1. Introduction
The spatial and temporal variability of precipitation during the Indian summer monsoon (ISM) is very important for the Indian economy, which is mainly based on agriculture. The ISM experiences, in addition to the dominant interannual variability, intraseasonal variability in the form of active and break spells of rainfall. Blanford (1886), in a pioneering work suggested the “intervals of drought” as the break periods during the peak monsoon months of July–August. Also, recent studies suggest that droughts are associated with longer breaks (Joseph et al. 2009; Raman and Rao 1981). Typically, during the monsoon breaks, the monsoon trough in the sea level pressure, normally extending from the head of the Bay of Bengal northwestward into Gujarat and adjoining Pakistan, is seen to propagate farther north into the foothills of Himalayas. This results in anomalously surplus rainfall in the Himalayan regions and below-normal rainfall to the south (Ramamurthy 1969; Krishnamurti and Ardanuy 1980; Krishnan et al. 2000, 2009; Rajeevan et al. 2008, 2010). The active condition of the ISM, on the other hand, is when the sea level pressure trough moves south of its normal position, resulting in above-normal rainfall along the climatological monsoon trough regions and in many parts of the peninsula (Sikka and Narsimha 1995; Rao 1976; Alexander et al. 1978; Das 2002; Rajeevan et al. 2010; Choudhury and Krishnan 2011). Compared with other scales, intraseasonal variability of the ISM represents a higher amplitude of the seasonal mean (Goswami 2011; Waliser 2006). Goswami et al. (2003) suggest that the emphasis of meridional shear of zonal winds and cyclonic vorticity along the monsoon trough results in increased (decreased) frequency of occurrence of low pressure systems during active (break) phase by the intraseasonal oscillations. The intraseasonal variability of ISM manifests as two broad peaks of variability, namely 10–20- and 30–60-day variabilities, with active and break phases that are linked to the northward migration of monsoon trough/ridge (Pai et al. 2009; Krishnamurti and Subrahmanyam 1982; Joseph and Sijikumar 2004; Krishnamurthy and Shukla 2007).
The revival of active conditions during the ISM is facilitated by the formation of synoptic disturbances in the Bay of Bengal, monsoon depressions, and low pressure systems that travel toward the northwest from Bay of Bengal into the Indian region (Chen et al. 2005; Sikka and Dixit 1972; Boos et al. 2015; Sikka and Gadgil 1980), many times along the monsoon trough, and cause copious rainfall. Krishnamurthy and Ajayamohan (2010) have shown that the absence of low pressure systems, such as lows, depressions, and cyclonic storms, represents the break phase and their presence represents an active phase of ISM.
From a dynamical perspective, some pioneering papers by Ramaswamy (1956, 1962) highlight the importance of anomalous southward shift of large-amplitude westerly troughs from the midlatitudes into the Indo-Pakistan region during breaks in the ISM. Importantly, further analyzing a case study studied by Ramaswamy (1962), Rao (1971) documents a manifestation of barotropic instability associated with increased horizontal shear due to the southward shift of the westerly troughs in the subtropical westerly jet at the midtropospheric level in the aforementioned break event and a subsequent revival associated with the formation of a synoptic disturbance. Rao (1971) hypothesized that manifestation of the barotropic instability during break leads to the formation of disturbances that in turn invigorate the ISM an active phase. Satyan et al. (1980) addressed the problem by using a two-layer quasigeostrophic model and carried out a stability analysis of the simulated monsoon zonal flow corresponding to break conditions. Satyan et al. (1980) also document the revival of the postbreak monsoon through formation of a synoptic disturbance. Further, while the upper-level flow in the simulations of Satyan et al. (1980) is found to be stable during the monsoon break conditions, it was found to be unstable a day before the formation of depression, supporting the argument of Rao (1971).
In the next few sentences, we briefly discuss some of the possible mechanisms such as the barotropic, baroclinic instabilities and other combined mechanisms, which have been suggested to explain the growth of the synoptic disturbances. The combined barotropic–baroclinic wind field study of the monsoon by Shukla (1977), using a 10-layered quasigeostrophic model, found that the barotropic mode is the only source for the upper-tropospheric growing mode at 150 hPa. Shukla (1978) numerically integrated the linearized perturbation equations for a three-layer quasigeostrophic model and performed a combined conditional instability of the second kind (CISK)–barotropic–baroclinic instability analysis, which shows the maximum growth rate occurs for the smallest scales. On the other hand, Goswami et al. (1980), while suggesting that a large meridional shear of the eastward component of winds at the 200-hPa level and a high cyclonic vorticity at low levels over the monsoon trough region during break periods favor growth of barotropic and baroclinic instabilities, adds that these instabilities cannot explain the initial growth for monsoon depressions. Therefore, the question remains whether instabilities generated by large-scale processes lead to subsequent revival of the monsoon through a barotropic instability mechanism and formation of a synoptic disturbance. In this paper, we attempt to answer this question. The availability of reanalysis datasets in the recent decades is a great opportunity in this sense. Analysis of multiple cases will also help us to refine any theoretically based thresholds and indices that represent a phenomenon. For example, theory (Kuo 1953; Starr and White 1954; Aihara 1959) suggests that barotropic instability occurs only in disturbances of very long wavelengths. The case study of a break monsoon Rao (1971) suggests that synoptic waves in the subtropical westerly jet in the Indian region with a wavelength greater than (less than) 3000 km are unstable (stable). We revisit this aspect in this study. The details of the datasets used and methods of analysis are described in the next section. We present our results and a discussion in section 3, followed by conclusions in section 4.
2. Data and methods
a. Data
For the present study, we have used monsoon break periods based on Rajeevan et al. (2006) of ISM for the period 1979–2007. Following Rajeevan et al. (2010), we choose the region bounded by 18.0°–28.0°N, 65.0°–88.0°E as the core monsoon region; indeed, on an interannual scale, the area-averaged rainfall in this region is highly correlated at 0.91 with that of interannual variation of the Indian summer monsoon (Rajeevan et al. 2010). The daily data employed in the study are zonal (U) wind at 200 hPa, meridional (V) wind, geopotential height, and sea level pressure (SLP). All of these products were obtained from National Centers for Environmental Prediction (NCEP) Reanalysis 2 (Kanamitsu et al. 2002). These datasets have a spatial resolution of 2.5° latitude × 2.5° longitude on a global grid and a temporal coverage of four-times-daily values from 1 January 1979 to 31 December 2007. In addition, the dates of the synoptic disturbances and locations were collected from the India Meteorological Department (2012; Cyclone eAtlas) data. In addition, the SLP data from the NCEP Reanalysis 2 data were used to reconfirm the dates of formation of the synoptic disturbances. We adopt the breaks and active event dates following Rajeevan et al. (2010).
b. Method
A complete list of the symbols/notations representing various variables/parameters in the study.
3. Results and discussion
a. Barotropic instability in the aftermath of breaks
From the works of Starr and White (1954) and Rao (1971), we can suppose that such a break condition will result in barotropic instability, which may in turn manifest as a synoptic disturbance for the revival of ISM. In this context, from Table 1, following Rajeevan et al. (2008), we list the dates of various postbreak revival events of ISM. Of the 41 total events (Table 2), 18 revivals occurred with the formation of low pressure in the Bay of Bengal (e.g., Fig. 1) and 7 others with the formation of low pressure on land (figures not shown). This result suggests that about 61% of the postbreak revivals are associated with formation of low pressure in the Bay of Bengal or land regions, providing a general support to the hypothesis of Rao (1971) and Raghavan (1973).
The formation of a synoptic disturbance on the particular day after every break event during the 1979–2007 period. An asterisk represents the revival of ISM without low formation.
Observed SLP distribution (hPa) on 10 Aug 2000, after a break period.
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
Now, eddy formation due to barotropic instability would necessitate a conversion of the 
Conversion of mean kinetic energy values (J s−1) at 200 hPa.
Conversion of kinetic energy anomaly values (J s−1) for the 1979–2007 period.
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
What is the potential mechanism for such manifestation of barotropic instability in these subseasonal events? As is known, barotropic disturbances derive energy from the mean kinetic energy. Energy considerations (e.g., Kuo 1951) show that for a disturbance to grow, it must tilt in a direction opposite to that of the meridional gradient of zonal wind. To be specific, a tilt from southwest to northeast (SW–NE) in a westerly zonal flow will meet this criterion. That is, waves with an SW–NE tilt will result in a maximum vorticity to the south [see (3), which is from Kuo (1949)]. From supplementary Figs. S1 and S2, it is seen most of the break days are also indeed associated with such an SW–NE tilt in the 200-hPa zonal flow. Such a tilt in the mean 200-hPa subtropical westerly jet over the Indian region on a typical break day (see Fig. 3a as an example, along with the corresponding geopotential field in Fig. 3b) is associated with a northward transfer of westerly momentum (Kuo 1949). In such a case, the zonally averaged eddy momentum transport 
(a) Zonal wind (m s−1) at 200 hPa on 4 Aug 2000, a typical break day. (b) The corresponding geopotential distribution (km).
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
(a) Eddy momentum flux transfer (m2 s−2), which is averaged zonally, during a break (1–9 Aug), before the break (14–23 Jul), and after the break (10–15 Aug), relative to the 1–9 Aug break in the year 2000. (b) Zonal wind profiles (m s−1) at 82.5°E and 200 hPa during a break day (4 Aug), on a day in the prebreak period (23 Jul), and on a postbreak day (11 Aug), all for the event presented in (a).
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
From the point of Rao (1971), it will be instructive to verify that the barotropic instability is a mechanism that would help the aforementioned eddies grow in such situations. To that end, the meridional vorticity distribution of the absolute vorticity ζ in the Indian region during the break events is presented in Fig. 5a, along with the corresponding composite in Fig. 5b. Importantly, we see maximum or minimum in absolute vorticity ζ around 29°N in the composite, with the individual values varying between 25° and 30°N. Manifestation of such maximum or minimum values is a necessary condition for the barotropic instability (Kuo 1951) from the individual case also indicates such manifestation (Fig. 5b). All this highlights the importance of the mean seasonal zonal wind structure, with westerlies to the north and easterlies to the south of the Indian subcontinent, in facilitating such a dynamical instability manifested by the breaks.
(a) Meridional distribution of the composite absolute vorticity (s−1) at 200 hPa, obtained by compositing it over all the break periods during 1979–2007. (b) As in (a), but composited over each break period during 1979–2007.
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
b. Wavelength threshold for manifestation of a postbreak synoptic disturbance
Ramaswamy (1962) and Rao (1971) claim from their individual case studies a decrease in channel width (D/2) between subtropical westerly and tropical easterly jets that manifest as a dynamical instability. We revisit this aspect by computing the D/2 during the break events in the study period. Our results (Table 4 and Fig. 6) show that 32 out of 41 break events (78%) indeed show a decrease in channel width. From this, we can deduce that a dynamical instability during the breaks is facilitated either as a result of a transient southward shift of the westerlies over the northern portions of the subcontinent and/or a transient northward shift of the tropical easterly jet stream over the peninsular region. Such a decrease in the channel width in the zonal width can also manifest with a weakening (strengthening) of the upper-level westerlies (easterlies) in the Indian region.
The channel width (D/2; °) between the subtropical westerly jet and tropical easterly jet at 200 hPa during the 1979–2007 period.
Latitudinal distance (°) between westerlies and easterlies at 200 hPa for various phases associated with observed break events.
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
Theory (Kuo 1953; Syōno and Aihara 1957) shows that barotropic instability occurs only in zonal waves of wavelength shorter than a critical wavelength Lc [see (1)]. Rao (1971), from his sole case study, estimates Lc of the upper-level westerly jet stream in the Indian region to be ~3000 km. However, given that it was only a single case and the relatively poor quality of the upper-air data during that period, we use the reanalyzed gridded datasets for multiple monsoon break cases to revisit this important finding by Rao (1971). Our analysis using (1) (Table 4) shows that (i) wavelengths in the upper-level westerlies north of Indian region during the summer monsoon reach a minimum value during breaks as compared to a few days prior to and after the event and (ii) the critical mean value of the aforementioned wavelength, obtained by averaging it over all break events, is 7411 km. The minimum Lc we find is just 5127 km (Fig. 7; also see Table 5).
Wavelength anomalies (km) of the zonal wind at 200 hPa, averaged over the span of each break event.
Citation: Journal of the Atmospheric Sciences 74, 5; 10.1175/JAS-D-16-0325.1
Calculated values of wavelength (Lc; km) before, during, and after break periods.
4. Conclusions
Ramaswamy (1962) and Rao (1971) show, through individual case studies that transition from break to active conditions occurs during the Indian summer monsoon (ISM) owing to the manifestation of barotropic instability, which leads to formation of a synoptic disturbance. Given the critical importance of break–active cycles in defining the seasonal rainfall envelope (Goswami et al. 2003; Goswami and Ajayamohan 2001) during the ISM, it is very important to revisit the conclusions of these case studies. With this goal in mind, using the atmospheric circulation datasets from the NCEP–NCAR Reanalysis 2 (Kanamitsu et al. 2002) for the period 1979–2007, we explore the potential role of monsoon break conditions in subsequent revival of the monsoon through formation of a synoptic disturbance in the Indian region. We adopt the monsoon active and break calendar documented by Rajeevan et al. (2008). We find that barotropic instability manifests in the Indian region during monsoon breaks in 61% of the cases. Such a revival is found to be associated with a reduction of the “zonal width” between the upper-level subtropical westerlies and tropical easterlies. Our correlation analysis between the wavelength of zonal winds in the Indian region and the rate of conversion of mean kinetic energy values for the study period is −0.285, statistically significant at 95% confidence level, which confirms the role of barotropic instability for formation of the postbreak synoptic disturbance (e.g., Aihara 1959). During the monsoon break period there is no rainfall over most of the country, and therefore the succeeding disturbances are not generated by the condensational heating. Thus, the argument that generation of monsoon depressions and synoptic disturbances due to the break-induced barotropic instability is reasonable. We also find that the mean wavelength of westerlies during boreal monsoon events north of the Indian region, which leads to the revival of the monsoons, is about 7400 km. While Rao (1971) suggests a threshold wavelength of 3000 km from his study, our analysis of the 41 cases suggests an apparent threshold from our sample to be above 5000 km.
As this study has been mainly carried out using the NCEP–NCAR Reanalysis 2 (Kanamitsu et al. 2002), in the future, we plan to explore these issues in other reanalysis datasets and various available medium-range hindcast runs (e.g., Mitra 2003a,b, 2009, 2013) and by conducting a few numerical sensitivity experiments.
We also need to remember that the Indian summer monsoon variability is controlled by several factors and drivers. In addition, formation of a disturbance depends on various other factors such as SST and moisture availability. The monsoon can also revive as a result of large-scale circulation changes, in which case the manifested instability may be different. From this context, the relevance of the other mechanisms, such as the baroclinic instability, in the remaining cases of the break–active transitions that happen without the formation of a synoptic disturbance needs further examination.
Acknowledgments
The authors gratefully acknowledge the India Meteorological Department (IMD), India, for the cyclone/synoptic disturbance chronology (eAtlas) data from www.rmcchennaieatlas.tn.nic.in, and the NOAA-Earth System Research Laboratory (ESRL), Climate Diagnostics Center, United States, for providing the National Centers for Environmental Prediction (NCEP Reanalysis 2) data from www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis2.html. We also acknowledge the anonymous reviewers for their critical comments.
APPENDIX
Barotropic Instability Problem
These are two ways of studying the development of disturbances: namely,
eigenvalue problem (Holton 2004) and
the initial-value problem (Kuo 1953; also see chapter 6 of Krishnamurti et al. 2013).
A complete list of the symbols/notations representing various variables/parameters in the appendix.
As can be understood, x and y are the coordinate axes taken positive toward east and north, respectively.
From the prescribed initial values of u, A, B, and 
a. Initial conditions
b. Boundary conditions—Meridional direction
c. Time tendency of amplitudes
d. Initial change of kinetic energy
The rate of change of kinetic energy may be regarded as the rate of amplification of the disturbances. If it is positive, kinetic energy tends to increase with time, and disturbance is said to be unstable. If it is negative, kinetic energy tends to decrease, and the disturbance is said to be stable or damping. If the rate of change of kinetic energy is zero, the kinetic energy remains constant, and the disturbance is said to be neutral.
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