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  • View in gallery

    Mooring-observed daily equatorial zonal current (m s−1) at 80°, 85°, and 93°E from March 2015 through April 2019. The dashed vertical lines mark each 1 Jan and 1 Jul.

  • View in gallery

    Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement during April 2015 to April 2019 (gray thin line). Thick red, blue, and black lines represent the seasonal, intraseasonal, and interannual components, respectively.

  • View in gallery

    The power spectrum of seasonal (blue) and intraseasonal (orange) components of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement.

  • View in gallery

    (a) STDs of zonal wind stress from CCMP during 2001–18 along the equator (1°S–1°N) for intraseasonal (blue line), seasonal (red line), and interannual (black line) components. (b) The seasonal zonal current on day 208 from BRAN (color). As an example, the ray paths tracking from the point at 73°E, 10 m are shown: the wind-generated Kelvin and reflected Rossby rays of the second meridional modes with the periods of 90 (blue dash–dotted line), 180 (red dash–dotted line), and 360 days (black dash–dotted line).

  • View in gallery

    Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (c) 0°, 85°E; and (e) 0°, 93°E from mooring measurement (black line) and their projection onto the second and fourth modes (mode 2 plus mode 4; blue line). Also shown are STDs of the first 10 modes projected by the observed 200–500-m-averaged zonal currents at (b) 0°, 80°E; (d) 0°, 85°E; and (f) 0°, 93°E.

  • View in gallery

    (a) (left) EOF-sp1 and (left center) EOF-sp2: the first and second EOF spatial modes for the monthly zonal velocities averaged between 0.25°S and 0.25°N from LOM_Maldives during 2001–18; 47% and 27% are the explained variances. (center) EOF-sp1(modes2–4) and (right center) EOF-sp2(modes2–4): as in EOF-sp1 and EOF-sp2, but using the sum of baroclinic modes 2–4 of the zonal velocities. (right) EOF-sp1(modes1, 5–25): as in EOF-sp1, but using the sum of baroclinic modes 1 and 5–25. Also shown are longitude–depth plots of the monthly zonal velocities (m s−1) averaged between 0.25°S and 0.25°N for (b) June, (c) July, and (d) August 2016 obtained from LOM_Maldives. For (b)–(d), shown are the sum of baroclinic modes (left) 1–25, (left center) 2–20, and (center) 2–4, along with (right center) mode 2 and (right) mode 4.

  • View in gallery

    Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement (black line), BRAN (red line), PIOM (blue line), and OFES (green line). We only show the reanalysis and OGCM results from 2009 so as to display the lines clearly.

  • View in gallery

    STDs of zonal velocities averaged at 200–1000 m, 0.25°S–0.25°N from (a) BRAN, (b) OFES, and (c) PIOM based during 2001–18. Blue, red and black lines represent the ISV, seasonal, and interannual components, respectively. STD of the ISV component from the OFES climatological run is also shown [dashed blue line in (b)]. Also shown are longitude–time plots of the seasonal components of zonal velocities (m s−1) averaged at 200–1000 m, 0.25°S–0.25°N, from (d) BRAN, (e) OFES, and (f) ROM. The y axis repeats for 3 years.

  • View in gallery

    Longitude–depth plots of STDs of zonal velocities (m s−1) averaged between 0.25°S and 0.25°N from BRAN during 2001–18 for (a) intraseasonal, (b) seasonal, and (c) interannual components.

  • View in gallery

    (a),(b) STDs of zonal velocities averaged at 200–1000 m, 0.25°S–0.25°N, from LOM experiments during 2001–18. Also shown are longitude–depth plots of the monthly climatological zonal velocities (m s−1) averaged between 0.25°S and 0.25°N for January, April, July, and October obtained from (c) LOM_MR, (d) LOM_DAMP, (e) LOM_Reflect (LOM_MR − LOM_DAMP), (f) LOM_Maldives, (g) LOM_Maldives_DAMP, and (h) LOM_Maldives_Reflect (LOM_Maldives − LOM_Maldives_DAMP) during 2001–18. Black lines are the 0 m s−1 contours.

  • View in gallery

    (left) The spatial structure of 200–1000 m averaged monthly climatology of pressure (color shading; 980 g cm−1 s−2) and current (vectors; m s−1) from LOM_MR during 2001–18. (right) The meridional structure of the EIC at section 85°E, marked by red vertical lines in the left column.

  • View in gallery

    The weakened rate of each mode, by comparing the monthly climatological zonal velocities averaged at 200–1000 m over 0.25°S–0.25°N, 50°–90°E from LOM_MR and LOM_Maldives during 2001–18.

  • View in gallery

    Amplitudes of semiannual harmonics of (a)–(f) mode 2 and (g)–(l) mode 4 along the equator (0.25°S–0.25°N) from (left) LOM_MR, (center) LOM_DAMP, and (right) LOM_Reflect (m s−1).

  • View in gallery

    Longitude–time plots of zonal currents (m s−1) along the equator (0.25°S–0.25°N) for mode 2 averaged at 600–640 m at 180-day period from (a) LOM_MR and (b) LOM_Maldives and for mode 4 averaged at 680–720 m from (c) LOM_MR and (d) LOM_Maldives. The depth is chosen according to the core location shown in Fig. 13. The dash–dot lines in (a) and (c) mark the phase of modes 2 and 4, respectively, which is defined by the month with the strongest eastward velocity.

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Determination of Spatiotemporal Variability of the Indian Equatorial Intermediate Current

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  • 1 State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China
  • | 2 Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou, China
  • | 3 Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, Colorado
  • | 4 School of Marine Sciences, Sun Yat-sen University, Guangzhou, China
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Abstract

Using 4-yr mooring observations and ocean circulation model experiments, this study characterizes the spatial and temporal variability of the Equatorial Intermediate Current (EIC; 200–1200 m) in the Indian Ocean and investigates the causes. The EIC is dominated by seasonal and intraseasonal variability, with interannual variability being weak. The seasonal component dominates the midbasin with a predominant semiannual period of ~166 days but weakens toward east and west where the EIC generally exhibits large intraseasonal variations. The resonant second and fourth baroclinic modes at the semiannual period make the largest contribution to the EIC, determining the overall EIC structures. The higher baroclinic modes, however, modify the EIC’s vertical structures, forming multiple cores during some time periods. The EIC intensity has an abrupt change near 73°E, which is strong to the east and weak to the west. Model simulation suggests that the abrupt change is caused primarily by the Maldives, which block the propagation of equatorial waves. The Maldives impede the equatorial Rossby waves, reducing the EIC’s standard deviation associated with reflected Rossby waves by ~48% and directly forced waves by 20%. Mode decomposition further demonstrates that the semiannual resonance amplitude of the second baroclinic mode reduces by 39% because of the Maldives. However, resonance amplitude of the four baroclinic mode is less affected, because the Maldives fall in the node region of mode 4’s resonance. The research reveals the spatiotemporal variability of the poorly understood EIC, contributing to our understanding of equatorial wave–current dynamics.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-20-0042.s1.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Gengxin Chen, chengengxin@scsio.ac.cn; Dongxiao Wang, dxwang@mail.sysu.edu.cn

Abstract

Using 4-yr mooring observations and ocean circulation model experiments, this study characterizes the spatial and temporal variability of the Equatorial Intermediate Current (EIC; 200–1200 m) in the Indian Ocean and investigates the causes. The EIC is dominated by seasonal and intraseasonal variability, with interannual variability being weak. The seasonal component dominates the midbasin with a predominant semiannual period of ~166 days but weakens toward east and west where the EIC generally exhibits large intraseasonal variations. The resonant second and fourth baroclinic modes at the semiannual period make the largest contribution to the EIC, determining the overall EIC structures. The higher baroclinic modes, however, modify the EIC’s vertical structures, forming multiple cores during some time periods. The EIC intensity has an abrupt change near 73°E, which is strong to the east and weak to the west. Model simulation suggests that the abrupt change is caused primarily by the Maldives, which block the propagation of equatorial waves. The Maldives impede the equatorial Rossby waves, reducing the EIC’s standard deviation associated with reflected Rossby waves by ~48% and directly forced waves by 20%. Mode decomposition further demonstrates that the semiannual resonance amplitude of the second baroclinic mode reduces by 39% because of the Maldives. However, resonance amplitude of the four baroclinic mode is less affected, because the Maldives fall in the node region of mode 4’s resonance. The research reveals the spatiotemporal variability of the poorly understood EIC, contributing to our understanding of equatorial wave–current dynamics.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JPO-D-20-0042.s1.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding authors: Gengxin Chen, chengengxin@scsio.ac.cn; Dongxiao Wang, dxwang@mail.sysu.edu.cn

1. Introduction

The Equatorial Intermediate Current (EIC) is a common phenomenon in the three major oceans. It locates beneath the thermocline generally down to 1200 m along the equator, driven by the zonal equatorial winds. Different from the quasi-permanent feature in the Pacific and Atlantic Oceans (Firing 1987; Kessler and McCreary 1993; Delcroix and Henin 1988; Fischer and Schott 1997; Gouriou et al. 2006; Wang et al. 2016), the EIC in the Indian Ocean shows seasonal reversal with a significant semiannual cycle (Gent et al. 1983; Jensen 1993; Huang et al. 2018a).

Based on moored current meters deployed in the western equatorial Indian Ocean between 47° and 62°E, Luyten and Roemmich (1982) first reported semiannual variability in zonal velocity below the thermocline (at 200, 500, and 750 m) with amplitude of 0.15 m s−1 and upward phase propagation in the western Indian Ocean. Using a line ocean model, Gent et al. (1983) reproduced the semiannual zonal velocity, and concluded that the observed zonal flow was a forced response to the semiannual component of the near-equatorial zonal winds. Jensen (1993) applied a numerical isopycnal ocean model to simulate the Indian Ocean circulation and suggested that a semiannual, resonant basin mode related to second baroclinic mode contributed to the strong EIC. Based on in situ observations in the eastern equatorial Indian Ocean and a continuously stratified linear ocean model (LOM), Huang et al. (2018a) verified the EIC’s semiannual variability and the equatorial basin resonance at the semiannual period. Huang et al. (2018b) further investigated vertical phase propagation of the EIC. The semiannual current and isotherm displacement variability are verified recently by Argo data (Zanowski and Johnson, 2019).

Despite the recent advancement, our knowledge on the EIC in the Indian Ocean remains limited, and variability of equatorial zonal current at intermediate depth layer is not fully understood. In addition to the semiannual component, it is unclear whether or not the EIC also exhibits intraseasonal and interannual variability, like the equatorial surface current and undercurrent (e.g., McPhaden, 1982; Thompson et al. 2006; Gnanaseelan et al. 2012; Gnanaseelan and Deshpande 2018; Masumoto et al. 2005; Chen et al. 2017, 2019). The observed 0.15 m s−1 amplitude of the EIC in the western basin (Luyten and Roemmich, 1982) is far smaller than the ~0.35 m s−1 amplitude of EIC at 80° and 85°E in the eastern basin (Huang et al. 2018a), implying that the EIC intensity has significant spatial variation. However, the spatial variability of the EIC and its causes have not been addressed.

By analyzing in situ observations, ocean reanalysis data and results from ocean general circulation models (OGCMs), this study characterizes the spatial and temporal variability of the EIC in the Indian Ocean. LOM experiments are further performed to provide insight into the underlying dynamics. The research provides new knowledge on the EIC, which will help advance our understanding of the equatorial current system and associated mass and salt exchanges between the eastern and western Indian Ocean.

2. Data and ocean models

a. Observations, reanalysis data and existing OGCM results

Three moorings were deployed at 0°, 80°E; 0°, 85°E; and 0°, 93°E to observe zonal current on the equator and provided data from April 2015 to April 2019. Each mooring equipped with two upward-looking acoustic Doppler current profiler (ADCP) records. The measurement range covers the upper ~500 m initially and then ~1000 m subsequently (Fig. 1), with vertical resolution of 8 m and sampling frequency of 1 h. Profiles with a water depth change greater than 10 m per hour are eliminated. Here, current velocities are linearly interpolated onto uniform 5-m intervals, and hourly measurements are averaged into daily data.

Fig. 1.
Fig. 1.

Mooring-observed daily equatorial zonal current (m s−1) at 80°, 85°, and 93°E from March 2015 through April 2019. The dashed vertical lines mark each 1 Jan and 1 Jul.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

The daily current data from the Bluelink Reanalysis (BRAN; Oke et al. 2013) are used to characterize the EIC features. BRAN is available from January 1994 to March 2019, with 1/10° horizontal grid spacing, and 51 vertical levels. Current data from OGCM for the Earth Simulator (OFES; Masumoto et al. 2004) are also analyzed. OFES, forced by National Centers for Environmental Prediction (NCEP) winds, heat, and water fluxes has a horizontal resolution of 1/10° and 54 vertical levels. It was first run with monthly climatological forcing for 50 years, denoted as climatological run (CLIM), and then a hindcast run forced by NCEP winds. The simulated fields were stored as 3-day snapshots data available from 1980 to 2019. To estimate the impact of oceanic internal variability on the EIC intraseasonal variability (ISV), the daily output in the last 8 years of the OFES CLIM run is also analyzed. These eddy-resolving datasets with high temporal resolution allow us to examine the EIC not only on seasonal and interannual time scales but also on intraseasonal time scale. Daily cross-calibrated multiplatform (CCMP) satellite ocean surface wind vectors from 2001 to 2018 (Atlas et al. 2011), version 2.0, are analyzed to understand wind stress at different time scales over the equatorial Indian Ocean.

b. Ocean models and experiments performed

To further verify the EIC features, the western Pacific and northern Indian Oceans Model (PIOM) is adopted (Liang et al. 2019). The PIOM is an implementation of the terrain-following, free-surface, primitive equations Regional Ocean Modeling System. The PIOM domain extends from 20°S, 35°E at the southwest corner to 52°N, 157°E at the northeast corner, with a horizontal resolution of 1/12° and 30 vertical levels. Taking the winter climatology of temperature and salinity from World Ocean Atlas 2013 as the initial condition, the model is spun up using National Oceanic and Atmospheric Administration (NOAA) climatological monthly forcing for 30 years. Restarting from the spun-up solution, PIOM is integrated forward in time from January 1990 to December 2017 with the NOAA and National Climatic Data Center blended daily wind fields, and from November 2018 to December 2019 with Windsat of Remote Sensing Systems (RSS). The period of January–October 2018 is the transition period, when the wind gradually changes to the Windsat of RSS linearly. Surface heat and freshwater forcing is from the NCEP Reanalysis II products with 6-h interval. OFES 3-day data from 1990 to 2017 and their 3-day climatologies are used to provide the model open boundary temperature, salinity, and velocity for 1990–2017 and 2018–19, respectively, using a modified radiation approach (Gan and Allen 2005). The daily BRAN data, 3-day OFES hindcast data, and the daily PIOM outputs from January 2001 to December 2019 are used in our analysis. We have also compared these datasets with the mooring observations for their respective overlapping periods: OFES and PIOM from April 2015 to April 2019 and BRAN from April 2015 to March 2019.

To help elucidate the EIC dynamics, a LOM is configured to the tropical Indian Ocean north of 29°S with a horizontal resolution of 55 km. Zonal and meridional velocities and pressure are the sum of the first 25 vertical normal modes. The linear model is first spun up for 20 years and then integrated forward in time for the period of 1959–2018 using the monthly, Japanese 55-Year Reanalysis–Drive Ocean (JRA55-do) wind stress forcing (Tsujino et al. 2018). This experiment, which does not include the Maldives, is referred to as LOM main run (LOM_MR). Details of the model can be found in Han et al. (2011) and Chen et al. (2015). Earlier studies have shown that the LOM is able to well represent the EIC and equatorial undercurrent in the tropical Indian Ocean (Chen et al. 2015; Huang et al. 2018a).

To isolate the influence of the Maldives on the EIC, experiment LOM_Maldives is performed, in which the Maldives are represented by two rectangular boxes: 73°–74°E, 2°–6°N and 73°–73.5°E, 0.5°–1°N (Han et al. 1999, 2011). The third experiment, LOM_DAMP, is the same as LOM_MR but with a damper in the eastern equatorial ocean (McCreary et al. 1996; Han et al. 1999). For the solution with the damper, the eastern boundary of the equatorial basin is extended to 115°E, and there is no forcing in this extended area. The damper is applied in the region x > 107.5°E, 7.5°S < y < 7.5°N, and it relaxes the zonal-velocity and pressure fields of each mode to zero there (Han et al. 1999). The damper efficiently absorbs the energy of incoming equatorial Kelvin waves, and thus no Rossby waves are reflected back into the ocean interior from the eastern boundary. While LOM_DAMP primarily measures the effects of directly forced Kelvin and Rossby waves, the solution difference LOM_Reflect (LOM_MR − LOM_DAMP) isolates the reflected Rossby wave effects (Chen et al. 2015). The fourth experiment, LOM_Maldives_DAMP is the same as LOM_DAMP but with the Maldives. We analyze the monthly outputs of the four experiments from January 2001 to December 2018.

3. Results

a. Components and vertical modes

Figure 1 shows the 4-yr (from April 2015 to April 2019) zonal currents observed by the three equatorial moorings. Semiannual signals can be visually identified and appear to be the dominant component at 80° and 85°E in the intermediate depth from 200 to 1000 m, whereas no significant semiannual variability is observed at 93°E. At 80° and 85°E, the EIC exhibits year to year variations, being strong and occupying the entire intermediate layer of 200–1000 m sometimes (e.g., July 2016 and January 2019 at 80°E; July 2017 at 85°E) but separated into cores in other times (e.g., July 2017 and 2018 at 80°E). To quantify the EIC variability, the mooring observations are bandpass filtered with a 20–105-day Lanczos digital filter to obtain their intraseasonal components. The seasonal components are derived by averaging the low-frequency time series, obtained through a 105-day low-pass Lanczos filter, into one 365-day seasonal cycle. To obtain their interannual components, we first remove the seasonal components and then perform a 380-day low-pass Lanczos filter. At all three sites, times series of the seasonal and intraseasonal components are much larger than the interannual component (Figs. 2a–c). The standard deviations (STDs) of seasonal and intraseasonal u velocities at 200–500 m at 80°, 85°, and 93°E are approximately 90%, 88%, and 86% of the STDs of the original velocities, respectively. Here, we thus focus on reporting the seasonal cycle and intraseasonal variability. The seasonal component is larger than the intraseasonal component at 80° and 85°E with STDs of 0.10 versus 0.04 m s−1 and 0.09 versus 0.05 m s−1, respectively. However, the seasonal component weakens to the east, and is weaker than the intraseasonal component at 93°E (0.04 vs 0.05 m s−1). As a result, the u velocity variation at 93°E is dominated by the intraseasonal component (cf. gray and thick blue lines in Fig. 2c).

Fig. 2.
Fig. 2.

Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement during April 2015 to April 2019 (gray thin line). Thick red, blue, and black lines represent the seasonal, intraseasonal, and interannual components, respectively.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

Spectral analysis verifies the above statements. The most energetic spectral peaks occur near the semiannual period (~166 days) at 80° and 85°E (Figs. 3a,b). However, the peak energy of the semiannual period weakens significantly at 93°E (Fig. 3c), which is only 16% of that at 80°E. In comparison, the intraseasonal components have multispectral peaks and show weak differences among the three mooring sites.

Fig. 3.
Fig. 3.

The power spectrum of seasonal (blue) and intraseasonal (orange) components of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

The components of zonal wind stress are different from that of the current (Fig. 4a). Intraseasonal component of zonal wind stress is the largest in the central and eastern basin. The seasonal component dominates wind variability west of 50°E, is comparable to the intraseasonal component from 55° to 70°E, but is apparently weaker than the intraseasonal component east of 75°E and is comparable to the interannual component east of east of 80°E. Thus, the local wind strength at different time scales does not directly determine the corresponding EIC amplitude, although the strongest intraseasonal wind in the eastern basin does contribute to the dominance of intraseasonal EIC at 93°E mooring location. The strong seasonal current results from the equatorial basin resonance at the semiannual period, when the Rossby wave reflected from the eastern boundary intensifies the directly forced equatorial waves in the basin interior (Huang et al. 2018a). In the process of downward penetration, the ray slopes are −ω/Nb(z) for the Kelvin ray and (2n + 1)ω/Nb(z) for the nth meridional mode Rossby wave, where ω denotes the frequency (ω = 2π/T) and Nb(z) denotes Brunt–Väisälä frequency profile (Han 2005). The angles of Kelvin and Rossby wave rays are thus proportional to their frequencies: the higher the frequency, the steeper the ray angle and the deeper the downward penetration. The ray paths in Fig. 4b are calculated from the BRAN with the choices of T = 180 (red dash–dot line), T = 90 (blue dash–dot line) and T = 360 days (black dash–dot line), tracking from the point, for example, at 73°E, 10 m. The semiannual EIC is weaker near the eastern ocean boundary at 93°E, since the eastward and downward Kelvin waves’ energy ray emanating from 73°E is above 200 m even at the eastern boundary, and reflected Rossby waves’ energy ray penetrates westward and downward at a shallower angle than that of the intraseasonal component, leaving 93°E in the shadow zone. The ray path of semiannual reflected Rossby waves encompasses the central equatorial basin at intermediate depth, causing large amplitude variability in the region. Indeed, the importance of boundary reflection in generating EIC has been shown in the analytic solutions of McCreary (1981). The seasonal zonal current on day 208 from BRAN (color in Fig. 4b), the time when the seasonal component averaged at 200–1000 m obtains its maximum amplitude, clearly verifies the strong EIC in the central basin. Its distinct spatial difference will be further examined in the next section. In comparison with the seasonal component, the ray path of the intraseasonal component has a deeper angle and thus has larger influence on the EIC in the eastern basin. Conversely, the ray path of the interannual component has a shallower angle, and thus has larger influence on the EIC in the western basin.

Fig. 4.
Fig. 4.

(a) STDs of zonal wind stress from CCMP during 2001–18 along the equator (1°S–1°N) for intraseasonal (blue line), seasonal (red line), and interannual (black line) components. (b) The seasonal zonal current on day 208 from BRAN (color). As an example, the ray paths tracking from the point at 73°E, 10 m are shown: the wind-generated Kelvin and reflected Rossby rays of the second meridional modes with the periods of 90 (blue dash–dotted line), 180 (red dash–dotted line), and 360 days (black dash–dotted line).

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

Previous studies suggested that the EIC was dominated by the second baroclinic mode (Jensen 1993; Huang et al. 2018a). Here, we further examine the contributions of different baroclinic modes to the EIC using the mooring observations. Vertical normal mode decomposition (Shankar et al. 1996) is performed with the climatologic density profile of World Ocean Atlas 2013 (WOA13). At each time step, the u velocities averaged at 200–500 m at the three mooring sites are projected onto the first 10 normalized vertical normal modes. The STDs of u from the first 10 modes suggest that, in addition to the leading second mode, the fourth mode also substantially contribute to the EIC (Fig. 5). STDs of the fourth mode reach 35%, 55%, and 78% of that of the second mode at the three mooring sites, respectively. Mode 2 plus mode 4 effectively capture both the amplitudes and the phases of the observed u velocities (Fig. 5).

Fig. 5.
Fig. 5.

Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (c) 0°, 85°E; and (e) 0°, 93°E from mooring measurement (black line) and their projection onto the second and fourth modes (mode 2 plus mode 4; blue line). Also shown are STDs of the first 10 modes projected by the observed 200–500-m-averaged zonal currents at (b) 0°, 80°E; (d) 0°, 85°E; and (f) 0°, 93°E.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

Such a strong second baroclinic mode contribution is attributable to its resonance with the 180-day wind and 90-day wind in the equatorial Indian Ocean (Han 2005; Huang et al. 2018a). When the periodic forcing satisfies T = 4L/(mCn), reflected waves intensify the directly forced waves and resonance occurs. Here, T is the forcing period, L is the basin width, m is a positive integer, and Cn is the Kelvin wave speed for the vertical mode n. For the equatorial Indian Ocean, L is approximate 6300 km. For T = 180 days, it yields resonance mode speed of Cn = 1.63 m s−1 when m = 1 and Cn = 0.81 m s−1 when m = 2. The resonance mode speeds are close to the Indian Ocean second and fourth baroclinic mode speeds of 1.67 and 0.75 m s−1, suggesting that the second and fourth modes are both resonance baroclinic modes and thus have amplified amplitudes. At the surface, while the n = 4 mode indeed showed a relative peak in zonal surface current as a response to semiannual wind forcing, this peak is much weaker than that of n = 2 mode (Fig. 7 of Han et al. 1999). In the thermocline, however, intermediate modes (n = 4–8) have significant contributions to the equatorial undercurrent (Chen et al. 2015). For the EIC discussed here, n = 4 mode shows an apparently strong contribution. This is associated with the n = 4 vertical mode structure, with larger amplitude in the thermocline and middle layer (Fig. S1 in the online supplemental material), as well as the weaker EIC amplitude compared to the surface currents. The importance of n = 4 mode resonance in contributing to the deep jets of the equatorial Atlantic, which has a similar zonal size of the equatorial Indian Ocean, has been shown by existing studies (e.g., Brandt et al. 2016; Claus et al. 2016).

Combinations of different baroclinic modes determine the vertical structures of the EIC. By analyzing outputs from LOM_Maldives for the entire 2001–18 periods and using empirical orthogonal function (EOF) analysis, we conclude that the dominated vertical structures of the EIC are the entire layer structures with core speed in the top layer (explained variance is 47%; the first panel in Fig. 6a) or middle layer (explained variance is 27%; the second panel in Fig. 6a), which are attributed to composition of the second and fourth baroclinic modes, with the help of the third baroclinic mode contributing to top layer of 200–300 m (the third and fourth panels in Fig. 6a; see baroclinic mode structures for each month in Fig. S2 of the online supplemental material). Even so, the higher modes still modify the EIC’s vertical structures sometimes. Taking the situation in June–August 2016 as an example, the EIC with eastward velocity in the eastern basin in July–August 2016 is dominated by modes 2–4 (Figs. 6b–d). However, modes 2–4 cannot reproduce the weak EIC with three cores in June 2016 (Fig. 6b). Modes 5–20 are indispensable to form the multiple-cores structure at that time.

Fig. 6.
Fig. 6.

(a) (left) EOF-sp1 and (left center) EOF-sp2: the first and second EOF spatial modes for the monthly zonal velocities averaged between 0.25°S and 0.25°N from LOM_Maldives during 2001–18; 47% and 27% are the explained variances. (center) EOF-sp1(modes2–4) and (right center) EOF-sp2(modes2–4): as in EOF-sp1 and EOF-sp2, but using the sum of baroclinic modes 2–4 of the zonal velocities. (right) EOF-sp1(modes1, 5–25): as in EOF-sp1, but using the sum of baroclinic modes 1 and 5–25. Also shown are longitude–depth plots of the monthly zonal velocities (m s−1) averaged between 0.25°S and 0.25°N for (b) June, (c) July, and (d) August 2016 obtained from LOM_Maldives. For (b)–(d), shown are the sum of baroclinic modes (left) 1–25, (left center) 2–20, and (center) 2–4, along with (right center) mode 2 and (right) mode 4.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

b. Spatial variations and the cause

Mooring observations reveal obvious spatial variability of the EIC, which mainly originates from the seasonal component. Here, we further examine the spatial structure of the EIC and dynamics accounting for its spatial variations. To this end, the outputs from BRAN, OFES and PIOM, are analyzed. Model/data comparison suggests that BRAN effectively captures the fundamental features of the EIC, especially for its seasonal component (Figs. 7a,b). At 80°E, BRAN intermediate currents agree well with the mooring data, with a correlation coefficient of 0.75 from April 2015 to March 2019, and observed and simulated STDs of 0.13 and 0.12 m s−1. At 85°E, BRAN intermediate currents agree well with the mooring data, with a correlation coefficient of 0.72 from April 2015 to March 2019, and observed and simulated STDs of 0.12 and 0.11 m s−1. The model outputs are difficult to quantify u velocities at 93°E, where the intraseasonal component dominates (Fig. 7c). The amplitude and phase of zonal currents from PIOM are comparable with that from BRAN and moorings (cf. blue, red, and black lines in Fig. 7). In comparison, OFES intermediate currents have smaller amplitudes.

Fig. 7.
Fig. 7.

Time series of 200–500-m-averaged zonal currents at (a) 0°, 80°E; (b) 0°, 85°E; and (c) 0°, 93°E from mooring measurement (black line), BRAN (red line), PIOM (blue line), and OFES (green line). We only show the reanalysis and OGCM results from 2009 so as to display the lines clearly.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

Figures 8a–c show the STDs of intraseasonal (red solid line), seasonal (blue solid line), and interannual (black solid line) u velocities averaged at 200–1000 m, 0.25°S–0.25°N, from the reanalysis and OGCM results. All of the models qualitatively reproduce the EIC features revealed by the moorings: the dominant roles of seasonal and intraseasonal components, the seasonal component occupying the central Indian Ocean but weakening to the east, and the intraseasonal component surpassing the seasonal one in the eastern Indian Ocean. The simulated discrepancies of the three models are mainly reflected in the weakening area of the seasonal component. For example, like the mooring observations, the seasonal component in BRAN is obviously stronger than the intraseasonal one at 80° and 85°E, but is weaker at 93°E. In comparison, the seasonal component in OFES and PIOM is comparable with the intraseasonal one at 85°E. Nevertheless, OFES and PIOM still successfully reproduce the strong seasonal component in the center Indian Ocean.

Fig. 8.
Fig. 8.

STDs of zonal velocities averaged at 200–1000 m, 0.25°S–0.25°N from (a) BRAN, (b) OFES, and (c) PIOM based during 2001–18. Blue, red and black lines represent the ISV, seasonal, and interannual components, respectively. STD of the ISV component from the OFES climatological run is also shown [dashed blue line in (b)]. Also shown are longitude–time plots of the seasonal components of zonal velocities (m s−1) averaged at 200–1000 m, 0.25°S–0.25°N, from (d) BRAN, (e) OFES, and (f) ROM. The y axis repeats for 3 years.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

To further verify features of u velocities at different time scales mentioned above, we show longitude–depth sections for the intraseasonal, seasonal and interannual u components using BRAN during 2001–18 (Fig. 9). The large STDs of seasonal component dominate u variability in the central basin, especially at 73°–90°E over the intermediate layer, but they are weak in the eastern basin, agreeing with the mooring observations and energy rays discussed above (Fig. 4b). The intraseasonal component weakens with the increase of depth, but it is the largest EIC component in the eastern basin as discussed above. The interannual component is weak throughout the basin.

Fig. 9.
Fig. 9.

Longitude–depth plots of STDs of zonal velocities (m s−1) averaged between 0.25°S and 0.25°N from BRAN during 2001–18 for (a) intraseasonal, (b) seasonal, and (c) interannual components.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

A striking phenomenon revealed by the reanalysis and OGCM results is that the seasonal component of the EIC weakens almost by half at ~73°E and further decreases toward the west (Figs. 8a–c, 4b, and 9b). This feature is consistent with the observations showing that zonal current in the intermediate layer has an amplitude of 0.15 m s−1 in the western basin (Luyten and Roemmich 1982) but much larger in the central-eastern basin (Fig. 1). Time–longitude plot of the seasonal component of the equatorial zonal velocity averaged at 200–1000 m verifies the weakened EIC west of the Maldives once again (Figs. 8d–f). As the EIC results primarily from the reflected Rossby waves from the eastern boundary (Huang et al. 2018a), the phase of the EIC propagates westward (Figs. 8d–f). The Rossby waves are weakened substantially at ~73°E by the Maldives, suggesting that the Maldives play an important role in causing the abrupt change in EIC intensity.

The Maldives impede westward energy propagation of Rossby waves while they have little influence on the transmission of equatorial Kelvin waves, and thus weaken the equatorial resonance and reduce zonal surface currents west of the Maldives (Han et al. 1999). As a result of the blocked Rossby waves, the EIC is not strong as suggested in Huang et al. (2018a). As the seasonal component is the main source of the EIC’s spatial variability, the monthly outputs from LOM are used for the investigation of the Maldives effect on the EIC [see Chen et al. (2015) and Huang et al. (2018a) for LOM validation]. STDs of the equatorial zonal velocity averaged at 200–1000 m (Fig. 10a) and longitude–depth plot of the equatorial zonal velocity (Fig. 10c) suggest that the strong EIC crosses the whole basin in LOM_MR. When the Maldives are included, however, the EIC weakens significantly (Figs. 10a,f). The STD of u velocity averaged at 50°–90°E from LOM_Maldives is only 53% of that from LOM_MR (Fig. 10a). The abrupt change in EIC intensity at ~73°E is reproduced by the LOM_Maldives (black line in Figs. 10a and 10f), verifying the role of the Maldives in spatial inconsistency of the EIC.

Fig. 10.
Fig. 10.

(a),(b) STDs of zonal velocities averaged at 200–1000 m, 0.25°S–0.25°N, from LOM experiments during 2001–18. Also shown are longitude–depth plots of the monthly climatological zonal velocities (m s−1) averaged between 0.25°S and 0.25°N for January, April, July, and October obtained from (c) LOM_MR, (d) LOM_DAMP, (e) LOM_Reflect (LOM_MR − LOM_DAMP), (f) LOM_Maldives, (g) LOM_Maldives_DAMP, and (h) LOM_Maldives_Reflect (LOM_Maldives − LOM_Maldives_DAMP) during 2001–18. Black lines are the 0 m s−1 contours.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

The EIC is mainly forced by the reflected Rossby waves, but not the directly forced Kelvin and Rossby waves (cf. lines in Fig. 10a; compare Figs. 10d and 10e). Assume that the intraseasonal, seasonal and interannual wind forcing for the equatorial Kelvin waves has large spatial scale with the same sign across the equator (either eastward or westward), reflected Rossby waves obtain the largest amplitude at the eastern boundary, because they are direct reflections of equatorial Kelvin waves, which achieve the maximum amplitude at the eastern boundary because Kelvin waves’ solution is proportion to the integral of zonal wind from west to east (Han 2005). When the westward-propagating Rossby waves arrive at the Maldives, some energy is reflected eastward and some transmitted to the west and some dissipated. The reflection weakens the EIC associated with the incoming Rossby waves east of the Maldives, and the blocked Rossby waves’ energy also yields weakened EIC west of the Maldives, accounting for the basin-wide weakened EIC. The LOM experiments clearly demonstrate the point that the Maldives substantially impede the reflected Rossby waves. The STD of u velocity averaged at 50°–90°E from LOM_Maldives_Reflect (LOM_Maldives − LOM_Maldives_DAMP; red dotted line in Fig. 10b), which isolates the influence of the Maldives on the reflected Rossby waves, is only 52% of that from LOM_Reflect (red solid line in Fig. 10b). The EIC amplitude in LOM_Maldives_Reflect is obviously smaller than that in LOM_Reflect (cf. Figs. 10h and 10e). By contrast, the EIC amplitude in LOM_Maldives_DAMP is comparable with that in LOM_DAMP (cf. Figs. 10d and 10g), with the STD of u velocity from LOM_Maldives_DAMP (blue solid line in Fig. 10b) being ~80% of that from LOM_DAMP (blue dotted line in Fig. 10b).

To further reveal the spatial structure of the EIC, we show horizontal maps of pressure and current averaged over 200–1000 m (left column in Fig. 11), and meridional structure of the current (right column in Fig. 11). Reflected Rossby waves from the eastern boundary set up the pressure gradient and induce the EIC in the eastern basin, as the situation for the equatorial undercurrent in the Indian Ocean (see Figs. 8a and 11 in Chen et al. 2015). The EIC at section 85°E mainly locates at 2°S–2°N, 200–1000 m, with core speed in the top layer or middle layer (right column in Fig. 11).

Fig. 11.
Fig. 11.

(left) The spatial structure of 200–1000 m averaged monthly climatology of pressure (color shading; 980 g cm−1 s−2) and current (vectors; m s−1) from LOM_MR during 2001–18. (right) The meridional structure of the EIC at section 85°E, marked by red vertical lines in the left column.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

c. Impact of the Maldives on the resonance modes

In this section, we further examine the impact of the Maldives on amplitudes of different baroclinic modes and thus the EIC intensity at seasonal time scale. Compared to LOM_MR, the u velocities averaged at 50°–90°E, 0.25°S–0.25°N, 200–1000 m of modes 1 and 3–10 from LOM_Maldives weaken 11%–18% with a mean value of 15% (Fig. 12). In comparison, the resonance mode 2 reduces by 39%. Why do the Maldives have larger impact on the resonance mode 2 but not the resonance mode 4 with the 180-day wind?

Fig. 12.
Fig. 12.

The weakened rate of each mode, by comparing the monthly climatological zonal velocities averaged at 200–1000 m over 0.25°S–0.25°N, 50°–90°E from LOM_MR and LOM_Maldives during 2001–18.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

To answer this question, we further examine semiannual harmonics of zonal velocities from modes 2 and 4 in the intermediate layer. Amplitudes of semiannual harmonic of model 2 zonal current occupy the entire intermediate layer, which are caused primarily by the reflected Rossby waves and contributed to a lesser extent by the directly forced Kelvin and Rossby waves in the central basin, while the directly forced waves play more importance roles than reflected waves in the eastern and western basins (Figs. 13a–13f). In comparison, amplitudes of semiannual harmonic of mode 4 have two cores, with one being located at 60°–70°E and the other, 85°–95°E (Figs. 13g,j). The western core results mainly from the directly forced response (Figs. 13h,k), while the eastern one is induced primarily by the reflected Rossby waves (Figs. 13i,l).

Fig. 13.
Fig. 13.

Amplitudes of semiannual harmonics of (a)–(f) mode 2 and (g)–(l) mode 4 along the equator (0.25°S–0.25°N) from (left) LOM_MR, (center) LOM_DAMP, and (right) LOM_Reflect (m s−1).

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

In the directly forced response, most energy in the intermediate layer results from directly forced Rossby waves, because equatorial Kelvin beam has a shallow angle when it propagates energy both eastward and downward (see Fig. 4). Rossby waves, however, propagate energy westward and downward, and thus Rossby waves forced by basin-scale winds obtain larger magnitudes to the west (Figs. 13b,e,h,k). The cores of mode 2 associated with directly forced response are more to the west than that of mode 4 (cf. Figs. 13b and 13h), because Rossby wave beams of mode 2 have a shallower angle.

Figure 14 shows longitude–time plots of zonal current averaged at its core depths of 600–640 m (Fig. 12) along the equator for mode 2 and 680–720 m for mode 4 at 180-day period from LOM_MR and LOM_Maldives. The dash–dotted lines in Figs. 14a and 14c mark the phase of modes 2 and 4, which is defined by the month with the strongest eastward velocity. The phase differences between modes 2 and 4 reach 2–3 months, suggesting that the two modes tend to weaken each other at semiannual period. The Maldives Inlands significantly weaken resonance amplitudes of mode 2 (cf. Figs. 14a and 14b) as the situation at surface layer (Han et al. 2011). However, they have weak impact on the resonance amplitudes of mode 4. This is because the Maldives—particularly the island of Suvadiva—are located near 73°E, which fall in the “node” region of the mode 4 resonance, just like the 90-day resonance of surface current (Han et al. 2011).

Fig. 14.
Fig. 14.

Longitude–time plots of zonal currents (m s−1) along the equator (0.25°S–0.25°N) for mode 2 averaged at 600–640 m at 180-day period from (a) LOM_MR and (b) LOM_Maldives and for mode 4 averaged at 680–720 m from (c) LOM_MR and (d) LOM_Maldives. The depth is chosen according to the core location shown in Fig. 13. The dash–dot lines in (a) and (c) mark the phase of modes 2 and 4, respectively, which is defined by the month with the strongest eastward velocity.

Citation: Journal of Physical Oceanography 50, 11; 10.1175/JPO-D-20-0042.1

4. Summary and discussion

The EIC locates beneath the thermocline generally down to 1200 m along the equator. Our knowledge on the EIC in the Indian Ocean remains quite limited. Using 4-yr mooring observations deployed by the Chinese Academy of Sciences and ocean circulation model experiments, this study characterizes the spatial and temporal variability of the EIC in the Indian Ocean and investigates the causes.

Mooring observations and model simulations suggest that the EIC is mainly composed of seasonal and intraseasonal components. Amplitude of the seasonal component presents obviously spatial discrepancy, and has an abrupt change at ~73°E associated with the Maldives. In comparison, the intraseasonal component has no significant spatial differences in intensity. The QuikScat and climatological runs from OFES demonstrate that the intraseasonal component in the western and eastern basins results from different processes (cf. red solid and red dashed lines in Fig. 7b). STDs of the EIC from the QuikScat and climatological runs are comparable, suggesting that the EIC ISV in the western basin is predominantly caused by the oceanic internal instabilities. In the eastern basin, the EIC ISV, however, is essentially attributed to atmospheric intraseasonal oscillations. Generation of the EIC ISV will be a good topic for future research.

In addition to the second baroclinic mode suggested by previous studies, the resonant fourth baroclinic mode with large amplitude in the thermocline and middle layer significantly contributes to the EIC amplitude and phase. Combinations of different baroclinic modes result in the changed vertical structures of the EIC. The first two dominated vertical structures of the EIC, induced by low-order modes 2–4, are the entire layer structures with core speed in the top layer (45%) or middle layer (28%). The EIC presents multiple-cores structures sometimes, benefiting from the higher baroclinic modes.

As the Maldives impede the propagation of equatorial Rossby waves (with little influence on equatorial Kelvin waves), they weaken the EIC magnitude. The STD of u velocity averaged for (50°–90°E, 0.25°S–0.25°N) and 200–1000 m from LOM_Maldives is only 53% of that from LOM_MR. The Maldives weaken the reflected Rossby waves substantially but have less influence on the directly forced Rossby waves. The STD of EIC with Maldives is only 52% of that without Maldives for reflected Rossby waves, but 80% for directly forced waves. The semiannual resonance of the second baroclinic mode reduces by 39%, in comparison with 11%–18% of modes 1, 3–10. The semiannual resonance of fourth baroclinic mode has two cores, with one located at 60°–70°E and the other at 85°–95°E. The Maldives have weak impact on the resonance amplitude of mode 4, because they are located in a “node” region of the resonance.

Acknowledgments

We thank the two anonymous reviewers for their constructive comments. OFES data were downloaded at http://apdrc.soest.hawaii.edu/datadoc/ofes/ofes.php. The OFES simulation was conducted on the Earth Simulator under the support of JAMSTEC. BRAN data were downloaded at https://wp.csiro.au/bluelink/global/bran/. WOA13 were downloaded at https://www.nodc.noaa.gov/OC5/woa13/woa13data.html. CCMP Version-2.0 vector wind analyses are produced by Remote Sensing Systems. Data are available at http://www.remss.com. This work is supported by NSFC 41822602, XDA 20060502, XDB42000000, GML2019ZD0306, NSFC 41976016, NSFC 41676010, 2017YFB0502700, NSFC 41506022, LTOZZ2002, Youth Innovation Promotion Association CAS (2017397), the Pearl River S&T Nova Program of Guangzhou (201806010105), and NHXX2018WL0101.

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