a. Observation and methods

The moored data were from the observation stations deployed in the northern South China Sea (Table 1) for Stations 1, 2, 3, and 4 (herein S1, S2, S3, and S4). The stations consist of both buoys and moorings (see Fig. 1 for the buoy and mooring design at S3 as an example). TCs Kalmaegi (2014), Rammasun (2014), Sarika (2016) and Haima (2016) were chosen for the validation of this study (Fig. 2) as they were close to our observation arrays, and the upper ocean temperature variation was measured by the temperature sensors on the stations. S1–S3 were deployed in 2014, capturing Kalmaegi and Rammasun; the SeaBird 37 recorders that observed temperature were at 20-m vertical intervals from the surface to ∼400 m and measurements were taken every 120 s. S2 (S1–S3) captured the temperature response to Rammasun (Kalmaegi); see Zhang et al. (2016, 2020) for more details of the stations. S4 was deployed in 2016, capturing TCs Sarika and Haima; the temperature sensors were at 5–20-m vertical intervals that were smaller (larger) at shallower (deeper) depths from the surface to ∼400 m on buoys and from ∼200 to 700 m, and these measurements were taken from every 1 s to every 300 s. The details of the observed temperature response refer to Zhang et al. (2016, 2018, 2019, 2020) and Wu et al. (2018, 2020).

Buoy and mooring design at station 3.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Buoy and mooring design at station 3.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Buoy and mooring design at station 3.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Tropical cyclones and observation stations.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Tropical cyclones and observation stations.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Tropical cyclones and observation stations.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Table 1

Location, water depth, and deployment of temperature sensors on buoys of the observation stations. Water depth of the observation stations was estimated by topography. S2, S4, S5, and S7 all consist of a buoy and mooring. Bold values indicate that the temperature sensor deployed at the depth was lost, has some error in data, or no data.

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This research used the Coupled Ocean Atmosphere Response Experiment 3.0 (COARE3.0) algorithm (Fairall et al. 2003) to calculate surface heat flux. The cloud cover data for shortwave radiation were from the U.S. National Centers for Environmental Prediction (NCEP) reanalysis products (http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.html); air temperature, sea surface pressure, humidity, rainfall were from the in-site observations at S1–S4.

In this study, the initial mixed layer depth (h₀) is calculated by the temperature that is 0.5°C lower than the sea surface temperature before a TC. The post-TC well-mixed layer depth (h₀ + h_E − h_U) is the depth with highest vertical temperature gradient under h₀. The term h_E is the well-mixed layer thickness. The uplift distance by upwelling (h_U) is the difference in the average depth of the 21°C (S1 and S3 for Kalmaegi and S2 for Rammasun) or 20°C (S2 for Kalmaegi and S4 for Sarika and Haima) isotherms before and after TCs and is positive for the uplift of the isotherm. The term h_U is negative for downwelling. The transition layer thickness (h_T) is taken as the thickness between h₀ + h_E − h_U and the temperature anomaly minimum under h₀ + h_E − h_U. The vertical temperature gradient for parameterization (T_z) is calculated by the average of the vertical temperature gradient of the initial temperature profile between h₀ and h₀ + h_E − h_U.

b. Tropical cyclones

The TC tracks were from the China Meteorological Administration (CMA; http://tcdata.typhoon.org.cn/en/zjljsjj_zlhq.html) (Ying et al. 2014). The TC tracks from other best-track datasets (e.g., Joint Typhoon Warning Center and the Japan Meteorological Agency) were similar (Zhang et al. 2016, 2019, 2020). In Table 2, the radius of maximum wind (r_max) was obtained from the Joint Typhoon Warning Center (JTWC) dataset. The across-track distance of the station to TC (y) was calculated using the China Meteorological Administration (CMA) best-track data when the tropical cyclone was closest to our observation array. A positive (negative) distance corresponds to the right (left) side of the track. The values of Kalmaegi (2014) correspond to stations 1–3, the values of Rammasun (2014) correspond to station 2, and the values of Sarika (2016) and Haima (2016) correspond to station 4. The term τ_max is the maximum wind stress of a TC.

Table 2

Information on tropical cyclones when closest to the observation array.

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As shown in Table 2, all four TCs were weak typhoons when traveling through our observation arrays, as the maximum wind speeds were from 36 to 42 m s⁻¹, which were classified as category 1 under the Saffir–Simpson hurricane wind scale (see https://www.nhc.noaa.gov/aboutsshws.php). Note that the maximum sustained wind in the CMA dataset is 2-min averaged, while the Saffir–Simpson scale uses 1-min averaged wind, so the category may be relatively weak estimated by the CMA best-track data. Kalmaegi (Rammasun) was relatively fast (slow), with a translation speed of 8.80 m s⁻¹ (4.68 m s⁻¹). Sarika and Haima moved at a moderate speed, with translation speeds of 6.53 and 6.80 m s⁻¹, respectively. All four TCs caused a significant near-inertial response in their lee, and the response biased to the right side of their tracks as their nondimensional translation speed (S) was greater than 1 (Zhang et al. 2020). The Rossby number for the mixed-layer current (R) was small (∼0.3) at the stations of Kalmaegi, Sarika, and Haima but large (R = 2.145) at S4 during Rammasun (mainly due to the shallow initial mixed layer depth than that of other TCs), which indicated that the effect of horizontal advection was not important at the stations during Kalmaegi, Sarika, and Haima but played a role at S2 during Rammasun.

a. Upper ocean temperature observations

TCs induced a significant upper ocean response at the observation stations (Figs. 3 and 4). There was background diurnal and semidiurnal tide and near-inertial response after the TCs, the temperature is averaged in one day before the TCs and one inertial period after the TCs to see the net temperature change (see Figs. 3d–f and 4j–l and Figs. 4d–f and 4j–l). The result of low-pass filtered temperature is similar; see Figs. A1 and A2 in the appendix for the 3-day low-pass filtered temperature before and after the TCs. After Kalmaegi, S1 and S3 (S2) show near-surface cold anomaly, subsurface cold (warm) anomaly and deeper ocean cold anomaly; see Figs. 3j and 3l (Fig. 3k). After Rammasun (Sarika and Haima), S2 (S4) shows a near-surface cold anomaly, subsurface warm anomaly, and deeper ocean warm anomaly.

Variations in (a)–(c) temperature and (g)–(i) temperature anomalies before and after Kalmaegi above 150 m at the observation stations. Also shown are the averaged (d)–(f) vertical temperature and (j)–(l) temperature anomaly profiles before (black lines; averaged 24–48 h before the TC) and after (red lines; averaged for the second inertial period) Kalmaegi at the observation stations. In (a)–(c) and (g)–(i), the black solid lines are the depths that are 0.5°C lower than the sea surface temperature, the horizontal black dashed lines are the 21°C isotherms for stations 1 and 3 and 20°C for station 2, the vertical black lines show the arrival time of Kalmaegi (day 0), and the vertical brown dashed lines represent the range of the second inertial period after Kalmaegi.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Variations in (a)–(c) temperature and (g)–(i) temperature anomalies before and after Kalmaegi above 150 m at the observation stations. Also shown are the averaged (d)–(f) vertical temperature and (j)–(l) temperature anomaly profiles before (black lines; averaged 24–48 h before the TC) and after (red lines; averaged for the second inertial period) Kalmaegi at the observation stations. In (a)–(c) and (g)–(i), the black solid lines are the depths that are 0.5°C lower than the sea surface temperature, the horizontal black dashed lines are the 21°C isotherms for stations 1 and 3 and 20°C for station 2, the vertical black lines show the arrival time of Kalmaegi (day 0), and the vertical brown dashed lines represent the range of the second inertial period after Kalmaegi.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Variations in (a)–(c) temperature and (g)–(i) temperature anomalies before and after Kalmaegi above 150 m at the observation stations. Also shown are the averaged (d)–(f) vertical temperature and (j)–(l) temperature anomaly profiles before (black lines; averaged 24–48 h before the TC) and after (red lines; averaged for the second inertial period) Kalmaegi at the observation stations. In (a)–(c) and (g)–(i), the black solid lines are the depths that are 0.5°C lower than the sea surface temperature, the horizontal black dashed lines are the 21°C isotherms for stations 1 and 3 and 20°C for station 2, the vertical black lines show the arrival time of Kalmaegi (day 0), and the vertical brown dashed lines represent the range of the second inertial period after Kalmaegi.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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As in Fig. 3, but for (top) Rammasun, (middle) Sarika, and (bottom) Haima at the observation stations. The horizontal black dashed lines are the 21°C isotherms for Rammasun and 20°C isotherms for Sarika and Haima.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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As in Fig. 3, but for (top) Rammasun, (middle) Sarika, and (bottom) Haima at the observation stations. The horizontal black dashed lines are the 21°C isotherms for Rammasun and 20°C isotherms for Sarika and Haima.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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As in Fig. 3, but for (top) Rammasun, (middle) Sarika, and (bottom) Haima at the observation stations. The horizontal black dashed lines are the 21°C isotherms for Rammasun and 20°C isotherms for Sarika and Haima.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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To further decompose the effects of mixing and vertical advection, a temperature 0.5°C lower than the SST is used as the variation in the well-mixed layer (h₀ + h_E − h_U), the depth of the 20° or 21°C isotherms as the variation in vertical advection (h_U), and the depth between the well-mixed layer temperature anomaly minimum under the well-mixed layer as the transition layer thickness (h_T); this method was similar to their decomposed depth or thickness in model simulations used in previous research (Zhang et al. 2016, 2018, 2019, 2020).

After Kalmaegi, S1–S3 all experienced net upwelling as the averaged isotherm uplifted below the mixed layer (Figs. 3d–f and Table 3). The deepened well-mixed layer quickly met the upwelling (Figs. 3a–c), with an uplift of the averaged isotherm under the forced mixed layer (Figs. 3d–f) and a negative heat anomaly in the forced mixed layer (ΔQ_init + ΔQ_sub), which were −33.034, −21.566, and −26.011 KJ cm⁻², respectively (Table 3). The heat anomaly above 150 m (ΔQ₁₅₀) was also negative, which were −49.661, −28.259, and −48.431 KJ cm⁻², respectively (Table 3). S1 and S3 were close to Kalmaegi’s track, and the upwelling was relatively strong and mixing was relatively weak, leading to only a net cold anomaly with no net warm anomaly in the upper ocean (Figs. 3j,l). S2 was relatively far from Kalmaegi’s track, and the upwelling was weak and mixing was strong, leading to subsurface warm anomaly (Fig. 3k).

Table 3

The averaged temperature response at the observation stations. The values in the table refer to the average temperature before and after the TCs, i.e., red solid lines in Figs. 3j–l and 4j–l as well as red dashed lines in Figs. A1j–l and A2j–l.

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The SST cold anomaly at S2 (−2.028°C) was also greater than that at S1 and S3 (−1.522° and −1.090°C) because the increased mixed layer depth at S2 (h_E = 26.32 m, h_T = 58.65 m) was greater than that at S1 and S3 (h_E = 21.03 and 23.04 m, h_T = 33.56 and 35.20 m).

Different from the stations after Kalmaegi, S2 and S4 experienced net downwelling after Rammasun, Sarika, and Haima (Fig. 4), and the deepened well-mixed layer quickly met the downwelling (Figs. 4a–c), with a downward push of the averaged isotherm under the forced mixed layer (Figs. 4d–f) and a positive heat anomaly in the forced mixed layer (ΔQ_init + ΔQ_sub), which was −6.859, 4.513, and 17.197 KJ cm⁻² respectively (Table 3). Heat content above 150 m was also positive (ΔQ₁₅₀), with values of 4.043, 6.785, and 26.734 KJ cm⁻² respectively (Table 3). The warm anomaly under the forced mixed layer was small at S4 after Sarika because the downwelling was weak (h_U = −1.59 m). Haima further deepened the mixed layer slightly (Figs. 4c,f), but there were few near-surface cold anomalies (Figs. 4i,l) because Sarika had already mixed and uniformed the near-surface water. However, the transition layer was thicker and downwelling was stronger after Haima than after Sarika, resulting in greater and deeper subsurface warm anomalies (Figs. 4i,l, Table 3). Specifically, Sarika and Haima successively pushed some warm water into the subsurface water and deeper water.

At all stations, the dominant terms controlling the air–sea heat flux during TCs were latent heat flux and shortwave radiation (solar radiation), as shown in Fig. 5. The latent heat flux increased because the intense TC wind strengthened evaporation and shortwave radiation decreased when the cloud of the TC covered (or partly covered) the sun. The ocean lost heat during the forced stage of the TCs because the decrease in shortwave radiation was associated with TC cloud cover and the increase in latent heat flux was associated with the strong TC wind. Surface heat flux (Q_flux) were −1.555, −0.121, and −3.206 KJ cm⁻² at S2, S4, and S5 during Kalmaegi, −0.702 KJ cm⁻² at S4 during Sarika and 0.514 KJ cm⁻² at S4 during Haima. However, the ocean seemed to gain heat at S4 during Rammasun (Q_flux = 2.541 KJ cm⁻²) as S2 was far from Rammasun’s center, where TC clouds were coarse and wind was weak. Air–sea heat flux was responsible for the colder SST and inversion of the near-surface vertical temperature profiles with a colder SST than subsurface temperature at the stations (Figs. 3d–f and 4d,f). It also influenced the pre-TC vertical temperature, as the initial mixed layer at S2 before Rammasun was shallow (h₀ = 9.74 m; Fig. 4d), and the pre-TC SST was colder than the subsurface temperature at S4 before Sarika (Fig. 4e), which was due to both the seasonal cycle of surface heat flux, which was in July (October), and the warming (cooling) of the sea surface at S2 (S4) before Rammasun (Sarika). Overall, the air–sea surface heat flux played a small role in SST but was not important for changes in the upper ocean heat. Note that the four TCs studied here were relatively strong TCs with a maximum wind speed (V_max) ≥36 m s⁻¹ and at least typhoon intensity, and the air–sea heat flux may be more important after weaker TCs (Potter et al. 2017; Zhang et al. 2021a).

(a)–(c)Sea surface shortwave radiation (black), longwave radiation (orange), sensible heat flux (blue), and latent heat flux (red) during Kalmaegi at S1, S2, and S3, respectively. (g)–(i) As in (a)–(c), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. (d)–(f) Heat content (KJ cm⁻²) above 80 m (0–80 m; red), greater than 26°C [≥26°C, tropical cyclone heat potential (TCHP); orange], accumulated surface heat flux (blue, Q_flux), and heat content within the mixed layer (ΔQ_init + ΔQ_sub) during Kalmaegi at S1, S2, and S3, respectively. (j)–(l) As in (d)–(f), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. Black dashed lines are zero lines. Accumulated surface heat flux values are the accumulated values of (a)–(c) and (g)–(i) regarding the change in water temperature, and the accumulated surface heat flux is set to 0 on day 0.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(c)Sea surface shortwave radiation (black), longwave radiation (orange), sensible heat flux (blue), and latent heat flux (red) during Kalmaegi at S1, S2, and S3, respectively. (g)–(i) As in (a)–(c), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. (d)–(f) Heat content (KJ cm⁻²) above 80 m (0–80 m; red), greater than 26°C [≥26°C, tropical cyclone heat potential (TCHP); orange], accumulated surface heat flux (blue, Q_flux), and heat content within the mixed layer (ΔQ_init + ΔQ_sub) during Kalmaegi at S1, S2, and S3, respectively. (j)–(l) As in (d)–(f), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. Black dashed lines are zero lines. Accumulated surface heat flux values are the accumulated values of (a)–(c) and (g)–(i) regarding the change in water temperature, and the accumulated surface heat flux is set to 0 on day 0.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(c)Sea surface shortwave radiation (black), longwave radiation (orange), sensible heat flux (blue), and latent heat flux (red) during Kalmaegi at S1, S2, and S3, respectively. (g)–(i) As in (a)–(c), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. (d)–(f) Heat content (KJ cm⁻²) above 80 m (0–80 m; red), greater than 26°C [≥26°C, tropical cyclone heat potential (TCHP); orange], accumulated surface heat flux (blue, Q_flux), and heat content within the mixed layer (ΔQ_init + ΔQ_sub) during Kalmaegi at S1, S2, and S3, respectively. (j)–(l) As in (d)–(f), but during Rammasun at S2, during Sarika at S4, and during Haima at S4, respectively. Black dashed lines are zero lines. Accumulated surface heat flux values are the accumulated values of (a)–(c) and (g)–(i) regarding the change in water temperature, and the accumulated surface heat flux is set to 0 on day 0.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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In addition to mixing, vertical advection and surface heat flux, the temperature and heat change can be changed by horizontal advection. As mentioned before, the Rossby number for the mixed-layer current [ $R={\tau }_{\text{max}}/({\rho }_0{h}_{\text{mix}}Uf)$] was relatively small at the stations during Kalmaegi, Sarika, and Haima (R ≈ 0.3) but relatively large (R = 2.145) at S4 during Rammasun, so horizontal advection was not important during the forced stage of Kalmaegi, Sarika, and Haima but played a role at S2 during Rammasun. Further validation and analysis of the processes and mechanisms during TCs using three-dimensional model simulations can be found in previous research (e.g., Zhang et al. 2016, 2018, 2019, 2020).

In brief, the upper ocean temperature response depended on the relative importance of mixing and vertical advection (upwelling and downwelling), surface heat flux modulated some of the SST before and after the TC, and horizontal advection was important when the Rossby number for the mixed-layer current (R) was large.

b. Long-term variation in the upper ocean temperature after a tropical cyclone

As a TC modulates the vertical temperature structure, mainly through heat pump and cold suction effects during its forced stage, a further unknown is how the temperature anomalies recover and vary after the TC.

It is generally recognized that the air–sea surface heat flux after a TC is responsible for the recovery of the SST and mixed layer anomalies (Emanuel 2001; Price et al. 1986, 2008; Zhang et al. 2021a). After Kalmaegi, the cooled initial mixed layer did not recover back to its initial condition for at least 47 days after the TC, with cold ΔQ_init and cold SST anomalies (Figs. 6a–f). This result may be because Kalmaegi traveled through the observation array on 15 September, and the seasonal cycle was spanned from autumn to winter after Kalmaegi. The surface heat flux tends to cool the near-surface ocean. After Rammasun, the sea surface heat flux warmed and recovered ΔQ_init, and the tropical cyclone heat potential (TCHP) returned to that before Rammasun in 5 days (Figs. 6h,i), but the near-surface ocean cooled again after that, which may be due to subsequent air–sea processes, such as TC Matmo (2014) from 22 to 23 July. Note that the strong cooling in the mixed layer near day 60 (nearly 15 September) at S4 was due to the effect of Kalmaegi. Specifically, the air–sea surface heat flux did not recover more than one and a half months after the TCs, although the seasonal cycle after Rammasun recovered the near-surface ocean temporarily. Except the air–sea surface heat flux, the background circulation of the South China Sea may lead to the near-surface temperature changes.

(a) Surface fluxes (W m⁻²), (b) ocean temperature anomalies above 100 m (ΔT; °C), and (c) change in heat content (KJ cm⁻²) at station 1 before and after Kalmaegi. (d)–(f) As in (a)–(c) but for station 3 for Kalmaegi. (g)–(i) As in (a)–(c), but for station 2 for Rammasun. Day 0 is the time when TC is closest to the observation station. In (a), (d), and (g), the black line is the shortwave radiation, the orange line is the longwave radiation, the blue line is the sensible heat flux, and the red line is the latent heat flux. In (c), (f), and (i), the orange line is the heat anomaly of the water warmer than 26°C, which is also the tropical cyclone heat potential (TCHP), the red line is the heat anomaly in the initial mixed layer (ΔQ_init), the blue line is the accumulated heat change caused by heat flux (Q_flux, with 0 KJ cm⁻² at day 0), the black solid line is ΔQ_init − Q_flux, and the black dashed line is the zero line. Anomalies are the original values minus their average from 24 to 48 h before the TC.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a) Surface fluxes (W m⁻²), (b) ocean temperature anomalies above 100 m (ΔT; °C), and (c) change in heat content (KJ cm⁻²) at station 1 before and after Kalmaegi. (d)–(f) As in (a)–(c) but for station 3 for Kalmaegi. (g)–(i) As in (a)–(c), but for station 2 for Rammasun. Day 0 is the time when TC is closest to the observation station. In (a), (d), and (g), the black line is the shortwave radiation, the orange line is the longwave radiation, the blue line is the sensible heat flux, and the red line is the latent heat flux. In (c), (f), and (i), the orange line is the heat anomaly of the water warmer than 26°C, which is also the tropical cyclone heat potential (TCHP), the red line is the heat anomaly in the initial mixed layer (ΔQ_init), the blue line is the accumulated heat change caused by heat flux (Q_flux, with 0 KJ cm⁻² at day 0), the black solid line is ΔQ_init − Q_flux, and the black dashed line is the zero line. Anomalies are the original values minus their average from 24 to 48 h before the TC.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a) Surface fluxes (W m⁻²), (b) ocean temperature anomalies above 100 m (ΔT; °C), and (c) change in heat content (KJ cm⁻²) at station 1 before and after Kalmaegi. (d)–(f) As in (a)–(c) but for station 3 for Kalmaegi. (g)–(i) As in (a)–(c), but for station 2 for Rammasun. Day 0 is the time when TC is closest to the observation station. In (a), (d), and (g), the black line is the shortwave radiation, the orange line is the longwave radiation, the blue line is the sensible heat flux, and the red line is the latent heat flux. In (c), (f), and (i), the orange line is the heat anomaly of the water warmer than 26°C, which is also the tropical cyclone heat potential (TCHP), the red line is the heat anomaly in the initial mixed layer (ΔQ_init), the blue line is the accumulated heat change caused by heat flux (Q_flux, with 0 KJ cm⁻² at day 0), the black solid line is ΔQ_init − Q_flux, and the black dashed line is the zero line. Anomalies are the original values minus their average from 24 to 48 h before the TC.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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The post-TC geostrophic adjustment and background circulation may be responsible for the subsurface and deeper ocean temperature variations as the heat does not exchange with air directly. The TC-induced subsurface cold or warm anomalies tended to move into deeper depths with time (Figs. 7m–p). There seemed to be two paths for the downward propagation of subsurface anomalies. The downward movement of the main (minor) path was slow (relatively fast) and only dozens of meters (hundreds of meters) in 2–3 weeks. A model simulation several days after Kalmaegi (Zhang et al. 2018) showed that the main path was due to the recovery of subsurface anomalies by horizontal advection, and the minor path was due to the downward propagation of near-inertial waves. However, the background circulation may be more important for temperature and heat change 10 days or more after the TCs.

(a)–(d) Temperature (T; °C), (e)–(h) temperature anomaly (ΔT; °C), and (i)–(l) net temperature anomaly (ΔTn; °C) before and after the tropical cyclones. Day 0 is the time when the tropical cyclone is closest to the observation station. The temperature anomaly is the temperature value minus its average from 24 to 48 h before the TC. The net temperature anomaly is the temperature anomaly low pass filtered that is lower than a 3-day period. Black arrows represent the propagation direction of the subsurface anomaly.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(d) Temperature (T; °C), (e)–(h) temperature anomaly (ΔT; °C), and (i)–(l) net temperature anomaly (ΔTn; °C) before and after the tropical cyclones. Day 0 is the time when the tropical cyclone is closest to the observation station. The temperature anomaly is the temperature value minus its average from 24 to 48 h before the TC. The net temperature anomaly is the temperature anomaly low pass filtered that is lower than a 3-day period. Black arrows represent the propagation direction of the subsurface anomaly.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(d) Temperature (T; °C), (e)–(h) temperature anomaly (ΔT; °C), and (i)–(l) net temperature anomaly (ΔTn; °C) before and after the tropical cyclones. Day 0 is the time when the tropical cyclone is closest to the observation station. The temperature anomaly is the temperature value minus its average from 24 to 48 h before the TC. The net temperature anomaly is the temperature anomaly low pass filtered that is lower than a 3-day period. Black arrows represent the propagation direction of the subsurface anomaly.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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a. Vertical temperature profile anomaly

If mixing is the only mechanism (Fig. 8a), the surface cold anomaly equals the subsurface warm anomaly, the upper ocean heat change is zero, and the heat change under the initial mixed layer (h₀) is always positive; this is the “heat pump” condition as described and studied in previous works (Emanuel 2001; Mei et al. 2013). If the “cold suction” effect is added, the upwelling (downwelling) uplifts (downdrifts) the temperature profile and makes the mixed layer shallower (deeper). In so doing, upwelling (downwelling) will induce integral cooling (warming) in the vertical column. As mentioned by previous research (e.g., Lu et al. 2021; Price 1981; Zhang et al. 2018), vertical advection (i.e., upwelling and downwelling) usually delays mixing by approximately half a day, and the interaction between mixing and vertical advection is small during fast-moving TCs. If upwelling (downwelling) is moderate, the vertical temperature profile is a cold–warm–cold anomaly with more subsurface warm anomalies than surface cold anomalies, see Fig. 8b (Fig. 8c). If upwelling is strong, there will be no subsurface warm anomalies and only cold anomaly in the vertical temperature profile (Fig. 8d). The isotherm may outcrop if upwelling is too strong (Fig. 8e), but this condition is rare because there always exists a surface mixed layer after a TC, although it may be very shallow. On the other hand, there may be only a warm anomaly under h₀ if downwelling is much stronger than mixing (Fig. 8f), and this condition was observed at S4 after Haima. Figure 8 presents the potential vertical temperature profile structures caused by the so-called heat pump (mixing) and cold suction (vertical advection) processes of a TC. Note that there is a transition layer (between h₀ + h_E and h₀ + h_E + h_T) with the water being partially mixed that below the vertically uniform well-mixed layer (h₀ + h_E), according to Price et al. (1986).

(a)–(f) Sketches of the vertical upper ocean temperature profiles modulated by (a) only mixing, (b) a combination of mixing and moderate upwelling, (c) a combination of mixing and downwelling, (d) a combination of mixing and strong upwelling that forces the mixed layer to be shallower than the initial mixed layer depth, (e) very strong upwelling with an outcropping isotherm so that only upwelling works, and (f) only downwelling. The term h₀ is the initial mixed layer depth; h_E and h_T are the well-mixed layer thickness and transition layer thickness, respectively; and h_U is the vertical movement of the isotherm by upwelling (positive value) or downwelling (negative value). The dashed (solid) line is the temperature profile before (after) TC forcing. The blue (red) shadow represents a cold (warm) anomaly. ΔQ_init and ΔQ_mix are the heat changes in the initial mixed layer and forced mixed layer, respectively, and ΔQ_sub is the heat change in the subsurface between the initial and forced mixed layers. (g) Sketch of the effect of mixing and vertical advection (upwelling and downwelling) and the distribution of vertical temperature anomaly profiles in the across-track section of a tropical cyclone.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(f) Sketches of the vertical upper ocean temperature profiles modulated by (a) only mixing, (b) a combination of mixing and moderate upwelling, (c) a combination of mixing and downwelling, (d) a combination of mixing and strong upwelling that forces the mixed layer to be shallower than the initial mixed layer depth, (e) very strong upwelling with an outcropping isotherm so that only upwelling works, and (f) only downwelling. The term h₀ is the initial mixed layer depth; h_E and h_T are the well-mixed layer thickness and transition layer thickness, respectively; and h_U is the vertical movement of the isotherm by upwelling (positive value) or downwelling (negative value). The dashed (solid) line is the temperature profile before (after) TC forcing. The blue (red) shadow represents a cold (warm) anomaly. ΔQ_init and ΔQ_mix are the heat changes in the initial mixed layer and forced mixed layer, respectively, and ΔQ_sub is the heat change in the subsurface between the initial and forced mixed layers. (g) Sketch of the effect of mixing and vertical advection (upwelling and downwelling) and the distribution of vertical temperature anomaly profiles in the across-track section of a tropical cyclone.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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(a)–(f) Sketches of the vertical upper ocean temperature profiles modulated by (a) only mixing, (b) a combination of mixing and moderate upwelling, (c) a combination of mixing and downwelling, (d) a combination of mixing and strong upwelling that forces the mixed layer to be shallower than the initial mixed layer depth, (e) very strong upwelling with an outcropping isotherm so that only upwelling works, and (f) only downwelling. The term h₀ is the initial mixed layer depth; h_E and h_T are the well-mixed layer thickness and transition layer thickness, respectively; and h_U is the vertical movement of the isotherm by upwelling (positive value) or downwelling (negative value). The dashed (solid) line is the temperature profile before (after) TC forcing. The blue (red) shadow represents a cold (warm) anomaly. ΔQ_init and ΔQ_mix are the heat changes in the initial mixed layer and forced mixed layer, respectively, and ΔQ_sub is the heat change in the subsurface between the initial and forced mixed layers. (g) Sketch of the effect of mixing and vertical advection (upwelling and downwelling) and the distribution of vertical temperature anomaly profiles in the across-track section of a tropical cyclone.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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b. Relative positions of the mixing and vertical advection

Because of the relative positions of mixing, upwelling, and downwelling, the vertical temperature profiles in Figs. 8a–f can exist on different across-track positions (see Fig. 8g). In the Northern Hemisphere, TCs cause strong upwelling on the right-rear part of a TC and downwelling in front of the TC and on both sides of the upwelling zone (Zhang et al. 2018). The vertical current shear instability is usually responsible for the deepening of the mixed layer (Lu et al. 2021). The TC induced mixing biases to the right side of the TC track because of the TC wind-current resonance (Price 1981, 1983; Price et al. 1986) and upwelling biases to the right side of the TC track because of the resonance of pressure gradient and current (Price 1983). Note that the rightward bias of mixing is greater than upwelling. As a result, a typical upper ocean temperature response biases to the right side of the TC track in the Northern Hemisphere (e.g., Lu et al. 2021; Price 1981; Price et al. 1986, 1994; Zhang et al. 2016, 2018).

The vertical temperature anomaly after a TC in the upwelling zone is similar to Fig. 8b when upwelling is moderate (S2 during Kalmaegi; Fig. 3k), similar to Fig. 8d when upwelling is strong (S1 and S3 during Kalmaegi; Figs. 3j,l). The condition that upwelling is too strong and isotherm outcrops (Fig. 8e) is not captured by our observation. The downwelling zones are on both sides of the upwelling zone (Fig. 8g), and the vertical temperature anomaly is similar to Fig. 8c, which is the condition of S4 during Rammasun (Fig. 4j) or S4 during Sarika (Fig. 4k). The vertical temperature anomaly turns to only warm anomaly under initial mixed layer as shown in Fig. 8f if mixing is small or no mixing, which is the condition of S4 during Haima (Fig. 4l). There will also be a “pure mixing” position with no vertical advection between the upwelling and downwelling zones, with a heat pump vertical temperature structure, although it seems not to be captured by our observation. In the Southern Hemisphere, the upper ocean response will bias the left side of the TC track with a mirrored flip of the left and right sides of Fig. 8g.

c. Temperature and heat change by mixing

Combining Eq. (3) with Eq. (2), the mixing-induced cold anomaly (ΔQ_cold) and warm anomaly (ΔQ_warm) are as follows:

$\mathrm{\Delta }{Q}_{\text{cold}}=-\mathrm{\Delta }{Q}_{\text{warm}}=\rho c_p\left(-\mathrm{\Delta }T{h}_0-\frac{\mathrm{\Delta }{T}^2}{2T_z}\right)=-\rho c_p\frac{h_E(h_E+h_T)(h_E{}^2+h_E{h}_T+4h_0{}^2+4h_0{h}_E+2h_T{h}_0)}{2{(2h_0+2h_E+h_T)}^2}{T}_z,$(6)

then the nondimensional mixing-induced cold anomaly ( $\mathrm{\Delta }{Q}_{\text{cold}}^{\prime }$) and warm anomaly ( $\mathrm{\Delta }{Q}_{\text{warm}}^{\prime }$) are

$\mathrm{\Delta }{Q}_{\text{cold}}^{\prime }=-\mathrm{\Delta }{Q}_{\text{warm}}^{\prime }=\frac{\mathrm{\Delta }{Q}_{\text{cold}}}{\rho c_p{h}_0{}^2{T}_z}=-\frac{H_E(H_E+H_T)(4+4H_E+H_E{}^2+2H_T{}^2+H_E{H}_T)}{2{(2+2H_E+H_T)}^2}.$(7)

Figure 9 shows the ΔSST′ and $\mathrm{\Delta }{Q}_{\text{cold}}^{\prime }$ on the nondimensional space of H_E and H_T. Figure 8a only shows ΔSST′ when H_U < 1 + H_E + H_T. TC induces only cold ΔSST', and its magnitude increases with the increases of H_E and H_T. Note that although H_E alters ΔSST' in a greater extent when H_E and H_T, H_T is usually several times greater than H_E (e.g., 2.5–40 times in our observation; Table 3), so the well-mixed layer and transition layer are both important for SST and upper ocean thermal change in the real world.

Nondimensional SST change [ $\mathrm{\Delta }\text{SS}{\text{T}}^{\prime }=\mathrm{\Delta }\text{SST}/(h_0{T}_z)$] and mixing-induced near-surface cold anomaly ( $\mathrm{\Delta }{Q}_{\text{cold}}{}^{\prime }$) on the parameter space of the nondimensional transition layer thickness ( $H_T=h_T/h_0$) and nondimensional well-mixed layer thickness ( $H_E=h_E/h_0$). Note that ΔSST′ in (a) is on the condition when the nondimensional upwelling depth H_U < 1 + H_E + H_T.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Nondimensional SST change [ $\mathrm{\Delta }\text{SS}{\text{T}}^{\prime }=\mathrm{\Delta }\text{SST}/(h_0{T}_z)$] and mixing-induced near-surface cold anomaly ( $\mathrm{\Delta }{Q}_{\text{cold}}{}^{\prime }$) on the parameter space of the nondimensional transition layer thickness ( $H_T=h_T/h_0$) and nondimensional well-mixed layer thickness ( $H_E=h_E/h_0$). Note that ΔSST′ in (a) is on the condition when the nondimensional upwelling depth H_U < 1 + H_E + H_T.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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Nondimensional SST change [ $\mathrm{\Delta }\text{SS}{\text{T}}^{\prime }=\mathrm{\Delta }\text{SST}/(h_0{T}_z)$] and mixing-induced near-surface cold anomaly ( $\mathrm{\Delta }{Q}_{\text{cold}}{}^{\prime }$) on the parameter space of the nondimensional transition layer thickness ( $H_T=h_T/h_0$) and nondimensional well-mixed layer thickness ( $H_E=h_E/h_0$). Note that ΔSST′ in (a) is on the condition when the nondimensional upwelling depth H_U < 1 + H_E + H_T.

Citation: Journal of Physical Oceanography 53, 2; 10.1175/JPO-D-22-0132.1

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d. Temperature and heat change by vertical advection

e. Validation by observation

The observation data at the stations are used to check the one-dimensional parameterization model results. The model-estimated ΔSST and heat change (Table 4) are close to those in observations after Kalmaegi, Sarika, and Haima (Table 3). However, after Rammasun, the model estimated ΔSST (−1.642°C) and heat content (ΔQ_init = −5.582 KJ cm⁻²; ΔQ_sub = 4.846 KJ cm⁻²) are warmer than observation (−3.682°C; −11.549 and 4.689 KJ cm⁻²). As shown in Table 1, the Rossby number for the mixed-layer current (R) was large (2.145), so the horizontal cold advection may be important at S2 after Rammasun, which is not considered in the one-dimensional parameterization model.

Table 4

Net temperature response at the observation stations by the one-dimensional theoretical model.

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Thus, the parameterizations are able to reproduce the SST and heat change in the upper ocean for fast-moving TCs when horizontal heat advection and air–sea heat flux is weak. Note that Table 4 uses one inertial period of average vertical movement of isotherms in the observation (h_U) for the calculation of H_U, and a simplified near-inertial movement of water. It also ignored the delay of vertical advection relative to mixing. The choice of mixed layer and vertical movement distance can improve the parameterization, but I do not pursue this issue further, as it would make the usage of the simplified model more complicated and require more observation data for validation.

a. Effect of surface heat flux

Different from expectations, the SST, heat content in the initial mixed layer (Q_init) and TCHP did not recover back to pre-TC conditions after the four TCs at the observation stations. Thus, it was determined that a TC breaks the local air–sea heat balance, which does not return to pre-TC conditions, especially during the cooling phase of the seasonal cycle (e.g., from summer to winter). In contrast, the SST seems to have entered another air–sea heat balance. As TCs influence the subtropical ocean every year, their cumulative effect may influence the local air–sea heat budget. For example, subtropical ocean surfaces may be warmer without TCs. However, more observations and studies are needed to determine whether the insufficient surface and near-surface recovery are unique or universal.

b. Combined effect of mixing and advection on heat

Because of the heat conservation, although the subsurface was not as warm as the pure heat pump assumption, the cold suction effect actually modulated the subsurface warm anomalies deeper into the ocean than the forced layer. Thus, TC modulated warm surface water into the subsurface and deeper waters. In particular, the TC-induced combined effect of the heat pump and cold suction and the downward propagation of the temperature anomaly after a TC may be an important way for surface heat to transfer into the ocean interior (e.g., the propagation of surface global warming signals into the ocean interior and deep ocean). Note that the combination effect of heat pump and cold suction cause net cold heat change near the TC core region, as the cooling caused by upwelling is narrow near the TC track and warming by downwelling is extensive that on both sides of upwelling region. After TCs, some heat anomaly may stay in the ocean along with the geostrophic adjustment. Lu et al. (2020) and Park et al. (2021) did some pioneering work about the geostrophic response that perturbs the underlying ocean eddy after a TC, which may merit applying a similar method for the temperature and heat modulation by geostrophic adjustment after a TC in further studies.

c. Control factors of the upper ocean temperature response

Generally, mixing depends on the intensity of TC wind stress, vertical advection depends on the intensity of the wind stress curl, and both depend on the upper ocean temperature structure. Previous research has shown that the upper ocean temperature response to TCs depends on the TC parameters (e.g., translation speed and wind speed) (Lu et al. 2021; Potter et al. 2017) and ocean conditions (e.g., SST, ocean stratification, and TC heat potential) (Busireddy et al. 2019; Potter and Rudzin 2021). Miyamoto et al. (2017) showed that the deepening of the mixed layer by a TC depends on a nondimensional number C_o, which is the ratio of TC-induced velocity shear per depth in the initial mixed layer to the static stability beneath the mixed layer. Large-scale phenomena, such as El Niño–Southern Oscillation (ENSO), the Pacific decadal oscillation (PDO), and the North Atlantic Oscillation (NAO), can also modulate the upper ocean feedback to TCs through the influence of ocean stratification and TC-induced mixing (Cao et al. 2021).

The parameterization in section 4 show that we can estimate the change of signal-point upper ocean temperature profile and heat content after a TC with initial temperature profile, mixing depth (H_E, H_T), and upwelling depth (H_U) after fast-moving TC with low Rossby number for the mixed-layer current. As H_E, H_T, and H_U are controlled by TC parameters and ocean conditions, it is possible to estimate post-TC ocean single-point vertical temperature profile and heat content change based on tropical cyclone (or wind) characteristics and initial ocean temperature condition. In summary, further research on TC parameters, ocean conditions, and background processes that influence TC-induced SST and upper ocean heat responses is merited.