied Typhoon Phanfone and confirmed that using the ECMWF dataset to calculate EDH during typhoons is a reliable method. Therefore, we utilized ERA5 data, as a supplement to the observational data, to derive the spatiotemporal distribution of EDH and other continuous environmental parameters across a broad maritime area during the lifetime of Typhoon Koinu. Table 1 lists the collection heights, units, and abbreviations of the meteorological data used.

During propagation through the atmosphere, EM waves undergo refraction due to the vertical distribution characteristics of AT and RH. As Equation 1 shows, this phenomenon can be described quantitatively by the refractive index n, which is defined as the ratio of the propagation speed of the EM waves in free space, co, to that in a medium v:

The atmospheric refractive index at Earth’s surface exhibits small numerical values ranging from 1.00025 to 1.0004, meaning that minute variations in the index represent substantial impact on EM wave propagation. To highlight these subtle yet critical variations, atmospheric refractivity N is introduced, which is influenced by meteorological factors and serves to amplify the representation of these changes as shown in Equation 2:

where T is atmospheric temperature, P is total atmospheric pressure, and e is water vapor partial pressure. After obtaining vertical profiles of humidity and pressure, e can be derived from the specific humidity q in Equation 3:

where ϵ=0.622 is a constant (molar mass ratio of water vapor to dry air). To account for Earth’s curvature, the modified refractivity M(z) is used by Equation 4:

where rc is Earth’s radius (m), z is height (m), N (in N-unit) and M(z) (in M-unit) are dimensionless quantities with artificially assigned units that serve as the primary metrics for quantifying refractivity. From (2) and (4), the vertical profile of M(z) requires the profiles of e, P, and T.

In recent years, numerous evaporation duct models have been developed, based on the Liu–Katsaros–Businger (LKB) model (Babin and Dockery, 2002) and the Monin–Obukhov similarity theory (MOST) (Fairall et al., 1996), to calculate the M-profile and EDH. While most evaporation duct prediction models are based on MOST, their specific implementations differ. Among them, the foundational LKB model and the Paulus–Jeske (P-J) model (Jeske, 1973; Paulus, 1985) have gained broad acceptance. To address inherent limitations within the LKB framework, improved models such as NAVSLaM (Frederickson et al., 2000) and the BYC model (Babin et al., 1997) have been developed. This study employed NAVSLaM, developed by the Naval Postgraduate School, which calculates the M-profile from key meteorological parameters to derive EDH. NAVSLaM has been validated extensively as a reliable tool for estimating both EDH and modified refractivity profiles, demonstrating particular utility in the unstable marine conditions prevalent during typhoons.

In a comparative buoy experiment by Babin and Dockery (2002) (Babin and Dockery, 2002) that evaluated four models—the NWA (Liu and Blanc, 1984), Naval Research Laboratory (NRL) (Cook and Burk, 1992), BYC (Babin et al., 1997), and NAVSLaM (Frederickson et al., 2000)—NAVSLaM showed superior agreement with measurements, attributable to its use of directly measured evaporation duct profiles. Through OTH propagation experiments in the South China Sea, Shu et al. (2025) demonstrated that NAVSLaM performs optimally under unstable atmospheric conditions, while the P-J model is more reliable under stable conditions; a finding that aligns with the predominant atmospheric conditions during the typhoon-influenced period of our study. Therefore, NAVSLaM was chosen to derive the spatial distribution of EDH owing to its recognized competency in the predominant atmospheric conditions pertaining during the passage of a typhoon.

Meteorological parameters such as AP, RH, SST, WS, and AT specified at a fixed height above the sea surface are input into NAVSLaM to calculate EDH, and the vertical profiles of WS ( u(z)), temperature ( T(z)), and specific humidity ( q(z)) are expressed using MOST which are given by Equations 5–7:

where z0u, z0θ, and z0q are the roughness lengths for WS, potential temperature, and specific humidity (typically, 1.5 × 10⁻⁴ m), respectively; uτ, θτ, and qτ are the Monin–Obukhov scaling parameters for WS, potential temperature, and specific humidity, respectively; κ is the von Kármán constant; Γdz is the dry adiabatic lapse rate term; L is the Monin–Obukhov length (a measure of atmospheric stability); The relevant scale parameters are calculated using the TOGA COARE 3.0 bulk flux algorithm (Fairall et al., 2003). COARE 3.0 bulk algorithm, upgraded from the 1996-released version 2.5, features optimized stability solution with adjusted stability functions, redefined scalar transfer coefficients based on the conserved mixing ratio, and modified roughness length parameterizations. These revisions slightly boost fluxes at wind speeds >10 m·s⁻¹, with two unevaluated surface gravity wave influence parameterizations added. ψm and ψh are stability correction functions (that vary with atmospheric stability); and ζ=z/L is the Monin–Obukhov stability parameter. Atmospheric stability can also be determined by the sea–air temperature difference. To derive the vertical profile of M(z), the atmospheric pressure profile is calculated as shown in Equation 8:

where g is gravitational acceleration, z1 is the reference height, z2 is any height in the surface layer, R = 287 J/kg/K is the universal gas constant, and Tv is the average virtual temperature between z1 and z2.

Based on numerical methods such as wave optics theory and geometric optics theory, various EM wave propagation models suitable for tropospheric environments have been developed. Notably, evaporation duct profiles are used widely to estimate maritime EM wave propagation characteristics, with representative models including the ray tracing (RT) model (Brekhovskikh, 1980; Curt A. Levis et al., 2011), the parabolic equation (PE) method (Ozgun et al., 2020), and the Advanced Propagation Model (APM).

These models exhibit distinct characteristics. The RT model offers high computational efficiency. The PE method can provide full-wave solutions and account for effects such as multipath propagation and diffraction in range-dependent environments, and it has been applied widely to prediction of tropospheric EM propagation. The APM is a hybrid modeling approach that divides the propagation path into different regions based on parameters such as elevation angle and distance, selecting the most appropriate sub-model for calculation in each region to balance accuracy and overall computational efficiency. For the propagation calculation of radio waves in the complex scenario of evaporation ducts, the PE model in the APM plays a key role. Therefore, the PE model will be elaborated on in detail below. For the partition and detailed description of the APM model, please refer to the relevant literature (Barrios et al., 2002; Derksen, 2016). By relying on the full-wave solution capability of the PE method, the APM can accurately characterize propagation characteristics in complex environments such as range-dependent refractivity fields. The standard PE equation is derived from the Helmholtz wave equation which is given by Equation 9:

where k0=w/c=2π/λ is the wave number of EM waves in free space, λ is wavelength, ψ is a horizontally or vertically polarized electric or magnetic field, M(x,z) is the refractive index of the medium, x is horizontal distance on the ground surface, and u(x,z) is the scalar component of the electric field. The Split-Step Fourier method has the advantages of better numerical stability, short computation time, and high efficiency which is used in Equation 10. It is the preferred method for solving EM wave propagation problems in large-scale spatial ranges, where the field is calculated step by step along the propagation path as shown in Equation 11. The field u(x,z) is computed incrementally along the propagation path:

where F[·] and F−1[·] denote the Fourier transform and inverse Fourier transform, respectively; p=ksinθ, p is the transform variable, θ is the angle deviating from the horizontal direction, and δx is the range increment. In this study, horizontal polarization is adopted, and an omnidirectional antenna is used as the transmission source; the corresponding initial field u(0,z) is expressed as shown in Equation 12:

For details on the construction of this initial field, please refer to the classic technical documents of the parabolic equation model (Barrios et al., 2002; Fairall et al., 2003; Ozgun et al., 2011). The path loss can be calculated by Equation 13:

The APM integrates the strengths of both the RT and the PE models, making it highly suitable for handling complex environments such as range-dependent refractivity fields and irregular terrain. It has been validated extensively and applied across various ducting environments (Wang et al., 2023c; Yang et al., 2024; Shu et al., 2025), demonstrating reliable performance in complex propagation scenarios. Given the horizontal inhomogeneity of evaporation ducts under typhoon conditions, and the complex propagation processes involved, this study employed the APM to simulate the impact of such inhomogeneity on EM wave propagation in typhoon scenarios.

Figure 2 presents the temporal evolution of the meteorological parameters recorded by wave gliders WG1, WG2, and WG3 throughout the typhoon event, together with the calculated EDH. The spatial distributions of the meteorological parameters and EDH simulated using the ERA5 dataset during the typhoon in four different stages are shown in Figures 3–6. At 21:00 on October 1, the wave gliders were located far away from the typhoon, as illustrated in Figures 3a, b, d. Specifically, a distinct typhoon eye structure can be clearly identified in Figures 3a, b. During October 1–3, WS increased from 7 m/s to around 11 m/s owing to peripheral typhoon influence ahead of the typhoon, as shown in Figure 2a. Between 00:00 on October 3 and 00:00 on October 4, WS recorded by WG2 increased from 11 m/s to 25 m/s as WG2 reached the high-WS zone (Figure 4a). As shown in Figures 4b–e, the wave gliders began to enter the high-WS zone on the periphery of the typhoon eye. At 03:00 on October 4, WG2 entered the eye region (22.31°N, 123.34°E; Figure 5a), where WS dropped abruptly to 4.36 m/s and AP decreased to 950 hPa, reflecting the calm core of the storm. At 06:00, WG2 had passed through the core and arrived at the high-WS zone on the opposite side, where WS peaked at 26.5 m/s (Figure 6a). As the typhoon moved northwestward, the wave gliders gradually moved away from the core region, with WS rapidly dropping to 3 m/s by 00:00 on October 5. AP rebounded to 1010 hPa later on October 5 (Figure 2b). During this entire period (October 3–5), sustained rainfall within the inner typhoon region kept RH consistently high, varying narrowly between 90% and 95% (Figure 2c). RH recorded by WG1 and WG3 rose to 90%–95% at around 12:00 on October 1, while RH measured concurrently by WG2 increased from 77% to approximately 90%, then decreased to around 80% at 00:00 on October 2, then increased again to 94% at 00:00 on October 3. As shown in Figures 2d, e, AT decreased from around 30 °C to 26 °C and SST dropped from 30 °C to 26 °C measured by WG2. Rainfall during the typhoon process might be one of the reasons for the temperature reduction; in addition, the latent heat absorbed by the typhoon from seawater evaporation is also an important factor contributing to the drop in SST.

Figure 7 illustrates the spatiotemporal distribution of the surface latent heat flux (SLHF) at different times, which characterizes the degree of seawater evaporation. It can be seen that SLHF exhibits significant differences in distribution across different stages of the typhoon. Before the typhoon’s arrival, SLHF has small absolute values, indicating relatively weak seawater evaporation during this period. With the typhoon’s approach, SLHF shows a distinct “typhoon structure” with a “typhoon eye”. In the outer region of the typhoon, the absolute values of SLHF are large, whereas those inside the typhoon eye are small, which demonstrates that seawater evaporation is intense in the outer typhoon region and weak in the typhoon eye.

This section analyzes the EDH distribution as determined from wave glider measurements and identifies the dominant meteorological factors across different typhoon periods. Comparative analysis was conducted for two distinct periods: the pre-typhoon period (October 1–3) and the during-typhoon period (October 3–5).

During the pre-typhoon period, EDH derived by WG2 decreased from 15 to 10 m, recovered to 15 m, and eventually declined to 7 m between 00:00 on October 1 and 00:00 on October 3, exhibiting a variation pattern directly opposite to that of RH, which synchronously followed an increase–decrease–increase trend, as shown in Figure 2f. Beginning at 00:00 on October 4, when WG2 entered the high-WS zone, EDH increased from 7 to 11 m as WS rose substantially, while WG1 also recorded a peak EDH near 16 m, as shown in Figure 2f. During the first half of October 4, when WG2 traversed the typhoon’s core region, WS and EDH exhibited notable covariation: EDH dropped to 5.7 m in the typhoon eye at 03:00, rose to 11 m in a high-WS area by 06:00, and eventually fell to 3 m as the typhoon departed by 11:00 on October 5, as shown in Figures 4-6. When the typhoon approached, WS superseded RH as the dominant factor controlling EDH, exhibiting positive correlation with EDH variations.

Furthermore, to study the correlations between EDH and meteorological factors, correlation analysis was conducted. The measured data were split into the pre- and during-typhoon periods to determine the correlations between EDH and meteorological factors during different typhoon stages. EDH is not sensitive to AP; therefore, scatter plots and correlations of RH, WS, AT, and SST against EDH before and during the passage of the typhoon are presents in Figure 8. Moreover, Table 2 summarizes the Spearman correlation coefficients between RH, WS, AT, SST and EDH at different typhoon stages. Notably, the data presented in Figure 8 and Table 2 are derived from the observations of WG2.

Before the typhoon’s approach (October 1–3), the Spearman correlation coefficient between RH and EDH was −0.83, as shown in Table 2. Its absolute value substantially exceeded that of other meteorological parameters during the same period, confirming the strong negative correlation. RH played the dominant regulatory factor for EDH before the typhoon’s arrival. This controlling influence is further visualized in Figure 8, where the fitted curve in the scatter plot demonstrates pronounced negative correlation between RH and EDH, indicating that RH played the predominant inhibitory role in modulating EDH in the pre-typhoon period. This suppression mechanism occurs because high RH restrains sea surface evaporation and limits moisture flux across the air–sea interface. This disrupts the formation of the humidity gradient and the maintenance of the refractivity structure that are required for evaporation duct development, which ultimately leads to restriction of EDH. However, it should be noted that the correlation coefficient of 0.7 between AT and EDH only indicates a correlation between the two variables, rather than directly reflecting the actual magnitude of AT’s impact on EDH. Under the extreme weather conditions of a typhoon, changes in WS and RH are relatively drastic. AT exhibited an overall downward trend, which may be affected by rainfall, and its variation trend was correlated with that of RH in the early stage of the typhoon. This is likely the primary reason for the correlation coefficient of 0.7.

During the typhoon process (October 3–5), the consistent corresponding pattern of movement between EDH and WS was confirmed statistically by a strong positive Spearman correlation ( ρ = 0.82). In contrast, the correlation between RH and EDH weakened markedly ( ρ = 0.05). The results clearly indicate that WS replaced RH as the core regulatory factor driving EDH variation during the typhoon’s passage. This shift is attributed to the fact that high WS disrupts sea surface stability, enlarges the effective evaporation area, and rapidly transports moisture upward from the sea surface, which creates a steeper humidity gradient near the sea surface, establishing conditions favorable for EDH extension.

Furthermore, it can be seen from Figure 3c and Figure 7c that the absolute value of SLHF is smaller in regions with high RH, indicating that high RH restrains sea surface evaporation. From Figures 7b–d: as the typhoon approaches, the SLHF exhibits a certain correlation with RH; However, the strong WS associated with the typhoon intensifies sea surface evaporation, the SLHF distribution is mainly correlated with WS. Thus, high WS promotes sea surface evaporation. In summary, the SLHF distribution demonstrates that high RH restrains sea surface evaporation, while high WS promotes it.

A notable phenomenon emerged through comparison of the two periods: although the average WS increased from 10 m/s (pre-typhoon period) to 13.57 m/s (during-typhoon period), the average EDH decreased from 11.9 to 8.7 m, as shown in Figure 2. This apparent contradiction is attributed to the concurrent rise in average RH from 86.2% to 92.7%, which fluctuated persistently above 90% during the typhoon. While the elevated WS seemed to enhance sea surface evaporation, the saturated marine boundary layer, characterized by persistently high RH, suppressed the sea–air humidity gradient and consequently weakened the refractivity gradient that is essential for EDH development. Consequently, the suppressing effect on EDH induced by the elevated RH might have overridden the enhancing effect of increased WS, leading to an overall lower EDH in the during-typhoon period than in the pre-typhoon period.

3.3 Sensitivity of EDH during the typhoon.

To further investigate the influence of WS and RH on EDH, we conducted sensitivity analysis to examine the relationships among WS, RH, and EDH, as shown in Figure 9. EDH is insensitive to AP; thus, it was set to a constant value of 1010 hPa. Additionally, owing to the limited fluctuations in AT and SST during the typhoon, representative values of 27 °C and 28 °C, respectively, were employed.

As shown in Figure 9, statistically significant positive correlation was found between EDH and WS when RH was held constant, whereas EDH decreased with increasing RH under fixed WS conditions. To elucidate their competing influences, we compared EDH at two points: Point A (RH = 70%, WS = 5 m/s) and Point B (WS = 25 m/s, RH = 95%). Results indicate that EDH at Point A was substantially higher than at Point B. This demonstrates that while high WS promotes seawater evaporation and favors a higher EDH, RH plays the more dominant role. At Point B, despite the high WS of 25 m/s, the saturated humidity environment (RH = 95%) strongly suppressed evaporation, ultimately leading to a lower EDH than under the drier, calmer conditions of Point A. This mechanism explains why the observed EDH was lower in the during-typhoon period than in the pre-typhoon period.