The 1994 Positive Indian Ocean Dipole Event as Investigated by the Transfer Routes of Oceanic Wave Energy

Zimeng Li aGraduate School of Environmental Studies, Nagoya University, Nagoya, Japan

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Hidenori Aiki bInstitute for Space-Earth Environmental Research, Nagoya University, Nagoya, Japan
cApplication Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Abstract

The present study investigates the interannual variability of the tropical Indian Ocean (IO) based on the transfer routes of wave energy in a set of 61-yr hindcast experiments using a linear ocean model. To understand the basic feature of the IO dipole mode, this paper focuses on the 1994 pure positive event. Two sets of westward transfer episodes in the energy flux associated with Rossby waves (RWs) are identified along the equator during 1994. One set represents the same phase speed as the linear theory of equatorial RWs, while the other set is slightly slower than the theoretical phase speed. The first set originates from the reflection of equatorial Kelvin waves at the eastern boundary of the IO. On the other hand, the second set is found to be associated with off-equatorial RWs generated by southeasterly winds in the southeastern IO, which may account for the appearance of the slower group velocity. A combined empirical orthogonal function (EOF) analysis of energy-flux streamfunction and potential reveals the intense westward signals of energy flux are attributed to off-equatorial RWs associated with predominant wind input in the southeastern IO corresponding to the positive IO dipole event.

Significance Statement

The present study gains a new insight into the mechanism of the Indian Ocean dipole events using a new diagnostic scheme for wave energy based on 61-yr hindcast experiments. The results have shown the existence of two sets of westward transfer of wave energy at the equator during 1994. One set of westward signals shows the same group velocity with theoretical equatorial Rossby waves that appear reasonably along the equator. The other set of westward signals at the equator represents a slightly slower group velocity than the theoretical equatorial Rossby waves, which is associated with abnormally extended southeasterly winds during the Indian Ocean dipole event.

© 2022 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: Zimeng Li, lizimeng1995@gmail.com; Hidenori Aiki, aiki@nagoya-u.jp

Abstract

The present study investigates the interannual variability of the tropical Indian Ocean (IO) based on the transfer routes of wave energy in a set of 61-yr hindcast experiments using a linear ocean model. To understand the basic feature of the IO dipole mode, this paper focuses on the 1994 pure positive event. Two sets of westward transfer episodes in the energy flux associated with Rossby waves (RWs) are identified along the equator during 1994. One set represents the same phase speed as the linear theory of equatorial RWs, while the other set is slightly slower than the theoretical phase speed. The first set originates from the reflection of equatorial Kelvin waves at the eastern boundary of the IO. On the other hand, the second set is found to be associated with off-equatorial RWs generated by southeasterly winds in the southeastern IO, which may account for the appearance of the slower group velocity. A combined empirical orthogonal function (EOF) analysis of energy-flux streamfunction and potential reveals the intense westward signals of energy flux are attributed to off-equatorial RWs associated with predominant wind input in the southeastern IO corresponding to the positive IO dipole event.

Significance Statement

The present study gains a new insight into the mechanism of the Indian Ocean dipole events using a new diagnostic scheme for wave energy based on 61-yr hindcast experiments. The results have shown the existence of two sets of westward transfer of wave energy at the equator during 1994. One set of westward signals shows the same group velocity with theoretical equatorial Rossby waves that appear reasonably along the equator. The other set of westward signals at the equator represents a slightly slower group velocity than the theoretical equatorial Rossby waves, which is associated with abnormally extended southeasterly winds during the Indian Ocean dipole event.

© 2022 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: Zimeng Li, lizimeng1995@gmail.com; Hidenori Aiki, aiki@nagoya-u.jp

1. Introduction

The Indian Ocean dipole (IOD) is an important factor for explaining interannual variability of sea surface temperature (SST) in the tropical Indian Ocean (IO) (Saji et al. 1999; Webster et al. 1999). The most dominant interannual variation in the IO is one originating from El Niño–Southern Oscillation (ENSO) in the Pacific Ocean as manifested by empirical orthogonal function (EOF) analyses of SST anomalies in previous studies. The IOD appears as the second EOF mode representing the zonal dipole structure of SST anomalies with opposite loading on the western and southeastern parts of the IO. The positive phase of IOD is associated with significant upwelling in the large parts of the southeastern basin and downwelling near the western basin. The IOD acts as a major driver for modulating the climate of countries surrounding the IO. For example, the East African regions suffered severe floods in 1994 (Behera et al. 1999) and 1997 (Webster et al. 1999) owing to these two positive IOD events. In Guan and Yamagata (2003), they mentioned that the East Asian countries experienced abnormal hot summer in response to the 1994 positive IOD. In 2010–11, two severe floods occurred in Australia that are attributed to the 2010–11 negative IOD event (Brigadier et al. 2016). Another extreme negative IOD event in 2016 contributed to the abnormal precipitation with below average rainfall in the East African and above average rainfall over the eastern IO (Lu et al. 2018). Recently, one of the strongest IOD events in records occurred in 2019. During 2019, a severe drought and catastrophic bushfire occurred in Australia. This extreme climate event is attributed to the 2-yr consecutive positive IOD and El Niño occurrence (Wang and Cai 2020).

The IOD is an inherent air–sea coupled mode in the tropical IO, not a part of ENSO (Vinayachandran et al. 1999; Saji and Yamagata 2003; Ashok et al. 2003; Hong et al. 2008). During the 1994 pure positive IOD event, the southeastern tropical IO experienced the unusual atmospheric and oceanic conditions with cold SST and strong southeasterly surface winds (Behera et al. 1999). Halkides and Lee (2009) and Tanizaki et al. (2017) examined the development of cooling SST in the southeastern tropical IO through mixed layer heat budget analyses in 1994. Vinayachandran et al. (1999) pointed out that these anomalous easterly winds in 1994 contributed to the weak Wyrtki (1973) jet during boreal spring. The 1994 positive IOD event initiated in May which is earlier than another positive IOD event owing to the intraseasonal disturbances in 1994 (Rao and Yamagata 2004).

The IOD is associated with thermocline depth anomalies that propagate as large-scale waves. Previous studies have adopted various methods to investigate the characteristics of equatorial Kelvin waves (KWs) and Rossby waves (RWs) in the IO at interannual time scales. The dynamics of KWs and RWs has a crucial impact on the development and termination of IOD which in turn alters SST (Yamagata et al. 2004; McPhaden and Nagura 2014; Delman et al. 2016). During the positive phase of IOD, easterly wind anomalies excite upwelling equatorial KWs propagating eastward, leading to the upwelling off Java and Sumatra coasts (Vinayachandran et al. 2001; Delman et al. 2014; Chen et al. 2016). Huang and Kinter (2002) analyzed heat content to demonstrate the western boundary reflection from RWs to KWs is a pivot in relaxing the SST anomaly in the eastern basin. Rao et al. (2002) demonstrated that the subsurface dipole corresponding to the IOD may help reverse the surface dipole through westward propagating RWs. Yuan and Liu (2008) found the western boundary reflection from RWs to KWs provides important negative feedback to the evolution of upwelling currents off the Java coast during the IOD events by analyzing sea level anomaly. Nagura and McPhaden (2010) examined interannual variability in the equatorial IO based on the zonal velocity and sea surface height (SSH). They demonstrated that the velocity anomalies reverse before the wind anomalies reverse during the decay of IOD events owing to reflected RWs from the eastern boundary. Yan et al. (2012) pointed out that the thermocline variation forced by eastward propagation of KWs is crucially important for the development and decay of IOD events. Another important issue is the influence of ENSO during IOD–ENSO concurrent years. It has been demonstrated that El Niño forcing is necessary to strengthen and maintain the westward propagating off-equatorial RWs in the southern tropical IO even after the IOD has demised (Chakravorty et al. 2013, 2014). Du et al. (2020) illustrated that the downwelling RWs in the southern tropical IO have a decisive effect on the 2019 extreme positive IOD event. Based on the significance of wave dynamics, it is necessary to analyze the propagation of waves through the view of wave energy which may offer a better understanding of the development of IOD.

The prime objective of the present study is to provide a new perspective for the interannual variability in the tropical IO based on the transfer routes of wave energy using a new scheme of Aiki et al. (2017, hereafter AGC17). This scheme has been successfully applied to trace the transfer episodes of wave energy in the IO at intraseasonal time scales (Ogata and Aiki 2019) and at seasonal time scales (Li and Aiki 2020, hereafter LA20), in the Atlantic Ocean at annual time scales (Song and Aiki 2020) and at intraseasonal time scales (Song and Aiki 2021), and in the Pacific Ocean at interannual time scales (Toyoda et al. 2021). This study represents the first application of the AGC17 scheme in the IO at interannual time scales and may be regarded as a counterpart of Toyoda et al. (2021).

The present manuscript is organized as follows. Section 2 provides the details of the model, data used, numerical experiments, and diagnostic scheme used for the study. Section 3 highlights the 1994 pure positive IOD event to illustrate the general features of model output in the IO at interannual time scales. In section 4, we analyze the transfer episodes of wave energy in 1994–95 and examine the evolution of wave energy by comparing with 1990 as an IOD neutral year. Section 5 presents a summary of our major results.

2. Model and method

a. Linear ocean model

We have performed a set of 61-yr hindcast experiments for interannual variability in the IO using a linear ocean model (LOM). The governing equations of the model are shown in the appendix. We have applied the same model to simulate the monsoonal variation of wave energy in the IO (LA20) and examine the vertical propagation of waves at seasonal time scales in the IO (Li et al. 2021). The model is forced by monthly wind stress from 1958 to 2018 derived from the Japanese 55-year Reanalysis (JRA-55) 10-m wind velocity with the bulk formula of Large and Pond (1981). The model domain spans from 25°S to 20°N, and from 30° to 120°E with realistic coastlines. The model coastlines are derived from 100-m isobath in the General Bathymetric Chart of the Oceans (GEBCO) dataset. The Indonesian Archipelago has been closed. No side friction has been applied at the coastal boundaries of the model domain. Eddy viscosity is as in LA20. The model yields three-dimensional output with a 1/4° grid spacing in both zonal and meridional directions. The vertical profile of density in the tropical IO is averaged over 20°S–20°N and 40°–110°E extended to 5500-m depth and computed from annual mean salinity and temperature in the World Ocean Atlas 2013. As done by LA20, we have assumed no motion near the ocean bottom and estimated the gravity wave speed of the nth vertical mode c(n) following the bottom-pressure decoupling theory of Tailleux and McWilliams (2001). The vertical mode decomposition indicates gravity wave speeds of 2.99, 1.69, and 1.03 m s−1 for the first three baroclinic modes, respectively. The model output is separated into 6100 snapshots with an interval of 3.65 days over 61 years.

b. Diagnostic scheme for wave energy

In the present study, we use a newly proposed diagnostic scheme described by AGC17 to trace the transfer episodes of wave energy by analyzing the directionality of wave group velocity vectors. As compared to previous diagnostic schemes, such as pressure flux schemes (Cummins and Oey 1997) and the Orlanski and Sheldon (1993) scheme, the AGC17 scheme has the advantage of smooth tropical and subtropical transition for all waves and at all latitudes (Ogata and Aiki 2019; Song and Aiki 2020; LA20; Toyoda et al. 2021; Song and Aiki 2021; Li et al. 2021; Aiki et al. 2021).

AGC17 have presented an approximated version of the energy flux, which has been referred to as level-2 expression to read
u(n)p(n)¯+(p(n)φapp¯/2)y,υ(n)p(n)¯(p(n)φapp¯/2)x,
2φapp(f/c(n))2φapp=q(n),
where ∇2 = ∂xx + ∂yy. The quantity φapp is the solution of potential vorticity inversion Eq. (1b).

3. Interannual variation of simulated results

a. Comparison between reanalysis and simulated results

The dipole mode index (DMI) is defined as the difference in sea surface temperature anomalies between the western (10°S–10°N, 50°–70°E) and southeastern (10°S–0°, 90°–110°E) parts of the tropical IO, which has turned out to be useful for identifying the occurrence of IOD (Saji et al. 1999). We have validated simulated sea surface geopotential anomalies against 20°C isotherm depth anomalies in the European Centre for Medium-Range Weather Forecasts (ECMWF) ocean reanalysis (ORAS3). Figure 1a shows the time series of DMI between model output and reanalysis results during 1959–2009. The depth of 20°C isotherm manifests the variability of thermocline. When the IOD is under the positive phase, the thermocline becomes anomalous shallow in the eastern IO corresponding to the upwelling near the Sumatra coast. In contrast, the thermocline deepens anomalously in the western IO corresponding to anomalous downwelling near the African coast. The simulated index (red line in Fig. 1a) is based on the model output of sea surface geopotential associated with the combination of three baroclinic modes in our hindcast experiments. Classification of IOD years in the present study is based on Saji et al. (1999). The IOD was under the positive phase during 1961, 1966, 1967, 1972, 1982, 1994, 1997–98, and 2006. Following the definition of ENSO events in Trenberth (1997), the 1961, 1966, 1967, and 1994 positive IOD events develop independent of ENSO, which are referred to as the pure IOD events (yellow shaded columns in Fig. 1a). The 1972, 1982, 1997–98, and 2006 positive IOD events co-occur with strong El Niño in the Pacific (green shaded columns in Fig. 1a). We have calculated lead–lag correlation coefficients between model output and reanalysis results (Fig. 1b) and obtained the highest correlation coefficient of 0.825 at no lag in the period of 1959–2009 and particularly up to 0.95 during 1994 (figure not shown). While the positive lags signify that LOM leads ORAS3. These results suggest that our model has done reasonable work in simulating the interannual variability associated with the IOD.

Fig. 1.
Fig. 1.

(a) Comparisons of dipole model indexes during 1959–2009. The blue line represents the 20°C isotherm depth (m, shown by the vertical axis ticks on the right) from ECMWF ORAS3. The red line represents sea surface geopotential simulated by linear ocean model (LOM; m2s−2 as shown by the vertical axis ticks on the left). Yellow shaded columns indicate pure positive IOD events, and green shaded columns indicate IOD–ENSO concurrent positive IOD events. (b) Lead–lag correlation between reanalysis results (blue line) and model output (red line). The simultaneous correlation coefficient of is 0.825. The positive lags signify that LOM leads ORAS3.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

b. General features of simulated results during 1994 positive IOD event

We have investigated the energy transfer episodes during the 1994 pure positive event. The results in the following sections are during the period 1994–95. First we examine how good the model simulation is able to reproduce or differs from the previous understanding of the development process of IOD events. Figures 2 and 3 show a set of Hovmöller diagrams at the equator for the first three baroclinic modes during 1990 and 1994–95, respectively, the former of which represents a neutral year in terms of IOD. The magnitude of the second baroclinic mode is greater than that of the first and third baroclinic modes in both periods (Jensen 1993; Polito and Liu 2003; Nagura and McPhaden 2010; Iskandar et al. 2014; Ogata and Aiki 2019; LA20; Chen et al. 2020). The result shows that during the neutral year of 1990, zonal velocity and geopotential anomaly are phase locked to the seasonal cycle along the equator in the second baroclinic mode (Figs. 2c,d). The zonal velocity along the equator reverses direction four times per year (Fig. 2c). During boreal spring and fall, westerly winds induce eastward currents referred to as Wyrtki jet, while the northeast and southeast monsoon winds trigger the westward currents during boreal summer and winter. The geopotential anomaly shows positive signals (indicating thermocline deepening) during boreal spring and fall and negative signals (indicating thermocline shallowing) during boreal summer and winter (Fig. 2d). Along the equator, the westerly component of wind stress is dominant during boreal spring and fall, while the easterly component of wind stress appears during boreal summer and winter.

Fig. 2.
Fig. 2.

Hovmöller diagrams along the equator for the simulated results during 1990 of our hindcast experiments associated with the (a),(b) first, (c),(d) second, and (e),(f) third baroclinic modes. (left) Simulated zonal velocity (color shading; m s−1) and wind stress (solid and dashed contours for westerly and easterly wind stress, respectively; interval of 0.005 N m−2). (right) Simulated geopotential anomaly (color shading; m s−1, rescaled as p(n)/c(n) to follow the definition of gravitational potential energy) and meridional velocity (solid and dashed contours for northward and southward currents, respectively; interval of 0.01 m s−1).

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

Fig. 3.
Fig. 3.

As in Fig. 2, but for 1994–95.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

In contrast, during 1994 along the equator, anomalous easterly winds appear first by May and intensify in the following months then attain a peak in August–September (Fig. 3c). This feature along the equator weakens and terminates by March 1995. These easterly winds derived from southeastern IO are restricted to the central-eastern equatorial IO. During the fall of 1994, easterly winds along the equator induce westward currents, corresponding to the predominant energy input by wind forcing (negative contours in Fig. 4e). A slightly slower pulse of zonal currents appears in the western basin (November 1994–April 1995) as compared with that of normal months that are associated with westward propagating RWs. These easterly winds in the positive phase induce westward transport coincident with the negative signals off Sumatra during the positive IOD. These negative geopotential anomalies are associated with upwelling KWs and resulting anomalous thermocline shoaling (Fig. 3d).

Fig. 4.
Fig. 4.

Seasonal evolution of wind stress vector (arrows; N m−2) and geopotential anomaly (color shading; m2 s−2) for the simulated results in February, May, August, and November of 1990 of our hindcast experiments. The results are associated with the combination of the first three baroclinic modes.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

Figures 4 and 5 show the time evolution of geopotential anomaly during 1990 and 1994, respectively. The geopotential anomaly in 1990 is characterized by seasonal cycle in the tropical IO. Upwelling signals appear during boreal winter and summer, while downwelling signals appear during boreal spring and fall in the central eastern equatorial IO. Wind stress vectors in February and August coincide with northeast and southwest monsoon winds, respectively. As compared to the neutral year, southeasterly winds initiate from May and dominate over the southeastern IO in May–October during 1994. These anomalously strong winds induce upwelling in the central-eastern tropical IO from June–December. The southeasterly winds become weak from November and terminate in December.

Fig. 5.
Fig. 5.

As in Fig. 4, but for a monthly interval from May 1994 to December 1994.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

4. Transfer routes of wave energy in the Indian Ocean

We now trace the transfer routes of wave energy through the directionality of wave group velocity vectors using the AGC17 scheme to examine the interannual variability in the IO based on the results of our hindcast experiments. In the following paragraphs, the results of energy-flux vectors are based on the second baroclinic mode and the results of energy-flux streamfunction and energy-flux potential are based on the combination of the first three baroclinic modes.

a. 1994 positive IOD event

Figure 6 shows a set of Hovmöller diagrams along 3°N, the equator, and 3°S for the second baroclinic mode during 1990 and 1994–95. During the neutral IOD year of 1990, the equatorial KWs appear four times per year, which is consistent with the life cycle of wave energy determined by LA20. The westerly winds during boreal spring and fall at the central equator generate downwelling KWs that propagate eastward toward Sumatra coast. Upwelling KWs along the equator during boreal summer and winter are triggered by the southwest monsoon and northeast monsoon, respectively. The energy flux at both 3°N and 3°S during 1990 (Figs. 6a,c) is characterized by seasonal variation. During 1994, the continuous easterly winds extending from the southeastern IO along the equator dominate from April 1994–March 1995 and induce upwelling KWs which propagate eastward, as manifested by the negative signals of geopotential anomaly (Fig. 3d) in the eastern basin of the equatorial IO. The absence of westerly winds at the central equator during the monsoon transition period (Fig. 3c) results in the absence of energy input by westerly wind at the central equator during boreal spring and fall (Fig. 6e). Considering the generation of wave energy, the absence of westerly winds at the central equator may account for the weak eastward signals of equatorial KWs at the central-eastern basin in April–May of 1994 (Vinayachandran et al. 1999) and the absence of equatorial KWs at the central-eastern basin in October–November of 1994. The easterly winds were sustained until early 1995 along the equator. Meanwhile, upwelling KWs during January–March of 1995 are basically in response to these easterly winds along the equator instead of being forced by the northeast monsoon.

Fig. 6.
Fig. 6.

Hovmöller diagrams along (left) 3°N, (center) the equator, and (right) 3°S for the results (a)–(c) during 1990 and (d)–(f) 1994–95 of our model experiment with the second baroclinic mode. Color shading shows the energy flux (W m−1) with positive and negative values indicating eastward and westward, respectively, as estimated by the AGC17 scheme. Contours show the energy input by wind forcing with an interval of 0.001 W m−1 with positive value indicating the westward currents accelerated and negative value indicating the eastward currents decelerated by easterly winds. Yellow and green lines indicate the theoretical phase speed of KWs and RWs, respectively. Light blue and magenta lines represent the slower phase speed of KWs and RWs, respectively. The solid and dashed lines correspond to the actual existence and nonexistence of KWs and RWs, respectively.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

The traveling period of a packet of KWs propagating eastward and then back as boundary-reflected equatorial long RWs propagating westward across the equatorial IO (from 45° to 100°E) is referred to as basin mode period (Jensen 1993; Han et al. 1999). It takes 0.26, 0.46, and 0.75 years for the first three baroclinic modes, respectively. Given that the basin mode period of the second baroclinic mode is about half a year and the theoretical phase speed of equatorial KWs is 3 times faster than that of equatorial long RWs. Equatorial KWs and long RWs take about 1.5 and 4.5 months, respectively, to cross the basin. During 1994, it seems that the traveling period for one round trip of KWs and RWs across the equatorial IO extends roughly to 8 months (August 1994–March 1995) in the second baroclinic mode (Fig. 4e). Since the eastward transfer of energy flux associated with the equatorial KWs takes 1.5 months (July–August in 1994) to cross the zonal extent of the equatorial IO as usual, the longer traveling period is attributed to the propagation of westward energy flux. At the central-eastern basin along the equator, the phase speed of RWs is consistent with the theoretical phase speed of equatorial long RWs (green solid line in Fig. 6e, August–October in 1994). This set of westward energy flux is attributed to the reflected equatorial RWs at the eastern boundary. At the central-western basin, the group velocity of westward transfer of energy flux is slightly slower (pink line in Fig. 6e) than at the central-eastern basin. For the formation of this slower set of westward energy flux, we first considered the possibility that the anomalous easterly winds at the equator may be responsible for this slower westward transfer of energy flux. Zonal currents from September 1994 to March 1995 are accelerated by the easterly winds, indicating the predominant energy input by wind forcing (negative contour in Fig. 6e). This may generate and intensify the westward transfer of energy flux associated with RWs at the equator. The eastward transfer of energy flux associated with KWs forced by these easterly winds in February–March of 1995 has the same phase as the theoretical second baroclinic mode of KWs. Thus these easterly winds could not generate the different group velocities of westward energy flux associated with RWs at the equator. We have then examined whether the off-equatorial RWs from the southeastern basin are the possible factor for the formation of this slower set of westward energy flux or not. Based on the Hovmöller diagrams of energy flux along 3°S, equator, and 3°N during 1994–95 based on the AGC17 scheme (Figs. 6d–f), we note that the eastward signals related to KWs at the equator during July–August of 1994 are attributed to these abnormal easterly winds. As these KWs arrive at the eastern boundary, they are reflected and diffracted to equatorial and off-equatorial RWs, respectively. Energy flux at 3°N is characterized by the seasonal cycle rather than interannual variation (Fig. 6d). The westward energy flux at 3°N does not influence the group velocity of westward energy flux at the equator in the other periods. Meanwhile, since the westward transfer of energy flux at 3°N forced by local wind forcing near 83°E is in phase with the seasonal cycle, and may not be in charge of the slower group velocity of westward energy flux at the equator. In the southeastern IO, the slightly slower phase signals of westward energy flux appear along 3°S (pink line in Fig. 6f) as compared to the general group velocity of westward energy flux in the other seasons and neutral year (black line in Figs. 6c,f). These are off-equatorial RWs forced by the southeasterly winds in the southeastern IO with the predominant energy input by wind forcing at the central-eastern region of 3°S (contour in Fig. 6f). This packet of westward RWs shifts toward the equator from the southeastern IO (Schopf et al. 1981) in response to the influence of southeasterly winds and is intensified by easterly winds at the equator. This could account for the appearance of a slightly slower phase speed of RWs at the central-western equatorial IO. There exists another slower group velocity of westward energy flux during November 1994–June 1995 also induced by the extended southeasterly winds. However, energy input by wind forcing weakens from November and disappears in December at 3°S, indicating the demise of southeasterly winds in the southeastern IO. This packet of off-equatorial RWs propagates westward along 3°S toward the African coasts. In brief, the results illustrate the different group velocities of westward transfer of energy flux associated with RWs co-occurs with the anomalous southeasterly winds in the southeastern IO. Namely, the southeasterly winds trigger the slightly slower group velocity of westward transfer of energy flux associated with RWs that is connected to the equator and to the western IO.

To examine the development process of wave energy during the 1994 IOD event, we use the Helmholtz decomposition of the AGC17 level-2 energy flux:
RyDx=ρ0u(n)p(n)¯+ρ0(p(n)φapp¯/2)y,
+RxDy=ρ0υ(n)p(n)¯ρ0(p(n)φapp¯/2)x,
where the scalar quantities R and D correspond to the rotational and divergent components of the energy flux, respectively (with a unit of W m−1). The distributions of R (referred to as energy-flux streamfunction) and D (referred to as energy-flux potential) are shown in Figs. 7 and 8, respectively. The positive contours and negative contours indicate wind input and energy dissipation in the corresponding region, respectively.
Fig. 7.
Fig. 7.

Monthly evolution of energy-flux streamfunction R (color shading; 109 W = 1 GW) and energy-flux potential D (solid and dashed contours represent positive and negative values, respectively; interval of 106 W) in (a) February, (b) May, (c) August, and (d) November of 1990 computed using the AGC17 scheme (2a)–(2b) based on the monthly mean. The results are associated with the combination of the first three baroclinic modes.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

Fig. 8.
Fig. 8.

As in Fig. 5, but for a monthly interval from May 1994 to December 1994.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

We have investigated evolution in 1990 (Fig. 7) and 1994 (Fig. 8) by analyzing the energy-flux streamfunction and potential based on a monthly mean. Both the northwest monsoon in February 1990 (Fig. 7a) and the southwest monsoon in August 1990 (Fig. 7c) generate the upwelling KWs near the African coasts propagating eastward. Westerly winds at the central equator induce downwelling KWs propagating toward the Sumatra coast (Figs. 7b,d). After these KWs arrive at the eastern boundary, they will bifurcate poleward. This is consistent with two sets of cyclonic circulations of wave energy in each hemisphere during the normal monsoon year demonstrated by LA20. Figure 8 shows the developing process of the 1994 pure positive IOD event where the westward signals of energy-flux streamfunction together with the moderate signals of wind input first appear by May in the southeastern IO (Fig. 8a). These features, such as westward signals and predominant wind input, intensify and migrate westward to the equator along the Indonesian archipelago during June–July (Figs. 8b,c). These westward signals are associated with the off-equatorial RWs and positive contours are attributed to energy input by southeasterly winds. These features reach the peak in August and are restricted in the southeastern regions (Fig. 8d). The intense westward signals and predominant wind input maintain power until September (Fig. 8e). With the weakening of southeasterly winds in the southeastern IO, the westward signals associated with off-equatorial RWs and energy input by southeasterly winds become weaker from October (Fig. 8f) and are about to terminate in November (Fig. 8g). This dipole event has a rapid demise in December (Fig. 8h).

b. Combined EOF analysis for wave energy

We have performed the combined EOF analysis for the anomalies of energy-flux streamfunction and potential. Here we have removed the climatological component of monthly data to examine the interannual variability of wave energy in the IO. The first combined EOF mode explains about 27% of the total variance of energy-flux streamfunction and potential in the IO. The spatial pattern of the first EOF mode (Fig. 9a) shows that the westward signals related with the off-equatorial Rossby waves appear in the southeastern IO. Simultaneously, the positive signals of energy-flux potential corresponding to the predominant wind input are dominated in the southeastern IO indicating the energy supplied by southeasterly winds. This kind of pattern appears as the most dominant mode and is consistent with the distinct features during a dipole event year, such as the well-developed pattern in August 1994 (Fig. 8d). Temporal projection of leading combined EOF mode represents interannual variations and is coincident with the results of 61-yr hindcast experiments. The times series of the first combined EOF mode represents some positive peaks during 1961, 1982, 1994, 1997, and 2006 (yellow and green shaded columns in Fig. 9c) that are consistent with the reproduced major positive IOD events as shown in Fig. 1a. The 1966, 1967, and 1972 positive IOD events described in Fig. 1a are less pronounced in temporal projection of the first EOF mode. Note that the 1964, 2010, and 2016 peaks are related to the negative IOD events.

Fig. 9.
Fig. 9.

(a),(b) Results of the combined EOF analysis for energy-flux streamfunction (top panels: color shading for positive values in pink and negative values in dark blue; 109 W = 1 GW) and energy-flux potential (bottom panels: color shading for positive values in orange and negative values in green; 106 W) computed using the AGC17 scheme. Horizontal patterns in (a) and (b) and temporal patterns in (c) and (d) are associated with the first and second EOF modes in the left and right panels, respectively. All results are associated with the combination of the first three baroclinic modes during the 61-yr hindcast experiment in the present study. Yellow and green shaded columns in (c) and (d) are adapted from Fig. 1a.

Citation: Journal of Physical Oceanography 52, 3; 10.1175/JPO-D-21-0189.1

The second and third combined EOF modes explain about 21.8% (Figs. 9b,d) and 10.63% (figure not shown) of the total energy-flux streamfunction and potential variance in the IO, respectively. The energy-flux streamfunction in the second mode shows the typical interannual behavior in the spatial pattern. The powerful westward transfer of wave energy related to the off-equatorial RWs is prevailing in the southeastern IO. The spatial pattern of energy-flux potential (Fig. 9b) in the second dominant mode shows positive loading in the eastern equatorial IO and negative loading in the Arabian Sea. The positive value of energy-flux potential indicates the wind input peak in the eastern equatorial IO. This intense energy input by anomalous winds in an IOD event plays a leading role in triggering the wave energy transfer. The energy-flux potential becomes negative in the Arabian Sea where wave energy is dissipated owing to eddy viscosity. The time evolution of combined EOF second mode (Fig. 9d) agrees with the 1994 and 2006 positive IOD events.

5. Conclusions

The present study has investigated the transfer routes of wave energy during the 1994 positive IOD event, in an attempt to examine the applicability of the AGC17 scheme to phenomena at interannual time scales. We have conducted 61-yr hindcast experiments in the IO to offer a good comparison with the reanalysis results of 20°C isotherm depth in ECMWF ORAS3. Analyzing the time evolution of energy flux along the equator during the 1994 pure positive IOD event, we have found two sets of westward transfer signals associated with RWs. The first set has the phase speed in agreement with the linear theory of equatorial RWs. This set is attributed to the boundary-reflected equatorial RWs at the eastern basin of the IO from equatorial KWs. The second set is slightly slower than the theoretical phase speed of equatorial RWs. This set is found to be given by off-equatorial RWs originating from southeasterly winds initiated from the southeastern IO, which may be responsible for the appearance of a slightly slower group velocity of westward energy flux along the equator. The energy flux along 3°N during 1994 is characterized by the seasonal cycle, while that along 3°S exhibits interannual variations under the influence of extended southeasterly winds.

We have examined the development process of wave energy during 1994 using the AGC17 scheme based on the monthly mean of 3.65-day snapshots. In the leading month, the positive signals of energy-flux streamfunction together with positive contours of energy-flux potential appear in the southeastern IO. The positive curl in the southeastern IO is in response to energy input by southeasterly winds. These signals develop and shift westward toward the equator along the Indonesian archipelago. Westward transfer signals of energy-flux streamfunction are coincident with the westward off-equatorial RWs generated by southeasterly winds. It has a markedly rapid peaking of the powerful off-equatorial RWs and predominant wind input in August and is maintained until September. Whether or not this slower RW propagation is also identified from reanalysis data with realistic thermocline distribution and with atmospheric heat forcing is subject to investigation in a future study using the AGC17 scheme. Southeasterly winds become weak leading to the cutoff of westward propagation signals from October. This dipole event ceased at the end of 1994. Using the combined EOF analysis of energy-flux streamfunction and potential, we have shown that the features during a positive IOD event, such as the intense westward signals associated with wind-generated off-equatorial RWs and predominant wind input by southeasterly winds in the southeastern IO, appear as the most dominant mode.

Acknowledgments.

We thank two anonymous reviewers and Tomomichi Ogata for their valuable comments on the previous version of this manuscript. This study was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI 18H03738.

Data availability statement.

The set of model outputs obtained during the last year of each of the three experiments performed in the present study will be archived at both https://www.diasjp.net/en/ and http://cidas.isee.nagoya-u.ac.jp/databases/index.shtml.en upon publication of this manuscript. A number of datasets were retrieved from the Asia-Pacific Data Research Center at the University of Hawai’i (http://apdrc.soest.hawaii.edu). These include temperature and salinity data from the World Ocean Atlas 2013 for the calculation of gravity wave phase speed, mixed-layer depth data from the Argo products. The wind velocity data of the Japanese 55-year Reanalysis (JRA-55) Project has been used for estimation of monthly wind forcing. The anomaly of 20°C isotherm depth data are derived from European Centre for Medium-Range Weather Forecasts (ECMWF) ocean reanalysis (ORAS3).

APPENDIX

Linear Ocean Model

The linear ocean model (LOM) is written as
ut(n)fυ(n)+px(n)=α(n)τxρ0hmixHbottom+SGSx,
υt(n)+fu(n)+py(n)=α(n)τyρ0hmixHbottom+SGSy,
pt(n)+(c(n))2(ux(n)+υy(n))=0,
for each baroclinic mode. The subscripts x, y, and t denote horizontal and temporal partial derivatives, respectively. The superscript n indicates baroclinic mode number. The terms u(n)(x, y, t) and υ(n)(x, y, t) represent the zonal and meridional velocity, respectively. The term p(n)(x, y, t) corresponds to geopotential. The variable f denotes the Coriolis parameter. The parameter ρ0 is set to 1027 kg m−3, indicating the reference value of seawater density. The wind stress is shown by the vector (τx, τy). The definition of α(n) is described in detail in appendix A of LA20. It yields 0.35, 0.44, and 0.27 for the first three baroclinic modes, respectively. The annual mean mixed layer depth in the tropical IO, hmix = 35 m, is calculated through Argo float data based on the temperature difference of 0.2°C. The reference depth of the bottom of the ocean Hbottom is 5500 m in the tropical IO. The effect of lateral eddy viscosity is marked as subgrid-scale terms (SGS) in (A1) and (A2), that is, as in LA20 and Li et al. (2021).
Forcing terms for the wave energy budget are as follows. The wind input is written as
α(n)hmixHbottom(u(n)τx¯+υ(n)τy¯),
and the eddy dissipation is written as
ρ0(u(n)SGSx¯+υ(n)SGSy¯)
These terms correspond to the energy flux potential mentioned in (2a) and (2b).

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Save
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    • Search Google Scholar
    • Export Citation
  • Ashok, K., Z. Guan, and T. Yamagata, 2003: A look at the relationship between the ENSO and the Indian Ocean Dipole. J. Meteor. Soc. Japan, 81, 4156, https://doi.org/10.2151/jmsj.81.41.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Behera, S. K., R. Krishnan, and T. Yamagata, 1999: Unusual ocean-atmosphere conditions in the tropical Indian Ocean during 1994. Geophys. Res. Lett., 26, 30013004, https://doi.org/10.1029/1999GL010434.

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    • Search Google Scholar
    • Export Citation
  • Brigadier, L., B. A. Ogwang, V. Ongoma, C. Ngonga, and L. Nyasa, 2016: Diagnosis of the 2010 DJF flood over Zambia. Nat. Hazards, 81, 189201, https://doi.org/10.1007/s11069-015-2069-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Chen, Z., X. Wang, and L. Liu, 2020: Reconstruction of three-dimensional ocean structure from sea surface data: An application of is QG method in the southwest Indian Ocean. J. Geophys. Res. Oceans, 125, e2020JC016351, https://doi.org/10.1029/2020JC016351.

    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
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  • Delman, A. S., J. Sprintall, J. L. McClean, and L. D. Talley, 2014: The influence of remote wind forcing and Kelvin Waves on the Java upwelling in positive IOD years. 2014 AGU Fall Meeting, San Francisco, CA, Amer. Geophys. Union, Abstract A11E-3064.

    • Search Google Scholar
    • Export Citation
  • Delman, A. S., J. Sprintall, J. L. McClean, and L. D. Talley, 2016: Anomalous Java cooling at the initiation of positive Indian Ocean dipole events. J. Geophys. Res. Oceans, 121, 58055824, https://doi.org/10.1002/2016JC011635.

    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Crossref
    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Han, W., J. P. McCreary, D. L. T. Anderson, and A. J. Mariano, 1999: Dynamics of the eastern surface jets in the equatorial Indian Ocean. J. Phys. Oceanogr., 29, 21912209, https://doi.org/10.1175/1520-0485(1999)029<2191:DOTESJ>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hong, C.-C., M.-M. Lu, and M. Kanamitsu, 2008: Temporal and spatial characteristics of positive and negative Indian Ocean dipole with and without ENSO. J. Geophys. Res., 113, D08107, https://doi.org/10.1029/2007JD009151.

    • Search Google Scholar
    • Export Citation
  • Huang, B., and J. L. Kinter, 2002: Interannual variability in the tropical Indian Ocean. J. Geophys. Res., 107, 3199, https://doi.org/10.1029/2001JC001278.

    • Crossref
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  • Fig. 1.

    (a) Comparisons of dipole model indexes during 1959–2009. The blue line represents the 20°C isotherm depth (m, shown by the vertical axis ticks on the right) from ECMWF ORAS3. The red line represents sea surface geopotential simulated by linear ocean model (LOM; m2s−2 as shown by the vertical axis ticks on the left). Yellow shaded columns indicate pure positive IOD events, and green shaded columns indicate IOD–ENSO concurrent positive IOD events. (b) Lead–lag correlation between reanalysis results (blue line) and model output (red line). The simultaneous correlation coefficient of is 0.825. The positive lags signify that LOM leads ORAS3.

  • Fig. 2.

    Hovmöller diagrams along the equator for the simulated results during 1990 of our hindcast experiments associated with the (a),(b) first, (c),(d) second, and (e),(f) third baroclinic modes. (left) Simulated zonal velocity (color shading; m s−1) and wind stress (solid and dashed contours for westerly and easterly wind stress, respectively; interval of 0.005 N m−2). (right) Simulated geopotential anomaly (color shading; m s−1, rescaled as p(n)/c(n) to follow the definition of gravitational potential energy) and meridional velocity (solid and dashed contours for northward and southward currents, respectively; interval of 0.01 m s−1).

  • Fig. 3.

    As in Fig. 2, but for 1994–95.

  • Fig. 4.

    Seasonal evolution of wind stress vector (arrows; N m−2) and geopotential anomaly (color shading; m2 s−2) for the simulated results in February, May, August, and November of 1990 of our hindcast experiments. The results are associated with the combination of the first three baroclinic modes.

  • Fig. 5.

    As in Fig. 4, but for a monthly interval from May 1994 to December 1994.

  • Fig. 6.

    Hovmöller diagrams along (left) 3°N, (center) the equator, and (right) 3°S for the results (a)–(c) during 1990 and (d)–(f) 1994–95 of our model experiment with the second baroclinic mode. Color shading shows the energy flux (W m−1) with positive and negative values indicating eastward and westward, respectively, as estimated by the AGC17 scheme. Contours show the energy input by wind forcing with an interval of 0.001 W m−1 with positive value indicating the westward currents accelerated and negative value indicating the eastward currents decelerated by easterly winds. Yellow and green lines indicate the theoretical phase speed of KWs and RWs, respectively. Light blue and magenta lines represent the slower phase speed of KWs and RWs, respectively. The solid and dashed lines correspond to the actual existence and nonexistence of KWs and RWs, respectively.

  • Fig. 7.

    Monthly evolution of energy-flux streamfunction R (color shading; 109 W = 1 GW) and energy-flux potential D (solid and dashed contours represent positive and negative values, respectively; interval of 106 W) in (a) February, (b) May, (c) August, and (d) November of 1990 computed using the AGC17 scheme (2a)–(2b) based on the monthly mean. The results are associated with the combination of the first three baroclinic modes.

  • Fig. 8.

    As in Fig. 5, but for a monthly interval from May 1994 to December 1994.

  • Fig. 9.

    (a),(b) Results of the combined EOF analysis for energy-flux streamfunction (top panels: color shading for positive values in pink and negative values in dark blue; 109 W = 1 GW) and energy-flux potential (bottom panels: color shading for positive values in orange and negative values in green; 106 W) computed using the AGC17 scheme. Horizontal patterns in (a) and (b) and temporal patterns in (c) and (d) are associated with the first and second EOF modes in the left and right panels, respectively. All results are associated with the combination of the first three baroclinic modes during the 61-yr hindcast experiment in the present study. Yellow and green shaded columns in (c) and (d) are adapted from Fig. 1a.

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