Prolonged thermocline warming by near-inertial internal waves in the wakes of tropical cyclones

Upper Ocean Conditions Before and After TC Forcing.

Upper ocean conditions after the passage of TCs are characterized by elevated mean values of KE, $\kappa$, $J_{\text{q}}$, and shear variance (Fig. 1C–F) compared to ocean conditions before TCs (cyan lines). Note that 95% confidence intervals for the time-depth means of $\kappa$ and $J_{\text{q}}$ in Table 1 are shown separately for the near-surface (0 to 50 m depth, white rows) and thermocline levels (50 to 250 m, turquoise rows), revealing that $J_{\text{q}}$ increased after TC passage by factors in the ranges [1.8, 21.4] and [1.7, 4.8] at the near-surface and thermocline levels. Low values of $J_{\text{q}}$ between 50 and 70 m for all periods in Fig. 1E indicate that turbulent heat transfer in the near-surface was relatively independent of transfer within the thermocline. In other words, there are two separate mixing processes happening above and below the ML base days to weeks after TC passage, and near-surface restratification is helping insulate thermocline heat, a necessary condition for net OHC to increase after TC passage (17).

Table 1.

Statistical summary of four periods of observation

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Based on a total of N individual casts, 95% confidence intervals for the average $\kappa$ and $J_{\text{q}}$ were computed for the near-surface (depth $<$ 50 m, white rows) and thermocline (50 to 250 m depth, green rows) layers during each of the periods defined in Fig. 2. Vertical variations in $\kappa$ and $J_{\text{q}}$ are plotted with confidence intervals in Fig. 1 D and E.

Vertical profiles of $J_{\text{q}}$ in Fig. 1E are consistent with increased OHU in the TC wake, while thermocline data further point to enhanced heat transfer across 150-m depth or between the seasonal and permanent thermoclines. The mean heat flux convergence and resulting warming rates $T_t^{turb}$ are $\sim$0.03 ${}^{°}$C d${}^{-1}$ in the upper 50 m, while thermocline measurements reveal contiguous layers with warming/cooling rates reaching $\pm 0.{015}^{°}$C d${}^{-1}$ (Fig. 1G, Materials and Methods). These values contrast with observations made before TC passage, when maximum values of $T_t^{turb}$ were roughly 25% of those measured after TC forcing (Fig. 1G). Overall, this evidence points to increased local OHU after TC forcing and prolonged deepening of upper thermocline heat, which would presumably reduce the amount of heat that will be locally lost to the atmosphere during winter.

Observed Collocation of NIWs, $\mathit{\kappa }$, and $J_{\text{q}}$.

Time-depth sections of $\mathbf{u}$, ${\mathbf{u}}_{\text{NI}}$, $\kappa$, and $J_{\text{q}}$ in Fig. 2 indicate that the observed increase in thermocline values of $\kappa$ and $J_{\text{q}}$ was associated with TC-generated NIWs. $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ rarely reached 0.15 m s${}^{-1}$ before TC passage (Fig. 2 E and I), but downward-propagating envelopes where $\Vert {\mathbf{u}}_{\text{NI}}\Vert >0.15$ m s${}^{-1}$ are evident in all post-TC measurements. More importantly, NIW envelopes are collocated with areas of enhanced $\kappa$ and $J_{\text{q}}$ (Fig. 2F–H and J–L). This collocation continues down to 300 m, as deep as our microstructure measurements go, but is likely to continue at greater depths as NIWs propagate into the deep ocean.

Changes in rotary wavenumber spectra of shear (Fig. 1F, Materials and Methods) before and after TC passage show a significant increase in variance associated with TC-generated internal waves. Shear associated with downward-propagating internal wave modes ($c_g$ down, Fig. 1F) increased after TC passage and at virtually all scales, while upward-propagating internal wave modes ($c_g$ up, Fig. 1F) did not consistently increase their shear variance. Evidence of increased shear due to downward-propagating NIWs may explain the collocation between mixing and NIWs in Fig. 2F–H and J–L, as shear instability is known to be the leading driver of mixing within NIW envelopes (27–29).

A meridional transect across the wakes of TCs Mangkhut, Trami, and Kong-Rey (Fig. 3 spans the across-TC-tracks period) reveals complex variations in NIW properties and mixing that result from patterns in NIW generation and propagation since TC passage. Tilted bands of alternating signs in v and $v_{\text{NI}}$ (Figs. 3A and 2G) are more intense and dominated by greater vertical scales at the northern end of the transect, which features more recent TC forcing than the southern end. Three distinct maxima in near-surface $\Vert \mathbf{u}\Vert$ are located near 13.8, 15.8, and 17.8${}^{°}$N (Fig. 3B) and likely associated with the passage of TCs Mangkhut, Kong-Rey, and Trami, which crossed 134.7${}^{°}$E near 14.1, 16.5, and 17.1${}^{°}$N roughly 23, 5, and 14 d before we sampled their respective latitudes (Fig. 3C). Thermocline $\Vert \mathbf{u}\Vert$ was as high as 1.1 m s${}^{-1}$ directly below mesoscale layers where shear squared ($S^2={\Vert \frac{\partial \mathbf{u}}{\partial z}\Vert }^2$) peaks and thus creates a favorable environment for enhanced turbulence (Fig. 3 C and D).

Elevated mean values of thermocline $J_{\text{q}}$ after TC passage (Fig. 1E and Table 1) were largely set by relatively few intermittent events with $J_{\text{q}}>$ 100 W m${}^{-2}$ that happened near local peaks in $S^2$ (Fig. 3C). We assess the impact of $S^2$ on $J_{\text{q}}$ by calculating the Richardson number $Ri=N^2/S^2$ and outlining areas where $Ri<0.5$ (gray contours in Fig. 3D). Here, N is the buoyancy frequency, and while the canonical threshold for shear instability is $Ri<0.25$, we use a higher value to compensate for the vertical resolution of $\mathbf{u}$. Notice that the background value of $J_{\text{q}}$ is negligibly small, but sporadic patches of increased $J_{\text{q}}$ are collocated with gray contours in Fig. 3D. This collocation is evidence that enhanced mixing resulted from shear instability in NIWs.

Regional Variations in NIW Activity and Mixing.

To generalize our time- and location-specific measurements, we assume that empirical relations between observed $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ and $\kappa$ (Fig. 4 A and B) are representative of those in other areas impacted by the same TCs. This way, we use HYCOM’s representation of thermocline $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ (SI Appendix) to inform the distribution of NIW activity throughout the Western Pacific and infer associated patterns in $\kappa$ and thermocline mixing (Fig. 4 C and D). Even though $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ is only an indirect proxy for turbulence and NIWs drive enhanced mixing through their effect on $S^2$ and Ri (Fig. 3 C and D), extending the observed relation between $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ and $\kappa$ helps us to broadly assess the impacts of TC-generated NIWs on the regional ocean heat budget.

Observed 4-d averages of thermocline $\kappa$ and $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ covaried during our experiment (Fig. 4A). In fact, the linear relation

yields a correlation coefficient $r=0.64$ when $a=33\pm 5\times {10}^{-5}$ and $b=0.9\pm 0.9\times {10}^{-5}$ (Fig. 4B, 95% CI). A comparison between HYCOM’s representation of NIW activity ($‖u_{\text{NI}}^{\text{HYCOM}}‖$) and 2 y-long moored records from our study region shows that HYCOM can roughly reproduce temporal patterns in $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ but can underestimate its value below 100 m (SI Appendix, Figs. S2 and S3). After noting this, we used $‖u_{\text{NI}}^{\text{HYCOM}}‖$ and the linear relation in Fig. 4A to estimate $\kappa$ and $J_{\text{q}}$ during our experiment in the Western Pacific (Fig. 4 C and D).

To emphasize the long timescales of NIW-driven mixing, HYCOM-based estimates of $\kappa$ and $J_{\text{q}}$ are shown in Fig. 4 C and D as 30-d averages between 12 September and 11 October (the same period used for $\mathrm{\Delta }KE$ in Fig. 1B). To facilitate interpretation of their climate significance, $\kappa$ and $J_{\text{q}}$ were interpolated onto the 22 and 26 ${}^{°}$C isotherms. Results for the 22 ${}^{°}$C isotherm are shown in Fig. 4 C and D, while results at the 26 ${}^{°}$C level are shown in SI Appendix, Fig. S4 a and b, and a time series of the $T_t^{\text{turb}}$ that results from differences between the two levels is shown in SI Appendix, Fig. S4C. The 22 ${}^{°}$C isotherm was chosen because it roughly separates between hotter water masses that take up heat from the atmosphere and colder ones that release their heat into the atmosphere (1). Similarly, the 26 ${}^{°}$C isotherm was chosen because it approximately marks an SST threshold at which air–sea fluxes can power TC intensification (47, 48).

Regional estimates of thermocline $\kappa$ have local peaks along the right sides of TC tracks (dashed lines in Fig. 4D), consistent with the asymmetry of NIW generation by TCs (42). While the influence of TCs Mangkhut, Trami, and Kong-Rey is most prominent, $\kappa$ is also 2 to 3 times greater than the background along the track of TC Jebi (blue dashed line), which passed by this area near 1 September. Similar patterns are observed in $J_{\text{q}}$, which is as high as 35 W m${}^{-2}$. These values are roughly consistent with observations, where mean values of $J_{\text{q}}$ at the 22 ${}^{°}$C isotherm are approximately 20, 40, and 20 W m${}^{-2}$ for the Left-side, across-TC-tracks, and Right-side periods, respectively (Fig. 1E).

To assess the climatic relevance of our results, we focus on values of $J_{\text{q}}$ inside the 10${}^{°}\times$ 6${}^{°}$ dashed box in Fig. 4D. There, the area-averaged NIW-driven $J_{\text{q}}$ across the 22 ${}^{°}$C isotherm was 20.5 $\pm$ 3.0 W m${}^{-2}$, which is roughly 5% greater than across the 26 ${}^{°}$C isotherm (SI Appendix, Fig. S4 A and B) and $\sim$80% of the climatological surface heat flux for September ($\approx$25 W m${}^{-2}$). The difference between $J_{\text{q}}$ at 22 and 26 ${}^{°}$C, which is small compared to the magnitude of $J_{\text{q}}$, would presumably cool the water between these isotherms at a rate $\approx 0.{01}^{°}$C month${}^{-1}$ (SI Appendix, Fig. S4C, Eq. 4), while the remaining $J_{\text{q}}$ remains available to warm the ocean below 22 ${}^{°}$C.

Integrated within the dashed box in Fig. 4D, NIW-driven $J_{\text{q}}$ transfers $\sim$0.015 PW across the 22 ${}^{°}$C isotherm, which is between 2.5 and 10% of the global TC contribution to OHU (15, 16, 18). Furthermore, this downward heat flux is $\sim$2% of the northward Pacific heat transport out of the tropics (49, 50) and $\sim$16% of the contribution by eddies (51). Considering that these estimates account for only a small fraction of the area impacted by the three TCs in this study, our analyses highlight the importance of NIWs in shaping the TC contribution to OHC and climate.

SST Cooling and TC-Driven Mixing.

Previous estimates of the TC contribution to OHC have used satellite measurements of SST cooling behind TCs to infer the TC-induced $\kappa$ via a characteristic mixing depth $z_{\text{L}}$. This method, exemplified in Fig. 5A, often defines $z_L$ as the depth above which the average pre-TC temperature is equal to the SST after TC passage ($T_{\text{TC}}$). Assuming a mixing timescale $t_{\text{mix}}\sim 24$ h to represent the duration of the forced stage, turbulence is then roughly quantified as $\kappa \approx z_{\text{L}}^2/t_{\text{mix}}$ (16, 20, 52). While this approach is physically sound and has proven useful to parameterize TC-driven mixing, it gives the impression that TC-driven mixing only acts to impact SST via ML deepening and that it only does it during the forced stage of TCs. However, observations in Figs. 1E and 2E–H show that turbulence in TC-generated NIWs drives a prolonged downward transfer of heat across the thermocline (Fig. 5B). If the contribution of TCs to ocean heat transport and remote climate is in fact determined by the amount of heat they transfer to water masses colder than the local wintertime SST (24), quantifying $J_{\text{q}}$ in the thermocline weeks to months after TC passage is essential to assessing the net impact of TCs on OHC and climate (Fig. 5).

Spatial patterns in SST cooling and $z_L$ are not indicative of the distribution of NIW activity and thermocline mixing. Blue contours in Fig. 4D outline areas where SST cooling in TC wakes exceeded 1 ${}^{°}$C, while black contours indicate areas where $z_L$ reached below the 22 ${}^{°}$C isotherm (Materials and Methods). Differences between these contours and our estimates of $J_{\text{q}}$ (Fig. 4D) show that SST-based techniques would indicate that no heat was transferred across the 22 ${}^{°}$C along the track of TC Mangkhut. The comparison yields similar results at the 26 ${}^{°}$C level (SI Appendix, Fig. S4B), highlighting how SST cooling and the prolonged NIW-driven mixing detailed by our observations are complementary but quite different facets of TC-driven mixing.

A schematic in Fig. 5 summarizes the different stages of mixing driven by TCs and their distinct impacts to upper ocean stratification. SST cooling results from mixing at the ML base during the forced stage of TCs (Fig. 5A) and tends to be collocated with $\mathrm{\Delta }KE$ (8). In contrast, the 3D distribution of NIWs is impacted by TC forcing, background stratification, and ocean currents with horizontal scales $\sim$25 km and greater (44, 45). Without a proper representation of NIWs and their mixing, ocean models are likely to underestimate the depth of anomalous OHC induced by TCs (Fig. 5B) and thereby misallocate anomalous air–sea fluxes in subsequent seasons and years (Fig. 5C). Two year-long comparisons between modeled and observed $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ in SI Appendix, Figs. S2 and S3 show that HYCOM (horizontal resolution $1/12\times 1/{12}^{°}$) underestimates $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ with increasing depth, yielding annually averaged values $>$30% lower than observations below 150 m. This is likely due to the low vertical resolution (50 to 100 m) of HYCOM’s permanent thermocline, suggesting that high-resolution model configurations and NIW-specific parameterizations alike (5, 53) are needed to accurately reproduce the TC contribution to OHC and meridional heat transport.

Shipboard Data.

Horizontal velocities $\mathbf{u}$ (Figs. 2A–D and 3B) were measured using a hull-mounted, 75-kHz acoustic Doppler current profiler (ADCP) and were processed using a third-order Butterworth filter within the frequency range [0.7f, 1.3f] to extract their near-inertial component ${\mathbf{u}}_{\text{NI}}$ (Fig. 2E–H), where f is the mean inertial frequency for locations sampled. The same filter was used to compute ${\mathbf{u}}_{\text{NI}}$ from moored records (SI Appendix, Fig. S2) and HYCOM output. Vertical wavenumber spectra of shear (Fig. 1F) were computed after applying WKB-stretching and scaling procedures in ref. 57, for which monthly stratification data from ARGO (58) were used.

Because the ship was only static from 21 September to October 3 and from October 9 to October 12, bandpass filters used to calculate $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ when the ship moved across TC wakes are likely to underestimate $\Vert {\mathbf{u}}_{\text{NI}}\Vert$. While ship motion induces a bias in the perceived phase propagation of NIWs (28, 59), small-scale spatial variations in $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ can further bias the results of bandpass filtering. Cross-track variations in $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ follow the length scale $\sim$100 km or twice the maximum wind radius of TCs (25, 26), but our ship moved at a cross-track velocity of up to 250 km for every inertial period (Fig. 3). Sampling at that speed, a 100 km-long peak in $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ would appear in measurements as an oscillation with frequency $>$2f. This may be the case for some of the local peaks near 150 m in Fig. 3B, where $\Vert \mathbf{u}\Vert$ goes from 0.4 to 0.9 m s${}^{-1}$ and back to 0.4 m s${}^{-1}$ in $\sim$150 km, or little more than half an inertial period.

More than 4,000 individual vertical profiles of temperature (T), stratification ($N^2$), and the turbulent dissipation rate ($\epsilon$) were obtained using the Chameleon microstructure profiler (60), which was deployed from the stern of R/V Thomas G. Thompson. Following (61), we used 3-h averages of $\epsilon$ and $N^2$, and set $\mathrm{\Gamma }=0.2$ (62, 63) to compute $\kappa$ as

Likewise, turbulent heat fluxes $J_{\text{q}}$ were computed as

while estimates of the turbulent warming rate $T_t^{\text{turb}}$ are given by

Here, ${\rho }_0=1024$ kg m${}^{-3}$ is the reference density of seawater and $c_p=4.1\times {10}^3$ J K${}^{-1}$ kg${}^{-1}$ is the heat capacity. $J_{\text{q}}$ and $T_{\text{turb}}^{\prime }$ were computed using hourly averages of the vertical temperature gradient $\frac{\partial T}{\partial z}$ and $\kappa$ as shown in Fig. 3D, and later averaged to the temporal periods specified in Figs. 1, 2, 4, and Table 1. Confidence intervals in Fig. 1 and Table 1 were computed via bootstrapping.

Reanalysis Data.

Data from the atmospheric ERA5 (64) and oceanic HYCOM (65) reanalyses provide context for shipboard observations and help inform their large-scale implications. We computed the cumulative transfer of kinetic energy into the ocean $\mathrm{\Delta }KE=\int \tau ·{\mathbf{u}}_{\mathit{surf}}dt$ as a proxy for net forcing, assuming that a fraction of $\mathrm{\Delta }KE$ becomes available for NIW generation (Fig. 1 A and B). Here, $\tau$ and ${\mathbf{u}}_{\mathit{surf}}$ are given 3-h data of wind stress and surface velocities from ERA5 and HYCOM respectively, while the dates $t_0$ and $t_1$ used are indicated as titles on top of Fig. 1 A and B.

$u_{\text{NI}}^{\text{HYCOM}}$ was obtained by applying a third-order Butterworth bandpass filter to the model’s velocity output using the local frequency range [0.7f, 1.3f]. Values of $‖u_{\text{NI}}^{\text{HYCOM}}‖$ were computed for multiple vertical levels and later validated by comparing them against corresponding measurements from two year-long moored records within our area of observations (SI Appendix, Figs. S2 and S3).

Thirty-day averages of $\kappa$ in Fig. 4C, SI Appendix, Fig. S4A were calculated by interpolating 4-d averages of $\Vert {\mathbf{u}}_{\text{NI}}\Vert$ on to the depth of the 22 ${}^{°}$C isotherm, applying the linear fit described in Fig. 4B to obtain $\kappa$, and averaging the results between 12 September and 11 October. Corresponding values of $J_{\text{q}}$ (Fig. 4D) were calculated as $c_p{\rho }_0\kappa \frac{\partial T}{\partial z}$ and averaged within the same period, where $\frac{\partial T}{\partial z}$ is the local vertical temperature gradient in HYCOM.

TC Tracks and Induced SST Cooling.

TC track and intensity data are from the US Navy’s Joint Typhoon Warning Center (JTWC) and summarized in SI Appendix, Fig. S1. TCs’ potential for NIW generation was assessed using the ratio $U_{\mathit{storm}}/c_g$, where $U_{\mathit{storm}}$ is the TC translation speed and $c_g$ is the local baroclinic mode-1 gravity wave speed roughly 3.2 m s${}^{-1}$, (66), which was computed using ARGO climatology data (58) and assuming constant stratification beneath 2,000 m.

SST cooling induced by TCs was computed as the difference between SST averages 3 to 10 d before and 1 to 4 d after TC passage (56) with daily SST data from ERA5. SST cooling was computed for every location within 200 km of TC tracks and corresponding dates of TC passage were defined as the dates of closest proximity to the TC eye. Results were used to plot the blue contours in Fig. 4D), which highlight areas where SST cooling from TCs Mangkhut, Trami, or Kong-Rey was greater than 1 ${}^{°}$C. Moreover, the characteristic mixing depth $z_L$ was computed using HYCOM temperature stratification data, and areas where $z_L$ went deeper than the pre-TC 22 ${}^{°}$C isotherm are shown as black contours in Fig. 4D, SI Appendix, Fig. S4C.