1. Introduction
Many studies of midlatitude Rossby waves have examined satellite measurements of SSH (e.g., Chelton and Schlax 1996; Isoguchi et al. 1997; Nagura and McPhaden 2021a; Périgaud and Delecluse 1992; Qiu 2002). SSH variability is mainly caused by first baroclinic mode waves, whose variability in pressure and horizontal velocity is trapped near the surface of the ocean (Killworth et al. 1997; Killworth and Blundell 2003). On the other hand, Argo profiling floats have provided in situ temperature and salinity data for the upper 2000 m (Roemmich et al. 2009). These observations have enabled investigations of wave propagation at subsurface and intermediate levels (Chu et al. 2007; Nagura 2018), and the resultant data complement information obtained from traditional in situ temperature observations (Liu and Zhang 1999). The benefit of Argo float observations is clear in the Indian Ocean, where in situ observations were sparse before the launch of the Argo program but have increased rapidly during the Argo era (Nagura and McPhaden 2018).
In this study, we examine wave propagation at subsurface levels. We use an ocean reanalysis dataset, the Estimated State of the Global Ocean for Climate research (ESTOC; Osafune et al. 2014a,b, 2015), which assimilates Argo float and other observations into an OGCM using a 4DVAR method (see section 2a for details). Figure 1 shows interannual anomalies in meridional velocity near the surface at 25°N and 25°S obtained from ESTOC, which show westward propagation in all basins. The westward phase speed is similar to that estimated by satellite altimetry (7 cm s−1; Chelton and Schlax 1996), which is the typical propagation speed of first baroclinic mode long Rossby waves. Meridional velocity anomalies at 1000-m depth propagate much more slowly, with a typical phase speed of ∼2 cm s−1 (Fig. 2). Slow propagation is observed in several areas globally: east of ∼150°W in the North Pacific Ocean (Fig. 2a); east of ∼110°W in the South Pacific Ocean (Fig. 2d); east of ∼70°E in the south Indian Ocean (Fig. 2c); and in the whole longitudinal range of the North and South Atlantic Oceans (Figs. 2b,e). To our knowledge, this slow propagation of meridional velocity at intermediate depths has not been reported previously. The amplitude of slowly propagating signals is largest in the south Indian Ocean. Along 25°S, between 70° and 110°E, the temporal and zonal mean meridional velocity at 1000-m depth is ∼11 cm s−1, whereas the zonal mean of the standard deviations of their anomalies is ∼9.7 cm s−1, indicating the nonnegligible amplitude of interannual anomalies.
Longitude–time diagrams of meridional velocity anomalies at 100-m depth along 25°N or 25°S in (a) the North Pacific Ocean, (b) the North Atlantic Ocean, (c) the south Indian Ocean, (d) the South Pacific Ocean, and (e) the South Atlantic Ocean obtained from the ESTOC control run. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Solid lines show the typical zonal phase speed of first baroclinic mode long Rossby waves (−7 cm s−1) estimated from satellite altimetry by Chelton and Schlax (1996).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
As in Fig. 1, but for meridional velocity anomalies at 1000-m depth. Solid lines are as in Fig. 1. Dashed lines show the typical zonal phase speed of meridional velocity anomalies at 1000-m depth along 25°S in the south Indian Ocean (−2 cm s−1; see Fig. 8 below).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
This study describes the propagation of waves in the south Indian Ocean on interannual time scales and examines their driving force. Although propagating signals also occur in temperatures, we focus on meridional velocity because slowly propagating signals are easier to identify in meridional velocity than in temperature (section 5c). Temperature variability is affected not only by wave propagation but also by long-term warming trends (e.g., Roemmich et al. 2015) and spiciness variability (e.g., Häkkinen et al. 2016; Nagura 2021), which may further complicate the interpretation of detected signals.
We conducted numerical experiments to identify the driving force of waves. ESTOC is a long-term ocean state estimation dataset that was generated through a data synthesis experiment using a 4DVAR method based on the “strong constraint.” This method provides the best time-trajectory fit to diverse observations by correcting only the initial and surface boundary conditions without imposing any artificial source or sink of mass, momentum, and buoyancy. The output is a model solution that is driven by the optimally estimated initial and surface boundary conditions. We generated perturbed surface boundary conditions with which to run the model.
The remainder of this paper is organized as follows. Section 2 describes ESTOC and the settings of numerical experiments. Section 3 describes the results of a statistical analysis and section 4 provides the results of numerical experiments. Section 5 presents an additional discussion of vertical modes, the transmission of waves from the Pacific to the Indian Ocean, and results obtained from datasets other than ESTOC. Finally, a summary of the main results is provided in section 6.
2. Model and methods
a. ESTOC
The OGCM used for ESTOC is version 3 of the Modular Ocean Model (Pacanowski and Griffies 2000). The model domain is quasi-global and covers the region between 75°S and 80°N on a latitude–longitude grid with intervals of 1°. The model has 45 vertical levels. The bottom topography is taken from the Scripps topography on a 1° global grid (Pacanowski and Griffies 2000). A turbulence closure model for the surface mixed layer (Noh 2004), a bottom boundary layer model (Nakano and Suginohara 2002), and an isopycnal mixing scheme (Gent and McWilliams 1990) are adopted. Interior vertical mixing is computed by a linear combination of three semiempirical schemes (Gargett 1984; Hasumi and Suginohara 1999; Tsujino et al. 2000). For pretuning, physical parameters including those related to diffusivity are estimated optimally using the Green’s function approach (Menemenlis et al. 2005; Toyoda et al. 2015) to reproduce the climatological distribution of water mass properties.
First, the model was spun up for 3000 years from a state of rest using climatological heat, freshwater, and momentum fluxes at the sea surface obtained from NCEP–NCAR Reanalysis 2 (Kanamitsu et al. 2002). Second, the model was driven from 1946 to 2014 using NCEP–NCAR Reanalysis 1 (Kalnay et al. 1996) with relaxation to climatological sea surface salinity obtained from the World Ocean Atlas 1998 (Conkright et al. 1999) and 10-day averages of SST obtained from the NOAA Optimally Interpolated (OI) SST (Reynolds et al. 2002) and Extended Reconstructed (ER) SST (Smith et al. 2008). This model run gave surface heat and freshwater flux corrected by relaxation. Third, the first-guess run was carried out using the state at the end of 1956 as the initial condition and corrected surface flux as the surface boundary conditions. Then, an optimized four-dimensional field was sought by modifying the initial and surface boundary conditions based on the adjoint model. The assimilation window spans the period from 1957 to 2014. Assimilated observations include temperature and salinity data obtained from the ENSEMBLES (EN4) dataset compiled by the Hadley Centre of the U.K. Met Office (Good et al. 2013), the NOAA OI/ER SST, and sea surface dynamic height anomalies obtained from satellite SSH provided by the Copernicus Marine and Environment Monitoring Service (CMEMS; Ducet et al. 2000). Note that the ENSEMBLES dataset includes Argo float observations. The temporal resolution of the control of air–sea flux was 10 days. The surface boundary conditions were given as momentum, heat, and freshwater flux. The final product is the output of the model that was driven by the optimally estimated initial and surface boundary conditions, which we refer to as the control run. The details of the data assimilation scheme have been described by Osafune et al. (2015). In this study, we use monthly averages of the output for the period from 1990 to 2014; satellite SSH is assimilated for most of this period. Anomalies are computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude.
b. Comparison with observations
In ESTOC, the surface boundary conditions were optimized using the ocean model and oceanic observations. A different approach is used in atmospheric reanalysis, which assimilates atmospheric data into an atmospheric model. To check for consistency, we compared wind stress curl and net surface heat flux anomalies between ESTOC and ERA5 (Hersbach et al. 2020). ERA5 data are monthly averages on a 0.25° × 0.25° grid, and they were interpolated onto a 1° × 1° grid for comparison.
Wind stress curl anomalies tend to be larger in magnitude in ESTOC than in ERA5 (Figs. 3a,c); this is particularly pronounced near the west and east coasts of Australia, in the interior of the south Indian Ocean between 20° and 30°S, and south of 35°S between 30° and 70°E. Surface heat flux anomalies in ESTOC tend to be comparable in magnitude to those in ERA5 (Figs. 3b,d). Discrepancies in the magnitude of surface heat flux anomalies occur in the interior of the south Indian Ocean (10°–20°S and 60°–105°E) and southwest of Australia, where the magnitude is smaller in ESTOC than in ERA5, and along the northwest coast of Australia, north of Madagascar, and in the equatorial Pacific Ocean, where the magnitude is larger in ESTOC. Correlation coefficients are mostly high for wind stress curl anomalies (Fig. 3e). Correlations for surface heat flux anomalies tend to be high in the Indonesian archipelago, along the west and northwest coasts of Australia, and in the equatorial Pacific Ocean (Fig. 3f). Correlation coefficients for surface heat flux anomalies are low at 25°–35°S and 40°–90°E, where the standard deviations of anomalies are small. Surface forcing anomalies are qualitatively consistent in the two datasets, although some quantitative discrepancies are noted.
Standard deviations of wind stress curl anomalies obtained from (a) ESTOC and (c) ERA5. (e) Correlation coefficients of wind stress curl anomalies between ESTOC and ERA5. (b),(d),(f) As in (a), (c), and (e), respectively, but for net surface heat flux anomalies. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. The comparison covers the period 1990–2014. Contour lines in (e) and (f) show the 95% confidence level (Student’s t test).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
We compared SSH anomalies between ESTOC and the satellite measurements provided by CMEMS (Ducet et al. 2000). Satellite SSH data are monthly averages on a 0.25° × 0.25° grid, and we interpolated them onto a 1° × 1° grid for comparison. Note that satellite SSH was assimilated into ESTOC. However, we maintain that the comparison is a useful exercise, as the 4DVAR method is based on the strong constraint, which seeks the solution that satisfies the model equations and best fits the observations, rather than obtaining the state that is in exact agreement with all assimilated observations. In this sense, the comparison with assimilated observations can be an indication of the validity of dynamics incorporated into the model. If, for example, wave propagation in the Indonesian seas is unrealistic in the model due to insufficient resolution of complex bathymetry, and if the resulting error cannot be corrected by altering the initial and surface boundary conditions, the 4DVAR scheme cannot eliminate errors, resulting in a discrepancy between the assimilation product and the observations. The comparison shows that the amplitude of SSH variability is smaller in ESTOC than in the satellite measurements for the tropical southern Indian Ocean (5°–20°S, 50°–90°E) and along the west coast of Australia (Figs. 4a,b). The correlation exceeds the 95% confidence level in most of the regions north of 30°S (Fig. 4c). Structures associated with mesoscale eddies are dominant in the satellite measurements south of 30°S; ESTOC cannot resolve these because of the coarse horizontal resolution. The high correlation in the Indonesian archipelago suggests that the phases of waves propagating through the archipelago are well simulated. Nagura and McPhaden (2021a) examined satellite SSH data and reported that SSH anomalies in the tropical northwestern Pacific Ocean (4°N, 150°E) lead those in the southeastern Indian Ocean (20°–35°S, 105°–115°E) by 2 months. They attributed this lead time to the propagation of waves from the former to the latter region. The lag time for SSH anomalies between the two regions estimated from ESTOC is also 2 months, with SSH anomalies in the northwestern Pacific Ocean leading. This further supports the validity of the ESTOC results.
Standard deviations of SSH anomalies obtained from (a) the ESTOC control run and (b) satellite measurements. (c) Correlation coefficients of SSH anomalies between the ESTOC control run and satellite measurements. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Standard deviations and correlation coefficients were computed for the period 1993–2014, for which both ESTOC output and satellite SSH are available. Contour lines in (c) show the 95% confidence level (Student’s t test). (d) Mean Brunt–Väisälä frequency squared averaged from 50° to 100°E along 25°S in the south Indian Ocean for WOA13 (solid line) and the ESTOC control run (dotted line). The mean Brunt–Väisälä frequency squared obtained from ESTOC is the average for the period 1990–2014.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Finally, we compared the mean stratification at 25°S in the south Indian Ocean between ESTOC and the World Ocean Atlas 2013 (WOA13; Locarnini et al. 2013; Zweng et al. 2013). WOA13 provides temperature and salinity data on a 1° × 1° grid. The Brunt–Väisälä frequency squared was computed using the International Thermodynamic Equation of Seawater 2010 (McDougall and Barker 2011). The Brunt–Väisälä frequency squared estimated from WOA13 has two peaks at depths of ∼100 and ∼900 m (solid line in Fig. 4d). The peak at ∼900-m depth delineates a thin layer of Antarctic Intermediate Water, and weak stratification at depths of 300–700 m represents a thick layer of Subantarctic Mode Water (Nagura and McPhaden 2018). These features are reproduced by ESTOC, although the subsurface peak is located at ∼650-m depth and is shallower than that in WOA13 (dotted line in Fig. 4d). This result indicates that ESTOC provides a reliable qualitative simulation of the observed mean stratification.
c. Numerical experiments
We conducted sensitivity experiments to identify the generation mechanisms of interannual variability in meridional velocity, in which we replaced surface boundary conditions with their climatologies. We refer to these experiments hereafter as “climatology experiments.” We also used artificially generated surface forcing data, which were obtained by adding idealized anomalies to climatologies. These experiments are referred to as “idealized experiments.” In addition, we conducted an experiment in which forcing fields were the same as those in the control run, but the model topography was edited artificially. All experiments are listed in Table 1. The climatology experiments are denoted by CLIM, AMOM, or ABUO, and the idealized experiments by IDEAL. In the experiments, the model was first spun up by unperturbed surface forcing from 1957 to 1980. The model was then driven with perturbed forcing fields after 1982. From 1980 to 1982, a linear weight was used to gradually shift from unperturbed to perturbed forcing. The climatology of surface boundary conditions was computed from 10-day averages and includes seasonal variability. The details of each set of experiments are described below.
1) Climatology experiments
First, all the forcing fields were replaced with their climatologies over the whole model domain (CLIM_GLB); the results of this experiment show spontaneous variability on interannual time scales. We then replaced all the forcing fields in the south Indian Ocean (SIO), the coastal region west of Australia (AUS), and the tropical Pacific Ocean (TPO) regions with their climatologies (CLIM_IO-PO; the regions designated as SIO, AUS, and TPO are shown in Fig. 5). Previous studies have reported that zonal wind anomalies in the equatorial Pacific Ocean related to ENSO excite SSH variability in the tropical Pacific Ocean, which propagates toward the west coast of Australia via the Indonesian archipelago before radiating to the interior of the south Indian Ocean (Clarke 1991; Clarke and Liu 1994; Feng et al. 2010, 2011; Nagura and McPhaden 2021b; Potemra 2001; Wijffels and Meyers 2004). Wind forcing in the south Indian Ocean also excites local SSH variability (Nagura and McPhaden 2021a; Volkov et al. 2020). The results of these studies indicate that surface forcing in both the tropical Pacific and south Indian Oceans excites variability in the south Indian Ocean; considering this, we conducted CLIM_IO-PO. Next, we estimated the impact of surface forcing in the respective regions of SIO, AUS, and TPO. In AMOM_SIO, only the momentum forcing in the SIO region has anomalies, and all other forcing fields were replaced with climatologies. (“AMOM_SIO” is shorthand for “anomalous momentum forcing in the SIO”.) Similar experiments were conducted for the AUS and TPO regions (AMOM_AUS and AMOM_TPO). We also carried out experiments in which only the buoyancy forcing has interannual anomalies (ABUO_SIO, ABUO_AUS, and ABUO_TPO, where “ABUO” means “anomalous buoyancy forcing.”)
Regions used for sensitivity experiments: the south Indian Ocean (SIO; 45°S–5°N, 35°–100°E); the coastal region west of Australia (AUS; 45°S–5°N, 100°–125°E), and the tropical Pacific Ocean (TPO; 15°S–15°N, 125°E–65°W).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
2) Idealized experiments
In the IDEAL_TPO_TAUX experiment, all surface forcing fields were climatologies, except that the idealized pattern of anomalies shown in Fig. 6b was added to the climatology of zonal wind stress. The spatial structure of idealized forcing mimics that of the first EOF mode of zonal wind stress anomalies (Fig. 6a), which explains 33% of the total variance. The first EOF mode is characterized by positive values between 150°E and 150°W near the equator and negative values in off-equatorial regions north of 10°N and south of 10°S. The off-equatorial anomalies are smaller in magnitude. These are approximately represented in the idealized forcing. The time series of the first EOF mode is highly correlated with SST anomalies in the Niño-3.4 region (5°S–5°N, 120°–170°W; r = 0.83, significant at the 99% confidence level), which indicates that this mode is related to ENSO. Idealized anomalies were computed as C0X(x, y)T(t), where C0 is a constant, X(x, y) is the spatial pattern shown in Fig. 6b, and T(t) is the temporal pattern. Note that the maximum amplitude of X and T is unity. The temporal pattern T(t) is zero before 1998, peaks in January 2000, and returns to zero after 2002 (Fig. 6h). Its time scale is set to ∼2.5 years on the basis of the results of autocorrelation of the principal component time series of the first EOF mode. The amplitude C0 is 2.0 × 10−2 N m−2, which is the typical magnitude of zonal wind stress anomalies in the equatorial Pacific Ocean.
Spatial patterns of (a) the first EOF mode of zonal wind stress anomalies in the TPO region (20°S–20°N, 120°E–60°W), (c) the second EOF mode of meridional wind stress anomalies in the southern part of the AUS region (15°–40°S, 100°–120°E), and (e) the first EOF mode of net surface heat flux anomalies in the southern part of the AUS region obtained from ESTOC. Before EOF analysis, monthly climatologies were subtracted and the time series were smoothed with a 13-month boxcar filter and detrended. Spatial patterns of the idealized (b) zonal wind stress anomalies used in IDEAL_TPO_TAUX, (d) meridional wind stress anomalies used in IDEAL_AUS_TAUY, (f) net surface heat flux anomalies used in IDEAL_AUS_HEAT, and (g) zonal wind stress anomalies used in IDEAL_SIO_TAUX. (h) Temporal pattern of idealized forcing. Note that the maximum amplitude of idealized anomalies in (b), (d), (f), (g), and (h) is unity. The method of EOF analysis is described by Emery and Thomson (2004).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
In IDEAL_AUS_TAUY, the idealized anomalies shown in Fig. 6d were added to climatological meridional winds. All of the other forcing fields were climatologies. The spatial pattern of idealized anomalies was designed by comparison with the second EOF mode of meridional wind stress anomalies off the west coast of Australia (Fig. 6c). The second EOF mode explains 20% of the total variance and is characterized by positive values off the northwest coast of Australia. The principal component time series of the second EOF mode is significantly correlated with the Ningaloo Niño index defined by Kataoka et al. (2014) at the 95% confidence level (r = −0.60), indicating that the second EOF mode is related to this climate mode (Feng et al. 2013; Marshall et al. 2015). We used the pattern in Fig. 6h for the temporal evolution of idealized anomalies for IDEAL_AUS_TAUY because the time scale of the second EOF mode of meridional wind stress anomalies off the west coast of Australia is comparable to that of the first EOF mode of zonal wind stress anomalies in the TPO region. The amplitude of the idealized forcing anomalies used in IDEAL_AUS_TAUY is 2.0 × 10−2 N m−2, which is the typical magnitude of meridional wind stress anomalies along the west coast of Australia.
The spatial structure of the idealized anomalies for IDEAL_AUS_TAUY mimics that of the second EOF mode. We also tried using an idealized pattern of forcing anomalies that resembles the first EOF mode of meridional wind stress anomalies, but it did not excite significant variability in meridional velocity in the subsurface of the south Indian Ocean. The first EOF mode, which explains 42% of the total variance, is characterized by a pattern of anomalies that were separate from the Australian coast (figure not shown), and these are not able to excite subsurface variability.
Previous studies have reported that buoyancy forcing excites high baroclinic mode waves, whereas wind forcing drives lower baroclinic modes (Huang 2000; Huang and Pedlosky 1999, 2000; Liu 1999b; Liu and Zhang 1999; Thompson and Ladd 2004). Surface buoyancy forcing affects entrainment velocity at the bottom of the surface mixed layer, whereas surface wind forcing drives vertical velocity at the base of the Ekman layer. The direct effect of surface buoyancy forcing penetrates deeper than that of surface wind forcing because the mixed layer is thicker than the Ekman layer at midlatitudes. The effect of surface buoyancy forcing was tested by IDEAL_AUS_HEAT, in which the idealized pattern of anomalies shown in Fig. 6f was added to climatological surface heat flux, with all other forcing fields being climatological. The spatial structure in Fig. 6f mimics that of the first EOF mode of surface heat flux anomalies, which explains 56% of the total variance and has localized negative values near the west coast of Australia (Fig. 6e). The principal component time series of this mode is significantly correlated with Niño 3.4 SST anomalies at the 95% confidence level (r = −0.64) but not with the Ningaloo Niño index (r = 0.20). This EOF mode is also correlated with cyclonic/anticyclonic surface wind anomalies in the southeastern Indian Ocean (figure not shown), which are often observed during ENSO events (e.g., Wang et al. 2003). We do not discuss the processes of surface heat flux variability further here, but we use the EOF mode as a pattern of dominant variability. The temporal pattern of idealized anomalies is shown in Fig. 6h, and the time scale of the first EOF mode of surface heat flux anomalies is comparable to this pattern. The amplitude of the anomalies is ∼12 W m−2, which is the approximate amplitude of the surface heat flux anomalies along the west Australian coast. Note that we imposed anomalous cooling in this experiment.
In IDEAL_SIO_TAUX, we added the idealized anomalies shown in Fig. 6g to the climatological zonal wind stress, with all other forcing fields being climatologies. Our aim is to show how the ocean responds to wind forcing in the ocean interior away from the coast. (The structure in Fig. 6g was designed arbitrarily and does not correspond to any EOF mode.) Previous theoretical studies have reported that Ekman pumping drives low baroclinic modes (Huang 2000; Liu 1999b). As described in section 4b, the results of IDEAL_SIO_TAUX show a surface-trapped pattern of meridional velocity anomalies, which is different from the results obtained from the other idealized experiments. Again, we used the pattern in Fig. 6h for the temporal evolution. The amplitude of idealized forcing was 2.0 × 10−2 N m−2. The meridional scale of idealized zonal wind stress anomalies was set such that the resulting wind stress curl is typical in magnitude for the south Indian Ocean (Fig. 3a).
3) Experiment with edited topography
Waves generated in the equatorial Pacific Ocean propagate through the Indonesian archipelago and along the west coast of Australia, then radiate to the interior of the south Indian Ocean. Topographic factors, such as the depths of Indonesian inner seas, sills, and Australian continental shelves, may affect transmission of the waves. The horizontal resolution of our model is low (1°), and the model topography does not fully resolve the topographic detail, and this may hamper accurate simulation of the wave transmission. To check sensitivity to the topography, we forced the model with the same initial and surface boundary conditions as those in the control run, but with the ocean floor flattened (Fig. 7). We flattened the model topography by converting the ocean grid to a land grid if the ocean floor was shallower than 100 m, and by setting the ocean floor to ∼5260 m if it was deeper than 100 m. These conditions were applied for the region 45°S–10°N, 50°E–160°W. The bottom depth in the target area varies slightly because the thickness of the bottom cell slightly changes from place to place owing to the use of partial cells (Pacanowski and Gnanadesikan 1998).
Depth of the ocean floor in (a) the control run and (b) the FLAT_BOTTOM experiment.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
3. Statistical analysis
In this section, we present the results of statistical analysis of the output of the control run. Figures 1 and 2 show that meridional velocity anomalies near the surface propagate at the phase speed of the first baroclinic mode, and those at the intermediate level propagate at a slower phase speed. We estimated phase speed in the longitude–time domain using the method of Barron et al. (2009). This method computes the standard deviation of anomalies along straight lines with various slopes and selects the one for which the standard deviation is minimized. The zonal phase speed of meridional velocity anomalies at 100-m depth is approximately −11 cm s−1 at 10°S and decreases to −1.5 cm s−1 at 40°S (Fig. 8, black line). This coincides roughly with the zonal phase speed estimated from satellite altimetry by Menezes and Vianna (2019), although the magnitude of the phase speed between 10° and 15°S is smaller in our estimate. Meridional velocity anomalies between 15° and 35°S at 1000-m depth propagate at a significantly slower rate compared with those at 100-m depth (Fig. 8, red line). No clear propagation signal is observed in the 1000-m meridional velocity anomalies south of 35°S (figure not shown), and the error for phase speed is large south of 37°S.
Zonal phase speed of meridional velocity anomalies at 100 m (black line) and 1000 m (red line) depths between 70° and 110°E as a function of latitude. Phase speed (solid line) and its error (dashed line) were estimated using the method of Barron et al. (2009). Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
The spectra of meridional velocity at 1000-m depth along 25°S show high energy at the annual period (Fig. 9a). The energy is high for periods longer than 2 years east of 70°E, with the highest energy occurring at periods of 4–8 years. This high energy is represented by the slowly propagating signals in Fig. 2c. West of 75°E, energy is high at periods shorter than 2 years, which is reflected in the short-term variability seen west of 75°E in Fig. 2c. Spectral energy averaged over periods longer than 3 years is high in the upper 100 m (Fig. 9b), which represents trapped surface signals. In addition, the averaged energy shows a subsurface peak at ∼500-m depth between 75°E and the eastern boundary of the basin, which confirms the presence of subsurface variability.
(a) Spectra of meridional velocity at 1000-m depth along 25°S as a function of longitude and period. (b) Spectral power of meridional velocity along 25°S averaged over periods longer than 3 years as a function of longitude and depth. Spectra were computed using the specx_anal function provided by the NCAR Command Language and normalized so that the area under the spectrum curve equals the variance of the input time series. Note that the color scales are logarithmic. The meridional velocity was smoothed with a 3-point triangle filter in longitude before the analysis.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
We estimated vertical structures using regression analysis. Figure 10 shows the meridional velocity anomalies at 25°S, 100°E regressed onto meridional velocity anomalies at the same point at depths of 100 m (black line) and 1000 m (red line). The anomalies regressed onto those at 100-m depth have the highest amplitude near the surface, decrease in amplitude with depth, and are indistinguishable from zero at ∼400-m depth. This structure likely reflects the first baroclinic mode, which has a surface-trapped pattern according to Killworth et al. (1997) and Killworth and Blundell (2003). The meridional velocity anomalies regressed onto those at 1000-m depth peak at ∼600-m depth and decrease in amplitude above and below this depth. This suggests that the subsurface variability has a different structure from the surface-trapped variability. Furthermore, the surface-trapped variability has a significant magnitude at 100-m depth, but the amplitude of subsurface variability is indistinguishable from zero at this depth. This justifies the use of meridional velocity at 100-m depth in Fig. 1 to describe the rapidly propagating signals. The subsurface variability is substantial, but the amplitude of the surface-trapped variability is negligible at 1000-m depth; therefore, we use meridional velocity at this depth in Fig. 2.
Meridional velocity anomalies at 25°S, 100°E regressed onto meridional velocity anomalies at the same point at depths of 100 m (black line) and 1000 m (red line). The dashed lines show the range of error for the 95% confidence level (Student’s t test). Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Figure 11 shows a sequence of meridional velocity anomalies regressed onto those at 25°S, 100°E and 1000-m depth with various time lags. At month −24, negative anomalies along 25°S occupy most of the interior regions east of 95°E, and positive anomalies are confined to the region near the eastern boundary below 300-m depth (Fig. 11a). At 1000-m depth, positive anomalies are trapped near the west coast of Australia between 15° and 30°S, whereas positive anomalies are aligned from northwest to southeast to the north of 15°S (Fig. 11b). At month −12, negative anomalies near the surface and positive anomalies in the subsurface emerge near the eastern boundary (Figs. 11c,d). At month 0, the subsurface positive anomalies reach around 25°S, 95°E and tilt toward the east in the vertical section (Fig. 11e). At this lag time, the positive anomalies are distributed from northwest to southeast at 1000-m depth (Fig. 11f). At month 12, the positive anomalies reach ∼90°E and their amplitude decreases. Negative anomalies propagate westward from the west coast of Australia below 300-m depth between months 0 and 12.
Meridional velocity anomalies (left) along 25°S and (right) at 1000-m depth regressed onto meridional velocity anomalies at 25°S, 100°E and 1000-m depth with various time lags. Filled circles show the locations of the base time series. Results are shown for lags of (a),(b) −24; (c),(d) −12; (e),(f) 0; and (g),(h) 12 months. Solid and dashed contours show values significant at the 95% confidence level (Student’s t test). Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
These results confirm the presence of two modes, one of which is trapped near the surface and propagates rapidly, and the other which peaks in amplitude in the subsurface and propagates at a slower phase speed. In the next section we identify the driving force of the subsurface variability using numerical experiments.
4. Numerical experiments
a. Climatology experiments
Figure 12a shows meridional velocity anomalies at 1000-m depth in the control run. If all the surface forcing fields are replaced with their climatologies, the amplitudes of the resulting anomalies are close to zero (Fig. 12b). This shows that the variability in meridional velocity at 1000-m depth is excited by anomalous surface forcing. The amplitudes of the anomalies are also small if the surface forcings in the TPO, AUS, and SIO regions are replaced with the climatologies (Fig. 12c), indicating the importance of forcing in these regions. The sum of the responses to surface momentum and buoyancy forcing in the SIO, AUS, and TPO regions (Fig. 12d) is almost identical to the results obtained from the control run, which confirms the efficacy of surface forcing in these regions and the linear nature of the response.
Longitude–time diagrams of meridional velocity anomalies at 1000-m depth along 25°S in the south Indian Ocean for (a) the control run, (b) CLIM_GLB, and (c) CLIM_IO-PO. (d) Sum of the results from AMOM_SIO, AMOM_AUS, AMOM_TPO, ABUO_SIO, ABUO_AUS, and ABUO_TPO. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. The dashed line is the same as that in Fig. 2.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Figures 13a–13c show the response to surface forcing in the respective regions. The largest contributor is forcing in the TPO region, the response to which shows a series of westward propagating anomalies emanating from the eastern boundary (Fig. 13c). The response to forcing in the AUS region (Fig. 13b) occasionally shows westward propagating anomalies with sizable amplitude, such as those in 1996–2002 and after 2010. Forcing in the SIO region mainly excites short-term variability west of 75°E and does not generate slowly propagating anomalies in the eastern basin (Fig. 13a).
Longitude–time diagrams of meridional velocity anomalies at 1000-m depth along 25°S in the south Indian Ocean for the sum of the results obtained from (a) AMOM_SIO and ABUO_SIO, (b) AMOM_AUS and ABUO_AUS, and (c) AMOM_TPO and ABUO_TPO, and for the results from (d) AMOM_SIO, (e) AMOM_AUS, (f) AMOM_TPO, (g) ABUO_SIO, (h) ABUO_AUS, and (i) ABUO_TPO. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. The dashed line is the same as that in Fig. 2.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Surface momentum forcing in the TPO region effectively excites the response in the southern Indian Ocean (Fig. 13f), whereas the response to surface buoyancy forcing in the TPO region is negligible (Fig. 13i). The response to momentum forcing in the AUS region (Fig. 13e) is comparable in magnitude to that of buoyancy forcing (Fig. 13h), but the former tends to be out of phase with the latter and the two offset each other to an extent. Surface momentum forcing in the SIO region excites short-term variability west of 75°E (Fig. 13d). The response to surface buoyancy forcing in the SIO region is small in magnitude (Fig. 13g). These results show that the primary forcing of the slowly propagating signals in the southern Indian Ocean is surface momentum flux in the TPO region and the secondary forcings are surface momentum and buoyancy flux in the AUS region.
For completeness, we show the response of meridional velocity at 100-m depth and SSH in Fig. 14. Surface forcing in the SIO region excites meridional velocity anomalies at 100-m depth in the central and western parts of the basin, which propagate at a phase speed close to the first baroclinic mode (Fig. 14a). Forcing in the AUS and TPO regions excites 100-m meridional velocity anomalies in the eastern part of the basin, and these tend to propagate at a slower phase speed (Figs. 14b,c). Our results show that forcing in the SIO, AUS, and TPO regions contributes to the excitation of meridional velocity anomalies at 100-m depth in the southern Indian Ocean. SSH anomalies in the western part of the basin are mainly influenced by surface forcing in the SIO region (Fig. 14d), whereas those in the eastern part of the basin are driven primarily by forcing in the TPO region (Fig. 14f). The amplitude of the response of SSH anomalies to surface forcing in the AUS region is relatively small (Fig. 14e). These results are consistent with those from previous studies of SSH variability (Eabry et al. 2021; Menezes and Vianna 2019; Nagura and McPhaden 2021a; Volkov et al. 2020; Zhuang et al. 2013). We compared the sum of the anomalies obtained from these sensitivity experiments with those from the control run for 100-m meridional velocity and SSH. The results compare well in phase, but some discrepancies were found for the amplitudes (figure not shown), which indicates the nonlinear nature of the responses for these variables. Further discussion on the response of surface variables is outside the scope of this work.
(top) Meridional velocity anomalies at 100-m depth and (bottom) SSH anomalies along 25°S for (a),(d) the sum of AMOM_SIO and ABUO_SIO; (b),(e) the sum of AMOM_AUS and ABUO_AUS; and (c),(f) the sum of AMOM_TPO and ABUO_TPO. Monthly climatologies were subtracted, and anomalies were smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Solid and dashed lines are as in Fig. 2.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
b. Idealized experiments
The above results show that surface momentum forcing in the TPO region is one of the drivers of 1000 m meridional velocity anomalies in the south Indian Ocean. In the IDEAL_TPO_TAUX experiment, eastward wind stress anomalies are imposed in the equatorial Pacific Ocean around the year 2000 (Figs. 6b,h). The imposed eastward winds drive an eastward current near the surface in the equatorial Pacific Ocean, which is accompanied by a weaker underlying westward current (Fig. 15). The presence of the subsurface countercurrent is consistent with the results from a linear, continuously stratified model (McCreary 1981). In the equatorial Pacific Ocean, this response is confined to the upper ∼300 m.
Zonal velocity anomalies obtained from IDEAL_TPO_TAUX along the equator in the Pacific Ocean in January 2000. Monthly climatologies were subtracted, and anomalies were smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Zonal velocity anomalies obtained from CLIM_GLB were subtracted.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Excited variability propagates into the southern Indian Ocean via the Indonesian archipelago, as reported in previous studies (e.g., Wijffels and Meyers 2004). Meridional velocity anomalies radiating from the west coast of Australia reach much deeper levels than zonal velocity anomalies in the equatorial Pacific Ocean (Fig. 16, left panels). Meridional velocity anomalies are negative in the upper 200 m and positive below near the eastern boundary in 2001 (Fig. 16a). Negative anomalies are tilted toward the east between 90°E and the eastern boundary along 25°S. Negative anomalies near the surface and the positive anomalies in the subsurface then migrate westward, with the near-surface negative anomalies propagating more rapidly (Figs. 16c,e,g). Positive anomalies are tilted to the east along 25°S. These characteristics are consistent with those obtained from the control run (Fig. 11, left column). Positive meridional velocity anomalies at 1000-m depth are trapped along the west coast of Australia between 15° and 35°S in 2001 (Fig. 16b) and then migrate westward (Figs. 16d,f,h). The westward migration is faster at lower latitudes, resulting in anomalies distributing from northwest to southeast. This horizontal distribution also resembles that obtained from the control run (Fig. 11, right column).
Meridional velocity anomalies obtained from IDEAL_TPO_TAUX (left) along 25°S and (right) at 1000-m depth. Monthly climatologies were subtracted, and anomalies were smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Meridional velocity anomalies obtained from CLIM_GLB were subtracted. Results are shown for (a),(b) June 2001; (c),(d) June 2002; (e),(f) June 2003; and (g),(h) June 2004.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
The longitude–time diagram in Fig. 17a shows the westward propagation of positive meridional velocity anomalies at 1000-m depth in IDEAL_TPO_TAUX. The phase speed is ∼2 cm s−1, which is close to that in the control run (Fig. 8, red line). Propagation of the negative anomalies occurs before and after propagation of the positive anomalies, but the negative anomalies have a smaller amplitude than the positive anomalies. The typical period of variability is 4–6 years, which is longer than the time scale for wind forcing (∼2.5 years). These results indicate that Pacific wind forcing generates slow subsurface propagation in the southern Indian Ocean.
Longitude–time diagrams of (a) meridional velocity anomalies at 1000-m depth, (b) meridional velocity anomalies at 100-m depth, and (c) SSH anomalies along 25°S in the south Indian Ocean obtained from IDEAL_TPO_TAUX. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Anomalies obtained from CLIM_GLB were subtracted. Solid and dashed lines are as in Fig. 2.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Pacific wind forcing also excites a response near the surface in the south Indian Ocean. The responses of 100-m meridional velocity and SSH show both rapidly and slowly propagating signals (Figs. 17b,c). In response to eastward wind forcing in the equatorial Pacific Ocean, positive 100-m meridional velocity anomalies and negative SSH anomalies are generated in the Indian Ocean along 25°S in 2000, and these propagate westward at the approximate phase speed of the first baroclinic mode. The generation of negative SSH anomalies by anomalous eastward wind forcing in the equatorial Pacific Ocean is consistent with the depression of SSH observed in the southeastern Indian Ocean during El Niño events (e.g., Feng et al. 2003; Nagura 2020). The positive 100-m meridional velocity and negative SSH anomalies take a few years to cross the basin. This rapid propagation is not observed in meridional velocity anomalies at 1000-m depth (Fig. 17a), suggesting that these signals are surface trapped. After 2001, a series of 100-m meridional velocity and SSH anomalies radiates from the eastern boundary, and these propagate at a slower phase speed. These results indicate that Pacific winds generate both surface-trapped and subsurface variability.
The results from the climatology experiments indicate that anomalous surface forcing in the AUS region excites variability in meridional velocity at 1000-m depth. The results from IDEAL_AUS_TAUY show that alongshore winds near the west coast of Australia (Fig. 6d) force meridional velocity anomalies, whose magnitude is largest near the surface (Fig. 18a). One year after the peak of wind forcing, meridional velocity anomalies are negative in the upper 200 m and positive below 200 m near the Australian coast (Fig. 18d), which propagate westward afterward (Figs. 18g,j). The phase speed of westward propagation of the subsurface positive anomalies is ∼2 cm s−1, which is consistent with the westward phase speed in the control run (Fig. 8, red line). Surface heat flux anomalies near the west coast of Australia (Fig. 6f) also generate westward-propagating meridional velocity anomalies (Figs. 18b,e,h,k). The vertical structure of the excited anomalies is characterized by surface-trapped variability in the upper ∼200 m and a subsurface peak in amplitude at ∼500-m depth, thus resembling the vertical structure obtained from the control run and the above idealized experiments. The westward phase speed of the meridional velocity anomalies at 1000-m depth in IDEAL_AUS_HEAT is also comparable to that in the control run. Meridional winds and surface heat flux off the west coast of Australia are thus effective drivers of subsurface variability.
Meridional velocity anomalies along 25°S in the south Indian Ocean obtained from (left) IDEAL_AUS_TAUY; (center) IDEAL_AUS_HEAT; and (right) IDEAL_SIO_TAUX. Meridional velocity anomalies obtained from CLIM_GLB were subtracted. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude. Results are shown for (a)–(c) January 2000, (d)–(f) January 2001, (g)–(i) January 2002, and (j)–(l) January 2003.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
In contrast, wind stress curl anomalies in the interior of the south Indian Ocean (Fig. 6g) generate surface-trapped anomalies of meridional velocity, and these propagate rapidly to the west (Figs. 18c,f,i,l). A positive anomaly occurs between 200- and 600-m depth to the east of 105°E in 2003, but its amplitude is much smaller than those of the surface-trapped signals in 2000 and 2001. This result indicates that interior wind forcing does not effectively excite subsurface variability, and this is consistent with the results of previous theoretical studies (Huang 2000; Liu 1999a).
5. Discussion
a. Vertical modes
The results presented in the previous sections show the presence of two vertical modes in meridional velocity. Here, we show that these two modes are representative of the first two baroclinic modes. We used the three-layer model of de Szoeke and Chelton (1999), which is represented by linearized, quasigeostrophic potential vorticity equations [Eq. (2.6) of de Szoeke and Chelton]. A flat bottom and rigid lid were imposed, which exclude the barotropic mode. The equations are written for long wavelength perturbations, and relative vorticity is ignored; the mean zonal velocity is included. The model parameters include the Coriolis coefficient and its meridional gradient, reduced gravity, the mean layer thicknesses, and the mean zonal velocity. We set the mean thicknesses of the upper and middle layers to 100 and 600 m, respectively, such that the layer interfaces are located at the local peaks in Brunt–Väisälä frequency (Fig. 4d, dotted line). The bottom depth is 4500 m. Reduced gravity is set to 0.05 m s−2 for the upper interface and 0.01 m s−2 for the lower interface; these are representative of the two peaks in Brunt–Väisälä frequency shown in Fig. 4d. The mean zonal velocities are 1.75, −0.69, and −0.30 cm s−1 for the top, middle, and bottom layers, respectively, and these were computed from the mean zonal velocity obtained from ESTOC. The eastward mean current in the top layer represents the south Indian countercurrent (Menezes et al. 2014), and the westward velocity in the lower two layers is the South Equatorial Current (Nagura and McPhaden 2018). The Coriolis coefficient and its meridional gradient were computed for 25°S. The system has two solutions, and these represent two baroclinic modes.
The resulting phase speed of the second baroclinic mode is −2.0 cm s−1, which is close to the estimate obtained for 1000-m meridional velocity from ESTOC (Fig. 8, red line). Pressure variability for the second baroclinic mode is opposite in phase between the top and middle layers (Fig. 19b), which results in a subsurface peak of meridional velocity anomalies, consistent with those observed in ESTOC (Fig. 10). Although the phase speed for the first baroclinic mode (−4.9 cm s−1) is slower than that estimated from the 100-m meridional velocity (Fig. 8, black line), its vertical structure is surface trapped (Fig. 19a), which is consistent with results obtained from ESTOC (Fig. 10, black line). These results suggest that the two modes of variability observed in ESTOC represent the first two baroclinic modes.
Vertical structure functions of pressure variability for the (a) first and (b) second baroclinic modes in the three-layer model of de Szoeke and Chelton (1999). The structure functions are normalized such that the value in the top layer is unity.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Liu (1999a) used a 2.5-layer model, which includes both the mean zonal and meridional flow. It was found that the path of energy propagation of the second baroclinic mode was parallel to the direction of the mean current, and the second baroclinic mode was thus referred to as the “advective mode.” In our case, the mean zonal and meridional velocities in the second layer (100–700-m depth) averaged over 25°S, 70°–110°E are approximately −0.6 and 0.8 cm s−1, respectively, and they are oriented to the northwest rather than being parallel to the westward propagation of the meridional velocity anomalies (Figs. 11 and 16, right columns). In addition, the frequency, zonal, and meridional wavelengths estimated from Fig. 11 did not fit the dispersion relation of Liu’s (1999a) advective mode. The reason for this failure is unclear, but it might have arisen because the same reduced gravity values were used for two-layer interfaces in Liu’s (1999a) study, which is inconsistent with Brunt–Väisälä frequency obtained from ESTOC (Fig. 4d). Further investigation is necessary to clarify how the mean current affects propagation of the second baroclinic mode.
b. Transmission of waves
As discussed in section 2c(3), waves propagating from the Pacific to the Indian Ocean can be affected by ocean-floor topography along the propagation path. To assess the sensitivity of our results to the ocean-floor topography, we conducted the FLAT_BOTTOM experiment, in which the seafloor in the western Pacific and Indian Oceans was flattened (Fig. 7b). Meridional velocity anomalies at 1000-m depth obtained from FLAT_BOTTOM (Fig. 20) compare well with those in the control run (Fig. 2c), except that small-scale, high-frequency variability west of 75°E is absent. Slowly propagating anomalies in the eastern basin were simulated in FLAT_BOTTOM and in the control run. We computed the pattern correlation between 1000-m meridional velocity anomalies in the control run and those in FLAT_BOTTOM. Here, pattern correlation was computed treating anomalies in the longitude–time section over 70°–110°E along 25°S as a single data series. The correlation coefficient was 0.74, and it was significant at the 99% confidence level. The neutral regression coefficient with a 95% confidence interval is 0.89 ± 0.19, which is indistinguishable from unity, although the anomalies in FLAT_BOTTOM are slightly smaller in magnitude than those in the control run. Note that the neutral regression coefficient is computed by minimizing the squared distances between the regression line and data points, and its result does not depend on which of two variables is used as the independent variable (Emery and Thomson 2004; Garrett and Petrie 1981). These results show that subsurface meridional velocity anomalies are not sensitive to topographic variations in the ocean floor. This suggests that topographic scattering or shelf waves have limited effects on the generation of slowly propagating signals.
As in Fig. 2c, but for the FLAT_BOTTOM experiment.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Another topic is a change in stratification along the path of wave propagation. The mean stratification in the equatorial Pacific Ocean is characterized by a steep vertical density gradient at the pycnocline, whereas stratification at the pycnocline is weaker at midlatitudes of the south Indian Ocean (Fig. 21a). This leads to a significant change in the vertical structures of baroclinic modes (Fig. 21b), which can transform waves as they propagate (e.g., Busalacchi and Cane 1988). Note that the vertical structure of midlatitude Rossby waves can be modified by the mean current (e.g., Killworth et al. 1997; de Szoeke and Chelton 1999), the effect of which is not considered in Fig. 21b. The dynamical details of wave transformation warrant further discussion in future studies.
(a) Mean Brunt–Väisälä frequency squared in the tropical Pacific Ocean (0°, 180°; solid line) and south Indian Ocean (25°S, 100°E; dashed line) obtained from the ESTOC control run. The temporal mean was computed for the period 1990–2014. (b) Vertical structures of the first (black), second (red), and third (blue) baroclinic modes computed from the mean stratification in the tropical Pacific Ocean (solid line) and south Indian Ocean (dashed line). Vertical modes were computed for the resting state, and the effect of the mean current was not considered.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
c. Other datasets
The results presented above were obtained from ESTOC. We also examined the output of ECCO version 4 (v4; Forget et al. 2015), which is another ocean state estimation dataset generated using the same method as ESTOC (i.e., a 4DVAR method based on the strong constraint). ECCO v4 is based on the Massachusetts Institute of Technology general circulation model (Adcroft et al. 2004; Marshall et al. 1997). This model uses a global “lat–lon–cap grid” that reverts to a simple latitude–longitude grid with 1° intervals between 70°S and 67°N. The 3D field of diffusivity was adjusted through data synthesis experiments. Its assimilation window is from 1992 to 2017. We used monthly averages interpolated onto a 0.5° × 0.5° grid.
The meridional velocity anomalies at 100-m depth obtained from ECCO v4 show westward propagation, with a phase speed close to that of the first baroclinic mode (Fig. 22a). Meridional velocity anomalies at 1000-m depth exhibit slower propagation between 1992 and 2005 to the east of ∼70°E (Fig. 22b). Slow propagation is clearer in meridional velocity anomalies at 1500-m depth (Fig. 22c). Zonal phase speed estimated using the method of Barron et al. (2009) shows that westward propagation of the meridional velocity anomalies at depths of 1000 and 1500 m is slower than those at 100 m between 15° and 30°S (Fig. 22d). Regression analysis shows that the 100-m meridional velocity anomalies represent variability trapped near the surface (Fig. 22e, black line), whereas those at depths of 1000 and 1500 m are related to variability that peaks in amplitude at around 800–1200-m depth (Fig. 22e, red and blue lines). These results are consistent with those from ESTOC and support the presence of two modes of variability. Note that quantitative discrepancies occur between the results from ESTOC and those from ECCO v4. For example, the amplitude of subsurface variability peaks at ∼600-m depth in ESTOC (Fig. 10), whereas the peak is at 800–1200-m depth in ECCO v4 (Fig. 22e). This discrepancy indicates that quantitative details are dependent on the dataset used, possibly as a result of differences in the configurations of the models and/or assimilation methods, such as the length of the assimilation window and/or the method of tuning diffusivity parameters. It is also possible that observations are not dense enough to constrain the details of the phenomenon.
Results obtained from ECCO v4. Meridional velocity anomalies along 25°S at depths of (a) 100, (b) 1000, and (c) 1500 m. Solid and dashed lines are as in Fig. 2. (d) Zonal phase speed (solid line) and its error (dotted line) for meridional velocity anomalies along 25°S between 70° and 110°E at depths of 100 m (black line), 1000 m (red line), and 1500 m (blue line) calculated using the method of Barron et al. (2009). (e) Meridional velocity anomalies at 25°S and 100°E regressed onto meridional velocity anomalies at the same location at depths of 100 m (black line), 1000 m (red line), and 1500 m (blue line). Dotted lines show the error bars estimated by Student’s t tests. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3-point triangle filter in longitude.
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
Figure 15a of Nagura (2020) shows the slow propagation of meridional velocity anomalies at an intermediate level along 22°S in the output from the Japan Meteorological Agency’s Multivariate Ocean Variational Estimation system (MOVE-g2i or GONDOLA100A; Toyoda et al. 2016, 2019), which is an ocean reanalysis generated by a 3DVAR method. The typical westward phase speed of meridional velocity anomalies obtained from MOVE-g2i is ∼1.3 cm s−1, which is slightly slower than that in ESTOC (Fig. 8) but qualitatively supports our conclusion that there is subsurface propagation that is slower than the first baroclinic mode. Nagura (2020) also reported that slow subsurface propagation was not observed in meridional velocity anomalies in the south Indian Ocean obtained from the ECMWF Ocean Reanalysis System, version 4 (ORAS4; Balmaseda et al. 2013). This absence suggests that the simulation of slow propagation may qualitatively depend on the assimilation schemes used, because both MOVE-g2i and ORAS4 were constructed using a 3DVAR method.
We further checked datasets generated by statistical gridding methods, but no slowly propagating signals were observed. We used temperature data obtained from Roemmich and Gilson’s (2009) dataset, the Grid Point Value of the Monthly Objective Analysis using Argo float data (MOAA-GPV; Hosoda et al. 2008), and the In Situ Analysis System (ISAS; Gaillard et al. 2016; Kolodziejczyk et al. 2017). The results obtained from the idealized ESTOC experiments indicate that surface wind and buoyancy forcings generate temperature anomalies at 1000-m depth, and these exhibit both fast and slow propagation (Figs. 23a–c). The results from the ESTOC control run show both fast and slow propagation in temperature anomalies at 1000-m depth, and the slow propagation is clearest in the eastern part of the basin (Fig. 23d). Temperature anomalies obtained from statistically gridded datasets are noisy and do not show any clear propagation (Figs. 23e–g). We checked temperature anomalies at different levels, and the results are consistent. This is likely due to the sparseness of in situ observations, which are insufficient for propagating signals to be resolved using statistical gridding. A more detailed observational study is necessary.
Longitude–time diagrams of temperature anomalies at 1000 m depth along 25°S in the south Indian Ocean for (a) IDEAL_TPO_TAUX, (b) IDEAL_AUS_TAUY, (c) IDEAL_AUS_HEAT, (d) the ESTOC control run, (e) the dataset of Roemmich and Gilson (2009), (f) MOAA GPV, and (g) ISAS. Anomalies were computed by subtracting monthly climatologies and smoothed with a 13-month boxcar filter in time and a 3° triangle filter in longitude. Anomalies obtained from CLIM_GLB were subtracted from those obtained from the ideal experiments. Solid and dashed lines are as in Fig. 2. Note that the color scale varies among (a)–(c), whereas the same scale is used for (d)–(g).
Citation: Journal of Physical Oceanography 52, 8; 10.1175/JPO-D-21-0290.1
6. Summary
This study examined the propagation of Rossby waves in the south Indian Ocean using the ocean reanalysis product ESTOC, which was constructed using the 4DVAR method. We focused on propagating signals in meridional velocity at midlatitudes on interannual time scales.
The results of statistical analysis show two modes of variability in meridional velocity anomalies in the south Indian Ocean. One mode is trapped near the surface and propagates to the west at a phase speed close to that of the first baroclinic mode (∼7 cm s−1 at 25°S). The other has a peak in amplitude at ∼600-m depth and propagates to the west at a slower phase speed (∼2 cm s−1 at 25°S). Such slowly propagating signals are observed at midlatitudes globally, but they are largest in amplitude in the south Indian Ocean. The typical time scale of the slowly propagating signals is 4–8 years, and they radiate from the west coast of Australia.
The results of the numerical experiments show that the primary forcing of slowly propagating signals in the south Indian Ocean is zonal wind anomalies in the equatorial Pacific Ocean related to ENSO. Zonal wind forcing in the equatorial Pacific Ocean excites a zonal jet trapped near the surface, which propagates to the Indian Ocean through the Indonesian archipelago and generates subsurface variability in the south Indian Ocean. Momentum and buoyancy forcings near the west coast of Australia can also excite slowly propagating subsurface signals in the south Indian Ocean. In contrast, wind forcing in the interior of the south Indian Ocean generates surface-trapped variability, but it is not an effective driver of slowly propagating subsurface signals.
Our discussion using the three-layer quasigeostrophic model suggests that surface-trapped variability and slowly propagating subsurface variability represent the first two baroclinic modes. Results obtained from another ocean reanalysis dataset (ECCO v4) also support our conclusion. Further study is necessary to clarify the dynamical details and climatic importance of the detected variability.
Acknowledgments.
The authors thank two anonymous reviewers for their helpful comments and Shuhei Masuda for helping us to set up one of the model experiments and his constructive comments. This work was supported by a JSPS Grant-in-Aid for Scientific Research (KAKENHI, JP18K03750).
Data availability statement.
The output of the ESTOC control run can be obtained at http://www.godac.jamstec.go.jp/estoc/j/description/03b.html. ERA5 data were obtained from https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5. Satellite altimetry data from CMEMS were obtained from ftp://my.cmems-du.eu/Core/SEALEVEL_GLO_PHY_L4_REP_OBSERVATIONS_008_047/dataset-duacs-rep-global-merged-allsat-phy-l4. WOA13 data are available at https://www.nodc.noaa.gov/OC5/woa13/. ECCO v4 data were obtained from https://ecco.jpl.nasa.gov/drive/files/Version4/Release4/interp_monthly. Roemmich and Gilson’s (2009) dataset was obtained at http://sio-argo.ucsd.edu/RG_Climatology.html. MOAA GPV is available at http://www.jamstec.go.jp/ARGO/argo_web/MapQ/Mapdataset_e.html. The ISAS dataset was obtained at https://www.seanoe.org/data/00412/52367.
REFERENCES
Adcroft, A., C. Hill, J.-M. Campin, J. Marshall, and P. Heimbach, 2004: Overview of the formulation and numerics of the MITGCM. Proc. ECMWF Seminar Series on Numerical Methods, Recent Developments in Numerical Methods for Atmosphere and Ocean Modelling, Reading, United Kingdom, ECMWF, 139–149, http://mitgcm.org/pdfs/ECMWF2004-Adcroft.pdf.
Balmaseda, M. A., K. Mogensen, and A. T. Weaver, 2013: Evaluation of the ECMWF ocean reanalysis system ORAS4. Quart. J. Roy. Meteor. Soc., 139, 1132–1161, https://doi.org/10.1002/qj.2063.
Barron, C. N., A. B. Kara, and G. A. Jacobs, 2009: Objective estimates of westward Rossby wave and eddy propagation from sea surface height analyses. J. Geophys. Res., 114, C03013, https://doi.org/10.1029/2008JC005044.
Busalacchi, A. J., and M. A. Cane, 1988: The effect of varying stratification on low-frequency equatorial motions. J. Phys. Oceanogr., 18, 801–812, https://doi.org/10.1175/1520-0485(1988)018<0801:TEOVSO>2.0.CO;2.
Chelton, D. B., and M. G. Schlax, 1996: Global observations of oceanic Rossby waves. Science, 272, 234–238, https://doi.org/10.1126/science.272.5259.234.
Chu, P. C., L. M. Ivanov, O. V. Melnichenko, and N. C. Wells, 2007: On long baroclinic Rossby waves in the tropical North Atlantic observed from profiling floats. J. Geophys. Res., 112, C05032, https://doi.org/10.1029/2006JC003698.
Clarke, A. J., 1991: On the reflection and transmission of low-frequency energy at the irregular western Pacific Ocean boundary. J. Geophys. Res., 96, 3289–3305, https://doi.org/10.1029/90JC00985.
Clarke, A. J., and X. Liu, 1994: Interannual sea level in the northern and eastern Indian Ocean. J. Phys. Oceanogr., 24, 1224–1235, https://doi.org/10.1175/1520-0485(1994)024<1224:ISLITN>2.0.CO;2.
Conkright, M. E., and Coauthors, 1999: World Ocean Database 1998: Documentation and quality control version 2.0. National Oceanographic Data Center Internal Rep. 14, 188 pp., https://repository.library.noaa.gov/view/noaa/1173/noaa_1173_DS1.pdf.
de Szoeke, R. A., and D. B. Chelton, 1999: The modification of long planetary waves by homogeneous potential vorticity layers. J. Phys. Oceanogr., 29, 500–511, https://doi.org/10.1175/1520-0485(1999)029<0500:TMOLPW>2.0.CO;2.
Ducet, N., P. Y. Le Traon, and G. Reverdin, 2000: Global high-resolution mapping of ocean circulation from TOPEX/Poseidon and ERS-1 and -2. J. Geophys. Res., 105, 19 477–19 498, https://doi.org/10.1029/2000JC900063.
Eabry, M. D., A. S. Taschetto, A. M. Maharaj, and A. Sen Gupta, 2021: What determines the lagged ENSO response in the south-west Indian Ocean? Geophys. Res. Lett., 48, e2020GL091958, https://doi.org/10.1029/2020GL091958.
Emery, W. J., and R. E. Thomson, 2004: Data Analysis Methods in Physical Oceanography. Elsevier, 638 pp.
Feng, M., G. Meyers, A. Pearce, and S. Wijffels, 2003: Annual and interannual variations of the Leeuwin Current at 32°S. J. Geophys. Res., 108, 3355, https://doi.org/10.1029/2002JC001763.
Feng, M., M. J. McPhaden, and T. Lee, 2010: Decadal variability of the Pacific subtropical cells and their influence on the south-east Indian Ocean. Geophys. Res. Lett., 37, L09606, https://doi.org/10.1029/2010GL042796.
Feng, M., C. Böning, A. Biastoch, E. Behrens, E. Weller, and Y. Masumoto, 2011: The reversal of the multidecadal trends of the equatorial Pacific easterly winds, and the Indonesian Throughflow and Leeuwin Current transports. Geophys. Res. Lett., 38, L11604, https://doi.org/10.1029/2011GL047291.
Feng, M., M. J. McPhaden, S.-P. Xie, and J. Hafner, 2013: La Niña forces unprecedented Leeuwin Current warming in 2011. Sci. Rep., 3, 1277, https://doi.org/10.1038/srep01277.
Forget, G., J.-M. Campin, P. Heimbach, C. N. Hill, R. M. Ponte, and C. Wunsch, 2015: ECCO version 4: An integrated framework for non-linear inverse modeling and global ocean state estimation. Geosci. Model Dev., 8, 3071–3104, https://doi.org/10.5194/gmd-8-3071-2015.
Gaillard, F., T. Reynaud, V. Thierry, N. Kolodziejczyk, and K. von Schuckmann, 2016: In situ-based reanalysis of the global ocean temperature and salinity with ISAS: Variability of the heat content and steric height. J. Climate, 29, 1305–1323, https://doi.org/10.1175/JCLI-D-15-0028.1.
Gargett, A. E., 1984: Vertical eddy diffusivity in the ocean interior. J. Mar. Res., 42, 359–393, https://doi.org/10.1357/002224084788502756.
Garrett, C., and B. Petrie, 1981: Dynamical aspects of the flow through the strait of Belle Isle. J. Phys. Oceanogr., 11, 376–393, https://doi.org/10.1175/1520-0485(1981)011<0376:DAOTFT>2.0.CO;2.
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155, https://doi.org/10.1175/1520-0485(1990)020<0150:IMIOCM>2.0.CO;2.
Good, S. A., M. J. Martin, and N. A. Rayner, 2013: EN4: Quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. J. Geophys. Res. Oceans, 118, 6704–6716, https://doi.org/10.1002/2013JC009067.
Häkkinen, S., P. B. Rhines, and D. L. Worthen, 2016: Warming of the global ocean: Spatial structure and water-mass trends. J. Climate, 29, 4949–4963, https://doi.org/10.1175/JCLI-D-15-0607.1.
Hasumi, H., and N. Suginohara, 1999: Effects of locally enhanced vertical diffusivity over rough topography on the world ocean circulation. J. Geophys. Res., 104, 23 364–23 374, https://doi.org/10.1029/1999JC900191.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Hosoda, S., T. Ohira, and T. Nakamura, 2008: A monthly mean dataset of global oceanic temperature and salinity derived from Argo float observations. JAMSTEC Rep. Res. Dev., 8, 47–59, https://doi.org/10.5918/jamstecr.8.47.
Huang, R. X., 2000: Climate variability inferred from a continuously stratified model of the ideal-fluid thermocline. J. Phys. Oceanogr., 30, 1389–1406, https://doi.org/10.1175/1520-0485(2000)030<1389:CVIFAC>2.0.CO;2.
Huang, R. X., and J. Pedlosky, 1999: Climate variability inferred from a layered model of the ventilated thermocline. J. Phys. Oceanogr., 29, 779–790, https://doi.org/10.1175/1520-0485(1999)029<0779:CVIFAL>2.0.CO;2.
Huang, R. X., and J. Pedlosky, 2000: Climate variability induced by anomalous buoyancy forcing in a multilayer model of the ventilated thermocline. J. Phys. Oceanogr., 30, 3009–3021, https://doi.org/10.1175/1520-0485(2001)031<3009:CVIBAB>2.0.CO;2.
Isoguchi, O., H. Kawamura, and T. Kono, 1997: A study on wind-driven circulation in the subarctic North Pacific using TOPEX/POSEIDON altimeter data. J. Geophys. Res., 102, 12 457–12 468, https://doi.org/10.1029/97JC00447.
Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471, https://doi.org/10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2.
Kanamitsu, M., W. Ebisuzaki, J. Woollen, S.-K. Yang, J. J. Hnilo, M. Fiorino, and G. L. Potter, 2002: NCEP-DOE AMPI-II Reanalysis (R-2). Bull. Amer. Meteor. Soc., 83, 1631–1644, https://doi.org/10.1175/BAMS-83-11-1631.
Kataoka, T., T. Tozuka, S. Behera, and T. Yamagata, 2014: On the Ningaloo Niño/Niña. Climate Dyn., 43, 1463–1482, https://doi.org/10.1007/s00382-013-1961-z.
Killworth, P. D., and J. R. Blundell, 2003: Long extratropical planetary wave propagation in the presence of slowly varying mean flow and bottom topography. Part I: The local problem. J. Phys. Oceanogr., 33, 784–801, https://doi.org/10.1175/1520-0485(2003)33<784:LEPWPI>2.0.CO;2.
Killworth, P. D., D. B. Chelton, and R. A. De Szoeke, 1997: The speed of observed and theoretical long extratropical planetary waves. J. Phys. Oceanogr., 27, 1946–1966, https://doi.org/10.1175/1520-0485(1997)027<1946:TSOOAT>2.0.CO;2.
Kolodziejczyk, N., P.-M. Annaig, and G. Fabienne, 2017: ISAS-15 temperature and salinity gridded fields. SEANOE, accessed 11 September 2020, https://doi.org/10.17882/52367.
Liu, Z., 1999a: Forced planetary wave response in a thermocline gyre. J. Phys. Oceanogr., 29, 1036–1055, https://doi.org/10.1175/1520-0485(1999)029<1036:FPWRIA>2.0.CO;2.
Liu, Z., 1999b: Planetary wave modes in the thermocline: Non-Doppler-shift mode, advective mode and Green mode. Quart. J. Roy. Meteor. Soc., 125, 1315–1339, https://doi.org/10.1002/qj.1999.49712555611.
Liu, Z., and R.-H. Zhang, 1999: Propagation and mechanism of decadal upper-ocean variability in the north Pacific. Geophys. Res. Lett., 26, 739–742, https://doi.org/10.1029/1999GL900081.
Locarnini, R. A., and Coauthors, 2013: Temperature. Vol. 1, World Ocean Atlas 2013, NOAA Atlas NESDIS 73, 40 pp., http://data.nodc.noaa.gov/woa/WOA13/DOC/woa13_vol1.pdf.
Marshall, A. G., H. H. Hendon, M. Feng, and A. Schiller, 2015: Initiation and amplification of the Ningaloo Niño. Climate Dyn., 45, 2367–2385, https://doi.org/10.1007/s00382-015-2477-5.
Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 5753–5766, https://doi.org/10.1029/96JC02775.
McCreary, J. P., 1981: A linear stratified ocean model of the equatorial undercurrent. Philos. Trans. Roy. Soc. London, 298, 603–635, https://doi.org/10.1098/rsta.1981.0002.
McDougall, T. J., and P. M. Barker, 2011: Getting started with TEOS-10 and the Gibbs Seawater (GSW) Oceanographic Toolbox. SCOR/IAPSO WG127, 28 pp., http://www.teos-10.org/pubs/Getting_Started.pdf.
Menemenlis, D., I. Fukumori, and T. Lee, 2005: Using Green’s functions to calibrate an ocean general circulation model. Mon. Wea. Rev., 133, 1224–1240, https://doi.org/10.1175/MWR2912.1.
Menezes, V. V., and M. L. Vianna, 2019: Quasi-biennial Rossby and Kelvin waves in the south Indian Ocean: Tropical and subtropical modes and the Indian Ocean dipole. Deep-Sea Res. II, 166, 43–63, https://doi.org/10.1016/j.dsr2.2019.05.002.
Menezes, V. V., H. E. Phillips, A. Schiller, N. L. Bindoff, C. M. Domingues, and M. L. Vianna, 2014: South Indian Countercurrent and associated fronts. J. Geophys. Res. Oceans, 119, 6763–6791, https://doi.org/10.1002/2014JC010076.
Nagura, M., 2018: Annual Rossby waves below the pycnocline in the Indian Ocean. J. Geophys. Res. Oceans, 123, 9405–9415, https://doi.org/10.1029/2018JC014362.
Nagura, M., 2020: Variability in meridional transport of the subtropical circulation in the south Indian Ocean for the period from 2006 to 2017. J. Geophys. Res. Oceans, 124, e2019JC015874, https://doi.org/10.1029/2019JC015874.
Nagura, M., 2021: Spiciness anomalies of Subantarctic Mode Water in the south Indian Ocean. J. Climate, 34, 3927–3953, https://doi.org/10.1175/JCLI-D-20-0482.1.
Nagura, M., and M. J. McPhaden, 2018: The shallow overturning circulation in the Indian Ocean. J. Phys. Oceanogr., 48, 413–434, https://doi.org/10.1175/JPO-D-17-0127.1.
Nagura, M., and M. J. McPhaden, 2021a: Interannual variability in sea surface height at southern midlatitudes of the Indian Ocean. J. Phys. Oceanogr., 51, 1595–1609, https://doi.org/10.1175/JPO-D-20-0279.1.
Nagura, M., and M. J. McPhaden, 2021b: Predicting interannual variability in sea surface height along the west coast of Australia using a simple ocean model. Geophys. Res. Lett., 48, e2021GL094592, https://doi.org/10.1029/2021GL094592.
Nakano, H., and N. Suginohara, 2002: Effects of bottom boundary layer parameterization on reproducing deep and bottom waters in a world ocean model. J. Phys. Oceanogr., 32, 1209–1227, https://doi.org/10.1175/1520-0485(2002)032<1209:EOBBLP>2.0.CO;2.
Noh, Y., 2004: Sensitivity to wave breaking and the Prandtl number in the ocean mixed layer model and its dependence on latitude. Geophys. Res. Lett., 31, L23305, https://doi.org/10.1029/2004GL021289.
Osafune, S., S. Masuda, and N. Sugiura, 2014a: Role of the oceanic bridge in linking the 18.6 year modulation of tidal mixing and long-term SST change in the North Pacific. Geophys. Res. Lett., 41, 7284–7290, https://doi.org/10.1002/2014GL061737.
Osafune, S., T. Doi, S. Masuda, N. Sugiura, and T. Hemmi, 2014b: Estimated state of ocean for climate research (ESTOC). JAMSTEC, accessed 6 July 2021, https://doi.org/10.17596/0000106.
Osafune, S., S. Masuda, N. Sugiura, and T. Doi, 2015: Evaluation of the applicability of the Estimated State of the Global Ocean for Climate Research (ESTOC) data set. Geophys. Res. Lett., 42, 4903–4911, https://doi.org/10.1002/2015GL064538.
Pacanowski, R. C., and A. Gnanadesikan, 1998: Transient response in a z-level ocean model that resolves topography with partial cells. Mon. Wea. Rev., 126, 3248–3270, https://doi.org/10.1175/1520-0493(1998)126<3248:TRIAZL>2.0.CO;2.
Pacanowski, R. C., and S. Griffies, 2000: MOM 3.0 Manual. Geophysical Fluid Dynamics Laboratory, 680 pp.