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    In situ observations of (a),(e) meridional velocity; and (b)–(d), (f)–(h) temperature (left) 80.5°E and (right) 90°E. The velocity time series are measured at the equator. The temperature time series are observations at 1.5°N in (b),(f); the equator in (c),(g); and 1.5°S in (d),(h). Data gaps are interpolated as described in the text. Temperature data are interpolated to the levels of ADCP observations. Cross marks at the left in the temperature plots indicate the depths of thermal sensors.

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    Variance-preserving spectra of meridional velocity in the upper 200 m for (a),(c) in situ observations; and (b),(d) the Ocean General Circulation Model for the Earth Simulator (OFES) OGCM at (left) 0°, 80.5°E and (right) 0°, 90°E. White vertical dashed lines mark the periods of 10, 20, and 50 days.

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    (a) Squared coherency and (c) phase difference for the observed meridional velocity between (0°, 80.5°E) and (0°, 90°E). The time series at 50-m depth at 0°, 80.5°E is used as an index. (b),(d) As in (a),(c), but for the OFES OGCM. The phase is shown only when the corresponding coherency is significant at the 99% level.

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    Dispersion relations for mixed Rossby gravity waves and the second and fourth meridional mode Rossby waves for the first baroclinic mode. The wavelengths and periods, estimated by coherence analysis between (0°, 80.5°E) and (0°, 90°E), are marked only if their coherence is significant at the 99% level. Results are shown for the meridional velocity at 50-m depth (blue marks) and the meridional gradient of temperature at 80-m depth (red marks). Asterisks and crosses are for the in situ observations and the OFES OGCM, respectively. The analysis period for meridional velocity (temperature gradient) is from 27 October 2004 to 17 October 2008 (from 17 September 2006 to 28 May 2008), which is the period when available records at 80.5° and 90°E overlap. Note that the OGCM results are output at 3-day intervals and that the variability around the 7-day period (marked by the red cross) is possibly not resolved well.

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    (a),(d) Mean temperature; (b),(e) variance-preserving spectra for temperature; and (c),(f) variance-preserving spectra for meridional gradient of temperature at 0°, 80.5°E for (top) in situ observations and (bottom) the OFES OGCM. Note that the scales for (c) and (f) are different.

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    Vertical profiles of (a),(b) mean meridional velocity [υ] (where square brackets denote long-term mean); (c),(d) mean meridional heat flux [υT]; and (e),(f) mean meridional heat advection at (top) 0°, 80.5°E and (bottom) 0°, 90°E. Red and blue lines are for in situ observations and the OFES OGCM, respectively. Green lines are the same as the blue lines except that the temperature gradient is computed between 1.5°S and 1.5°N to be consistent with the observational estimates. Dotted lines show the contributions from the mean field, which are defined as [υ][T] for (c),(d) and −[υ] for (e),(f).

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    The 10–30 day variability in OFES OGCM meridional velocity at 0°, 80°E and 120-m depth. Overplotted are one standard deviation (red line), and the northward velocity events whose magnitude exceeds one standard deviation (red diamonds).

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    (a)–(e) Composites of 10–30-day variability in OFES OGCM horizontal velocity (vectors) and temperature (colors) at 120-m depth for (from top to bottom) day −6, −3, 0, +3, and +6. Black circles show the location of the velocity index shown in Fig. 7. The full period of the model integration (1999–2009) is used to make the composites. (f)–(j) As in (a)–(e), but for horizontal patterns of velocity (vectors) and dynamic pressure (colors) for free mixed Rossby gravity waves of the first baroclinic mode at period of 14 days. The theoretical wave patterns are plotted in such a way that meridional velocity on the equator peaks at x = 0° and day 0.

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    The long-term mean of eddy meridional heat advection averaged over 50–150-m depth in the OFES OGCM. Eddy heat advection is defined as the total advection minus the contribution from the mean field .

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    (a),(c) Amplitudes and (b),(d) phases of cross spectra between meridional velocity and meridional temperature gradient at 0°, 80.5°E for in situ observations in (a),(b) and the OFES OGCM in (c),(d). The phase of the observational (or OGCM) results is shown only if the corresponding amplitude >0.1 (0.2).

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    Composites of the meridional momentum budget terms at 0°, 80.5°E and 120-m depth obtained from the OFES OGCM. The analysis period is from 1999 to 2009, and a 10–30-day bandpass filter is applied before the analysis. The composites are based on the northward velocity events shown in Fig. 7. Results are shown for the tendency term of meridional velocity (black), the momentum advection term (blue), the meridional pressure gradient force term (red), and the viscosity term (dotted). The viscosity term is computed as the residual of the budget. The Coriolis force term is negligible and has thus been omitted.

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    (a)–(c) 10–30-day variability in meridional temperature gradient (; colors) and meridional pressure gradient (; contours) along the equator for day −3, 0, and +3, respectively. (d) Time series of (solid line) and (dotted line) at (0°, 80°E) and 105-m depth. All the variables are obtained from the OFES OGCM output for 1999–2009 and composited based on the northward velocity events in Fig. 7. The contour interval for pressure gradient is 2 × 10−5 cm2 s−1. Negative values are shown with dotted–dashed lines. Zero contours are omitted. In (d), the scale for () is shown on the left (right).

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    As in Figs. 12a–c, but for temperature (colors) and vertical velocity (contours) along 2°N. The contour interval is 5 × 10−4 cm s−1. Vertical velocity is zonally smoothed with a 7-point boxcar filter.

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    Phase (solid line) and amplitude (dotted line) of the leading mode of a complex empirical orthogonal function analysis applied to the 10–30-day variability of equatorial (averaged between 0.5°S and 0.5°N) meridional wind stress. QSCAT winds are converted to wind stress using a standard bulk formula. The explained variance of the leading mode is about 35%. The scale of the phase (amplitude) is shown on the left (right).

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    Vertical velocity along 2°N obtained from (a) the OFES OGCM and (b)–(d) the linear continuously stratified model. The OGCM results are composited based on the northward velocity events obtained from output for 1999–2009. The linear model is forced by an idealized meridional wind forcing, whose period is 20 days and whose zonal wavelengths are 60°, 30°, and 120° in (b),(c), and (d), respectively. The solutions of the linear model represent the sums over the first 50 baroclinic modes of the mixed Rossby gravity waves. The contour interval is 5 × 10−4 cm s−1. Negative values are shaded and zero contours are omitted. Thick dashed lines show a reference inclination of 50 m (10°)−1.

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Meridional Heat Advection due to Mixed Rossby Gravity Waves in the Equatorial Indian Ocean

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  • 1 Japan Agency for Marine-Earth Science and Technology/Research Institute for Global Change, Kanagawa, Japan
  • | 2 Japan Agency for Marine-Earth Science and Technology/Research Institute for Global Change, Kanagawa, and The University of Tokyo/Graduate School of Science, Tokyo, Japan
  • | 3 Japan Agency for Marine-Earth Science and Technology/Research Institute for Global Change, Kanagawa, Japan
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Abstract

This study examines heat advection due to mixed Rossby gravity waves in the equatorial Indian Ocean using moored buoy observations at (0°, 80.5°E) and (0°, 90°E) and an ocean general circulation model (OGCM) output. Variability associated with mixed Rossby gravity waves is defined as that at periods of 10–30 days, where both observations and the OGCM results show high energy in meridional velocity and meridional gradient of temperature. The 10–30-day variability in meridional velocity causes convergence of heat flux onto the equator, the net effect of which amounts to 2.5°C month−1 warming at the depth of the thermocline. Detailed analysis shows that the wave structure manifested in temperature and velocity is tilted in the xz plane, which causes the phase lag between meridional velocity and meridional temperature gradient to be a half cycle on the equator and results in sizable thermocline warming. An experiment with a linear continuously stratified model shows that the contributions of many baroclinic modes, and the right zonal wavelength of wind forcing, are essential in generating the correct wave structure. It is also shown that contributions of mixed Rossby gravity waves to cross-equatorial heat transport are negligible, as temperature variability associated with this wave mode has a node on the equator.

Corresponding author address: Motoki Nagura, Japan Agency for Marine-Earth Science and Technology/Research Institute for Global Change, 2-15 Natsushima-cho, Yokosuka-city, Kanagawa 237-0061, Japan. E-mail: nagura@jamstec.go.jp

Abstract

This study examines heat advection due to mixed Rossby gravity waves in the equatorial Indian Ocean using moored buoy observations at (0°, 80.5°E) and (0°, 90°E) and an ocean general circulation model (OGCM) output. Variability associated with mixed Rossby gravity waves is defined as that at periods of 10–30 days, where both observations and the OGCM results show high energy in meridional velocity and meridional gradient of temperature. The 10–30-day variability in meridional velocity causes convergence of heat flux onto the equator, the net effect of which amounts to 2.5°C month−1 warming at the depth of the thermocline. Detailed analysis shows that the wave structure manifested in temperature and velocity is tilted in the xz plane, which causes the phase lag between meridional velocity and meridional temperature gradient to be a half cycle on the equator and results in sizable thermocline warming. An experiment with a linear continuously stratified model shows that the contributions of many baroclinic modes, and the right zonal wavelength of wind forcing, are essential in generating the correct wave structure. It is also shown that contributions of mixed Rossby gravity waves to cross-equatorial heat transport are negligible, as temperature variability associated with this wave mode has a node on the equator.

Corresponding author address: Motoki Nagura, Japan Agency for Marine-Earth Science and Technology/Research Institute for Global Change, 2-15 Natsushima-cho, Yokosuka-city, Kanagawa 237-0061, Japan. E-mail: nagura@jamstec.go.jp

1. Introduction

Cross-equatorial flow in the Indian Ocean is dominated by intraseasonal variability, which has been observed by moored current measurements (Luyten and Roemmich 1982; Reppin et al. 1999; Sengupta et al. 2004; Masumoto et al. 2005; Horii et al. 2011) and drifting buoys (Reverdin and Luyten 1986). Its energy spectrum shows a wide peak at 10–30-day periods in the western basin (Luyten and Roemmich 1982; Reverdin and Luyten 1986; Tsai et al. 1992), whereas it is dominated by biweekly variability near the surface and by 10–50-day variability at subsurface in the eastern basin (Reppin et al. 1999; Sengupta et al. 2004; Masumoto et al. 2005; Horii et al. 2011). Most studies attributed the intraseasonal variability to generation of mixed Rossby gravity waves (e.g., Sengupta et al. 2004). A possible energy source is dynamical instability mainly in the western basin (Kindle and Thompson 1989; Ogata et al. 2008) and wind forcing in the eastern basin (Moore and McCreary 1990; Sengupta et al. 2004; Miyama et al. 2006; Ogata et al. 2008).

The motivation of those studies was an assumption that intraseasonal variability in cross-equatorial flow contributes significantly to heat transport in the Indian Ocean. Halkides et al. (2007) disproved this assumption, showing based on numerical experiments that contribution of intraseasonal oscillations to cross-equatorial heat transport is small on the seasonal time scale. However, intraseasonal variability simulated by their model does not compare very well with observations. In this study, we estimate meridional heat transport and heat advection caused by mixed Rossby gravity waves in the Indian Ocean using in situ observations and an ocean general circulation model (OGCM) output. We also discuss associated dynamics, conducting an idealized experiment with a linear continuously stratified model.

Based on the consensus that mixed Rossby gravity waves dominate, we can guess their contributions to heat transport. If we assume a 1.5-layer model in which a warm active layer overlays a cool inert layer, depression (or elevation) of the interface causes a positive (negative) temperature anomaly at the depth of the interface, and a higher (lower) pressure anomaly above the interface. Thus, in the framework of a 1.5-layer model, temperature anomalies accompany pressure anomalies of the same sign. According to linear wave theory (e.g., Moore et al. 1998), pressure anomalies have a node on the equator in the case of mixed Rossby gravity waves, which leads to υp and thus υT being always zero on the equator (where υ denotes meridional velocity, p is pressure, and T is temperature). This indicates that the mixed Rossby gravity wave does not contribute to cross-equatorial heat transport. In terms of convergence–divergence of heat transport, the linear theory for mixed Rossby gravity waves for a single baroclinic mode predicts υ leading (and thus ) by a quarter cycle on the equator, which makes the long-term mean of zero, as
e1
where square brackets denote long-term mean; L denotes a certain long period; and are amplitudes for velocity and meridional temperature gradient, respectively; and are phases for υ and , respectively; and is frequency. Therefore, we might guess that mixed Rossby gravity waves contribute neither to cross-equatorial heat transport nor to convergence–divergence of heat flux on the equator. In this study we show that the former holds but the latter is not the case, owing to the contribution of multiple baroclinic modes and thus breakdown of the 1.5-layer model assumption.

Section 2 gives detailed descriptions of the observational data and numerical models used here. Section 3 shows the results and discusses the associated dynamics. Section 4 summarizes the main results and discusses their implications for climate.

2. Data and model

a. Observational data

In situ observations of meridional velocity are obtained from records of upward looking acoustic Doppler current profilers (ADCPs) deployed at (0°, 80.5°E) and (0°, 90°E), which are conducted as a part of the Research Moored Array for African–Asian–Australian Monsoon Analysis and Prediction (RAMA; McPhaden et al. 2009). Daily averages of velocity data are available in the upper 175 m at 5-m vertical resolution from 27 October 2004 to 17 October 2008 at 80.5°E, and in the upper 340 m at 10-m vertical resolution from 14 November 2000 to 17 January 2011 at 90°E (Figs. 1a,e). However, data are contaminated at depths shallower than 35 m at 80.5°E and 40 m at 90°E by acoustic signals reflected at the sea surface, and so are discarded. Data gaps, which are at most 1 day long, are filled by linear interpolation.

Fig. 1.
Fig. 1.

In situ observations of (a),(e) meridional velocity; and (b)–(d), (f)–(h) temperature (left) 80.5°E and (right) 90°E. The velocity time series are measured at the equator. The temperature time series are observations at 1.5°N in (b),(f); the equator in (c),(g); and 1.5°S in (d),(h). Data gaps are interpolated as described in the text. Temperature data are interpolated to the levels of ADCP observations. Cross marks at the left in the temperature plots indicate the depths of thermal sensors.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Daily temperature time series are obtained from RAMA moored buoys deployed at the equator, 1.5°S and 1.5°N along 80° and 90°E (Figs. 1b–d and 1f–h). Each buoy has 13–19 thermal sensors, the typical depths of which are 10, 20, 40, 60, 80, 100, 120, 140, 180, and 300 m. For the days when temperature data are available at more than 10 levels, temperature profiles are interpolated vertically to the levels of ADCP observations. Also, data gaps with length up to 2 days are filled by linear interpolation. To maximize data length, data gaps at the equator are filled by interpolating data at 1.5°S and 1.5°N to the equator. This meridional interpolation is validated by the high correlation between temperature observed at the equator and that interpolated meridionally (r = 0.7–0.9). The meridional gradient of temperature at the equator is calculated by central differencing, that is,
eq1

To compute heat flux υT and heat advection we need velocity records at the equator and temperature records at 1.5°S, the equator, and 1.5°N. A continuous time series is required as well to apply spectral analysis. Because of these requirements, the analysis period is from 6 September 2006 to 7 July 2008 at 80.5°E (671 days) and from 17 September 2006 to 28 May 2008 at 90°E (620 days). These periods should be long enough to estimate variability at 10–30-day periods.

b. OGCM

The OGCM we use is the OFES developed at the Japan Agency for Marine-Earth Science and Technology (JAMSTEC; Masumoto et al. 2004; Sasaki et al. 2006, 2008). The OFES is based on the Modular Ocean Model, version 3, developed at the Geophysical Fluid Dynamics Laboratory/National Oceanic and Atmospheric Administration (NOAA; Pacanowski and Griffies 1999). The model domain is from 75°S to 75°N with a horizontal grid spacing of 0.1° and 54 vertical levels. The K-profile parameterization scheme (Large et al. 1994) and a biharmonic operator are adopted for the calculation of vertical and horizontal viscosity, respectively. OFES is first spun up using daily averages of reanalysis data obtained from the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) (Kalnay et al. 1996) for the period from 1950 onward, and then integrated from 4 July 1999 to 27 October 2009 using Quick Scatterometer (QuikSCAT or QSCAT) satellite winds. The bulk formulae proposed by Rosati and Miyakoda (1988) are used for the calculation of surface heat fluxes. The surface salinity flux is calculated using NCEP–NCAR reanalysis data. In addition, model surface salinity is restored to the climatological monthly means of the World Ocean Atlas 1998 (WOA98; Boyer et al. 1998a,b,c). In this study, we analyze fields output at 3-day intervals. The analysis period is the same as that for the observations unless otherwise stated.

c. Linear model

In section 3c, we discuss mixed Rossby gravity waves excited by an idealized wind forcing. The model used is a continuously stratified linear model on an equatorial β plane, which is expressed by the shallow water equations for a baroclinic mode (e.g., McCreary 1984):
e2
where the subscript n denotes nth baroclinic mode; u and υ are zonal and meridional velocities; p is dynamic pressure defined as pressure divided by mean density; c is the wave speed; and A is a damping coefficient obtained under the assumption that vertical viscosity is inversely proportional to the Brunt–Väisälä frequency (McCreary 1981). In this study A = 8.84 × 10−4 cm2 s−3 following Miyama et al. (2006). Zonal wind forcing is ignored for simplicity. It does play a role in exciting mixed Rossby gravity waves in the Indian Ocean, but the dominant forcing comes from meridional wind stress (Miyama et al. 2006). Zonal velocity, meridional velocity, and pressure are obtained by summing up the contributions from each baroclinic mode:
eq2
where denotes the vertical structure function. In this study we use the first 50 baroclinic modes. The vertical mode parameters ( and ) are computed using the mean density stratification in the region of 5°S–5°N, 40°–100°E in the upper 4000 m, which is obtained from the WOA 2009 (Antonov et al. 2010; Locarnini et al. 2010). The wave speeds for the first four modes are 2.53, 1.63, 0.93, and 0.66 m s−1. These values are consistent with those obtained in earlier studies (e.g., Nagura and McPhaden 2010). The spatial structure of the meridional wind forcing, G(x, y), is defined as
eq3
where denotes the amplitude of wind forcing (= 1 × 10−2 N m−2); is the mean density of seawater (= 1025 kg m−3); is the zonal wavenumber of the forcing; and H is the depth of the ocean (= 4000 m). We chose 40° as the western end of the forcing, mimicking the geometry of the Indian Ocean. The equations are analytically solved following the methods described by McCreary (1984) and Miyama et al. (2006). We ignore boundary reflections, which usually play a minor role in the interior of the basin in the case of mixed Rossby gravity waves.

3. Results

a. Spectrum

Observed meridional velocity on the equator shows elevated energy at shorter periods (10–20 days) at 50–80-m depth, and at longer periods (15–30 days) at 80–150 m (Figs. 2a,c), as reported in earlier studies (e.g., Reppin et al. 1999). Energy is small at periods shorter than 10 days and longer than 30 days. The OGCM tends to overestimate energy but it is able to reproduce the basic features of the spectra (Figs. 2b,d).

Fig. 2.
Fig. 2.

Variance-preserving spectra of meridional velocity in the upper 200 m for (a),(c) in situ observations; and (b),(d) the Ocean General Circulation Model for the Earth Simulator (OFES) OGCM at (left) 0°, 80.5°E and (right) 0°, 90°E. White vertical dashed lines mark the periods of 10, 20, and 50 days.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Observed meridional velocity shows high zonal coherency along the equator at biweekly periods (Fig. 3a). Variability at 90°E leads that at 80.5°E (Fig. 3c), indicating westward phase propagation. The phase difference roughly follows the dispersion relation for mixed Rossby gravity waves (Fig. 4), confirming the dominance of this wave mode. The phase difference is larger at deeper levels, showing upward phase propagation, which is consistent with the linear theory of mixed Rossby gravity waves (McCreary 1984). Zonal coherence is small at periods longer than 20 days, possibly because of contributions from small-scale eddies (Ogata et al. 2008). The OGCM results compare well with observations, except for weaker coherency at about 150-m depth (Figs. 3b, 3d, and 4).

Fig. 3.
Fig. 3.

(a) Squared coherency and (c) phase difference for the observed meridional velocity between (0°, 80.5°E) and (0°, 90°E). The time series at 50-m depth at 0°, 80.5°E is used as an index. (b),(d) As in (a),(c), but for the OFES OGCM. The phase is shown only when the corresponding coherency is significant at the 99% level.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Fig. 4.
Fig. 4.

Dispersion relations for mixed Rossby gravity waves and the second and fourth meridional mode Rossby waves for the first baroclinic mode. The wavelengths and periods, estimated by coherence analysis between (0°, 80.5°E) and (0°, 90°E), are marked only if their coherence is significant at the 99% level. Results are shown for the meridional velocity at 50-m depth (blue marks) and the meridional gradient of temperature at 80-m depth (red marks). Asterisks and crosses are for the in situ observations and the OFES OGCM, respectively. The analysis period for meridional velocity (temperature gradient) is from 27 October 2004 to 17 October 2008 (from 17 September 2006 to 28 May 2008), which is the period when available records at 80.5° and 90°E overlap. Note that the OGCM results are output at 3-day intervals and that the variability around the 7-day period (marked by the red cross) is possibly not resolved well.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Temperature variability on the equator is small in magnitude at 10–30-day periods but large at periods of about 50 and 180 days (Figs. 5b,e). The 50- and 180-day variability are likely related to the Madden–Julian oscillation and the semiannual Wyrtki Jet, respectively. In contrast, energy is concentrated in 10–30-day periods for meridional temperature gradient (Figs. 5c,f). These patterns are consistent with the known spatial structure of mixed Rossby gravity waves, which have maximum meridional pressure gradient on the equator while the variability of pressure itself is zero there. Furthermore, energy is mostly confined to the depth of the thermocline (50–150 m; Figs. 5a,d), suggesting vertical movements of the thermocline as the cause of temperature variability. The OGCM results compare well with observations, except that the OGCM also includes large energy at periods less than 10 days. In addition, the simulated variability of meridional temperature gradient is one order larger in magnitude than observations, which is possibly due to the finer meridional grid spacing of the model (0.1°) compared to the meridional interval of observations (3°). The phase lag of the meridional temperature gradient between (0°, 80.5°E) and (0°, 90°E) is consistent with the dispersion relation for mixed Rossby gravity waves (Fig. 4), although coherency is small (figure not shown).

Fig. 5.
Fig. 5.

(a),(d) Mean temperature; (b),(e) variance-preserving spectra for temperature; and (c),(f) variance-preserving spectra for meridional gradient of temperature at 0°, 80.5°E for (top) in situ observations and (bottom) the OFES OGCM. Note that the scales for (c) and (f) are different.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

b. Meridional heat transport

The mean meridional heat flux [υT] at 80.5°E on the equator shows a southward peak at about 50-m depth in observations and in the model (Fig. 6c). The OGCM results compare well with observations in magnitude and vertical structure, except that the OGCM shows southward heat flux below 120-m depth whereas observations indicate northward heat flux there. At 90°E, the mean meridional heat flux has southward local peaks at about 50- and 110-m depth (Fig. 6d). The simulated heat flux at 90°E has a southward bias even though its vertical structure is similar to observations. The contribution from the mean circulation [υ][T] dominates the mean heat flux, which indicates that intraseasonal variability does contribute little to the mean cross-equatorial heat transport. Consistently, the vertical profiles of mean meridional heat flux and mean meridional velocity (Figs. 6a,b) are almost identical. These results support those of Halkides et al. (2007).

Fig. 6.
Fig. 6.

Vertical profiles of (a),(b) mean meridional velocity [υ] (where square brackets denote long-term mean); (c),(d) mean meridional heat flux [υT]; and (e),(f) mean meridional heat advection at (top) 0°, 80.5°E and (bottom) 0°, 90°E. Red and blue lines are for in situ observations and the OFES OGCM, respectively. Green lines are the same as the blue lines except that the temperature gradient is computed between 1.5°S and 1.5°N to be consistent with the observational estimates. Dotted lines show the contributions from the mean field, which are defined as [υ][T] for (c),(d) and −[υ] for (e),(f).

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

In contrast, eddy heat advection accounts for almost all mean meridional heat advection (Figs. 6e,f). This indicates that heat flux caused by intraseasonal variability does not cross the equator, but converges onto it. Warming due to heat advection peaks at about 80–120-m depths, which is the depth of the thermocline. The simulated results are significantly larger than observational estimates, but this discrepancy can be reconciled if we calculate the meridional gradient of temperature in the simulation between 1.5°S and 1.5°N as in observations (green lines in Figs. 6e,f). This indicates that the results derived from observations underestimate the magnitude of heat advection. We also repeated the calculation with model output for the full period (1999–2009) and obtained virtually the same results, which indicates that the shortness of the analysis period does not lead to crucial errors.

To see the horizontal structure, we composite subsurface temperature and velocity (Figs. 8a–e) using the 10–30-day variability in OGCM meridional velocity at 0°, 80°E as our index. Events are defined as periods when this index exceeds plus one standard deviation (Fig. 7). We confirmed that composites based on southward velocity peaks, defined in an analogous way, give essentially the same results. Results are also essentially the same if we use meridional velocity at 0°, 90°E as an index. For the composite analysis, the full time series of the model integration is used.

Fig. 7.
Fig. 7.

The 10–30 day variability in OFES OGCM meridional velocity at 0°, 80°E and 120-m depth. Overplotted are one standard deviation (red line), and the northward velocity events whose magnitude exceeds one standard deviation (red diamonds).

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

The composited subsurface temperature is antisymmetric about the equator (Figs. 8a–e), which is similar to pressure variability associated with mixed Rossby gravity waves (Figs. 8f–j). What is different between the OGCM results and the theoretical structure of a free wave of a single baroclinic mode is the phase relationship between meridional velocity and temperature. Theory predicts that, on the equator, meridional velocity and meridional pressure gradient should be 90° out of phase. In the OGCM, however, they are 180° out of phase. For example, at day −3, temperature anomalies are positive south of the equator and negative in the north, and velocity along the equator is northward in 80°–90°E. This pattern causes convergence of heat flux onto the equator. A similar pattern of opposite sign can be found at day 6. According to Eq. (1), the long-term mean of meridional heat advection is maximized if meridional velocity υ and meridional temperature gradient are 180° out of phase [i.e., in Eq. (1)]. The resulting warming due to eddy heat advection is trapped near the equator (Fig. 9).

Fig. 8.
Fig. 8.

(a)–(e) Composites of 10–30-day variability in OFES OGCM horizontal velocity (vectors) and temperature (colors) at 120-m depth for (from top to bottom) day −6, −3, 0, +3, and +6. Black circles show the location of the velocity index shown in Fig. 7. The full period of the model integration (1999–2009) is used to make the composites. (f)–(j) As in (a)–(e), but for horizontal patterns of velocity (vectors) and dynamic pressure (colors) for free mixed Rossby gravity waves of the first baroclinic mode at period of 14 days. The theoretical wave patterns are plotted in such a way that meridional velocity on the equator peaks at x = 0° and day 0.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Fig. 9.
Fig. 9.

The long-term mean of eddy meridional heat advection averaged over 50–150-m depth in the OFES OGCM. Eddy heat advection is defined as the total advection minus the contribution from the mean field .

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

The phase relationship between υ and can be confirmed by examining their cross spectrum, which is defined as , where (Emery and Thomson 2004). The results show that 10–30-day variability contributes most to the mean meridional heat advection at 50–150-m depths, with υ leading by half a cycle (Fig. 10). We present a dynamical explanation for this phase relationship in the next subsection.

Fig. 10.
Fig. 10.

(a),(c) Amplitudes and (b),(d) phases of cross spectra between meridional velocity and meridional temperature gradient at 0°, 80.5°E for in situ observations in (a),(b) and the OFES OGCM in (c),(d). The phase of the observational (or OGCM) results is shown only if the corresponding amplitude >0.1 (0.2).

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

c. Dynamics

In this subsection, we first examine the phase relationship between meridional velocity υ and meridional pressure gradient , and then proceed to the phase lag between and meridional temperature gradient .

The phase relationship between υ and is defined by the equation of meridional momentum:
eq4
where f is the Coriolis parameter; and are horizontal and vertical viscosity coefficients, respectively; and is the horizontal gradient operator. We estimated the momentum budget terms using output form the OFES OGCM and found that the momentum advection term and the viscosity term are negligible (Fig. 11). Thus the dominant balance is , which indicates that υ leads by a quarter cycle.
Fig. 11.
Fig. 11.

Composites of the meridional momentum budget terms at 0°, 80.5°E and 120-m depth obtained from the OFES OGCM. The analysis period is from 1999 to 2009, and a 10–30-day bandpass filter is applied before the analysis. The composites are based on the northward velocity events shown in Fig. 7. Results are shown for the tendency term of meridional velocity (black), the momentum advection term (blue), the meridional pressure gradient force term (red), and the viscosity term (dotted). The viscosity term is computed as the residual of the budget. The Coriolis force term is negligible and has thus been omitted.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

The relationship between pressure and temperature is defined by the hydrostatic equation:
e3
where is pressure (not dynamic pressure), ρ is density, S is salinity, and g is the acceleration due to gravity. The equation of state can be approximated as
e4
where is mean density, and α and β are positive coefficients proportional to the thermal expansion coefficient and the saline contraction coefficient, respectively. Assuming that the model has a rigid lid and that sea surface height gradients do not contribute to pressure gradient, pressure at a depth z can be derived by substituting Eq. (4) into Eq. (3) and integrating the resulting equation from the level of no motion –D to z:
eq5
Taking the meridional gradient, we obtain
e5
We computed using climatological salinity instead of salinity snapshots and obtained virtually the same results at 10–30-day periods, which indicates that salinity effects are negligible on this time scale. Thus, Eq. (5) can be reduced to
eq6
As dynamic pressure p is defined as ,
e6
that is, is proportional to the vertical integral of .

The OGCM results for 10–30-day variability show positive (or negative) above positive (negative) (Figs. 12a–c), which is consistent with Eq. (6). The pattern of is tilted toward the east. For example, at day 0, negative is located at about 50-m depth at about 85°E, whereas it is at about 100–150-m depths at 70°E (Fig. 12b). In other words, at deep levels leads that at shallow levels, as the pattern propagates westward following the phase speed of mixed Rossby gravity waves. As a result, leads if we compare them at a fixed level (Fig. 12d). The resulting phase difference between and is about a quarter cycle. As υ leads by a quarter cycle and leads by a quarter cycle, υ leads by a half cycle.

Fig. 12.
Fig. 12.

(a)–(c) 10–30-day variability in meridional temperature gradient (; colors) and meridional pressure gradient (; contours) along the equator for day −3, 0, and +3, respectively. (d) Time series of (solid line) and (dotted line) at (0°, 80°E) and 105-m depth. All the variables are obtained from the OFES OGCM output for 1999–2009 and composited based on the northward velocity events in Fig. 7. The contour interval for pressure gradient is 2 × 10−5 cm2 s−1. Negative values are shown with dotted–dashed lines. Zero contours are omitted. In (d), the scale for () is shown on the left (right).

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Similar tilted structures can be seen in vertical velocity and temperature along 2°N (Fig. 13). Masumoto et al. (2008) and Horii et al. (2011) pointed out, based on in situ observations, that upwelling (or downwelling) associated with mixed Rossby gravity waves leads upward (downward) movement of isotherms, which is supposed to result in cool (warm) temperature anomalies at the depth of the thermocline. Our results in Fig. 13 are consistent with their observations.

Fig. 13.
Fig. 13.

As in Figs. 12a–c, but for temperature (colors) and vertical velocity (contours) along 2°N. The contour interval is 5 × 10−4 cm s−1. Vertical velocity is zonally smoothed with a 7-point boxcar filter.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

The tilted structure and the resulting phase lag between and do not occur if the 1.5-layer model assumption is valid, as is described in the introduction. This means that the consideration of many baroclinic modes is essential to understand the tilted structure. If a wave in the xz plane can be expressed as , the line of constant phase is , and its inclination is defined as , where k and m are zonal and vertical wavenumbers, respectively. The zonal wavenumber k may depend on the wave’s dispersion relation and the zonal structure of wind forcing. The vertical wavenumber m depends on the mean stratification and contributions of the respective baroclinic modes. We force the linear continuously stratified model with an idealized wind stress pattern [Eq. (2)] and sum up the solutions of the first 50 baroclinic modes. The forcing period is 20 days, which is the period at which the coherence between υ and is highest (Fig. 10). We use 60° for the zonal wavelength of the forcing, based on the structure of the observed meridional wind stress (Fig. 14). The resulting inclination of vertical velocity in the xz plane is about 50 m (10°)−1 (Fig. 15b), which compares well with the OGCM results (Fig. 15a). If we use a shorter (or longer) zonal wavelength for the forcing, the line of constant phase becomes steeper (less steep; Figs. 15c,d). This tendency is accounted for by the fact that the inclination varies with the zonal wavenumber of the response according to , and that the zonal wavenumber of the response is proportional to that of the forcing. Thus, the tilted structure of vertical velocity is attributable to the contribution of multiple baroclinic modes, and the actual inclination depends on the zonal structure of the wind forcing.

Fig. 14.
Fig. 14.

Phase (solid line) and amplitude (dotted line) of the leading mode of a complex empirical orthogonal function analysis applied to the 10–30-day variability of equatorial (averaged between 0.5°S and 0.5°N) meridional wind stress. QSCAT winds are converted to wind stress using a standard bulk formula. The explained variance of the leading mode is about 35%. The scale of the phase (amplitude) is shown on the left (right).

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Fig. 15.
Fig. 15.

Vertical velocity along 2°N obtained from (a) the OFES OGCM and (b)–(d) the linear continuously stratified model. The OGCM results are composited based on the northward velocity events obtained from output for 1999–2009. The linear model is forced by an idealized meridional wind forcing, whose period is 20 days and whose zonal wavelengths are 60°, 30°, and 120° in (b),(c), and (d), respectively. The solutions of the linear model represent the sums over the first 50 baroclinic modes of the mixed Rossby gravity waves. The contour interval is 5 × 10−4 cm s−1. Negative values are shaded and zero contours are omitted. Thick dashed lines show a reference inclination of 50 m (10°)−1.

Citation: Journal of Physical Oceanography 44, 1; 10.1175/JPO-D-13-0141.1

Masumoto et al. (2008) and Horii et al. (2011) detected intraseasonal variability in vertical velocity by computing convergence–divergence of observed horizontal currents in the region of 1.5°S–0°, 79°–82°E. They speculated that this variability is associated with mixed Rossby gravity waves because the divergence–convergence patterns were dominated by meridional velocity. Figure 15 in this paper illustrates the generation of vertical velocity in association with mixed Rossby gravity waves and supports the hypothesis by Masumoto et al. and Horii et al.

4. Summary and discussion

Meridional velocity in the equatorial Indian Ocean is dominated by intraseasonal variability at 10–30-day periods, which earlier studies attributed to mixed Rossby gravity waves excited by wind forcing or dynamical instability (e.g., Sengupta et al. 2004). In the current study, we estimate the mean heat advection induced by mixed Rossby gravity waves and discuss its dynamics. The results, based on both moored buoy observations at (0°, 80.5°E) and (0°, 90°E) and an OGCM simulation, show that intraseasonal variability of meridional velocity causes heat flux convergence onto the equator at 50–150 m depth. This warms up the equatorial thermocline at a rate of 2.5°C month−1 in the long-term mean. Cross-equatorial heat transport, on the other hand, is not affected by meridional velocity variability at all. The zonal phase lag of the equatorial meridional velocity between 80.5° and 90°E fits the dispersion relation for mixed Rossby gravity waves. Zero cross-equatorial heat flux (υT = 0) on the equator is explained by the fact that the temperature variability associated with mixed Rossby gravity waves has a node on the equator. Our analysis shows that meridional velocity υ leads meridional gradient of temperature by half a cycle on the equator, which results in a sizable long-term mean of the advection term .

The phase difference between υ and can be explained as follows. First, the momentum budget analysis shows that the tendency of meridional velocity is mostly accounted for by the meridional pressure gradient force . This results in a phase difference of a quarter cycle between υ and , with υ leading. Second, the structure of is tilted in the xz plane because of the contribution of many baroclinic modes, which results in at deep levels leading at shallow levels. As is expected from the hydrostatic equation [Eqs. (3–6)], at a certain depth is proportional to the vertical integral of from the level of no motion to the depth. As a result, leads by a quarter cycle. Because of these two relations, υ leads by a half cycle. An idealized experiment with a linear continuously stratified model shows that the zonal wavelength of the wind forcing is the factor controlling the inclination in the xz plane.

As mentioned above the maximum thermocline warming due to mixed Rossby gravity waves in the Indian Ocean is about 2.5°C month−1 (Fig. 6). For comparison, subsurface cooling due to climatological upwelling in the equatorial Pacific Ocean amounts to about 5°C month−1, if we assume typical values for upwelling velocity and vertical temperature gradient [2 × 10−5 m s−1 and 10°C (100 m)−1, respectively; Johnson et al. 2001]. Thus, in terms of magnitude, thermocline warming due to mixed Rossby gravity waves in the equatorial Indian Ocean can be half as large as the upwelling-related cooling in the equatorial Pacific. Thus mixed Rossby gravity waves have the potential to affect the thermal structure of the equatorial Indian Ocean by warming the thermocline and changing basic stratification. In addition, modulation of mixed Rossby gravity waves, such as seasonal or interannual amplitude variations, can cause temperature variability on those time scales.

To further elucidate the impact of mixed Rossby gravity waves on Indian Ocean climate, we examined their relationship with barrier-layer thickness using in situ observations. We found a significant coherence between meridional velocity at 0°, 90°E and barrier layer thickness at 1.5°S, 90°E (figure not shown). This can be explained by the fact that the thermocline is deepened south of the equator when velocity on the equator is northward (Fig. 8c), causing the top of the isothermal layer to be further from the bottom of the mixed layer and giving rise to a thicker barrier layer. Further analysis will be needed to thoroughly assess the influence of mixed Rossby gravity waves on climate.

Acknowledgments

The authors would like to acknowledge encouraging comments from anonymous reviewer and the editor. We also thank the JAMSTEC and the NOAA/Climate Program Office and the Office of Climate Observation for their efforts to establish and maintain the RAMA buoy array. We also thank members of the OFES group of the JAMSTEC for development of the model.

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