Observable Large-Scale Impacts of Tropical Cyclones on the Subtropical Gyre

a. The SSH trough induced by a TC

The baroclinic geostrophic response on an f plane has been investigated in detail in LWS20. Although the TC moving direction and β effects play a negligible role in the generation of the geostrophic response (LWS20), they are vital for the post-TC evolution of the perturbed ocean. The features of the geostrophic response are summarized in the two-layer model presented in Geisler (1970).

In the two-layer model, the initial thickness of the upper layer is set to H₁ and the two-layer density difference Δρ with the upper-layer density being ρ. Assume that a TC with a fixed intensity translates at a constant U toward −X along Y = 0 (Fig. 1). The moving direction is θ north of west; generally, 0 ≤ θ ≤ 90° in the Northern Hemisphere. The TC causes the vertical displacements (i.e., upwelling/downwelling) of the two-layer interface, which involve the near-inertial and geostrophic components. Here the geostrophic component is represented as h and according to LWS20 its governing equation in X = 0 section can be described as

$-\frac{{\partial }^{2}h}{\partial Y^2}+\frac{1}{L_d^2}h=\frac{f}{\rho U{C}^2}{\displaystyle {\int }_{-U{t}_0}^{U{t}_0}{\text{curl}}_z\mathit{\tau }dX},$(1)

where f is the Coriolis parameter, L_d = C/f is Rossby deformation radius, and curl_zτ is the wind stress curl of the TC and the time interval [−t₀, t₀] is the forcing duration of ∼12 h (Price et al. 1994). As seen from Eq. (1), the upwelling/downwelling and the associated temperature, salinity and SSH changes are built by a TC in this forcing duration of ∼12 h via the geostrophic response. Owing to the very short forcing duration, the associated SSH changes seem to be generated abruptly at the passage of the TC, resulting in the existence of the artificial smoothness by using merged altimetry datasets to observe them (Lu et al. 2023).

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Schematic description of the TC-induced SSH trough. The moving direction, i.e., the −X direction, is θ north of west. The black dashed line and black dots denote the track and 6-hourly TC centers, respectively. The width and length of the trough are 2L_h and L_track.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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As seen from Eq. (1), the positive curl_zτ must lead to positive h and further the SSH (η) trough due to η = −hΔρ/ρ. For a constant forcing along the track, ∂h/∂X = 0 and ∂η/∂X = 0, so the baroclinic response manifests the along-track thermocline ridge and the along-track SSH trough. The geostrophic streamfunction and potential vorticity (PV) can be defined as ψ_TC = −g′h/f = gη/f and $q_{\text{TC}}={\partial }^2{\psi }_{\text{TC}}/\partial Y^2-(1/L_d^2){\psi }_{\text{TC}}$, respectively, where g is gravity acceleration and g′ = gΔρ/ρ is the reduced gravity. Owing to ∂h/∂X = 0, both ∂ψ_TC/∂X and ∂q_TC/∂X also vanish, suggesting that ψ_TC and q_TC also possess along-track distribution.

As revealed in LWS20, the thermocline ridge or the SSH trough due to the upwelling is confined within |Y| ≤ L_h, sketched in Fig. 1, where the cross-track length scale L_h ≈ 100 km. The thermocline trough or the SSH rise associated with the downwelling is very weak. As can be seen from Fig. 1, a TC has the ability to perturb mesoscale eddies (large-scale ocean) in the cross-track (along-track) direction and the total track length (L_track) play a key role in the large-scale impacts. Generally, L_track ranges from several hundred to several thousand kilometers so that the large-scale impacts should not be ignored.

b. Quasigeostrophic motions after the TC passage

Three processes are involved in Eq. (3):

1. Quasigeostrophic adjustment driven by J(ψ_TC, q_basin) and J(ψ_basin, q_TC). Since ψ_basin and q_basin is independent of the TC while ψ_TC and q_TC have along-track patterns, the contours of ψ_TC(ψ_basin) and q_basin(q_TC) must not coincide so that J(ψ_TC, q_basin) ≠ 0 and J(ψ_basin, q_TC) ≠ 0. This suggests that the large-scale quasigeostrophic adjustment must occur after the TC passage.

2. Forced baroclinic Rossby waves. If the pre-TC ocean was presumed to be quiescent, Eq. (3) would be reduced to

   $\frac{\partial q_{\text{TC}}}{\partial t}+J({\psi }_{\text{TC}},q_{\text{TC}})+\beta \frac{\partial {\psi }_{\text{TC}}}{\partial x}=0,$(4)

   which depicts forced baroclinic Rossby waves.
3. Free baroclinic Rossby waves. If the ocean is not passed by a TC, its motion is dominated by

   $\frac{\partial q_{\text{basin}}}{\partial t}+J({\psi }_{\text{basin}},q_{\text{basin}})+\beta \frac{\partial {\psi }_{\text{basin}}}{\partial x}=0.$(5)

This equation describes free baroclinic Rossby waves emanating from the east boundary of the ocean basin.

c. The linear baroclinic Rossby waves

After a TC passage, the evolution of the induced SSH trough should be closely related to its moving direction denoted by θ in Fig. 1. For θ = 0°, L_dk_x ≈ L_d/L_track ≈ 0 and $C_p=C_g=-\beta L_d^2$, suggesting that in this case the SSH trough moves westward at the speed of $\beta L_d^2$ as the nondispersive Rossby waves. With θ increasing from 0° to 90°, L_dk_x gradually increases and causes the increasing C_p − C_g. The SSH trough thus manifest as dispersive Rossby waves, and the dispersion increases with the increasing θ. In fact, L_dk_x reaches its maximum L_d/2L_h for θ = 90°, still smaller than 1. Thus, the SSH trough always moves westward as long waves. If k_x is fixed, the increase of L_d with the decreasing latitude suggests that the northward SSH trough has the stronger dispersion at the lower latitude. The above conclusions can also be interpreted by $\beta (\partial \hspace{0.17em}{\psi }_{\text{TC}}/\partial x)$ in Eq. (4), i.e., βυ, where υ is the northward component of geostrophic currents. Because υ increases with the increasing θ (Fig. 1), the increased βυ suggests the enhanced Rossby wave dispersion. Similarly, υ increases with the decreasing latitude for the fixed ∂η/∂x, also causing the enhanced Rossby wave dispersion at the lower latitude.

a. Model configuration

To illustrate the evolutions of the SSH trough for different θ, we configured OGCM experiments on the β plane at the central latitude of 15°N using Hybrid Vertical Coordinate Ocean Model (HYCOM; Bleck 2002). The vertical mixing in the numerical experiments was chosen to be the K-profile scheme (Large et al. 1994). The advection–diffusion equations for temperature and salinity were treated by a variant (Drange and Bleck 1997) of the MPDATA scheme presented by Smolarkiewicz (1984). The horizontal resolution was 10 km, and the model was discretized using a 30-layer stretched vertical grid. The temperature and salinity were specified by Argo dataset ISAS20 (Gaillard et al. 2016) at 15°N, 152°E in March 2015. The model was run using the same grid in the (X, Y) coordinate but the results were displayed in the (x, y) coordinate. The Coriolis parameter on the β-plane experiments was set to f = f₀ + β₀y = f₀ + β₀ (−X sinθ + Y cosθ), where f₀ = 3.77 × 10⁻⁵ s⁻¹ and β₀ = 2.21 × 10⁻¹¹ m⁻¹ s⁻¹ for 15°N. To suppress the near-inertial waves, a radiation boundary condition was imposed along the four boundaries. In addition, we used a weak forcing with a small U to represent the real TC because near-inertial waves are hardly generated for U < C (Geisler 1970). We formulated the weak TC using the double exponential profile model in Willoughby et al. (2006) and made it move from X = 500 to −500 km at U = 6.94 km h⁻¹. The maximum wind speed (V_max) of this weak TC was specified to be 25.38 m s⁻¹. The induced geostrophic response is virtually the same as that forced by the TC in LWS20 with V_max = 35 m s⁻¹ and U = 13.2 km h⁻¹ since the geostrophic response is directly proportional to $V_{\text{max}}^2/U$, as seen from Eq. (1). The numerical experiments are listed in Table 1. The initial geostrophic response was generated on the f plane by the TC forcing (Init_GR). Then we examined the 60-day evolution of this geostrophic response on the β plane without any atmospheric forcing. Note that the evolution time here is slightly different from the passage time of the TC. This treatment is convenient to examine how the evolutions of the same SSH trough are affected by the moving direction, downwelling and nonlinearity (Table 1). In the LIN_NnoDown experiment, the directly omitted downwelling does not cause the substantial changes of the remaining SSH and temperature–salinity anomaly because according to the classical theory of geostrophic adjustment, if the perturbation scale is far larger than L_d (Gill 1982; Huang and Jin 2002), the pressure perturbation (here the omitted downwelling) will be largely retained and the geostrophic currents will adjust to the pressure.

Table 1.

Experiment descriptions.

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We primarily demonstrate large-scale features based on the simulated SSH. Only the temperature anomaly, PV anomaly (PVA) and northward currents output from LIN_N were analyzed for the vertical structure of the evolved geostrophic response. The temperature anomaly and PVA were estimated relative to the initial values in quiescent ocean by using the methods in LWS20.

In addition to the above idealized experiments, the evolution of the SSH trough induced by Typhoon Higos (2015) with the real track and typhoon forcing was simulated to compare with altimetry observations. Most of the configuration for this case was the same as that in the idealized experiments. However, the initially quiescent ocean with the stratification at (13°N, 152°E) in February 2015 was forced by the typhoon with the real track and intensity. Another difference was that the model was configuration in longitude–latitude coordinate and the horizontal resolution was 0.08°.

b. The jet and the SSH rise emerged from linear evolutions

More clearly, the evolutions of the SSH trough depend heavily on the moving direction (Fig. 2). The SSH trough for θ = 0° virtually maintained the initially generated state (Figs. 2a,b) because it propagates as nondispersive long Rossby waves (section 2c). As θ = 45° or 90°, the initially 200-km-width SSH trough moved but dispersed significantly toward the west (Figs. 2c–f). Furthermore, after the short-term evolution a small-width along-track SSH rise emerged behind the respective trough (Figs. 2c,e). Subsequently, a secondary, weak along-track SSH trough was generated on the tail of the SSH rise during the longer evolution (Figs. 2d,f). The higher SSH gradient between the primary SSH trough and the SSH rise can be viewed as an along-track jet (Figs. 2c–e). In essence, these phenomena are the consequence of dispersive Rossby waves. As indicated in Eqs. (6) and (7), the lower wavenumber Rossby waves move westward faster than the higher wavenumber Rossby waves. Thus, for each y-section SSH trough, the longer wave components traveled faster so that the SSH gradients at the west (east) side were weakened (deepened). The deepened SSH gradient at the east side of the primary SSH trough forms an along-track jet, which is very similar to that of nonlinear self-advection occurring in the β-plane evolution of an isolated eddy (Early et al. 2011; McWilliams and Flierl 1979; Smith and O’Brien 1983). Since the higher wavenumber Rossby waves move more slowly, during the evolution they gradually seceded from the initial wave packet, i.e., the primary SSH trough, and formed Rossby wave wakes including the SSH rise and the secondary SSH trough. This process is the same as the emerged Rossby wave wakes behind the isolated eddy evolution (Early et al. 2011; McWilliams and Flierl 1979).

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The linear evolutions of the SSH trough for (a),(b) θ = 0°; (c),(d) θ = 45°; and (e),(f) θ = 90°. (left) The 30-day evolution and (right) the 60-day evolution. The pink lines denote the track of the TC, and the gray lines in (c)–(f) denote the section of y = 0.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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According to the nature of dispersive Rossby waves, the widths and strengths of the primary SSH trough, the SSH rise, and the jet for θ = 45° or 90° should vary with the time, represented in Fig. 3 by the features of LIN_NW and LIN_N in y = 0 section. With the dispersion of the primary SSH trough, its width (L_trough) gradually grew (Fig. 3a). At the beginning, the width of the SSH rise (L_rise) was very large, ∼800 km, due to the contribution of downwelling (Fig. 3a). Then L_rise rapidly decreased in 10 days and then slowly decreased to an approximately steady value of 200–300 km. Owing to the wider initial perturbation for θ = 45°, L_trough and L_rise in this case were always wider than those for θ = 90° (Fig. 3a). The strength of the primary SSH trough, denoted by the minimum SSH (${\eta }_{\text{trough}}^{\text{min}}$), gradually decayed with the dispersion (Fig. 3b). In contrast, the strength of the SSH rise, denoted by the maximum SSH (${\eta }_{\text{rise}}^{\text{max}}$), gradually grew (Fig. 3c). Because of the appearance of the secondary SSH trough (Fig. 2f), $\hspace{0.17em}{\eta }_{\text{rise}}^{\text{max}}$ for θ = 90° turned to decrease after 50 days. The jet strength, denoted by the maximum geostrophic current near the jet ($U_g^{\text{max}}$), reached the peak of 50 cm s⁻¹ at approximately 10 days but gradually decayed with the dispersion after 30 days. In addition to the ignorable contribution of downwelling illuminated in the next subsection, all the changes shown in Figs. 3c and 3d mainly result from the dispersion of the primary SSH trough, consistent with the linear theory in section 2c. In particular, the dispersion for θ = 90° is remarkably stronger than that for θ = 45° (Fig. 3b), causing the rapider growth (decay) of the rise (jet) strength (Figs. 3c,d). It needs to be emphasized that the widths and strengths of the primary SSH trough, the SSH rise and the jet are clearly linked with the latitude (Figs. 2c–f) because of the higher dispersion at lower latitude (section 2c).

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Widths and strengths of the primary SSH trough, the SSH rise, and the jet for θ = 45° and 90° in the y = 0 section: (a) the widths of the primary SSH trough (L_trough) and the SSH rise (L_rise); (b) the strengths of the primary SSH trough denoted by the minimum SSH (${\eta }_{\text{trough}}^{\text{min}}$); (c) the strengths of the SSH rise denoted by the maximum SSH (${\eta }_{\text{rise}}^{\text{max}}$); (d) the strengths of the jet denoted by the maximum geostrophic current near the jet ($U_g^{\text{max}}$).

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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As classified in Camargo et al. (2007b), most of the moving directions for typhoons below 20°N belongs to θ ≤ 45° while the northward-moving typhoons mainly occurs above 20°N. These facts imply that the SSH trough in the WNP should usually disperse very slowly. In other words, the strengths and widths of the large-scale signals may vary slowly and not affect severely their observability in the WNP.

c. Contribution of downwelling

Figure 3a shows that the downwelling seemingly makes a contribution to the SSH rise. This contribution is evaluated by comparing the outputs of LIN_N and LIN_NnoDown. The simulated SSH trough looks like an athletics track (Fig. 4a) and the wider downwelling was located outside the narrower upwelling zone (Fig. 4b). However, the strength of the downwelling, with the maximum SSH of only ∼1.8 cm, was far smaller than that of the upwelling, consistent with Price (1981) and Jaimes and Shay (2015). The simulated evolution of the SSH trough by LIN_NnoDown (Figs. 4c,e) was almost the same as that by LIN_N (Figs. 2e,f). By contrast, in the sense of the linear dynamics, Figs. 4d and 4f approximately represent the evolution of the SSH rise in the downwelling zone, which was rather different than the evolution of the total SSH response in Figs. 2e and 2f. Moreover, the SSH contribution of downwelling was smaller than 1 cm during the evolution. Altogether, the Rossby wave wakes such as along-track SSH rise and jet primarily results from the dispersion of the primary SSH trough and the contribution of downwelling is ignorable.

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(a),(c),(e) SSH (cm) output from LIN_NnoDown and (b),(d),(f) SSH differences of LIN_N-LIN_NnoDown. The (top) 0-, (middle) 30-, and (bottom) 60-day evolutions. The pink line denotes the track of the TC. The start and end centers of the TC is plotted in (a) and (b) by “+”.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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d. Effects of nonlinearity

The linear evolutions in Fig. 2 are in fact dominated by the part ∂q_TC/∂t + β∂ψ_TC/∂x = 0 in Eq. (4); thus, the nonlinear effects of J(ψ_TC, q_TC) are omitted. Figure 5 shows the nonlinear evolutions to compare with Fig. 2. The results reveal that although Rossby wave dispersion is the main mechanism, the nonlinearity plays two roles in the evolutions. First, the nonlinear effects make the cyclonic ocean eddies (COEs) in the SSH troughs and the anticyclonic ocean eddies (AOEs) in the SSH rises to be formed because the local high concentrated PV can absorb the ambient like-sign PV to generate large coherent eddies by nonlinear interaction (McWilliams 1984). Consequently, the amplitudes of these COEs (AOEs) were slightly larger than the strengths of the corresponding SSH troughs (rises) in Fig. 2, while the strengths of the SSH troughs (rises) without eddies in Fig. 5 were obviously weaker than the corresponding strengths in Fig. 2. Under the action of the nonlinearity, the jet in Figs. 5c and 5d broke down finally and the COEs (AOEs) in the along-track SSH trough (rise) turned to be isolated. In this circumstance, the along-track patterns were not typically observable again. Second, similar to the self-advection in the evolution of an isolated eddy (Early et al. 2011; Smith and O’Brien 1983), the nonlinear advection associated with the along-track jet may inhibit Rossby wave dispersion. This inhabitation leads to the disappearance of the secondary SSH trough in Fig. 5d as compared with Fig. 2d. As explained in Early et al. (2011), Rossby wave dispersion drives the high SSH pattern toward the east but for θ = 45° the nonlinear advection linked with the jet does toward the northwest, so the nonlinear advection counteracts with Rossby wave dispersion. For θ = 90° the northward nonlinear advection has no effect on Rossby wave dispersion. For this reason, Rossby wave dispersion is very clear in Figs. 5e and 5f. By contrast, the interaction of the isolated COEs and AOEs dominates the evolution in Figs. 5c and 5d due to the inhibited Rossby wave dispersion.

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The nonlinear evolutions of the SSH trough for (a),(b) θ = 0°; (c),(d) θ = 45°; and (e),(f) θ = 90°. (left) The 30-day evolution and (right) the 60-day evolution. The pink lines denote the track of the TC.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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e. Vertical structure

The vertical structure of the evolution is illustrated by temperature anomaly, υ and PVA in y = 0 section output from LIN_N (Fig. 6). A salient feature is that the TC-induced impacts are mainly restricted in the upper thermocline, which has been noted in LWS20. The initial vertical patterns (Figs. 6a,d,g) are almost the same as those in LWS20. The maximum temperature anomaly appeared at the depth of ∼150 m and the temperature response can reach 400 m (Fig. 6a). In addition, the geostrophic currents were located in 0–200-m depth (Fig. 6d), while the positive PVA in 100–200-m depth (Fig. 6g). With the evolution, the cold temperature anomaly and positive PVA in the primary SSH trough gradually decayed and the warm (cold) temperature anomaly and negative (positive) PVA in the SSH rise (the secondary trough) emerged (Figs. 6b,c,h,i). Accordingly, the strong geostrophic currents were also associated with the SSH rise and the secondary SSH trough (Figs. 6e,f). The TC-induced effects were still located in the upper thermocline although they slightly penetrated deeper in the vertical (Fig. 6). This shallower structure of the TC-induced impacts has a profound effect on the westward propagation speed of the observed large-scale signals, which will be discussed in section 5c.

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(a)–(c) Temperature anomaly (°C), (d)–(f) υ (m s⁻¹), and (g)–(i) PVA (10⁻¹⁰ m s⁻¹) in the y = 0 section output from LIN_N. The (left) 0-, (center) 30-, and (right) 60-day evolutions, respectively. Note that PVA has no values in mixed layer. The dashed black lines denote the track of the TC.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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a. Data

The best track dataset, International Best Track Archive for Climate Stewardship (IBTrACS v04r00; Knapp et al. 2010), was used to derive V_max and to calculate U and L_track for the typhoons (Table 2). The typhoon intensity was denoted by the Saffir–Simpson scale categories from tropical storm (TS) to category 5. The initial SSH decreases are primarily located within ±L_h of the track (Fig. 1) so that a coverage named as COVER100 was calculated based on the track by setting L_h = 100 km (LWS20). The observed large-scale signals were identified from all-satellite-merged SSH dataset with 0.25° resolution downloaded from Copernicus Marine and Environment Monitoring Service (CMEMS). The along-satellite-track SSH data also from CMEMS were adopted to analyze the SSH changes along satellite tracks.

Table 2.

The mean SSH changes in COVER100 ($\overline{\mathrm{\Delta }\eta }$) over 4°–20°N, 122°E–180°. The mean, maximum, and minimum values of V_max and U as well as L_track in this region are given.

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b. Methods

2) Mean SSH change in COVER100

In some cases, the large-scale signals cannot be identified from merged altimetry datasets. To quantify the TC-induced contributions, we estimated the mean SSH change ($\overline{\mathrm{\Delta }\eta }$) in the COVER100. We only calculated $\overline{\mathrm{\Delta }\eta }$ over 4°–20°N, 122°E–180° caused by the typhoons staying in this region more than 2 days because they have L_track of over 500 km. There are 18 typhoons satisfying the above criteria among a total of 27 typhoons in 2015 (Table 2). Among the 18 typhoons, the large-scale signals were observable for 11 cases but unobservable for 7 cases (Table 2). The pre-TC and post-TC SSH patterns for the unobservable cases are given in the online supplemental material.

Here the procedure to estimate $\overline{\mathrm{\Delta }\eta }\hspace{0.17em}$ is demonstrated using the case of Typhoon Mekkhala (Fig. 7a). If a typhoon stayed N days in 4°–20°N, 122°E–180°, we first partitioned the COVER100 in each day into N subregions (Fig. 7a). Then the mean SSH from −30 to 30 days in each subregion was estimated as $\overline{\eta }(i,j)$, where 1 ≤ i ≤ N and −30 ≤ j ≤ 30. As demonstrated by $\overline{\eta }(2,j)$ in Fig. 7b, the artificial smoothness related to optimal interpolation used in the merged altimetry datasets lead to the gradually decrease near t = 0 rather than theoretically abrupt decrease (Lu et al. 2023). According to the nature of the optimal interpolation (Pujol et al. 2016), the ranges of the artificial smoothness should be approximately symmetrical about t = 0. Thus, we estimated the mean SSH change in a subregion as $\mathrm{\Delta }{\overline{\eta }}_i=\overline{\eta }(i,D)-\overline{\eta }(i,-D)$. Further, the mean SSH change in the COVER100 was $\hspace{0.17em}\overline{\mathrm{\Delta }\eta }={{\displaystyle \sum }}_{i=1}^N(\mathrm{\Delta }{\overline{\eta }}_i\times {\text{NG}}_i)/{{\displaystyle \sum }}_{i=1}^N{\text{NG}}_i$, where NG_i is the grid number in i subregion. The estimated $\overline{\mathrm{\Delta }\eta }$ is obviously sensitive to the choice of D (Fig. 7c). A smaller D cannot circumvent the artificial smoothness thus underestimating the TC-induced impacts. A larger D may enable the effects of other processes to be counted in. A reasonable choice was D = 10 days based on the sensitivity tests for all the cases in Table 2.

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The procedure to estimate $\overline{\mathrm{\Delta }\eta }$ for Typhoon Mekkhala. (a) Partitioning the COVER100 into subregions. (b) $\overline{\eta }(2,j)$, where the gray line denotes the passage time of the typhoon (t = 0) and the blue line is t = ±10 days. (c) The effect of D on $\overline{\mathrm{\Delta }\eta }$ .

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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a. Typhoon Mekkhala, θ ≈ 0°

A weak typhoon Mekkhala appeared in January 2015, and moved almost westward (Fig. 8), so θ ≈ 0° for this case. The preexisting mesoscale variability is so low (Fig. 8a) that the along-track SSH trough induced by this weak typhoon with TS scale is identifiable (Figs. 8b,c). The SSH trough mainly occurred in the COVER100, confirming that the cross-track length scale is ∼100 km. As seen in Table 2, the induced large-scale impacts were considerable due to the larger L_track (1738 km) and the moderate $\overline{\mathrm{\Delta }\eta }$ (−6.22 cm). Although the typhoon intensity is the same during its lifetime, the changed U caused a series of COEs (Fig. 8b). The SSH trough with many COEs embedded is very similar to the simulated results in Figs. 5a and 5b. These COEs were entangled with the ambient eddies a month later after the typhoon so that the SSH trough cannot be clearly identified again (Fig. 8d). In summary, this case validates that the large-scale signal for θ ≈ 0° is a SSH trough with a series COEs.

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Altimetry-based evolution of the SSH (cm) trough induced by Typhoon Mekkhala. The typhoon track (gray line), 6-hourly typhoon center (color dots), and intensity (color in the dots) are plotted in each panel. The color dots in the legend in (b) denote the typhoon intensity category on the Saffir–Simpson scale. The typhoon time (month/day/hour) is plotted in each panel. The pink dashed lines delineate the COVER100.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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b. Typhoons Bavi and Mayasak, θ ≈ 20°

As pointed out in section 2c, once θ increases from 0°, Rossby wave dispersion should emerge in the evolution of the SSH trough. Owing to no SSH rise and no jet for θ ≈ 0° (Figs. 2a,b, 5a,b, and 8b,c), it is necessary to answer for what minimum θ the SSH rise and jet will emerge. The supplemental numerical experiment show that the SSH rise and jet appear for θ = 15° (Fig. S8 in the online supplemental material). This result is also validated by altimetry observation for typhoons Bavi and Mayasak in March 2015. These two typhoons made a long journey over the WNP (Figs. 9b,c); both of their moving directions are θ ≈ 20°.

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(a)–(c) Altimetry-based evolution of the SSH (cm) trough induced by Typhoons Bavi and Maysak. SSHT1 is the SSH trough induced by previous Typhoon Higos, while C1 and C2 are the COEs by Higos. Two COEs (C3 and C4) are generated by Maysak. The pre-TC SSH field is plowed by Bavi and Maysak into two large SSH rises (SSHR1 and SSHR2) and one SSH trough (SSHT_large), the borders of which are B1 and B2. A small SSH trough (SSHT2) is formed by Bavi and Maysak. Note that SSHT_large denotes the entire SSH trough below B1 and B2 in (c). The typhoon track (gray line), 6-hourly typhoon center (color dots), and intensity (color in the dots) are plotted in each panel. The color dots in the legend in (a) denote the typhoon intensity category on the Saffir–Simpson scale. The birth and death times (month/day/hour) of Bavi and Maysak are given in (b) and (c), respectively.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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Prior to Bavi, the eddy activities were very weak except the along-track SSH trough (SSHT1) induced by Typhoon Higos (Figs. 9a and 10a–d). Although all the intensities of Bavi were the Saffir–Simpson scale of TS, most of the SSH trough induced by Bavi was visible (Fig. 9b). The mesoscale variability underlying Maysak was slightly stronger than that below Bavi and initially Maysak moved overlying a part of the SSH trough (SSHT2) induced by Bavi (Fig. 9c). However, the higher intensities of Maysak also generated an observable SSH trough (Fig. 9c). With the evolution of the SSH trough induced by Bavi, an along-track SSH rise and an along-track jet emerged clearly and both of them tended to be strengthened (Fig. 9c). An along-track jet and an along-track SSH rise seems to be formed from the SSH trough induced by Maysak but they were not very clear (Fig. 9c). Compared with Figs. 2 and 5, the secondary SSH troughs induced by the two typhoons cannot be identified possibly because of their weak strengths and the existed background mesoscale variability. Consistent with the simulated results, the strengths of the primary SSH troughs induced by the two typhoons were gradually weakened due to Rossby wave dispersion. Consequently, the weakened SSH trough was easily obscured by the background eddy field thus being unobservable (Figs. 9b,c). By contrast, the observed lifetimes of the jet and the SSH rise are far longer than that of the SSH trough (Fig. 9c).

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(a)–(d) Altimetry-based and (e)–(h) simulated evolutions of the SSH (cm) trough induced by Typhoon Higos. The typhoon track (gray line), 6-hourly typhoon center (color dots) and intensity (color in the dots) are plotted in each panel. The color dots in the legend in (a) denote the typhoon intensity category on the Saffir–Simpson scale. The typhoon time (month/day/hour) is plotted in each panel. The pink dashed lines delineate the COVER100.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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Interestingly, the observed results for typhoons Bavi and Maysak resemble the linear evolutions very much in Figs. 2c and 2d rather than the nonlinear evolutions in Figs. 5c and 5d. During the nonlinear evolutions (Figs. 5c,d), the nonlinearity should cause a series strong COEs (AOEs) in the SSH trough (rise), which cannot be found in the observed evolutions, seeing Figs. 9c and 13a below. In particular, two COEs, C3 and C4, directly generated by Maysak were rapidly disrupted by Rossby wave dispersion. Unlike the simulated evolutions, in theory the observed evolutions must exist the effects of the free Rossby waves [Eqs. (3)–(5)]. Similar to the dispersion of forced Rossby waves, the dispersions of the free Rossby waves may inhibit the nonlinearity in the evolutions of the SSH trough.

As seen from the observed along-track signals for typhoons Bavi and Maysak (Fig. 9), the SSH field in the WNP was clearly plowed into three parts: the large SSHT below the borders B1 and B2 (SSHT_large) including SSHT1 and SSHT2, the SSHR above the border B1 (SSHR1) and the SSHR semiclosed by the border B2 (SSHR2).

c. Typhoon Higos, θ ≈ 40°

Owing to the low SSH variability prior to Typhoon Higos (Fig. 10a), an SSH trough with two COEs (C1 and C2) was clearly seen (Figs. 10b,c). The moving direction was θ ≈ 40°, so the observations are well comparable to the idealized experiments for θ = 45°. Similar to Figs. 2c and 2d, the along-track jet emerged from the evolution of the SSH trough is discerned in Figs. 10b–d. However, the SSH rise seems visible but not very clear (Fig. 10c), possibly because the nonlinearity inhibits the forced Rossby wave dispersion (Fig. 5c). By comparing Fig. 5c with Fig. 10d, a remarkable difference can be found in westward propagation of the jet. After 30-day propagation, the simulated jet was still near the track (Fig. 5c), while the observed jet far away the track (Fig. 10d). It was hypothesized that the emerging COEs make the simulated jet slow down. To test this hypothesis, EXP_Higos (Table 1) was implemented and the SSH trough with two COEs were reproduced well (Figs. 10e,f). As indicated in Lu et al. (2023), the SSH extreme within the TC-induced COE can be viewed as the strength of the TC-induced geostrophic response. The simulated COE extreme for C1 (∼−14 cm) was slightly lower than the observed value (∼−12 cm) and the simulated value for C2 was well consistent with that from altimetry observation (Fig. 11a), suggesting that the geostrophic response to the typhoon was well simulated. However, the westward propagation speeds of the COEs were obviously slower (Figs. 10g,h) than what was observed in Figs. 10c and 10d, also seeing Fig. 11b.

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Comparisons of (a) COE SSH extremes and (b) westward propagation speeds derived from the observed and simulated COEs generated by Typhoon Higos. C1 and C2 are generated on 11 and 8 Feb, denoted by the dashed lines. Westward propagation speeds are estimated using the COE centers.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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If the westward propagation speeds of forced and free Rossby waves are $c_g^{\text{TC}}$ and $\hspace{0.17em}{c}_g^{\text{Basin}}$, respectively, according to the linear theory in White (1977) and Qiu et al. (1997), the observed westward propagation speeds should be $c_g^{\text{TC}}+c_g^{\text{Basin}}$. However, the simulations only describe the forced Rossby waves so that the simulated westward propagation speed is $c_g^{\text{TC}}$. In this sense, the slower simulated speed seems reasonable. Equations (6) and (7) indicate that $c_g^{\text{TC}}$($c_g^{\text{Basin}}$) is a function of $-\beta L_d^2$ ($-\beta L_d^{\text{Basin}}{}^2$), where $L_d^{\text{Basin}}$ is basin-scale Rossby deformation radius. As shown in section 3e, the geostrophic response occurs in the upper thermocline of ∼100–200-m depth, while the basin-scale signals occur in the main thermocline of ∼500–800-m depth, causing the L_d ≈ 60 km to be smaller than $L_d^{\text{Basin}}\approx 90\text{km}$ and further $c_g^{\text{TC}}<c_g^{\text{Basin}}$. Global observations in Chelton and Schlax (1996) and Chelton et al. (2007) indicate that $c_g^{\text{Basin}}$ can be estimated by $-\beta L_d^{\text{Basin}}{}^2$.

Using $L_d^{\text{Basin}}$ derived from Chelton et al. (1998), $-\beta L_d^{\text{Basin}}{}^2$ is estimated for C1 and C2 (Table 3). Assuming that we take the simulated westward propagation speeds of C1 and C2 as $c_g^{\text{TC}}$, the westward propagation speeds predicted by White (1977) and Qiu et al. (1997) are $-\beta L_d^{\text{Basin}}{}^2+c_g^{\text{TC}}$. However, Table 3 shows that the observed westward propagation speed is close to $-\beta L_d^{\text{Basin}}{}^2$ and considerably lower than $-\beta L_d^{\text{Basin}}{}^2+c_g^{\text{TC}}$.

Table 3.

Observed and simulated westward propagation speeds. The $-\beta L_d^{\text{Basin}}{}^2$ is estimated by $L_d^{\text{Basin}}$ derived from Chelton et al. (1998). The observed and simulated results is estimated by the mean values between 23 Feb and 15 Mar in Fig. 11b.

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This inconsistency in the observed and theoretical westward propagation speeds may be because the evolution of the SSH trough in a real ocean exists the vertical interactions between the forced and free Rossby waves. As hypothesized in section 5b, at least one of the roles of the vertical interaction is that free Rossby waves inhibit the nonlinearity in the SSH trough as the forced Rossby waves. For the Higos case, the inhibited nonlinearity can be seen from the fact that the simulated SSH trough was broken down early (Figs. 10g,h) but the observed SSH trough was long-lived (Figs. 10c,d). Unfortunately, the linear theory of White (1977) and Qiu et al. (1997) fails to treat the vertical interactions because in the theory the forced and free Rossby waves were assumed to occur in the same isopycnal layer. Indeed, a theory is required to understand the role of free Rossby waves but is beyond the scope of this study. Note that the observed strengths (Fig. 11a) and width (Fig. 10b) of the SSH trough are well consistent with the theory in LWS20 and the simulated results in Figs. 10e–h. Thus, the free Rossby waves may only affect the evolution of the SSH trough, not affecting the features related to the generation of the SSH trough such as its strength and width.

d. Typhoon Champi, θ ≈ 90°

After its formation on 14 October 2015, Typhoon Champi first moved westward as a weak and fast-moving typhoon and then turned to the north as a strong and slow-moving typhoon on 17 October 2015 (Fig. 12a). The observed SSH response induced by the westward-moving Champi was insignificant, while a strong SSH trough with a strong COE (C7) embedded appeared after 17 October 2015 (Fig. 12b). The northward SSH trough was approximately 1000 km long, very suited for validating the simulated cases in for θ ≈ 90° (Figs. 2e,f and 5e,f). Consistent with the simulated results, an along-track jet (B4) and an SSH rise (SSHR4) was generated on the east side of the SSH trough (Figs. 12a,b). Owing to the higher latitude, the Rossby wave dispersion is very weak (section 2c). However, after the long-term dispersion, the strengths of the SSH trough and C7 were still weakened and obscured by the ambient eddy field (Fig. 12c). The jet and the SSH rise were more robust than the SSH trough, less affected by the ambient eddy field (Fig. 12c), in line with the observation for Typhoon Bavi (Fig. 9c). As shown in Figs. 2 and 3, the strengths of the SSH rise and the jet decay due to the emerged secondary SSH trough. This can be supported by the fact that the strengths of the SSH rise and the jet in Fig. 12c were not to increase in contrast with Fig. 12b. However, we cannot assert that the secondary SSH trough on the tail of the SSH rise was the result of the Rossby wave dispersion (Fig. 12c).

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(a)–(d) Altimetry-based evolution of the SSH (cm) trough induced by Typhoon Champi. The typhoon track (gray line), 6-hourly typhoon center (color dots), and intensity (color in the dots) are plotted in (a). The color dots in the legend in (a) denote the typhoon intensity category on the Saffir–Simpson scale. The typhoon time (month/day/hour) is plotted in (a). The SSH rise (SSHR4), the jet (B4), and a COE (C7) are generated by this typhoon.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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Before Typhoon Champi, SSHR3 and B3 were formed and strengthened by several typhoons in July–August, seeing Fig. 15 below. Champi plowed the previous SSHR3 and B3 to generate SSHR4, B4, and C7 (Figs. 12a,b). Owing to the long-lived nature of geostrophic balance, the large-scale SSH patterns plowed by the previously observed large-scale signals moved westward until they encountered the Kuroshio. Most of them lasted until at least 31 December 2015; in particular, SSHR4 and B4 persisted until 15 February 2016 (Figs. 12c,d). Subsequently, SSHR4 degraded to an AOE, continuously moved westward and finally merged with the ambient AOE in mid-July 2016 (Fig. S9). It is clear that the impacts of Champi lasted about 9 months, from mid-October 2015 to mid-July 2016 (Fig. 12 and Fig. S9). The long-lived impacts mean that even if the local ocean is not passed over currently by any TC, the upper dynamics still can be affected by previous TCs. Although the TC-induced large-scale impacts should persist for long, the lifetime of the impacts induced by a specific typhoon is uncertain because it is determined by the distance between the impacts and west boundary currents and the interactions between the impacts and the ambient large-scale currents.

a. The along-track jet and the along-track SSH rise strengthened by Typhoon Dolphin

Unlike Figs. 2c and 2d, the along-track jet induced by Typhoon Dolphin seems not to emerge from the SSH trough (Fig. 13). Dolphin actually moved overlying the along-track jet (B1) induced by Typhoon Bavi. Before the arrival of Typhoon Dolphin, the jet may have been strengthening with the evolution, so it remains unclear whether the strengthened jet in Fig. 13b is closely related to Dolphin. To clarify this issue, the SSH (η_ΑST) along three satellite tracks (L1–L3 in Fig. 13b) and their changes (Δη_ΑST) are given in Fig. 14. The results show that Dolphin caused appreciable SSH decreases along the three tracks. Considering the existed errors of the TC track in best track datasets and the existed near-inertial signals in the post-TC original along-satellite-track data, both the original and merged SSH decreases along L1–L3 are thought to be approximately symmetrical about the track (Figs. 14d–f). The superposition of these approximately symmetrical SSH decreases to the pre-TC SSH did not lead to the symmetrical post-TC SSH (i.e., SSH trough) owing to the preexisting large cross-TC-track SSH gradients (Figs. 14a–c). Nevertheless, the contributions of Typhoon Dolphin strengthened the preexisting SSH gradients, particularly predominant in Figs. 14b and 14c. Thus, the large-scale impacts of Dolphin still existed in the forms of the strengthen B1 and the SSH rise on the right side of B1 (SSHR1). In addition, Dolphin further plowed the SSH field in 16°–20°N (Fig. 13b).

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Altimetry-based along-track jet induced by Dolphin (a) pre-TC SSH (cm) field and (b) post-TC SSH (cm) field. Three satellite tracks (L1, L2, and L3) in COVER100 are chosen to estimate the SSH changes along them. The typhoon track (gray line), 6-hourly typhoon center (color dots), and intensity (color in the dots) are plotted in each subfigure. The color dots in the legend in (a) denote the typhoon intensity category on the Saffir–Simpson scale. The typhoon time (month/day/hour) is plotted in each panel. The pre-TC and post-TC time (day) of each track relative to the typhoon passage is given along each track.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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(a)–(c) Pre-TC and post-TC SSH (cm) observations along three satellite tracks induced by Dolphin and (d)–(f) the associated Δη_ΑST for (left) L1, (center) L2, and (right) L3. The solid and dashed lines denote the original and merged data, respectively.

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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b. The combined large-scale impacts induced by multiple typhoons

In July 2015, two sequential typhoons, Chan-hom and Nangka, which mainly moved over the previous SSHR1 (Fig. 15a), caused significant sea surface cooling and mixed layer response (Wu and Li 2018). Over SSHR1, the intensities of Chan-hom were so weak that in this stage the along-track SSH trough induced by Chan-hom was not clearly observed (Fig. 15b). By contrast, although the along-track SSH trough induced by Typhoon Nangka was not identifiable over SSHR1, the associated along-track jet (B3) is roughly visible (Figs. 15a,b). Typhoons Chan-hom and Nangka passed successively over a preexisting AOE (A1), causing it to be disrupted and a large SSHT (SSHT3) to be generated (Figs. 15a,b). The emerged SSHT3 means that the observable impacts of Chan-hom and Nangka can extend to 24°N. The previous SSHR1 was plowed by Nangka into two parts: the smaller part was still termed as SSHR1 and the larger part was named as SSHR3 (Fig. 15b).

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SSH (cm) field plowed by five typhoons in July–August 2015: (a) before Chan-hom and Nangka; (b) before Soudelor and after Chan-hom and Nangka; (c) after Goni and Atsani. An AOE (A1) is labeled in (a). SSHR3 and B3 are formed by Soudelor by plowing the SSHR1. SSHT3 is induced by Chan-hom and Nangka, while SSHT3 is induced by Atsani. The COEs (C5 and C6) are induced by Goni. The other labeled SSH patterns are the same as in Fig. 6. The typhoon track (gray line), 6-hourly typhoon center (color dots), and intensity (color in the dots) are plotted in each panel. The color dots in the legend in (a) denote the typhoon intensity category on the Saffir–Simpson scale. The birth time and the departure time (month/day/hour) from the study region for Chan-hom and Nangka are given in (a), those for Soudelor in (b), and those for Goni and Atsani in (c).

Citation: Journal of Physical Oceanography 53, 9; 10.1175/JPO-D-22-0230.1

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The observable signals can be found for three typhoons in August 2015 (Figs. 15b,c). The tracks of two sequential typhoons, Soudelor and Goni, are approximately parallel to those of Chan-hom and Nangka. Consequently, SSHT3 and a preexisting COE (C5) were significantly enlarged and enhanced (Figs. 15b,c), and a super COE (C6) was generated by triggering baroclinic instability. In addition, the strengths of both SSHR3 and the jet B3 were also enhanced. Only a part of the along-track SSH trough (SSHT4) induced by Typhoon Atsani is observable (Figs. 15b,c). However, the SSH rise and the jet above SSHT4 were connected to SSHR3 and B3, respectively. These connections also altered the large-scale SSH field significantly. Affected by the downwellings of Soudelor and Goni, both SSHR1 and SSHR2 were squeezed and tended to merge (Fig. 15c). SSHT_large was not directly acted on by the five typhoons in July–August 2015, but it was also did indirectly by interacting continuously with SSHR1, SSHR2, and C6 (Figs. 15a–c).

c. Unobservable large-scale impacts

If none of the observable large-scale signals exist after the TC passage, do the large-scale impacts exist? As seen from $\overline{\mathrm{\Delta }\eta }$ in Table 2, all typhoons but Noul can more or less induce the SSH decreases. Although some typhoons only can induce the decreases of ∼2–3 cm, the associated large-scale impacts are still considerable because the impacts can be roughly quantified by $\overline{\mathrm{\Delta }\eta }\times \hspace{0.17em}{L}_{\text{track}}\times 2\hspace{0.17em}{L}_h$. Owing to the longer L_track of ∼1000–4000 km (Table 2), a smaller $\overline{\mathrm{\Delta }\eta }$ also means the significant changes of available potential energy.

The TC-induced contributions of some typhoons may actually be underestimated by $\overline{\mathrm{\Delta }\eta }$. For example, $\overline{\mathrm{\Delta }\eta }$ for Typhoon Higos is smaller than that for Typhoon Mekkhala. According to LWS20, both the higher V_max and slower U for Higos should generate the larger $\overline{\mathrm{\Delta }\eta }$ than for Mekkhala. However, the SSH trough induced by Higos rapidly moved westward and the SSH rise entered the COVER100 (Fig. 10b), leading to a smaller $\overline{\mathrm{\Delta }\eta }$. Similarly, the small $\overline{\mathrm{\Delta }\eta }$ for Typhoon Dolphin may also be due to the rapid westward propagation of the jet and the SSH rise (Fig. 13).

The large-scale signals of the seven typhoons in Table 2 cannot be observed because of the preexisting strong mesoscale variability (Figs. S1–S7). Except for Typhoon Noul, the estimated $\overline{\mathrm{\Delta }\eta }$ for the other six cases were negative, located between −1.79 and −12.67 cm. Thus, most of these typhoons still make the appreciable large-scale impacts on the subtropical gyre. In other words, the unobservable signals may not mean that the large-scale impacts are nonexistent, but merely that they cannot be seen intuitively.

The group-mean $\overline{\mathrm{\Delta }\eta }$ were estimated by ${{\displaystyle \sum }}^{\text{}}(\overline{\mathrm{\Delta }\eta }\hspace{0.17em}\times L_{\text{track}})/{{\displaystyle \sum }}^{\text{}}\hspace{0.17em}{L}_{\text{track}}$ from Table 2: −5.52 and −3.65 cm for the “observable” and “unobservable” groups, respectively. It is straightforward that the stronger geostrophic response may be more observable than the weaker geostrophic response. However, the observability should depend heavily on the vertical structure of the temperature–salinity anomaly associated with the background eddy field. The temperature–salinity anomaly induced by a TC certainly appears in the upper thermocline, while the background temperature–salinity anomaly is undetermined. For the same background SSH pattern, if the depth of the related maximum density anomaly is different, the observed large-scale impacts from altimetry datasets also differ because SSH primarily reflect the vertical integration of the density anomaly in mesoscale ocean.