• Bentamy, A., , Y. Quilfen, , F. Gohin, , N. Grima, , M. Lenaour, , and J. Servain, 1996: Determination and validation of average wind fields from ERS-1 scatterometer measurements. Global Atmos. Ocean Syst., 14 , 129.

    • Search Google Scholar
    • Export Citation
  • Cane, M., , and D. Moore, 1981: A note on low-frequency equatorial basin modes. J. Phys. Oceanogr., 11 , 15781584.

  • Cane, M., , and E. Sarachik, 1981: The response of a linear baroclinic equatorial ocean to periodic forcing. J. Mar. Res., 39 , 651693.

  • Clarke, A. J., , and X. Liu, 1993: Observations and dynamics of semiannual and annual sea levels near the eastern equatorial Indian Ocean boundary. J. Phys. Oceanogr., 23 , 386399.

    • Search Google Scholar
    • Export Citation
  • Fu, L-L., 2004: Latitudinal and frequency characteristics of the westward propagation of large-scale oceanic variability. J. Phys. Oceanogr., 34 , 19071921.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., , K. O’Neill, , and M. A. Cane, 1983: A model of the semiannual oscillation in the equatorial Indian Ocean. J. Phys. Oceanogr., 13 , 21482160.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Han, W., 2005: Origins and dynamics of the 90-day and 30–60-day variations in the equatorial Indian Ocean. J. Phys. Oceanogr., 35 , 708728.

    • Search Google Scholar
    • Export Citation
  • Han, W., , J. P. McCreary, , D. L. T. Anderson, , and A. J. Mariano, 1999: Dynamics of the eastward surface jets in the equatorial Indian Ocean. J. Phys. Oceanogr., 29 , 21912209.

    • Search Google Scholar
    • Export Citation
  • Han, W., , D. M. Lawrence, , and P. J. Webster, 2001: Dynamical response of equatorial Indian Ocean to intraseasonal winds: Zonal flow. Geophys. Res. Lett., 28 , 42154218.

    • Search Google Scholar
    • Export Citation
  • Han, W., , T. Shinoda, , L-L. Fu, , and J. P. McCreary, 2006: Impact of atmospheric intraseasonal oscillations on the Indian Ocean dipole during the 1990s. J. Phys. Oceanogr.,, 36 , ,, 670690.

    • Search Google Scholar
    • Export Citation
  • Jensen, T. G., 1993: Equatorial variability and resonance in a wind-driven Indian Ocean model. J. Geophys. Res., 98 , 2253322552.

  • Kindle, J. C., , and J. D. Thompson, 1989: The 26- and 50-day oscillations in the western Indian Ocean: Model results. J. Geophys. Res., 94 , 47214736.

    • Search Google Scholar
    • Export Citation
  • Koopmans, L. H., 1974: The Spectral Analysis of Time Series. Academic Press, 366 pp.

  • Le Blanc, J-L., , and J-P. Boulanger, 2001: Propagation and reflection of long equatorial waves in the Indian Ocean from TOPEX/Poseidon data during the 1993–1998 period. Climate Dyn., 17 , 547557.

    • Search Google Scholar
    • Export Citation
  • Le Provost, C., 2001: Ocean tides. Satellite Altimetry and Earth Sciences, L.-L. Fu and A. Cazenave, Eds., Academic Press, 267–304.

  • Lighthill, M. J., 1969: Dynamic response of the Indian Ocean to the onset of the southwest monsoon. Philos. Trans. Roy. Soc. London, 265A , 4593.

    • Search Google Scholar
    • Export Citation
  • Luyten, J. R., , and D. H. Roemmich, 1982: Equatorial currents at semiannual period in the Indian Ocean. J. Phys. Oceanogr., 12 , 406413.

    • Search Google Scholar
    • Export Citation
  • McPhaden, M. J., 1982: Variability in the central equatorial Indian Ocean. Part I: Ocean dynamics. J. Mar. Res., 40 , 157176.

  • Moore, D. W., , and J. P. McCreary, 1990: Excitation of intermediate-frequency equatorial waves at a western ocean boundary: With application to observations from the Indian Ocean. J. Geophys. Res., 95 , 52195231.

    • Search Google Scholar
    • Export Citation
  • O’Brien, J. J., , and H. E. Hurlburt, 1974: Equatorial jet in the Indian Ocean: Theory. Science, 184 , 10751077.

  • Quilfen, Y., , B. Chapron, , A. Bentamy, , J. Gourrion, , T. El Fouhaily, , and D. Vandemark, 1999: Global ERS 1 and 2 and NSCAT observations: Upwind crosswind and upwind downwind measurements. J. Geophys. Res., 104 , 1145911469.

    • Search Google Scholar
    • Export Citation
  • Rao, R. R., , and R. Sivakumar, 2000: Seasonal variability of near-surface thermal structure and heat budget of the mixed layer of the tropical Indian Ocean from a new global ocean temperature climatology. J. Geophys. Res., 105 , 9951015.

    • Search Google Scholar
    • Export Citation
  • Reddy, P. R. C., , P. S. Salvekar, , A. A. Deo, , and D. W. Ganer, 2004: Westward propagating twin gyres in the equatorial Indian Ocean. Geophys. Res. Lett., 31 .L01304, doi:10.1029/2003GL018615.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., , and T. M. Smith, 1994: Improved global sea surface temperature analyses using optimum interpolation. J. Climate, 7 , 929948.

    • Search Google Scholar
    • Export Citation
  • Schott, F. A., , and J. P. McCreary Jr., 2001: The monsoon circulation of the Indian Ocean. Progress in Oceanography, 51 , Pergamon,. 1123.

    • Search Google Scholar
    • Export Citation
  • Sengupta, D., , R. Senan, , and B. N. Goswami, 2001: Origin of intraseasonal variability of circulation in the tropical central Indian Ocean. Geophys. Res. Lett., 28 , 12671270.

    • Search Google Scholar
    • Export Citation
  • Stammer, D., , C. Wunsch, , I. Fukumori, , and J. Marshall, 2002: State estimation in modern oceanographic research. Eos, Trans. Amer. Geophys. Union, 83 , 289294295.

    • Search Google Scholar
    • Export Citation
  • Tsai, P. T. H., , J. O’Brien, , and M. E. Luther, 1992: The 26-day oscillation observed in the satellite sea surface temperature measurements in the equatorial western Indian Ocean. J. Geophys. Res., 97 , 96059618.

    • Search Google Scholar
    • Export Citation
  • Vincent, P., , S. D. Desai, , J. Dorandeu, , M. Ablain, , B. Soussi, , P. S. Callahan, , and , 2003: Jason-1 geophysical performance evaluation. Mar. Geod., 26 , 167186.

    • Search Google Scholar
    • Export Citation
  • Waliser, D. E., , R. Murtugudde, , and L. E. Lucas, 2003: Indo-Pacific Ocean response to atmospheric intraseasonal variability: 1. Austral summer and the Madden–Julian Oscillation. J. Geophys. Res., 108 .3160, doi:1029/2002JC001620.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1977: Response of an equatorial ocean to a periodic monsoon. J. Phys. Oceanogr., 7 , 497511.

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    Spectra of SSH (upper curve; cm2 cycles−1 day−1) and zonal wind stress [lower curve; 0.1 × (dyne cm−2)2 cycles−1 day−1]. The spectra were averaged over 10°S–10°N, 40°–100°E. The periods for the major spectral peaks are indicated. The 95% error bar for the spectra is shown.

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    The same spectra as shown in Fig. 1 with the high-frequency part (periods shorter than 140 days) displayed in a linear scale. SSH (cm2 cycles−1 day−1) is shown with a solid line, and zonal wind stress is shown with a dashed–dotted line [0.003 × (dyne cm−2)2 cycles−1 day−1]. The periods of interests are indicated.

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    The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the high-passed SSH.

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    High-passed SSH (cm) represented by the leading CEOF as a function of time (from years 1993 to 1996) and longitude along (a) the equator, (b) 4.5°N, and (c) 4.5°S. The data-void regions near 70°E are due to the Maldives Islands.

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    The std dev of the semiannual bandpassed (a) zonal and (b) meridional wind stress (cgs units).

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    (a) The amplitude of the theoretical basin mode (m = 1) along the equator (nondimensional units of amplitude). (b) The phase (°) of the mode as a function of latitude (12°S–12°N) and longitude (40°–100°E).

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    The phase along the equator from (a) the theoretical basin mode (m = 1) and (b) the leading SSH CEOF.

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    SSH (arbitrary unit) represented by the theoretical basin mode (m = 1) as a function of time and longitude along (a) the equator and (b) 4.5°N.

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    (a) The first two vertical EOFs of the semiannual zonal velocity (normalized) from the ECCO assimilation products at 0°, 90°E (solid line, the first mode; dashed line, the second mode). (b) Time evolution of the vertical structure represented by the first two EOFs of the semiannual zonal velocity (m s−1) at 0°, 90°E. The horizontal axis shows the ECCO model’s vertical levels, of which the corresponding depths are shown at the top.

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    The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the 90-day bandpassed SSH. (c) Std dev of the 90-day bandpassed zonal wind stress (cgs units).

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    The phase (°) of the (a) second (m = 2) and (b) third (m = 3) theoretical basin modes as functions of latitude (12°S–12°N) and longitude (40°–100°E).

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    The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the high-passed SSH with periods shorter than 75 days. (c) Std dev of the 60-day bandpassed zonal wind stress (cgs units).

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    Power spectrum of the temporal variability of the leading CEOF of the high-pass-filtered SSH (periods shorter than 75 days).

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    (a) Amplitude and (b) phase of the leading CEOF of the 120-day bandpassed SSH observations. (c) Std dev of the 120-day bandpassed zonal wind stress (cgs units).

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    (a) Amplitude and (b) phase of the leading CEOF of the 75-day bandpassed SSH observations. (c) Std dev of the 75-day bandpassed zonal wind stress (cgs units).

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    The std dev of SST (°C) in the period band of 170–190 days.

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    (a) Scatterplot of SST vs the magnitude of the wind stress in the period band of 170–190 days in the region west of 60°E between 10°S and 10°N. Note that the temporal means are removed from both variables. (b) Same as in (a), but for the SST vs SSH.

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    (a) The standard deviation of the 90-day bandpassed SST (°C). (b) Coherence amplitude of the SSH vs SST at the period of 90 days. The 95% level of the significant coherence is 0.53. (c) Coherence phase (°). Positive values indicate that the SSH is leading the SST.

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    (a) The std dev of the 60-day bandpassed SST (°C). (b) Coherence amplitude of the SSH vs SST at the period of 60 days. The 95% level of the significant coherence is 0.53. (c) Coherence phase (°). Positive values indicate that the SSH is leading the SST.

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Intraseasonal Variability of the Equatorial Indian Ocean Observed from Sea Surface Height, Wind, and Temperature Data

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  • 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
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Abstract

The forcing of the equatorial Indian Ocean by the highly periodic monsoon wind cycle creates many interesting intraseasonal variabilities. The frequency spectrum of the wind stress observations from the European Remote Sensing Satellite scatterometers reveals peaks at the seasonal cycle and its higher harmonics at 180, 120, 90, and 75 days. The observations of sea surface height (SSH) from the Jason and Ocean Topography Experiment (TOPEX)/Poseidon radar altimeters are analyzed to study the ocean’s response. The focus of the study is on the intraseasonal periods shorter than the annual period. The semiannual SSH variability is characterized by a basin mode involving Rossby waves and Kelvin waves traveling back and forth in the equatorial Indian Ocean between 10°S and 10°N. However, the interference of these waves with each other masks the appearance of individual Kelvin and Rossby waves, leading to a nodal point (amphidrome) of phase propagation on the equator at the center of the basin. The characteristics of the mode correspond to a resonance of the basin according to theoretical models. For the semiannual period and the size of the basin, the resonance involves the second baroclinic vertical mode of the ocean. The theory also calls for similar modes at 90 and 60 days. These modes are found only in the eastern part of the basin, where the wind forcing at these periods is primarily located. The western parts of the theoretical modal patterns are not observed, probably because of the lack of wind forcing. There is also similar SSH variability at 120 and 75 days. The 120-day variability, with spatial patterns resembling the semiannual mode, is close to a resonance involving the first baroclinic vertical mode. The 75-day variability, although not a resonant basin mode in theory, exhibits properties similar to the 60- and 90-day variabilities with energy confined to the eastern basin, where the SSH variability seems in resonance with the local wind forcing. The time it takes an oceanic signal to travel eastward as Kelvin waves from the forcing location along the equator and back as Rossby waves off the equator roughly corresponds to the period of the wind forcing. The SSH variability at 60–90 days is coherent with sea surface temperature (SST) with a near-zero phase difference, showing the effects of the time-varying thermocline depth on SST, which may affect the wind in an ocean–atmosphere coupled process governing the intraseasonal variability.

Corresponding author address: Lee-Lueng Fu, Jet Propulsion Laboratory 300-323, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109. Email: llf@pacific.jpl.nasa.gov

This article included in the In Honor of Carl Wunsch special collection.

Abstract

The forcing of the equatorial Indian Ocean by the highly periodic monsoon wind cycle creates many interesting intraseasonal variabilities. The frequency spectrum of the wind stress observations from the European Remote Sensing Satellite scatterometers reveals peaks at the seasonal cycle and its higher harmonics at 180, 120, 90, and 75 days. The observations of sea surface height (SSH) from the Jason and Ocean Topography Experiment (TOPEX)/Poseidon radar altimeters are analyzed to study the ocean’s response. The focus of the study is on the intraseasonal periods shorter than the annual period. The semiannual SSH variability is characterized by a basin mode involving Rossby waves and Kelvin waves traveling back and forth in the equatorial Indian Ocean between 10°S and 10°N. However, the interference of these waves with each other masks the appearance of individual Kelvin and Rossby waves, leading to a nodal point (amphidrome) of phase propagation on the equator at the center of the basin. The characteristics of the mode correspond to a resonance of the basin according to theoretical models. For the semiannual period and the size of the basin, the resonance involves the second baroclinic vertical mode of the ocean. The theory also calls for similar modes at 90 and 60 days. These modes are found only in the eastern part of the basin, where the wind forcing at these periods is primarily located. The western parts of the theoretical modal patterns are not observed, probably because of the lack of wind forcing. There is also similar SSH variability at 120 and 75 days. The 120-day variability, with spatial patterns resembling the semiannual mode, is close to a resonance involving the first baroclinic vertical mode. The 75-day variability, although not a resonant basin mode in theory, exhibits properties similar to the 60- and 90-day variabilities with energy confined to the eastern basin, where the SSH variability seems in resonance with the local wind forcing. The time it takes an oceanic signal to travel eastward as Kelvin waves from the forcing location along the equator and back as Rossby waves off the equator roughly corresponds to the period of the wind forcing. The SSH variability at 60–90 days is coherent with sea surface temperature (SST) with a near-zero phase difference, showing the effects of the time-varying thermocline depth on SST, which may affect the wind in an ocean–atmosphere coupled process governing the intraseasonal variability.

Corresponding author address: Lee-Lueng Fu, Jet Propulsion Laboratory 300-323, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, CA 91109. Email: llf@pacific.jpl.nasa.gov

This article included in the In Honor of Carl Wunsch special collection.

1. Introduction

The highly periodic monsoon wind cycle of the equatorial Indian Ocean makes this ocean basin an ideal place to study the dynamics of an ocean’s response to wind forcing. The seminal paper by Lighthill (1969) set the theoretical framework for studying the ocean’s response to the onset of monsoon wind. Cane and Sarachik (1981) addressed the subject of periodic forcing and discussed a wide range of solutions to the theoretical problem. Cane and Moore (1981) derived analytical solutions for idealized equatorial basin modes, which can be resonantly excited at certain frequencies depending on the size of the basin and the ocean’s stratification. The size of the equatorial Indian Ocean happens to yield resonant frequencies close to a subset of those of the seasonal cycle and its higher-order harmonics.

The resonant response of the equatorial Indian Ocean at the semiannual period was demonstrated by a number of modeling studies (Jensen 1993; Han et al. 1999). Han et al. (1999) discussed the relation between the resonance and the semiannual Wyrtki jet. The existence of the semiannual basin mode was also noted by Gent et al. (1983) and Clarke and Liu (1993). The variability at higher intraseasonal frequencies was studied by Han et al. (2001) and Han (2005) through comparisons of model simulations with observations. Enhanced variance in both sea level and zonal current near a period of 90 days was noted in the studies. The resonance mechanism of Cane and Moore (1981) was invoked to explain the 90-day variability.

Most of the previous studies focused on the reflection of Kelvin waves at the eastern boundary of the basin and the interference between the reflected Rossby waves with Kelvin waves in reinforcing the wind-forced ocean response. Numerical experiments were performed by Han et al. (1999) and Han (2005) to test the effects of the eastern boundary reflection. In these experiments, a damper was placed at the eastern boundary to absorb the incoming Kelvin waves so as to eliminate the reflected Rossby waves. Without the reflected Rossby waves, the model-simulated variability at both the semiannual and 90-day periods was drastically reduced, demonstrating the workings of a resonant mode established by wave reflection at the eastern boundary.

There has been relatively little study of the roles of the western boundary in the formation of the basin modes. Based on analyses of altimetry data, Le Blanc and Boulanger (2001) illustrated the reflection of Rossby waves into Kelvin waves at the western boundary of the equatorial Indian Ocean at the semiannual period. Because of the relatively small size of the Indian Ocean basin, the effects of the wave reflection and interference are felt over the entire basin and the spatial patterns of a basin mode are established. Han et al. (2001) and Han (2005) presented the zonal and meridional transects of the intraseasonal variability at periods of 20–100 days based on model simulations and altimeter observations, but did not explore the synoptic characteristics of the variability in terms of coherent modal patterns.

The spatial and temporal coverage of satellite altimeter data provides an excellent opportunity to study the details of the basin-wide variability of the ocean. The purpose of the present study is to analyze the decade-long altimetry data record from the Ocean Topography Experiment (TOPEX)/Poseidon (T/P) and Jason missions for describing the modal characteristics of the intraseasonal variability of the equatorial Indian Ocean. The relationships between these modes and sea surface wind stress and temperature are also analyzed. The questions to be addressed include the following. What are the dominant periods of wind forcing and their geographic patterns? What are the dominant periods of the ocean’s response and their geographic patterns? Is the ocean’s response consistent with the resonance theories? Are there any effects of the ocean’s response on sea surface temperature, which may affect the wind forcing as a feedback mechanism? The rest of the paper is organized as follows. The spectral characteristics of sea surface height and wind observations are described in section 2, followed by discussions (sections 37) of the spatial patterns of the sea surface height and wind stress variability associated with each of the identified spectral peaks. The relations of sea surface height and wind stress with sea surface temperature are discussed in section 8, followed by a summary with discussion in section 9.

2. Spectral description of the sea surface height and wind stress observations

To illustrate the dominant time scales of sea surface height (SSH) and wind stress, displayed in Fig. 1 are spatially averaged frequency spectra of the zonal wind stress and SSH in the equatorial Indian Ocean. The spectrum of the meridional wind is similar to that of the zonal wind and thus is not shown. The domain of the average is bounded by 10°S–10°N, 40°–100°E. The wind stress data were obtained from the European Remote Sensing Satellite (ERS) radar scatterometers (Quilfen et al. 1999). The wind velocity observations from the scatterometers’ 50-km-resolution cells were first converted into wind stress and then mapped to weekly 1° × 1° grids using an objective analysis technique (Bentamy et al. 1996). The data coverage spans 1991–2000.

The SSH data were obtained from the T/P and Jason radar altimeters with data coverage spanning 1993–2004. The T/P data covered a period from 2 October 1992–10 August 2002. The Jason data became available along the same ground tracks of T/P after January 2002. A relative bias of 13 cm between the two altimeter measurements was established from analysis of the overlapping data records (Vincent et al. 2003). After subtracting the relative bias from the Jason data, the two data records were combined to create global SSH time series with a record length of 12 yr. After making standard corrections, including tidal and inverted barometer corrections, the SSH residuals from the mean sea surface model supplied in the data records were linearly interpolated to a set of grid points 6.2 km apart (roughly 1-s flight time) along each repeat track. At each grid point, a 12-yr mean was removed from the data. The residual SSH data were then interpolated to 3-day, 1° × 1° grids using a Gaussian weighting scheme (Fu 2004). The spatial scales represented by the SSH and wind stress 1° × 1° fields are larger than 500 km. At these scales, both spectra show strong annual peaks. The annual variability of the equatorial Indian Ocean in relation to the atmospheric forcing is well documented (Schott and McCreary 2001) and hence not a subject of this study.

At frequencies higher than the annual, there is a series of peaks in both spectra at the intraseasonal frequencies associated with the higher-order seasonal harmonics. The most outstanding is the semiannual peak. Visually, the semiannual SSH peak is sharper than the annual SSH peak, which is less outstanding relative to the annual wind stress peak. To illustrate the peaks at higher frequencies more clearly, displayed in Fig. 2 are the portions of the spectra with periods shorter than 140 days in a linear scale. A scale factor was multiplied to the wind stress spectrum for comparison purposes. The 90-day peak in the SSH spectrum is the most outstanding relative to the wind spectrum, which is flat near the 90-day period. There are two peaks in the SSH spectrum near 60 days: one at 62.5 days and the other at 58.8 days. These are close to the aliased periods for the M2 (62.11 days) and S2 (58.74 days) tides, respectively. We need to be careful in interpreting the results at these periods because of the residual tidal errors in the altimeter data. The aliased period for the K1 tide is 171.2 days, which is separated from the semiannual period in the 12-yr-long data record. It will become clear later that the spatial patterns of the semiannual variability and the 60-day variability are not of tidal origins. There are also peaks at 120 and 75 days in both spectra. The spatial patterns of the variability associated with all these spectral peaks are to be discussed in the following sections.

3. The semiannual variability

The semiannual variability of the equatorial Indian Ocean is often discussed in the literature in association with the Wyrtki jets (Schott and McCreary 2001). The dynamics of the Wyrtki jets have recently been extensively studied by Han et al. (1999) using a hierarchy of models. The study demonstrates that the jets and the semiannual variability are primarily driven by wind. The paper emphasizes the importance of the reflection of Kelvin waves at the eastern boundary and a resonance mechanism involving the reflected Rossby waves. However, as noted in the introduction, the role of the western boundary and the basin-wide structure of the variability were not addressed in that study.

To focus on the spatial variability at intraseasonal frequencies, the SSH data were high-pass filtered to remove the variance at periods longer than 300 days. A complex-valued empirical orthogonal function (CEOF) analysis was applied to the high-passed data to obtain the patterns of the spatial and temporal variabilities. The leading mode accounts for 39% of the variance of the high-pass-filtered data with an rms amplitude of 3.8 cm. As expected from Fig. 1, the dominant time scales of this mode are centered at the semiannual period. The spatial patterns of the amplitude and phase of the mode are shown in Fig. 3. Despite the potential aliasing effects of the residual K1 tidal errors (less than 2 cm), the spatial patterns of the mode bear no resemblance to those of the K1 tide (Le Provost 2001). The pattern of the amplitude is similar to the simulation performed by O’Brien and Hurlburt (1974), who solved an initial-value problem using a numerical model. Their focus was on the initiation of the Wyrtki jet by the onset of wind forcing. The periodicity of the jet was not addressed in that study.

The SSH variability in the western basin shown in Fig. 3 is enhanced and characterized by the shape of the letter C. This C-shaped pattern indicates the effects of the western boundary in reflecting Rossby waves (Le Blanc and Boulanger 2001). The phase of the mode reveals westward propagation in the regions off the equator and eastward propagation along the equator. These features suggest the roles of Kelvin waves on the equator and Rossby waves off the equator. A recent modeling study similar to O’Brien and Hurlburt (1974) also demonstrated the existence of the main features of the CEOF in the model simulation (Reddy et al. 2004).

To examine the details of the wave propagation, the SSH represented by the leading CEOF is plotted as a function of time and longitude in Fig. 4. The SSH patterns at the equator and 4.5°S do not resemble those of simple Kelvin and Rossby waves, respectively. The SSH patterns at 4.5°N show more consistently westward propagation, like Rossby waves. As discussed later (and illustrated in Fig. 8), the interference among the large number of waves involved in the formation of the basin mode has masked the appearance of individual Kelvin and Rossby waves. It is clear that there is a stagnation region near 70°–80°E. This region is characterized by low amplitude and convergence of phase as shown in Fig. 3. Such a region is called an amphidrome in the tidal literature and is caused by the wave interference mentioned above. The valley of the SSH amplitude along the equator from 50° to 80°E (Fig. 3a) corresponds to the Wyrtki jet. The meridional curvature of the SSH at the equator is proportional to the zonal velocity of the surface geostrophic current. The Wyrtki jet is located in a region where the semiannual zonal wind stress (bandpassed in periods of 170–190 days) reaches a local maximum (Fig. 5a). The semiannual meridional wind (Fig. 5b) is relatively weak in the region. It is apparent that the semiannual variability of the entire basin, including the Wyrtki jet, is characterized by a basin mode strongly constrained by the geometry of the basin.

The nature of the resonance of equatorial basin modes was first discovered in theoretical studies (Cane and Sarachik 1981; Cane and Moore 1981). An elegant analytical solution was obtained by Cane and Moore (1981) for an equatorial ocean basin with an unbounded domain in the meridional direction. Although this geometry is not a good approximation of the equatorial Indian Ocean, the solution is convenient and adequate for providing a perspective for interpreting the observations.

The solution of Cane and Moore can be represented as the summation of an infinite number of equatorially trapped waves. When the width of the basin, the periods, and the speeds of the waves satisfy a certain condition, then the normal modes of the basin are established. The resonance condition can be written as P = 4L/(mcn), where P is the wave’s period, L is the basin width, cn is the speed of Kelvin waves for the nth baroclinic vertical mode, and m is a positive integer. For m = 1, the resonance period P is essentially the travel time for Kelvin waves and the reflected first meridional-mode Rossby waves making a round trip of the basin of the ocean. Note that the phase speed of the first meridional-mode Rossby waves is one-third of that of Kelvin waves (Gill 1982), yielding P = L/cn + L/cn/3. Therefore, the response of the ocean to a wind forcing of period P is reinforced by the Kelvin and Rossby waves generated by the forcing because these waves are always in phase with the forcing. For m > 1, the resonance is associated with higher-order modes involving subdomains of the basin.

For the equatorial Indian Ocean, L = 6330 km, c1 = 274 cm s−1, and c2 = 167 cm s−1, we have the following resonant periods: for the first baroclinic mode, P = 107 days, 53.5 days, 35.7 days, . . . , and for the second baroclinic mode, P = 175.5 days, 87.7 days, 58.5 days, . . . . Note that the resonant periods for the second baroclinic mode are close to some of the periods of the peaks in the wind stress spectrum including the semiannual peak (Fig. 1). Therefore, the semiannual variability represented by the leading CEOF is likely a normal mode response of the ocean involving the second baroclinic vertical mode. This second baroclinic mode resonance of the equatorial Indian Ocean was first demonstrated by Jensen (1993) and extensively discussed by Han et al. (1999) using numerical models.

Because of the various assumptions and approximations underlying Cane and Moore’s theory, including the basin geometry, the long-wave approximation, and the lack of realistic frictional effects, the spatial patterns of their solutions are not realistic. Without friction, the amplitude of the mode is independent of latitude because of the assumed infinite meridional dimension. Shown in Fig. 6a is the zonal dependence of the amplitude of the mode with m = 1. The amplitude minimum is at the middle of the basin as the observations show in Fig. 3. The phase of the mode (Fig. 6b) has a much more complicated pattern than that of the observations. The rapid phase variation in the middle of the basin off the equator is caused by high meridional modes, whose presence in reality is unlikely because of the enhanced dissipation at small scales. There is a convergence of phase at the center of the basin, somewhat resembling the observed phase shown in Fig. 3. There is an abrupt change of phase by 90° at the center of the basin on the equator (Fig. 7a). A similar, but much more gradual, phase change is exhibited by the observations (Fig. 7b). Displayed in Fig. 8 are the time–longitude plots of the mode of Cane and Moore with m = 1 at the equator and off the equator, showing similar patterns exhibited in Fig. 4. In particular, the apparent discontinuities of the highs and lows associated with the amphidrome in the middle of the basin are the results of the interference of the various waves generated at the two boundaries of the basin. In fact, these discontinuities are the characteristics of a basin mode.

To examine the vertical structure of the variability, the products from the Jet Propulsion Laboratory (JPL) component of the Estimating the Circulation and Climate of the Ocean (ECCO) Consortium (Stammer et al. 2002) were analyzed. The T/P and Jason data have been assimilated into an ocean general circulation model for estimating the three-dimensional state of the ocean. In the equatorial oceans, the model’s horizontal resolution is ⅓° latitude and 1° longitude. The model has 46 levels in the vertical direction. Ten years of the ECCO zonal velocity at 90°E on the equator were bandpass filtered (periods from 170 to 190 days) to extract the semiannual signals at all depths. An EOF analysis was applied to the filtered velocity time series. The two leading vertical modes account for 40% and 34% of the variance, respectively. The modal structures are shown in Fig. 9a. Each mode has two zero crossings at depths of less than 2000 m. If the other zero crossings at deeper depths where the velocities are relatively weak are ignored, the modal structures are similar to a second baroclinic mode. The combination of the two modes represents an upward-propagating wave (Fig. 9b), similar to the findings from the observations reported by Luyten and Roemmich (1982) and McPhaden (1982). Wunsch (1977) discussed the issue of vertically propagating waves versus standing modes regarding low-frequency forced motions in the equatorial Indian Ocean. At the semiannual period, the slowness of the vertically propagating waves makes it difficult to establish a standing mode based on Wunsch’s argument. In any case, the vertical scales are close to that of a second baroclinic mode, leading to the required zonal wave speeds for the resonance discussed above.

4. The 90-day variability

The period of the second resonant mode (m = 2) is 87.7 days. Near this period both the SSH and wind stress have a spectral peak (Fig. 2). Reflecting the characteristics of a resonance, the SSH peak is much more pronounced than the wind stress peak, which is marginally significant at the 95% level. This 90-day oscillation was studied by Han et al. (2001) and Han (2005). The analyses performed in these studies were focused on the variability along the equator and along selected meridional sections. The two-dimensional coherent patterns of the variability were not addressed.

To study the 90-day variability, the SSH data were high-pass filtered to retain the variance with periods shorter than 110 days. CEOF analysis was applied to the filtered data. Figure 10 shows the leading mode, which accounts for 28% of the high-passed variance with an rms amplitude of 2 cm. Consistent with the SSH frequency spectrum (Fig. 1), the dominant period of the leading mode is 90 days. Also shown is the standard deviation of the zonal wind stress filtered in the period band of 80–100 days. The meridional wind (not shown) in the region is similar to the zonal wind in pattern but weaker in magnitude by a factor of 2. The two cells of high SSH amplitude at 5°N and 5°S are located close to the local maxima of the wind forcing. The high amplitude of the SSH next to Sumatra is apparently caused by remote forcing through Kelvin waves and their reflections at the boundary. The reflected Rossby waves reinforce the ocean’s direct response to wind forcing when the waves have propagated westward back to the location of the forcing. This is because the total travel time for Kelvin waves and the reflected Rossby waves making one round trip of half of the basin is about 90 days, the period of the forcing. The phase has an amphidrome on the equator at about 86°E. Figure 11a shows the phase of the Cane and Moore mode for m = 2. The observations indicate that only the eastern half of the mode is excited. The theoretical amphidrome is located west of the ocean’s eastern boundary by one-quarter of the basin’s width, very close to 86°E as the observations indicate.

As indicated in the wind stress spectrum, the forcing at 90 days is relatively weak. However, the Kelvin waves generated in the eastern basin are quickly reflected back as Rossby waves, which, as noted above, are reinforced by the forcing after moving back to the forcing region because of the synchronized arrival of the waves with respect to the forcing. This process leads to the formation of the eastern half of the mode. Although there are also some local maxima of wind stress distributions in the western half of the basin, they are not able to excite the western half of the mode. The locations of the wind maxima are probably too far from the equator for the mode formation.

5. The 60-day variability

The SSH spectrum at periods near 60 days does not have a pronounced peak as the one near 90 days. There are two small peaks at 62.5 and 58.8 days. It is noted earlier that the SSH variabilities at these periods are susceptible to residual tidal errors. The wind stress spectrum is flat in this frequency range. There are many discussions of the variability of the Indian Ocean at time scales from 15 to 60 days (e.g., Han et al. 2001, 2006; Kindle and Thompson 1989; Moore and McCreary 1990; Sengupta et al. 2001; Waliser et al. 2003). The general conclusions indicate that the ocean variability is primarily driven by the intraseasonal wind and that the instability of ocean currents also plays a role. None of the studies addressed the possibility of a resonance. According to the theory of Cane and Moore (1981), the ocean has a resonance mode at a period near 60 days with m = 3.

Figure 12 shows the leading CEOF of high-passed SSH with periods shorter than 75 days. This mode accounts for 26% of the high-passed variance with an rms amplitude of 1.5 cm. The spectrum of the temporal variability of the CEOF is shown in Fig. 13. The variance is concentrated between 50 and 70 days, with no discernible peaks at the aliased tidal periods. The spatial patterns are similar to those of the 90-day variability, with the energy concentrated in the eastern end of the basin. The model results of Waliser et al. (2003) showed a similar pattern of SSH variability. A pattern of phase convergence is observed with an amphidrome near 90°E on the equator. The resonance mode of Cane and Moore with m = 3 has three cells (Fig. 11b) as opposed to two cells with m = 2. Apparently only the easternmost cell is excited. This is consistent with the distribution of the zonal wind stress, which is bandpass filtered in 50–70 days (Fig. 12c). The meridional wind is similar and not shown. Most of the wind forcing is located in the eastern half of the basin. The theoretical amphidrome of the easternmost cell is located on the equator with a distance of ⅙ of the basin’s width from the eastern boundary, at about 90°E. The agreement between the observations and the theory suggests the importance of the eastern boundary reflection of Kelvin waves into Rossby waves, which are reinforced by the wind forcing located in the central and eastern basin. It is apparent that the CEOF represents part of a basin mode with the characteristics of Cane and Moore’s mode with m = 3. There are no discernible effects of residual tidal errors on the CEOF. The patterns of the M2 and S2 (Le Provost 2001) tides bear no resemblance to the CEOF in the region.

6. The 120-day variability

Both the wind stress and SSH spectra have prominent peaks at periods close to 120 days. A CEOF analysis was performed on the SSH data filtered in a period band of 110–130 days. Displayed in Fig. 14 are the amplitude and phase of the leading CEOF along with the standard deviation of the zonal wind stress similarly filtered. The leading CEOF accounts for 41% of the filtered variance with an rms amplitude of 1.1 cm. The meridional wind is similar and not shown. The SSH amplitude pattern is not quite like any of those discussed previously, because the 120-day period is not associated with a resonance. However, the closest resonant period is 107 days for the first baroclinic mode with m = 1 (see section 3). There is indeed some resemblance between the phase pattern and that shown in Fig. 3 for the semiannual mode (corresponding to m = 1 as well), with an amphidrome near 75°E on the equator. The wind stress in the northwestern part of the basin is probably responsible for the partial excitation of the mode. When compared with the spectral peaks at 180 and 90 days (Fig. 1), the 120-day SSH peak, lacking the strength of a resonant peak, is relatively weak in comparison with the wind stress peak at 120 days.

In the region east of 80°E, especially south of the equator, the phase pattern is probably affected by the local wind forcing, which disrupts the phase pattern of the basin mode. Because the wind forcing in the region is too far south from the equator, it is not effective in exciting the basin mode. Moreover, the mismatch between the forcing period and the resonant period surely plays a role in the lack of a full-blown basin mode.

7. The 75-day variability

The spectral characteristics of the 75-day variability of SSH and wind stress are similar to those of the 120-day variability. Shown in Fig. 15 are the amplitude and phase of the leading CEOF of the SSH variability filtered in a period band of 70–80 days, along with the standard deviation of the zonal wind stress similarly filtered. The CEOF accounts for 53% of the filtered variance with an rms amplitude of 1 cm. The patterns of the zonal wind stress are similar to those at 90 and 60 days (Figs. 10c and 12c). The meridional wind (not shown) is generally weak in this period band. The SSH amplitude and phase to the east of 70°E are also similar to those shown in Figs. 10 and 12 for the periods of 90 and 60 days, respectively. The phase has an amphidrome close to 86°E, which is the location of the amphidrome of the SSH at 90 days. It is apparent that the mechanism of the ocean’s response to wind forcing at 75 days is similar to that governing the variability at 90 and 60 days. Although the period of 75 days is not a resonant period of a basin mode, the workings of the Kelvin and Rossby waves near the eastern boundary of the basin have a similar effect on the 75-day variability as they have on the 60- and 90-day variabilities.

The spatial patterns of the SSH variability to the west of 70°E, however, are different from those at 90 and 60 days. The phase patterns here are more complex. In the southwest region the phase shows westward propagation with an amphidrome near 10°S, 50°E. This phase pattern suggests the effects of the northern tip of the island of Madagascar (near 12°S, 49°E). North of the equator, there is also some westward propagation between 55° and 70°E, probably caused by locally forced Rossby waves.

8. Effects on sea surface temperature

It is interesting to investigate the possible roles of the energetic intraseasonal variability in affecting the sea surface temperature (SST), which in turn affects the wind forcing. Han et al. (2006) showed evidence of such effects on the evolution of the Indian Ocean zonal mode. The largest intraseasonal SST variability in the equatorial Indian Ocean is located in the western basin where the monsoon wind cycle is strongest. The semiannual SST variability is primarily caused by the latent heat loss due to the two monsoon wind cycles in a year (Rao and Sivakumar 2000). The semiannual SSH basin mode is primarily driven by the zonal wind stress (Fig. 5a) to the east of the maximum of the semiannual SST variability (Fig. 16). However, there are no significant effects of SSH on SST at the semiannual period as discussed below.

The Reynolds SST products available from the National Oceanic and Atmospheric Administration (NOAA) (Reynolds and Smith 1994) were used to investigate the relationships among SST, SSH, and wind. Simultaneous observations of the three variables over the period of 1993–2000 were used for the study. The data were filtered in a period band of 170–190 days to examine the relationship of SST with wind and SSH near the SST maximum in the western region of the basin. Shown in Fig. 17a is a scatterplot of SST versus the magnitude of wind stress in the region between 10°S and 10°N and to the west of 60°E. Basically, the SST follows the magnitude of wind stress in the semiannual period band. When the wind stress increases, the SST decreases, and vice versa. The exceptionally tight band of data points in the center of the distribution are from the region south of 5°N. To the north of 5°N, there is a phase lag between the SST and wind with the SST lagging by about 30°, or 15 days. Figure 17b shows a scatterplot of SST versus SSH in the semiannual band, revealing a complicated relationship. The coherence (not shown) between the SST and SSH in the semiannual band is generally high in the region, but there is not a clear linear relation between the two variables. The pattern of the scatter indicates a complex phase shift between the two variables. Note that SST and SSH are both directly forced by the wind and the resulting indirect relation between them is probably responsible for the scatter and complex phase shown in Fig. 17b.

At the 90-day period, the maximum SST variability (Fig. 18a) is located next to the northwestern boundary where the wind variability is strong (Fig. 10c). At this location the SST is coherent with the wind stress magnitude with a phase lag as in the case of the semiannual period. There are several secondary SST maxima between 5° and 10°S, from 50° to 100°E (Fig. 18a). At these locations, the SST is not related to the wind as discussed above. Instead, the SST is coherent with the SSH with near-zero phase (Figs. 18b and 18c). The coherence was computed from averaging over 10 adjacent frequency bands. For a coherence value of 0.6, for example, the 95% confidence limit for the phase estimate is about 40° (Koopmans 1974). A phase with absolute values less than 40° is thus indistinguishable from zero. The phase confidence limit goes up to 60° for a coherence value of 0.5. Note that 0.53 is the 95% level of the significant coherence for 10 degrees of freedom.

As shown in Fig. 18b, the locations of significant coherence along 80°E roughly correspond to the SSH maxima shown in Fig. 10, suggesting a certain relation between the SSH and SST at the 90-day period. This is apparently caused by the relation between the SST and the depth of the thermocline, which varies with SSH. For example, a decrease in the SSH is related to the rise of the thermocline, and the associated upward motion brings up the cold deep water to the surface, causing the SST to decrease. Tsai et al. (1992) provides an example of the relation between the SST and equatorial waves in the equatorial Indian Ocean. In the absence of a strong horizontal gradient of the SST in the equatorial Indian Ocean, vertical advection might be a more effective mechanism than horizontal advection in affecting SST.

Coherence between SST and wind stress magnitude was also analyzed for the 60-day period (not shown). Significant coherence was found for the SST variability at 5°–10°S, 50°–75°E (see Fig. 19a for the SST variability). The phase suggests similar effects of wind on the SST as discussed earlier for the semiannual and the 90-day variability. The SST variability near the northwestern boundary of the basin shows no significant coherence with wind, however. The interesting finding is that the SST variability at 5°–10°S, 80°–100°E is significantly coherent with the SSH with near-zero phase (Figs. 19b and 19c). So is the weak SST variability just south of Sri Lanka (5°N, 80°E). These are the locations of the 60-day SSH variability shown in Fig. 12a, indicating possible effects of SSH on SST. The roles of ocean dynamics in affecting the SST at intraseasonal scales in the equatorial Indian Ocean have been demonstrated by the modeling study of Waliser et al. (2003). They showed much enhanced SST variability in an ocean general circulation model relative to that in a slab mixed-layer model when the ocean is forced by the same wind field.

The SST variabilities at 75 and 120 days were also analyzed. The 120-day variability is mostly coherent with the magnitude of the wind stress in the same manner as the semiannual SST variability, except near the equator close to the western boundary where the SST varies with SSH with near-zero phase. The partially excited basin mode may have some effects on the SST in the region. In terms of the relation with SSH variability, the 75-day SST variability is somewhat similar to the 60-day SST variability in the region east of 80°E, showing similar effects of the SSH on SST.

9. Summary and discussion

The variability of SSH in the equatorial Indian Ocean is examined in relation to the wind forcing at intraseasonal frequencies. Spectral peaks are found in both SSH and zonal wind stress observations at several high-order harmonics of the seasonal cycle. At the semiannual period, SSH is characterized by a basin mode that exhibits many properties of a resonance mode predicted by the theory of Cane and Moore (1981). Although the existence of this resonance in the Indian Ocean has been noted by several previous studies, the details of the mode’s spatial patterns of amplitude and phase are presented for the first time. The patterns of the amplitude of the mode reveal the effects of the ocean’s zonal boundaries on the Kelvin and Rossby waves involved in the establishment of the mode. The patterns of the phase exhibit an amphidrome on the equator in the center of the basin, with phase lines showing the time evolution of the mode resulting from the superposition of various equatorial waves. The analysis of a model simulation constrained by the SSH observations shows that the vertical structure of the semiannual variability is dominated by vertically propagating waves as reported in previous studies. The vertical wavenumber of the waves is consistent with that of the second baroclinic mode as required for resonance at the semiannual period given the width of the equatorial Indian Ocean.

At the period of 90 days, the SSH variability exhibits a modal pattern similar to that of the semiannual mode but with half the size in the zonal dimension. The extent of the mode is basically confined to the eastern half of the basin. The theory of Cane and Moore (1981) calls for a second resonance mode at this period with a double-cell structure of two identical submodes in each zonal half of the basin. Apparently, only the eastern half of the mode is excited, probably because of the particular distribution of the wind forcing.

At the period of 60 days, the SSH variability also has a similar modal pattern with one-third the size in the zonal dimension. The extent of the mode is mostly confined to the eastern one-third of the basin. The theory of Cane and Moore (1981) calls for a third resonance mode at this period with a triple-cell structure of three identical submodes in each one-third of the basin. Apparently, only the easternmost of the mode is excited, which is probably also due to the particular distribution of wind forcing.

There are also peaks at 75 and 120 days in both the SSH and wind stress spectra. The spatial patterns of the 120-day variability somewhat resemble those of the semiannual variability. Although there is no resonant response of the ocean at 120 days, this period is close to the resonant period of 107 days corresponding to the first basin mode (m = 1) involving the first baroclinic vertical mode. The 75-day SSH variability exhibits spatial patterns in the eastern basin that are similar to the variabilities at 60 and 90 days, although 75 days is not a resonant period of the basin according to Cane and Moore (1981). The amphidrome of the 75-day variability is located close to that of the 90-day variability. The spatial distribution of the wind stress at 75 days is also similar to that at 90 and 60 days, again leading to the speculation on the roles of the geographic distribution of the wind forcing in establishing the modal patterns in the eastern part of the basin.

From the findings described above, it is apparent that only the semiannual SSH variability exhibits a coherent mode involving the entire equatorial Indian Ocean. The 120-day variability shows only vague signs of a basin mode because of the mismatch between the period and a resonant period. The SSH variability at the other higher frequencies can be characterized by a coherent mode only at the eastern part of the basin. The presence of an eastern boundary seems more effective in establishing such modal characteristics than does a western boundary. One may also argue that the geographic distribution of wind forcing at these frequencies is more favorable for exciting modes in the eastern basin, but this may not be an independent factor because of the apparent effects of the SSH variability on SST as discussed in section 8.

The geographic confinement of the high-frequency SSH modes (periods of 90 days and shorter) indicates that these modes are not affected by the western boundary. Their formation is basically owed to the synchronization of the forcing period with the round-trip travel time of the equatorial waves from the forcing location to the eastern boundary. Therefore, for localized wind forcing of a given period P with sufficient strength, a local mode of the ocean response may be established with an amphidrome located on the equator at a distance d from the eastern boundary with d = Pcn/8. As demonstrated by the SSH variability at 90, 75, and 60 days, these are localized modes maintained by the wind forcing through a resonance mechanism similar to that described by Cane and Moore (1981).

There is evidence of significant coherence between the SST and SSH at periods shorter than 120 days. Although a significant part of the SST variability is related to the variability of the magnitude of wind stress in terms of latent heat loss of the ocean, the coherence and phase between the SSH and SST suggest the roles of ocean dynamics in the SST variability. The fact of a near-zero phase difference between the SSH and SST reflects the modulation of SST by the vertical motion of the ocean associated with the time-varying thermocline depth. When the SSH decreases, the thermocline rises and the associated upward motion of the water brings up the cold deep water, leading to a decrease in SST. The effect of the SSH on SST may provide a feedback mechanism to the wind forcing, which interacts with the SST. Although the atmosphere is considered the main source for the intraseasonal wind variability over the Indian Ocean, the ocean’s feedback through its dynamical effects on the SST should be considered in an ocean–atmosphere coupled mechanism governing the intraseasonal variability of the Indian Ocean.

Acknowledgments

I have benefited from many insightful discussions with Weiqing Han of the University of Colorado. Her work provided a source of extensive references for this study. Ichiro Fukumori, the leader of the JPL component of the ECCO Consortium, kindly provided the velocity products for the study. Akiko Hayashi of JPL has always been my valuable source of programming assistance. I also benefited from discussions with Claire Perigaud, Tong Lee, and Duane Waliser of JPL. The research presented in the paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautic and Space Administration. Support from the TOPEX/Poseidon, Jason, and OSTM projects is acknowledged.

REFERENCES

  • Bentamy, A., , Y. Quilfen, , F. Gohin, , N. Grima, , M. Lenaour, , and J. Servain, 1996: Determination and validation of average wind fields from ERS-1 scatterometer measurements. Global Atmos. Ocean Syst., 14 , 129.

    • Search Google Scholar
    • Export Citation
  • Cane, M., , and D. Moore, 1981: A note on low-frequency equatorial basin modes. J. Phys. Oceanogr., 11 , 15781584.

  • Cane, M., , and E. Sarachik, 1981: The response of a linear baroclinic equatorial ocean to periodic forcing. J. Mar. Res., 39 , 651693.

  • Clarke, A. J., , and X. Liu, 1993: Observations and dynamics of semiannual and annual sea levels near the eastern equatorial Indian Ocean boundary. J. Phys. Oceanogr., 23 , 386399.

    • Search Google Scholar
    • Export Citation
  • Fu, L-L., 2004: Latitudinal and frequency characteristics of the westward propagation of large-scale oceanic variability. J. Phys. Oceanogr., 34 , 19071921.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., , K. O’Neill, , and M. A. Cane, 1983: A model of the semiannual oscillation in the equatorial Indian Ocean. J. Phys. Oceanogr., 13 , 21482160.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Han, W., 2005: Origins and dynamics of the 90-day and 30–60-day variations in the equatorial Indian Ocean. J. Phys. Oceanogr., 35 , 708728.

    • Search Google Scholar
    • Export Citation
  • Han, W., , J. P. McCreary, , D. L. T. Anderson, , and A. J. Mariano, 1999: Dynamics of the eastward surface jets in the equatorial Indian Ocean. J. Phys. Oceanogr., 29 , 21912209.

    • Search Google Scholar
    • Export Citation
  • Han, W., , D. M. Lawrence, , and P. J. Webster, 2001: Dynamical response of equatorial Indian Ocean to intraseasonal winds: Zonal flow. Geophys. Res. Lett., 28 , 42154218.

    • Search Google Scholar
    • Export Citation
  • Han, W., , T. Shinoda, , L-L. Fu, , and J. P. McCreary, 2006: Impact of atmospheric intraseasonal oscillations on the Indian Ocean dipole during the 1990s. J. Phys. Oceanogr.,, 36 , ,, 670690.

    • Search Google Scholar
    • Export Citation
  • Jensen, T. G., 1993: Equatorial variability and resonance in a wind-driven Indian Ocean model. J. Geophys. Res., 98 , 2253322552.

  • Kindle, J. C., , and J. D. Thompson, 1989: The 26- and 50-day oscillations in the western Indian Ocean: Model results. J. Geophys. Res., 94 , 47214736.

    • Search Google Scholar
    • Export Citation
  • Koopmans, L. H., 1974: The Spectral Analysis of Time Series. Academic Press, 366 pp.

  • Le Blanc, J-L., , and J-P. Boulanger, 2001: Propagation and reflection of long equatorial waves in the Indian Ocean from TOPEX/Poseidon data during the 1993–1998 period. Climate Dyn., 17 , 547557.

    • Search Google Scholar
    • Export Citation
  • Le Provost, C., 2001: Ocean tides. Satellite Altimetry and Earth Sciences, L.-L. Fu and A. Cazenave, Eds., Academic Press, 267–304.

  • Lighthill, M. J., 1969: Dynamic response of the Indian Ocean to the onset of the southwest monsoon. Philos. Trans. Roy. Soc. London, 265A , 4593.

    • Search Google Scholar
    • Export Citation
  • Luyten, J. R., , and D. H. Roemmich, 1982: Equatorial currents at semiannual period in the Indian Ocean. J. Phys. Oceanogr., 12 , 406413.

    • Search Google Scholar
    • Export Citation
  • McPhaden, M. J., 1982: Variability in the central equatorial Indian Ocean. Part I: Ocean dynamics. J. Mar. Res., 40 , 157176.

  • Moore, D. W., , and J. P. McCreary, 1990: Excitation of intermediate-frequency equatorial waves at a western ocean boundary: With application to observations from the Indian Ocean. J. Geophys. Res., 95 , 52195231.

    • Search Google Scholar
    • Export Citation
  • O’Brien, J. J., , and H. E. Hurlburt, 1974: Equatorial jet in the Indian Ocean: Theory. Science, 184 , 10751077.

  • Quilfen, Y., , B. Chapron, , A. Bentamy, , J. Gourrion, , T. El Fouhaily, , and D. Vandemark, 1999: Global ERS 1 and 2 and NSCAT observations: Upwind crosswind and upwind downwind measurements. J. Geophys. Res., 104 , 1145911469.

    • Search Google Scholar
    • Export Citation
  • Rao, R. R., , and R. Sivakumar, 2000: Seasonal variability of near-surface thermal structure and heat budget of the mixed layer of the tropical Indian Ocean from a new global ocean temperature climatology. J. Geophys. Res., 105 , 9951015.

    • Search Google Scholar
    • Export Citation
  • Reddy, P. R. C., , P. S. Salvekar, , A. A. Deo, , and D. W. Ganer, 2004: Westward propagating twin gyres in the equatorial Indian Ocean. Geophys. Res. Lett., 31 .L01304, doi:10.1029/2003GL018615.

    • Search Google Scholar
    • Export Citation
  • Reynolds, R. W., , and T. M. Smith, 1994: Improved global sea surface temperature analyses using optimum interpolation. J. Climate, 7 , 929948.

    • Search Google Scholar
    • Export Citation
  • Schott, F. A., , and J. P. McCreary Jr., 2001: The monsoon circulation of the Indian Ocean. Progress in Oceanography, 51 , Pergamon,. 1123.

    • Search Google Scholar
    • Export Citation
  • Sengupta, D., , R. Senan, , and B. N. Goswami, 2001: Origin of intraseasonal variability of circulation in the tropical central Indian Ocean. Geophys. Res. Lett., 28 , 12671270.

    • Search Google Scholar
    • Export Citation
  • Stammer, D., , C. Wunsch, , I. Fukumori, , and J. Marshall, 2002: State estimation in modern oceanographic research. Eos, Trans. Amer. Geophys. Union, 83 , 289294295.

    • Search Google Scholar
    • Export Citation
  • Tsai, P. T. H., , J. O’Brien, , and M. E. Luther, 1992: The 26-day oscillation observed in the satellite sea surface temperature measurements in the equatorial western Indian Ocean. J. Geophys. Res., 97 , 96059618.

    • Search Google Scholar
    • Export Citation
  • Vincent, P., , S. D. Desai, , J. Dorandeu, , M. Ablain, , B. Soussi, , P. S. Callahan, , and , 2003: Jason-1 geophysical performance evaluation. Mar. Geod., 26 , 167186.

    • Search Google Scholar
    • Export Citation
  • Waliser, D. E., , R. Murtugudde, , and L. E. Lucas, 2003: Indo-Pacific Ocean response to atmospheric intraseasonal variability: 1. Austral summer and the Madden–Julian Oscillation. J. Geophys. Res., 108 .3160, doi:1029/2002JC001620.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1977: Response of an equatorial ocean to a periodic monsoon. J. Phys. Oceanogr., 7 , 497511.

Fig. 1.
Fig. 1.

Spectra of SSH (upper curve; cm2 cycles−1 day−1) and zonal wind stress [lower curve; 0.1 × (dyne cm−2)2 cycles−1 day−1]. The spectra were averaged over 10°S–10°N, 40°–100°E. The periods for the major spectral peaks are indicated. The 95% error bar for the spectra is shown.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 2.
Fig. 2.

The same spectra as shown in Fig. 1 with the high-frequency part (periods shorter than 140 days) displayed in a linear scale. SSH (cm2 cycles−1 day−1) is shown with a solid line, and zonal wind stress is shown with a dashed–dotted line [0.003 × (dyne cm−2)2 cycles−1 day−1]. The periods of interests are indicated.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 3.
Fig. 3.

The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the high-passed SSH.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 4.
Fig. 4.

High-passed SSH (cm) represented by the leading CEOF as a function of time (from years 1993 to 1996) and longitude along (a) the equator, (b) 4.5°N, and (c) 4.5°S. The data-void regions near 70°E are due to the Maldives Islands.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 5.
Fig. 5.

The std dev of the semiannual bandpassed (a) zonal and (b) meridional wind stress (cgs units).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 6.
Fig. 6.

(a) The amplitude of the theoretical basin mode (m = 1) along the equator (nondimensional units of amplitude). (b) The phase (°) of the mode as a function of latitude (12°S–12°N) and longitude (40°–100°E).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 7.
Fig. 7.

The phase along the equator from (a) the theoretical basin mode (m = 1) and (b) the leading SSH CEOF.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 8.
Fig. 8.

SSH (arbitrary unit) represented by the theoretical basin mode (m = 1) as a function of time and longitude along (a) the equator and (b) 4.5°N.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 9.
Fig. 9.

(a) The first two vertical EOFs of the semiannual zonal velocity (normalized) from the ECCO assimilation products at 0°, 90°E (solid line, the first mode; dashed line, the second mode). (b) Time evolution of the vertical structure represented by the first two EOFs of the semiannual zonal velocity (m s−1) at 0°, 90°E. The horizontal axis shows the ECCO model’s vertical levels, of which the corresponding depths are shown at the top.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 10.
Fig. 10.

The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the 90-day bandpassed SSH. (c) Std dev of the 90-day bandpassed zonal wind stress (cgs units).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 11.
Fig. 11.

The phase (°) of the (a) second (m = 2) and (b) third (m = 3) theoretical basin modes as functions of latitude (12°S–12°N) and longitude (40°–100°E).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 12.
Fig. 12.

The spatial distribution of the (a) amplitude (arbitrary unit) and (b) phase (°) of the leading CEOF of the high-passed SSH with periods shorter than 75 days. (c) Std dev of the 60-day bandpassed zonal wind stress (cgs units).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 13.
Fig. 13.

Power spectrum of the temporal variability of the leading CEOF of the high-pass-filtered SSH (periods shorter than 75 days).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 14.
Fig. 14.

(a) Amplitude and (b) phase of the leading CEOF of the 120-day bandpassed SSH observations. (c) Std dev of the 120-day bandpassed zonal wind stress (cgs units).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 15.
Fig. 15.

(a) Amplitude and (b) phase of the leading CEOF of the 75-day bandpassed SSH observations. (c) Std dev of the 75-day bandpassed zonal wind stress (cgs units).

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 16.
Fig. 16.

The std dev of SST (°C) in the period band of 170–190 days.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 17.
Fig. 17.

(a) Scatterplot of SST vs the magnitude of the wind stress in the period band of 170–190 days in the region west of 60°E between 10°S and 10°N. Note that the temporal means are removed from both variables. (b) Same as in (a), but for the SST vs SSH.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 18.
Fig. 18.

(a) The standard deviation of the 90-day bandpassed SST (°C). (b) Coherence amplitude of the SSH vs SST at the period of 90 days. The 95% level of the significant coherence is 0.53. (c) Coherence phase (°). Positive values indicate that the SSH is leading the SST.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

Fig. 19.
Fig. 19.

(a) The std dev of the 60-day bandpassed SST (°C). (b) Coherence amplitude of the SSH vs SST at the period of 60 days. The 95% level of the significant coherence is 0.53. (c) Coherence phase (°). Positive values indicate that the SSH is leading the SST.

Citation: Journal of Physical Oceanography 37, 2; 10.1175/JPO3006.1

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