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Journal of Tropical Oceanography >

2020 , Vol. 39 >Issue 2: 1 - 10

DOI: https://doi.org/10.11978/2019038

Marine Hydrology

The main heaving modes in the Pacific Ocean

  • Qihua Peng , 1, 2 ,
  • Ruixin Huang 1, 3 ,
  • Weiqiang Wang 1 ,
  • Dongxiao Wang 1
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  • 1. State Key Laboratory of Tropical Oceanography (South China Sea Institute of Oceanology, Chinese Academy of Sciences), Guangzhou 510301, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA;

Received date: 2019-04-17

  Request revised date: 2019-05-05

  Online published: 2020-03-10

Supported by

Foundation item: Strategic Priority Research Programs of the Chinese Academy of Sciences(XDA20060500)

National Natural Science Foundation of China(41521005, 41676013)

National Key Research and Development Project(2016YFC1401401)

Independent project of State Key Laboratory of Tropical Oceanography(LTOZZ1702)

Copyright

Copyright reserved © 2019. Office of Acta Agronomica Sinica All articles published represent the opinions of the authors, and do not reflect the official policy of the Chinese Medical Association or the Editorial Board, unless this is clearly specified.
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Abstract

The spatial-temporal variability of heaving mode in the ocean is critical to understanding climate variability on interannual and decadal time scales. Using reanalysis data and a reduced gravity model, we investigated the leading heaving modes in the Pacific Ocean. The heaving signals are dominated by two modes: the first mode in which thermocline depth anomalies in the eastern and western equatorial Pacific have opposite signs, and the second mode in which thermocline depth anomalies in the equatorial and subtropical Pacific Ocean have opposite signs. The time evolution of these two heaving modes and the physics leading to these two modes were explored. Results indicate that the first mode is directly linked to equatorial zonal wind anomalies, and the second mode is induced by the wind stress curl anomaly in the subtropics. Furthermore, these two leading heaving modes have profound impacts on basin-scale heat transport (with an amplitude of 51014W) and ocean heat content redistribution (with an amplitude of 1.5×1020J) through ocean waves and Ekman transport, highlighting the importance of heaving modes in modifying the variabilities of the climate system and climate change.

Key words： Heaving mode; Pacific Ocean; ocean wave; heat transport; climate change

Cite this article

Qihua Peng , Ruixin Huang , Weiqiang Wang , Dongxiao Wang . The main heaving modes in the Pacific Ocean[J]. Journal of Tropical Oceanography, 2020 , 39(2) : 1 -10 . DOI: 10.11978/2019038

In general, anomalous climate signals in the world oceans can be classified into three basic categories: warming (cooling), freshening (salinification) and heaving, as postulated by Bindoff and McDougall (1994). The meaning of heaving mode in the world oceans was further explored through simple reduced gravity models (Huang, 2015). Since the simple reduced gravity model is based on the assumption of adiabatic motion, the heaving modes simulated by such models are adiabatic heaving modes. It is, however, difficult to separate the motion in the ocean into adiabatic and diabatic components. In this study, we adopted a working assumption: heaving is vertical motion of isopycnal/isotherm. Heaving may be primarily induced by wind stress perturbation without any heat and salt exchanges with the environment. Indeed, heat and salt exchanges can also lead to vertical motion of isopycnal/isotherm; however, the exact nature of heaving modes defined in this way is left for further study.
The oceans play a vital role in the climate system because they can store and transport tremendous amount of heat. In fact, the oceans store up to 90% of the heat buildup caused by increased greenhouse gas concentrations (Trenberth et al, 2013; Chen et al, 2014). The redistribution of the heat in the ocean can affect the properties of the overlying atmosphere, the radiation balance, hence modifying the ongoing climate change (Levitus et al, 2000; Balmaseda et al, 2013). Indeed, both thermohaline circulation and wind-driven circulation are important in redistributing the ocean heat content (Ganachaud et al, 2000; Willis et al, 2004; Lumpkin et al, 2007; Lee et al, 2011; Chen et al, 2014; Liu et al, 2016). On the one hand, the thermohaline circulation is important in heat transport, such as the Atlantic thermohaline circulation (THC) (Clark et al, 2002). On the other hand, heat transport can also be directly related to wind-driven adiabatic motion, i.e., the heaving of the isopycnal faces. Indeed, the effect of wind-related surface ocean anomalies can be transported to remote areas through adjustment of global ocean circulation and wave dynamics. As a result, heaving can induce large-scale ocean heat content redistribution, ranging from basin scale to inter-basin scale.
The recent global surface warming hiatus (add citations) is a good example to highlight the importance of heaving mode. It is evident that the hiatus is closely associated with the negative phase of the interdecadal Pacific oscillation (IPO), manifested as a La Niña-like cooling and intensified easterly wind over the equatorial Pacific (Kosaka et al, 2013; England et al, 2014; Meehl et al, 2014; Trenberth et al, 2014). Huang (2015) and Liu et al (2016) further suggested that the redistribution of heat content in the ocean, induced by heaving mode, is closely tied to the surface warming hiatus. Thus, heaving mode is important in climate change, and a better understanding of heaving signals is of great scientific interest and social relevance.
The theoretical basis and possible impacts of heaving mode have been systematically discussed by several studies. Huang (2015) investigated the adjustment of basin-scale warm water to different wind stress perturbations. The author suggested that the vertical movement of isopycnal can induce three-dimensional redistribution of heat content in the ocean and further affect the climate. His results imply that heaving modes can make vital contributions to the transient meridional overturning circulation (MOC) (with a non-negligible magnitude of 0.4×106 m3·s-1), poleward heat flux (with an amplitude of 2.8×1013 W) and vertical heat flux (with an amplitude of 1.0×1013 W), which have significant impacts on the global climate.
Based on Huang (2015), Tan et al (2015) proposed that the zonal overturning circulation (ZOC) and its associated zonal heat flux (ZHF) induced by heaving in the Pacific Ocean are important in the climate system. Based on idealized model setting, they suggested that the intensified equatorial easterly on decadal time scale can lead to a negative ZOC with a non-negligible magnitude (-0.3×106 m3·s-1) and a considerable westward ZHF with an amplitude of -1.12×1013 W, indicating that the anomalous ZOC and ZHF may consist of a major part of climate signals on decadal time scale.
These works have established the theoretical basis of heaving mode. Although experiments based on such idealized box models revealed important aspects of heaving modes in the ocean, the structures of heaving modes in the world oceans are waiting to be revealed using realistic climate data. Indeed, the main spatial-temporal variabilities of heaving signals in the real oceans, the underlying mechanisms, and the resultant heat transport are still unclear.
In the present study, we investigate the above questions using both reanalysis data and a reduced gravity model. Specifically, the reanalysis data are used to identify the main spatial patterns of heaving modes and associated wind stress perturbations in the Pacific Ocean. Our results show that there are two leading heaving modes in the Pacific Ocean, and both of these modes are characterized by significant wind perturbations in the Pacific Ocean. In addition, reduced gravity model experiments indicate that these leading modes are directly related to the adjustment of wind-driven circulations in the upper ocean through large-scale wave dynamics and Ekman dynamics. Furthermore, our model results reveal that the two leading heaving modes can induce large amount of heat transport in the Pacific Ocean, playing key roles in the climate system.
The rest of the paper is organized as follows. In section 1, we present an overview of the data and reduced gravity model. In section 2, we explore the main spatial-temporal variabilities of primary heaving modes in the Pacific Ocean and their associated physical processes. We also clarify the implications of these main heaving modes. In section 3, we discuss the asymmetric pattern and decadal trend of the second heaving mode. Finally, conclusions are given in section 4.

1 Methodology

1.1 Data and methods

The Simple Ocean Data Assimilation reanalysis (SODA 2.1.6) for the period 1958—2008 (Carton et al, 2008) is used for this study. Their model is based on the Parallel Ocean Program (POP) version 2.1, with an original resolution of 0.25°×0.4° and 40 vertical levels, but outputs were conservatively remapped onto a uniform 0.5°× 0.5° grid.
To diagnose the leading heaving modes in the SODA data, we carry out a combined empirical orthogonal function (CEOF) analysis on the main thermocline depth anomalies, which is represented by the depth of 15℃ isotherm (D15) (Capotondi et al, 2003; Deser et al, 2012), and on wind stress anomalies. The CEOF results (Figs. 1 and 2) thus denote the thermocline signals induced by wind stress perturbations. Note that the shifting of isotherms is due to the combination of the adiabatic movements induced by wind stress perturbations and the diabatic effects of internal heating/cooling; thus, such signals consist of both adiabatic heaving signals and diabatic signals. To separate the adiabatic heaving signals from the other diabatic signals, we perform several experiments to confirm the dominance of heaving signals in the leading CEOF modes (see section 1.2).
Fig. 1 CEOF1 (26%) of D15 anomalies (shading; dimensionless) and wind stress anomalies (vector; units: N·m-2) regressed against PC1 (a) and the corresponding PC time series (standardized) for CEOF1 (b)
Fig. 2 CEOF2 (20%) of D15 anomalies (shading; dimensionless) and wind stress anomalies (vector; units: N·m-2) regressed against PC2 (a) and the corresponding PC time series (standardized) for CEOF2 (b)

1.2 Model experiments

A simple reduced gravity model is used to investigate the heaving mode induced by wind perturbation. The patterns produced by the model can be compared with those diagnosed from the SODA data. The reduced gravity model is based on the adiabatic assumption that the total amount of warm water volume (WWV) in the upper layer is conserved. In the model, the momentum and continuity equations (Qiu et al, 2012) are:
$\frac{\partial u}{\partial t}+\zeta k \times u=-\Delta E+A_{h} \Delta^{2}u+\frac{\tau}{\rho_{0}H}$
$\frac{\partial H}{\partial t}+\Delta \cdot (Hu)=0$
where u=(u, v) is horizontal velocity, $\zeta=f+k \cdot \Delta \times u$ is absolute vorticity, $E=g'H+(u^2+\nu ^2)/2$ is the total energy, τ is surface wind stress vector, Ah is the horizontal eddy viscosity coefficient, H is the time-varying upper-ocean layer thickness, and ρ0 is the reference density.
The model domain is 120°E—70°W, 40°S—40°N; the resolution is 0.25°× 0.25°. The model is initialized with a uniform layer thickness of 300 m and has parameter values g′=0.03 m·s-2 and Ah=8000 m2·s-1. The model is forced by monthly wind stress data of 1958—2008 from the European Centre for Medium Range Forecasts (ECMWF) atmospheric reanalysis (ERA-40). It takes 50 years for the model to reach a quasi-equilibrium state, which is used as the reference state.
To study the relationship between the leading thermocline modes and associated wind stress perturbations, we carry out four experiments (Tab. 1). In each experiment, the model is restarted from the reference state at year 50, and forced by composite wind stress of the leading modes. The differences between the state of each of these experiments and the reference state are used to show the effects of wind stress perturbations on the leading thermocline modes.
Tab. 1 Description of model experiments
Experiment Forcing
EXP1 Composite winds during the positive phase of CEOF1
EXP2 Composite winds during the negative phase of CEOF1
EXP3 Composite winds during the positive phase of CEOF2
EXP4 Composite winds during the negative phase of CEOF2

2 Results

2.1 Spatial-temporal heaving variability in the Pacific Ocean

The leading CEOF mode of the thermocline and wind stress, accounting for 26% of the total variance, features a typical zonal dipole mode of D15 in the equatorial Pacific Ocean (Fig. 1a). The spatial pattern is similar to the thermocline depth anomalies during El Niño-Southern Oscillation (ENSO) events (Meinen et al, 2000; McGregor et al, 2013). The corresponding wind perturbations are characterized by strong anomalous westerlies centered in the central and western equatorial Pacific (Fig. 1a). PC1 is highly correlated with Nino 3.4 (r=0.85), demonstrating the strong link between this mode and ENSO.
To confirm the dynamic connection between the zonal tilt of thermocline anomalies in CEOF1 and the wind anomaly, we performed two experiments with the reduced gravity model (see Tab. 1). When forced by the superposition of the climatological wind and the composite wind anomalies of CEOF1, the model can reproduce the east-west dipole structure of thermocline anomalies in both phases (Figs. 3b and 3d). This is quite similar to the composites of the reanalysis data (Figs. 3a and 3c), demonstrating that this zonal dipole mode is primarily induced by anomalous wind stress. Therefore, the first mode is essentially an adiabatic heaving mode.
Fig. 3 Composite D15 anomalies (shading; units: m) of CEOF1 diagnosed from SODA (left panels) and from EXP1/EXP2 (right panels). Top panels are for the positive phase, and bottom panels, for the negative phase. Contours in the left panels indicate composite wind stress curl (contour interval=1×10-8 N·m-3, positive in black and negative in green), and vectors in the right panels denote composite wind stress anomalies (units: N·m-2). The output is obtained on day 120, a time for the Kelvin and Rossby waves to adjust to large D15 anomalies in the eastern and western equatorial Pacific Ocean
The CEOF2, accounting for 20% of the total variance, features a “sandwich” structure in the meridional direction, consisting of two positive thermocline depth bands over the subtropical regions in both hemispheres divided by a negative thermocline depth band near the equator (Fig. 2a). The concurrent wind stress anomalies are characterized by a complicated structure: anticyclone winds over a broad band of the subtropics, easterly wind anomalies in the western equatorial Pacific, and westerly wind anomalies in the southeastern equatorial region (Fig. 2a). Note that both D15 and wind stress anomalies are not confined to the tropical regions but extend farther poleward. Most remarkably, the corresponding PC2 shows a linearly increasing trend, implying a persistent reduction of warm water over the equatorial region and an increase of warm water in the subtropical regions since 1958. To our knowledge, this broad heaving mode has not been previously discussed in the literature.
EXP3 and EXP4 are performed to explore the contribution of wind anomalies in the second mode. Forced by the climatological wind plus the anomalous winds shown in Figs. 4b and 4d, our model can reproduce the key features of the second mode in both positive and negative phases. Specifically, the simulated results exhibit a decrease (increase) of D15 in the equatorial band whereas an increase (increase) of D15 exists in the subtropical regions, which is quite similar to the reanalysis results (Figs. 4a and 4c). This confirms that the second mode is primarily due to wind anomalies, and dominated by adiabatic heaving signals.
Fig. 4 Composite D15 anomalies (shading; units: m) of CEOF2 diagnosed from SODA (left panels) and from EXP3/EXP4 (right panels). Contours in the left panels indicate composite wind stress curl (contour interval=1×10-8 N·m-3, positive in black and negative in green), and vectors in the right panels denote composite wind stress anomalies (units: N·m-2). The output is obtained on day 360, a time for the Rossby waves and currents (much slower than Kelvin waves) to adjust to large D15 anomalies in the equatorial and subtropical Pacific Ocean

2.2 The physical processes underlying the heaving patterns

Figures 3 and 4 show that these two leading modes are nearly symmetric for the positive and negative phases. For the sake of brevity, we restrict our discussion to the positive phase of these two modes.
2.2.1 The first heaving mode
The motivation of this research is not only to characterize the structure of the thermocline and associated wind stress anomalies, but also to understand the mechanism and climate significance of these two modes. We examine the evolution of thermocline in the first heaving mode here. Given the close connection of the mode with the ENSO thermocline undulation, we infer the wave dynamics associated with ENSO may play a role. Even though the evolution of thermocline during ENSO is well documented (e.g., Jin, 1997; Bunge et al, 2014; Zhang et al, 2016; Wang et al, 2018), we still present it here so as to compare it with the mechanism of the second heaving mode discussed next.
Similar to the ENSO dynamics, wave dynamics play a vital role in generating the east-west dipole thermocline structure during the first heaving mode: westerly wind stress anomalies in the central and western Pacific generate strong eastward propagating downwelling equatorial Kelvin waves (Fig. 5a, thick line) and westward propagating upwelling Rossby waves off the equator in the western Pacific (Fig. 5a, dashed line). These waves have opposite impacts on the thermocline depth anomalies (Fig. 6a) and finally create the zonal dipole mode of D15 in the equatorial Pacific Ocean.
Fig. 5 Hovmöller diagrams for simulated D15 anomalies (shading; units: m) from EXP1 along the equator (a) and the latitude band of 10°N (c). (b) and (d) are the same as (a) and (c), except for the outputs of EXP3. The solid black line indicates Kelvin wave propagation, and the dashed black line denotes Rossby wave propagation
Fig. 6 Schematics for the first heaving mode (a) and the second heaving mode (b). Composite wind stress anomalies (vector; units: N·m-2) of the two modes are plotted. The wavy lines (downwelling in red and upwelling in blue) denote ocean waves (including Kelvin waves and Rossby waves), and the dashed vectors indicate wind-driven currents. The ellipses (downwelling-favorable wind anomalies in red and equatorial wind perturbations in yellow) indicate the key wind stress perturbation regions
2.2.2 The second heaving mode
The second mode is also characterized by downwelling equatorial Kelvin waves and upwelling Rossby waves (Figs. 5b and 5d). However, unlike the first heaving mode, the location of the westerly wind perturbation associated with the second heaving mode is closer to the eastern boundary (Fig. 2a). As a result, the downwelling Kelvin waves arrive at the eastern boundary in only 20 days. In contrast, the concurrent upwelling Rossby waves propagate continuously towards the west coast throughout the Pacific basin, resulting in a broad band of negative D15 anomalies near the equator (Figs. 4a and 4b). In addition, there are strong anomalous easterlies near the equator to the south of the anticyclone over the northwestern Pacific Ocean (Fig. 6b), which can also trigger upwelling Kelvin waves (not shown), and hence also raise the thermocline over the equatorial band.
Upon arriving at the coast, the positive D15 anomalies (equatorial Kelvin waves) propagate poleward as coastal Kelvin waves. Outside the equator, parts of the poleward downwelling coastal Kelvin waves transform into westward-propagating downwelling Rossby waves. The phase speed of these waves along 10°N is about -0.20 m·s-1 (Fig. 5d), consisting with the theoretical Rossby wave phase speed. These downwelling Rossby waves further contribute to deepening thermocline over the northeastern subtropical Pacific Ocean.
Interestingly, there is a significant accumulation of warm water in the subtropical Pacific west of 160°W (Fig. 5d, green box), and there are no westward-propagating downwelling Rossby waves in this region (Fig. 5d). Indeed, the thermocline anomalies in the northwestern Pacific Ocean are dynamically consistent with the anticyclone (the western North Pacific subtropical anticyclone) (Fig. 4b) in the area of the Philippine Sea (Wang et al, 1999; Wang et al, 2001; Xie et al, 2009; Du et al, 2009). The associated negative anomalous wind stress curl (Fig. 4a) drives strong downward motion in the Ekman layer [ωek=cyrl(τ/fρ0), where ωek is the vertical velocity at the bottom of Ekman layer], deepening thermocline there (Wang et al, 1999; Ishida et al, 2008; Yang et al, 2011; Huang et al, 2018; Yang et al, 2018). Indeed, negative wind stress curl is not confined to the northwestern Pacific but extends to a broad band of the subtropical Pacific regions in the two hemispheres, which is dynamically consistent with a wide range of D15 anomalies over the subtropical regions.
Overall, our results reveal that for the second heaving mode, the upwelling equatorial waves play a key role in raising the thermocline in the equatorial region, and both downwelling Rossby waves and local negative wind stress curl anomalies contribute to the deepening of thermocline over a broad band of the subtropical Pacific (Fig. 6b).

2.3 Impacts of heaving patterns

The adjustment of thermocline of the two leading heaving modes in the Pacific Ocean implies strong zonal and meridional heat transports, which are defined as follows:
$HT_{zonal}(x,t)=\rho_{0}C_{p}T \cdot [\int_{y_{s}}^{y_{n}}u(x,y,t) \cdot h(x,y,t)dy-\int_{y_{s}}^{y_{n}}u(x,y,0) \cdot h(x,y,0)dy]$
$HT_{meri}(y,t)=\rho_{0}C_{p}T \cdot [\int_{x_{w}}^{x_{c}}\nu(x,y,t) \cdot h(x,y,t)dx-\int_{x_{w}}^{x_{c}}\nu(x,y,0) \cdot h(x,y,0)dx]$
where HTzonal and HTmeri donate zonal and meridional heat transports, respectively. In (4), ρ0= 1035 kg·s-3 is the reference density, Cp = 4186 J·kg-1·°C-1 is the heat capacity, T=15°C is the mean temperature of the upper layer; ys and yn are the southern and northern boundaries, respectively; xe and xw are the eastern and western boundaries, respectively; u(x, y, t) and v(x, y, t) are zonal and meridional velocities at time t, respectively; u(x, y, 0) and v(x, y, 0) are climatological zonal and meridional velocities, respectively; h(x, y, t) is the thermocline depth at time t, and h(x, y, 0) represents climatological thermocline depth.
The zonal and meridional heat transports lead to heat content redistribution, defined as follows:
$HC_{zonal}(x,t)=\int_{y_{s}}^{y_{n}} \rho_{0}C_{p}T \cdot \Delta h(x,y,t) \Delta x dy$
$HC_{meri}(y,t)=\int_{x_{w}}^{x_{c}} \rho_{0}C_{p}T \cdot \Delta h(x,y,t) \Delta y dx$
where ∆h is the difference of thermocline depth between the control run and sensitive experiment. ∆x (∆y) is the grid size in the x-direction (y-direction).
Figures 7a and 7b show that the first heaving mode can induce large heat transports in both zonal and meridional directions. In the zonal direction, the adjustment of equatorial waves can induce strong net eastward heat transport through affecting zonal currents and thermocline depth (Fig. 7b). The amplitude of these net heat transports is nearly 0.5 PW (1 PW =1015 W), which can further induce strong heat content redistribution with an amplitude of 1×1020 J (Fig. 8b). In the meridional direction, the poleward propagating coastal Kelvin waves and Sverdrup transport (Jin, 1997) can efficiently remove heat from the equatorial eastern Pacific to higher latitudes (Fig. 7a). The resultant heat content redistribution is about -8×1019 J in the equatorial Pacific and 4×1019 J in the subtropical Pacific.
Fig. 7 Total heat transport (shading; units: W) of EXP1 in the meridional (a) and zonal directions (b). (c) and (d) are the same as (a) and (b), except for EXP3
Fig. 8 Heat content redistribution (shading; units: J) of EXP1 in the meridional (a) and zonal directions (b). (c) and (d) are the same as (a) and (b), except for EXP3
For the second heaving mode, as the eastward heat transport (e.g., during 1~120 days) counteracts against the westward heat transport (during 150~360 days) (Fig. 7d), the resultant net zonal heat transport and heat content redistribution are relatively small (Fig. 8d). Nevertheless, the amplitude of poleward heat transport is large (Fig. 7c). As mentioned above, the negative wind stress curl can induce robust Ekman downwelling and deepen thermocline in the subtropical regions, driving poleward Ekman transport from the equatorial band to higher latitudes. Besides, the poleward downwelling coastal Kelvin waves at the eastern boundary also move heat from the equator to higher latitudes. The above poleward heat transports finally result in considerable heat content redistribution with a magnitude of -2×1020 J in the equatorial Pacific and 1×1020 J in the subtropical Pacific (Fig. 8c), highlighting the key role of this heaving mode in redistributing heat in the oceans.

3 Discussion

In this study, we systematically investigate the mechanmism and impacts of the second heaving mode. Some interesting features are revealed for this heaving mode.
Both reanalysis data and model outputs show that the D15 anomalies are strongly asymmetric with respect to the equator in the western Pacific: thermocline anomalies are characterized by large positive values in the northwestern Pacific (120°— 160°W, 0°—20°N) whereas weak negative values appear in the southwestern Pacific (120°—160°W, 20°S—0°) (Fig. 4a). Indeed, the pattern of thermocline depth anomalies is dynamically consistent with the wind stress curl pattern. Here, we suggest that the asymmetric wind stress curl (Fig. 4a) plays a crucial role in this cross-equatorial asymmetric D15 pattern. Specifically, there is robustly negative wind stress curl over the northwestern Pacific, inducing strong downward motion in the upper ocean and hence deepening the thermocline there. Nevertheless, the negative wind stress curl over the southwestern Pacific is much smaller, leading to much smaller thermocline anomalies there.
Notably, PC2 exhibits an increasing trend since 1958 (Fig. 2b), implying a decrease of WWV over the equatorial band and an increase of WWV over the subtropical regions. Previous studies found that WWV plays a vital role in the development and decay of ENSO (Wyrtki, 1985; Jin, 1997). This decadal shift of warm water, which is mainly induced by the second heaving mode, can definitely affect the evolution and diversity of the ENSO (Zhang et al, 2007; Timmermann et al, 2018; Xie et al, 2018; Peng et al, 2019). Investigation on the relation between this decadal trend and ENSO is underway.

4 Conclusions

In the present study, we utilized SODA data and a reduced gravity model to reveal two leading heaving modes in the Pacific Ocean. The first heaving mode is
characterized by east-west dipole thermocline depth anomalies, and the second heaving mode exhibits a distinctive “sandwich” pattern in the meridional direction, with thermocline depth anomalies in the equatorial band and the opposite sign in the subtropical Pacific.
For the first heaving mode, the westerly wind stress perturbations over the central and western equatorial Pacific trigger eastward-propagating downwelling equatorial Kelvin waves and westward- propagating upwelling Rossby waves. These Kelvin waves and Rossby waves have inverse impacts on the thermocline depth anomalies on the two sides, and finally result in the zonal dipole mode of D15 in the equatorial Pacific Ocean. Since many of these features for the first heaving mode have been documented previously, we present them here to provide a basis for understanding similar behaviors associated with the second leading heaving mode.
For the second heaving mode, the upwelling ocean waves near the equator lead to the reduction of warm water in the equatorial band. As a result, the thermocline moves up near the equator. Besides, the downwelling Rossby waves in the subtropical regions and the negative wind stress curl work constructively to deepen the thermocline in the subtropical Pacific. As a result, the thermocline depth anomalies exhibit opposite signs between the equatorial band and subtropical region.
One of the most important impacts of heaving mode is the redistribution of warm water and thus heat content in the oceans (Huang, 2015). Our model results reveal that both leading heaving modes have profound impacts on the transport and redistribution of ocean heat content. Specifically, the first heaving mode can induce significant heat content redistribution in the zonal and meridional directions with an amplitude of 1.0×1020 J. In contrast, the second heaving mode has profound impact only on the meridional heat content redistribution (~2×1020 J). The decadal trend of the second heaving mode implies a significant decrease of WWV near the equatorial band, which may have profound impacts on ENSO evolution and diversity. Overall, our results highlight the importance of heaving in modifying the variabilities of the climate system and climate change.

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