1. Introduction
The summer monsoon is the wet season of the Indian subcontinent and is the lifeline for billions of people living on the rim of the Indian Ocean. Intraseasonal variability, which is commonly known as the monsoon intraseasonal oscillation (MISO), is pronounced during the Indian summer monsoon (Goswami 2005; Shukla 2014). Many studies have confirmed that MISO stems from the tropical Indian Ocean, as a result of the northward-propagating intraseasonal variabilities. Yasunari (1980) was one of the pioneers, and comprehensive descriptions of MISO were given by Annamalai and Slingo (2001), Goswami (2005), and Waliser (2006). Several processes and mechanisms have been identified to be important for the northward-propagating intraseasonal variabilities, such as the surface heat flux (Webster 1983), the interaction between the perturbations and the background easterly wind shear (Jiang et al. 2004), the eddy-mediated regime transitions (Bordoni and Schneider 2008), the convective momentum transport (CMT; Kang et al. 2010), and the ocean–atmosphere interactions (Yano and McBride 1998; Kemball-Cook and Wang 2001; Fu and Wang 2004; Zhou and Murtugudde 2014; Xi et al. 2015). Recently, a central Indian Ocean (CIO) mode was proposed in Zhou et al. (2017) as an intrinsic coupled mode that can explain the intraseasonal variabilities in the Indian monsoon. The CIO mode is represented by the covariability of intraseasonal sea surface temperature (SST) anomalies and intraseasonal low-level wind anomalies over the central Indian Ocean, and it captures the mechanistic links between the dynamic and thermodynamic fields. The CIO mode acts like a T junction and plays a role in the transition between the eastward-propagating intraseasonal variabilities (commonly known as the Madden–Julian oscillation) and the northward-propagating MISO. As a result, a high correlation between the CIO mode and the intraseasonal precipitation over the Bay of Bengal in boreal summer is found. The CIO mode and related processes have been diagnosed in Zhou et al. (2017) at intraseasonal time scales. As can be expected of this multiscale system, the CIO mode also has distinct features at seasonal–interannual time scales. Such low-frequency variability of the CIO mode and the driving mechanism are analyzed in this study. Decadal and multidecadal time scales and trends under global climate change will be diagnosed in a separate study especially in the context of the negative trend in the Indian summer monsoon and the erroneous representation of this trend in CMIP5 models (Saha et al. 2014; Roxy et al. 2015; Sabeerali et al. 2015).
At interannual time scales, El Niño–Southern Oscillation (ENSO) and the Indian Ocean dipole–zonal mode (IODZM) dominate over the Indo-Pacific region although some recent studies have posited that the tropical Atlantic can also influence the Indian monsoon variability (Pottapinjara et al. 2014, 2016). The long-term variability of the Indian summer monsoon is influenced by ENSO and IODZM. A negative correlation was found between ENSO and the Indian summer monsoon (Webster and Palmer 1997; Krishnamurthy and Kirtman 2003), but the relation appears to be nonstationary at decadal time scales (Kumar et al. 1999; Krishnamurthy and Goswami 2000). Especially in recent decades, the relation between ENSO and the Indian summer monsoon has weakened because of the influence of IODZM (Slingo and Annamalai 2000; Ashok et al. 2001; Sarkar et al. 2004), but the debate over the decadal shifts in Indian summer monsoon onset, withdrawal, and length of the rainy season continues (Sabeerali et al. 2014; Sahana et al. 2015). During the positive IODZM phase, warm SST anomalies over the western tropical Indian Ocean lead to anomalous updraft and surplus rainfall, compensating the El Niño–induced rainfall deficit over the monsoon region (Ashok et al. 2004). The relations between the Indian summer monsoon, ENSO, and IODZM extracted from observations and reanalysis products are confirmed by both theoretical and modeling studies (e.g., Li et al. 2003; Lau and Nath 2004). Because of the tangled interactions between the Indian and the Pacific Oceans, an appropriate combination of ENSO and IODZM is likely to have a better representation of the slow variability of Indian summer monsoon (Gadgil et al. 2004; also see Chen 2011; Lian et al. 2014) and may also need to consider the Atlantic zonal mode. By analogy, it is natural to expect that the interannual variability of the CIO mode is possibly influenced by both ENSO and IODZM as well. This is indeed the case and we report the detailed processes in this study. Any potential Atlantic influences on the CIO are not considered here.
For the rest of this paper, the data and methods are introduced in section 2. The seasonal and interannual variabilities as well as the dynamics are discussed in sections 3 and 4, respectively. The conclusions and discussion are presented in section 5.
2. Data and methods
Atmospheric variables, such as wind and precipitation for 1982–2014, are obtained from the daily National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis (Kalnay et al. 1996). The atmospheric variables are also obtained from daily ERA-Interim data, the global atmospheric reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF; Uppala et al. 2005) for ensuring the robustness of our findings. SST data for 1982–2014 are obtained from the ¼° daily NOAA Optimum Interpolation SST (Reynolds et al. 2007), and the outgoing longwave radiation (OLR) data are available for 1982–2013 from the NOAA satellite data (Liebmann and Smith 1996). All intraseasonal variabilities are obtained with a 20–100-day-bandpass Butterworth filter.
The index for the CIO mode is the principal component (PC) of the first combined empirical orthogonal function (EOF) mode of the daily intraseasonal SST and daily intraseasonal zonal winds at 850 hPa, as described in Zhou et al. (2017). The domain for the EOF analysis is over the whole Indian Ocean, covering 20°N–20°S, 40°–120°E. Each field is normalized by subtracting its regional mean and then dividing by its regional variance within the above domain before doing the EOF analysis, so that the SST and winds become dimensionless and are comparable in magnitude. The CIO mode index (CI) is shown in Fig. 1a with a blue curve. Although CI mainly captures the intraseasonal variabilities, there are also clear low-frequency variabilities in CI. To highlight the latter, the envelope of CI (EI) is computed using the Hilbert transform; that is, EI = |
(a) The CI (blue line; i.e., the PC of the first combined EOF mode) and its envelope (EI; red lines) obtained with the Hilbert transform. The top red line denotes positive EI and the bottom red line denotes negative EI. (b) Zoom in of (a) for the randomly selected year of 1992.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
In the following analysis, a two-sample Student’s t test, assuming that the two samples have unknown and unequal variances, is applied to test the statistical significance of the differences between two groups at a 95% confidence level.
3. Seasonal variability of the CIO mode
The climatological seasonal variability (daily data averaged from 1982 to 2014) of EI is shown in Fig. 2. It is obvious that the CIO mode is active during Indian summer monsoon from June to September but suppressed during boreal winter from December to March. Note that large (small) EI in Fig. 2 does not indicate a positive (negative) phase of the CIO mode. Instead, large (small) EI indicates that the amplitudes of the CIO mode for both the positive and the negative phases are enhanced (suppressed) during boreal summer (winter). In other words, the background state is favorable (unfavorable) for the CIO mode during boreal summer (winter). Thus, the question that will be addressed in this study is—what in the background state facilitates energizing the CIO mode during the Indian summer monsoon? Another distinct feature of the seasonal variation of EI in Fig. 2 is the dip in EI from early May to early June, which, however, is not likely to be attributable to the monsoon break periods or the “bogus” monsoon onset. Figure 2 shows the climatological seasonal variation of EI. While the break spells (Krishnan et al. 2000; Rajeevan et al. 2010) and the bogus onset of monsoon (Fasullo and Webster 2003) are both intraseasonal features, they are largely removed in the climatological mean. (The possible reason for the dip is discussed later using Fig. 7.)
The climatological seasonal variation of EI, which is the mean daily index from 1982 to 2014.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
(a) KE′ at 850 hPa (J kg−1) averaged over boreal summer from June to September. (b) As in (a), but averaged over boreal winter from December to March. (c),(d) As in (a),(b), but for [KE′ × 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
Terms of the kinetic energy budget in Eq. (1) at 850 hPa (J day−1 kg−1) averaged over boreal summer from June to September for (a) the horizontal advection, (b) [KE′ × PE′], and (c) the work done by the pressure gradient force.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
It is well known that the necessary condition for barotropic instability is that the meridional gradient of quasigeostrophic potential vorticity (QGPV; dq/dy = β − ∂2U/∂y2, where q is QGPV, β is the meridional gradient of the Coriolis parameter, and U is the background zonal velocity) changes sign within the study region (Vallis 2006). Figure 5 shows dq/dy in the lower troposphere at 850 hPa during the Indian summer monsoon and during boreal winter. During the Indian summer monsoon, positive and negative values occur alternatively in the meridional direction from about 10°S to the northern Bay of Bengal (~20°N), which is indicative of the necessary condition for the barotropic instability being satisfied. On the contrary, dq/dy during boreal winter is mostly negative, and the necessary condition for barotropic instability in the Northern Hemisphere does not occur. However, in the Southern Hemisphere, the zonal belt of a negative–positive–negative pattern of dq/dy can satisfy the necessary condition for barotropic instability and lead to large [KE′ × 
Meridional gradient of QGPV at 850 hPa (10−11 m−1 s−1) for the (a) Indian summer monsoon (from June to September) and (b) boreal winter (from December to March).
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
The vertical profiles of [KE′ × 
Vertical profile of the mean [KE′ × 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
The seasonal variabilities of 
Daily mean 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
The components for 
(a) All terms (day−2) in Eq. (4) along 5°N and (b) the three major components (day−2) in Eq. (4): LHS denotes the 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
4. Interannual variability of the CIO mode
Besides the seasonal variability, the CIO mode (EI) also has a pronounced interannual variability, as shown in Fig. 9 (solid line). The mean [KE′ × 
EI averaged from June to September in each year (solid line). Mean [KE′ × 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
Since ENSO and IODZM are two dominant interannual modes of variabilities over the Pacific and Indian Oceans, respectively, it is desirable to examine the influences of ENSO and IODZM on the interannual variability of the CIO mode. Note that we focus on the modulation of the CIO mode at interannual time scales and not on the interactions between ENSO and IODZM (Annamalai et al. 2003, 2005; Izumo et al. 2010). Since the CIO mode is active during the Indian summer monsoon but suppressed during boreal winter, we only focus on boreal summer in the following analysis. El Niño and La Niña are defined using the daily Niño-3.4 index (the daily mean SST over the Niño-3.4 region). The days during the Indian summer monsoon from 1982 to 2014 are categorized into two groups. The group that is composed of days with a Niño-3.4 index larger than the mean plus (minus) one standard deviation (STD) denotes the El Niño (La Niña) condition. Each group accounts for about 15% of total days during the Indian summer monsoon from 1982 to 2014. Goddard and Dilley (2005) and Camargo and Sobel (2005) used the upper 25% of total days for El Niño and lower 25% of total days for La Niña. Thus, the current criterion is stricter than the one they used. The difference of SST between El Niño and La Niña is shown in Fig. 10a. The warm anomalies from the central to the eastern Pacific Ocean are outstanding, and the El Niño and La Niña are clearly captured. The IODZM is identified with the daily dipole mode index (DMI) following Saji et al. (1999). By analogy to the criterion for El Niño and La Niña, the positive IODZM phase is defined when the DMI is larger than the mean plus one STD of the daily DMI during the Indian summer monsoon from 1982 to 2014, and the negative IODZM phase is defined when the DMI is smaller than the mean minus one STD. Figure 10b shows the SST difference between the positive and negative IODZM phases, and the IODZM pattern is also clearly reproduced. The SST differences between the IODZM phases and between the ENSO phases (Fig. 10) are quite different from the pattern of the CIO mode (Fig. 3a; Zhou et al. 2017). At the intraseasonal time scale, the CIO mode represents the ocean–atmosphere coupled features and the SST variation plays an important role in its evolution. In contrast, the low-frequency variabilities of the kinetic energy associated with the CIO mode are mainly due to the large-scale atmospheric circulation as shown above. Hence, the following analysis also focuses on the kinetic energy and the zonal wind structure in the atmosphere. However, this does not exclude the oceanic influences via other possible mechanisms, such as the oceanic impacts on the atmospheric boundary layer and the oceanic contribution to the accumulation of the available potential energy by modifying the surface heat flux.
SST differences (°C) during the Indian summer monsoon (from June to September) (a) between El Niño and La Niña and (b) between positive and negative IODZM phases. The differences in the hatched regions are not significant at a 95% confidence level.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
The difference in 
Meridional gradient of zonal wind ∂u/∂y at 850 hPa, averaged between 80° and 90°E, during positive and negative IODZM phases.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
Mean [KE′ × 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
Difference in winds δu at 850 hPa (vectors; m s−1) and d2(δu)/dy2 (color shading; 10−11 m−1 s−1) between the positive and the negative IODZM phases. The differences in the hatched regions are not significant at a 95% confidence level.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
The difference in 
Meridional gradient of zonal wind ∂u/∂y at 850 hPa, averaged between 80° and 90°E, during El Niño and La Niña.
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
(top) Difference in [KE′ × 
Citation: Journal of Climate 30, 16; 10.1175/JCLI-D-16-0616.1
5. Conclusions and discussion
The CIO mode is found to be closely related to the MISO and heavy monsoonal rainfall during the Indian summer monsoon. The processes associated with the CIO mode at intraseasonal time scales have been discussed in Zhou et al. (2017). In addition to the intraseasonal variabilities, the CIO mode also has pronounced seasonal and interannual variabilities. The low-frequency variabilities of the CIO mode are attributable to barotropic instability, which is triggered when the meridional shear of the background zonal winds are large enough to overcome the meridional gradient of the planetary vorticity. The energy conversion from zonal mean kinetic energy to the kinetic energy of intraseasonal variabilities energizes the intraseasonal variabilities during the Indian summer monsoon and leads to an active CIO mode. The horizontal eddy flux is the major component for the variation of the meridional gradient of zonal winds, which is consistent with the traditional conclusion for the global mean zonal velocity as discussed in Holton and Hakim (2013), albeit mostly in the context of midlatitude circulation. At interannual time scales, ENSO and IODZM are two dominant modes over the Indo-Pacific region. IODZM tends to shift the latitudinal position of the CIO mode by modifying the meridional shear of the zonal winds, since large-scale zonal winds are induced by the SST anomalies in the western and eastern nodes of IODZM. ENSO has moderate impacts on the interannual variability of the CIO mode; El Niño tends to weaken the CIO mode and La Niña tends to enhance it, via the changes in the low-level zonal wind shear over the central Indian Ocean. Overall, the impacts of ENSO and IODZM on the CIO mode at the interannual time scale are both moderate, which is consistent with the fact that the relations between ENSO/IODZM and Indian summer monsoon are weak and unreliable (e.g., Kumar et al. 1999; Krishnamurthy and Kirtman 2003). The weak statistical correlation between ENSO/IODZM and Indian summer monsoon was also shown in Zhou et al. (2017). At the intraseasonal time scale, Zhou et al. (2017) showed that the CIO mode represents a mechanistic link between the CIO mode and the Indian summer monsoon; that is, the CIO mode has an impact on the MISO via creating a coherent environment between the SST anomalies and the cyclonic gyre over the central Indian Ocean and modifying the vertical structure of the wind field. In this study, we conclude that the seasonal and the interannual variabilities of the CIO mode are also consistent with those of the Indian summer monsoon.
The seasonal variability of the CIO mode is quite consistent with that of the Indian monsoon. It represents the seasonal shift of the ITCZ and precipitation between the Northern and Southern Hemispheres. The observations and reanalysis products for SST and low-level winds (e.g., at 850 hPa) are fairly reliable. The simulation and prediction of these large-scale variables are also satisfactory. Thus, a better understanding of the relation between the CIO mode and the Indian summer monsoon is likely to facilitate the simulation and prediction of the intraseasonal features of the Indian monsoon and their low-frequency variabilities, especially the monsoon onset and withdrawal. At interannual and longer time scales, the evolution of the Indian monsoon system follows the shift of the ITCZ between the two hemispheres as well. The global energy balance determines the ITCZ locations at interannual and longer time scales (Schneider et al. 2014). Zhou et al. (2017) showed that the CIO mode, which captures the atmosphere–ocean interactions at the intraseasonal time scale, plays an important role in the MISO phenomenon. Current results show that the barotropic energy conversion resulting from the large-scale wind structures is undoubtedly a key process in the energy budget over the Indian Ocean during the Indian summer monsoon. In the multiscale but “seamless” climate system, the CIO mode is certainly influenced by the background state variability, such as ENSO and IODZM, as discussed in this study. On the other hand, it is also foreseen that the CIO mode may have feedbacks to the background state, which requires further studies in the future.
A caveat of this study is that the potential energy budget associated with the low-frequency variabilities of the CIO mode is not shown because of the uncertainty of key variables in the reanalysis products. The latent heat release and the moist processes are critical for the variation of the potential energy. But large uncertainty exists not only in reanalysis products but also in observations. For example, Zhang et al. (2010) showed inconsistency in shallow diabatic heating between four different Tropical Rainfall Measuring Mission (TRMM) datasets. Therefore, it is hard to yield reliable estimates of the potential energy budget using existing observations or reanalysis products. An idealized layer model (which has been widely used in theoretical studies, such as in Moorthi and Arakawa 1985; Chatterjee and Goswami 2004; Sobel and Maloney 2012; Liu and Wang 2013; Zhou and Kang 2013; and many others) should be a useful tool for detecting the influences of moist processes on the CIO mode at various time scales. It can also be useful for further examining the mechanisms of the CIO mode and the sensitivity of the CIO mode to the parameterization of moist processes. In all, much more work is needed for a better understanding of the CIO mode and its relation with the Indian monsoon in the multiscale climate system.
This work is supported by grants from the National Natural Science Foundation of China (41376034, 41321004, 41690121, and 41690120), the National Basic Research Program (2013CB430302), and the IPOVAR Project (GASI-IPOVAI-01-02 and GASI-IPOVAI-02). RM gratefully acknowledges the CYGNSS grant from NASA and the National Monsoon Mission funds for partial support. We deeply appreciate the comments from the editor and the reviewers on all aspects of our analysis, which helped sharpen our message.
APPENDIX
Derivations of the Zonal Momentum Equation
The derivation of the zonal mean zonal velocity equation is similar to the one presented in Holton and Hakim (2013), except that the advection and vertical eddy flux, which were neglected in their study, are retained in this study. In addition, since the zonal mean is taken within a bounded region (such as the Indian Ocean) rather than over the whole globe, the influences from the western and the eastern boundaries are considered.
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