The intraseasonal fluctuation of Indian summer monsoon rainfall and its relation with monsoon intraseasonal oscillation (MISO) and Madden Julian oscillation (MJO)

The intraseasonal fluctuations of Indian summer monsoon rainfall (ISMR) are mainly controlled by northward propagating monsoon intraseasonal oscillation (MISO) and eastward propagating Madden Julian oscillation (MJO). In the current study, we examine the relationship between the intraseasonal fluctuations (active and break spells) of ISMR with the phase propagation and amplitude of MISO and MJO. We notice that active spells generally occur during MISO phases 2–5 (MJO phases 3–6), and break spells mainly occur during MISO phases 6–8 (MJO phases 6–8 and 1). The association of active/break spells with MISO phases is more prominent than with MJO phases. We show the phase composite of unfiltered and regression-based reconstructed rainfall for eight MISO and MJO phases, which is consistent with the earlier findings. We notice that the reconstructed field shows a systematic and well-organised northward propagation compared to the unfiltered field. Phase composite also indicates a lead-lag relationship between MISO and MJO phases. MISO phase composite shows more robust northward propagation than the MJO phase composite. MISO reconstructed rainfall explained more percentage variance than MJO reconstructed rainfall with reference to 20–90-day filtered rainfall. It is found that long active (> 7 days) predominantly occurs when either MISO or MJO, or both of them are active, and the associated signal is somewhere in between phases 2 and 5. A long break occurs when both (MISO and MJO) or at least one (MJO/MISO) is feeble, or even though associated signals are strong, they are primarily located in phases 1, 6, 7 and 8.


Introduction
In recent years, much attention is being paid towards intraseasonal prediction as it fills the gap between synoptic weather scale and seasonal scale. The intraseasonal prediction has a wide range of applications over many sectors, such as agriculture, health, hydrology and power (Pattanaik et al. 2019). Out of these different sectors, it has one of the most significant roles in the agricultural sector as the Indian economy is highly interlaced with agriculture. Although the majority of the rain occurs over the Indian mainland from June to September (JJAS), it has a sizeable spatio-temporal variability within the season. Skilful prediction of this intraseasonal variability could help in decision-making in the agricultural sector, such as planting schedule, harvesting crop and fertiliser application (Meinke and Stone, 2005). The daily time series of standardised rainfall anomalies averaged over the core monsoon zone (Rajeevan et al., 2010) for the Indian monsoon season (JJAS) prominently show the intraseasonal fluctuations during the season. These fluctuations, i.e. above normal (below normal) rainfall activity over the core monsoon zone, are known as the active (break) spell of the Indian summer monsoon (Annamalai and Slingo, 2001;Gadgil and Joseph, 2003;Rajeevan et al., 2010). Prediction of these active and break spells (occurrence of the spell and their duration and intensity) at the adequate lead time (at least 2-4-week lead) has immense socio-economic importance. The prediction of intraseasonal variability is related to several factors, and the predictability primarily arises due to the low frequency oscillations during boreal summer. Many researchers (Goswami, 2005;Lawrence and Webster, 2002;Sikka and Gadgil, 1980;Yasunari, 1979) have reported that low frequency intraseasonal fluctuations over the Indian monsoon region are largely controlled by two dominant modes of variability: (a) the convectively coupled, planetary scale, eastward propagating MJO Madden andJulian, 1994, 1972;Salby and Hendon, 1994) and (b) the northward propagating MISO (Lau and Chan, 1986;Sikka and Gadgil, 1980;Wang et al., 2005). These two are the most dominating modes of intraseasonal oscillation. MISO exists only during boreal summer, whereas MJO exists around the year. Although MJO is weak during boreal summer (peaks in boreal winter Hendon and Salby, 1994;Madden, 1986)), it still influences climate and weather phenomena throughout the year, not only limited to the tropics but even in the sub-tropical region (Bond and Vecchi, 2003;Jones, 2000;Matthews, 2004;Mo and Higgins, 1998). During boreal summer, the eastward moving MJO influences the active-break cycle of the Asian monsoon (Lawrence and Webster, 2002;Yasunari, 1979). However, many studies (Goswami, 2005;Sikka and Gadgil, 1980) have advocated that among different modes of intraseasonal oscillations, the active and break spells of Indian summer monsoon are significantly controlled by the northward propagating 30-60-day mode. Many studies (Jones et al., 2004;Wang and Rui, 1990) have argued that a significant portion of the northward propagating mode during boreal summer is not associated with the eastward propagating mode. However, Lawrence and Webster (2002) found that a large percentage of northward moving convection is related to eastward propagating mode, although they also found some independent northward propagating convection. Kar et al. (1997) have investigated the relationship of the northward moving rain-band with the eastward moving components using the Japan Meteorological Agency (JMA) model and commented that the northward propagation of rainfall is not solely associated with eastward moving intraseasonal oscillations. Pai et al. (2011) have studied the association of intraseasonal fluctuations (active/break) of ISMR with the phases of MJO using IMD high-resolution rainfall data and RMM indices of Wheeler and Hendon (2004). They commented that around 83% of the break spells are favoured during MJO phases 1, 2, 7 and 8, and about 70% of the active spells are set in during MJO phases 3-6. Mishra et al. (2017) have also reported similar findings to Pai et al. (2011). Marshall and Hendon (2015) have studied the relationship between the MJO phase and frequency of the active/break days of the Australian summer monsoon. They summarised that active episodes are much more frequent during MJO phases 5-7, and the break phases are prevalent during MJO phases 8, 1 and 2 for the Australian summer monsoon.
In the current study, we considered the two most dominant modes of intraseasonal oscillation (ISO), namely, MJO and MISO, and tried to understand the relationship of Indian monsoon active/break with them.

Data and methodology
India Meteorological Department (IMD) gridded highresolution (0.25 × 0.25) rainfall data (Pai et al., 2014) over Indian land for the period 1998-2018 was used for this study. This data was initially developed up to the year 2010 and later extended for recent years. IMD-TRMM merged gridded rainfall datasets (Mitra et al., 2009) are also utilised wherever we require data beyond Indian land. For dynamical fields, the NCEP-NCAR reanalysis datasets (Kalnay et al., 1996) from 1 3 1998 to 2018 are used. Outgoing long-wave radiation (OLR) datasets from Advanced Very High Resolution Radiometers (AVHRR) aboard NOAA polar orbiting satellites (Liebmann and Smith, 1996) are also utilised for the same period.

Identification of active and break days
To identify the active and break days of ISMR, we have calculated daily standardised rainfall anomaly averaged over the core monsoon zone (as proposed by Rajeevan et al. (2010)) based on the 1998 to 2018 period. Active (break) is identified when the standardised rainfall anomaly averaged over the core monsoon zone is more than 0.9 (less than − 0.9) for consecutive 4 days and the average anomaly over the region during the period crosses 1.2 (less than − 1.2). The active and break identification is carried out from 10 June to 15 September because the delayed onset and early withdrawal of monsoon may lead to the misinterpretation of result (Joseph et al., 2009;Krishnan et al., 2000).

MJO and MISO principal components (PCs) and phases
For MJO monitoring, we have utilised the PCs based on the extended empirical orthogonal functions (EEOF) analysis of combined fields (velocity potential at 200 hPa, zonal wind at 200 hPa and 850 hPa) as described in Dey et al. (2019). They have also shown canonical MJO phase composite structure for various MJO phases. For monitoring northward propagating MISO, we have computed the MISO PCs using EEOF analysis of daily unfiltered rainfall analogous to Suhas et al. (2013). Although Sahai et al. (2014)

Active and break spell during 1998-2018
In

Association of active and break days with MJO and MISO phase
To examine the association of active and break days with the various phases of northward propagating MISO and eastward propagating MJO, we considered all active (193 days) and break (194 days) days during 1998-2018. We plotted the scatter diagrams of MISO1 and MISO2 in phase space for all active days (Fig. 1a) and break days (Fig. 1b) during 1998-2018. The black circle of a unit radius in Fig. 1a and Fig. 1b delineates strong and weak MISO categories. The frequency of active and break days with the various phases of MISO is shown in Fig. 1c and Fig. 1d, respectively. During frequency computation, we have excluded points that fall inside the unit circle (that represents a weak MISO). Figure 1 indicates that the frequency of active (break) days is high during MISO phases 2-5 (6-8). Strong association between active and break days with the MISO phase is apparent. Figure 2 is similar to Fig. 1 but for the PCs of MJO (based on Dey et al. (2019)). Figure 2 indicates that the frequency of active (break) days is high during MJO phases 3-6 (6-7-8-1).  Figure 3 shows the composite of daily unfiltered rainfall anomalies (mm/day) for eight MISO (Fig. 3a) and MJO (Fig. 3b) phases. It is evident from Fig. 3 that there is a phase lag in the MISO phase composite compared to the MJO phase composite. The phase 1 composite for MISO matches more or less with the phase 2 composite for MJO, and the phase 2 composite for MISO matches with the phase 3 composite for MJO, and so on. Phase 1 composite of MISO (phase 2 composite for MJO) shows large negative anomalies over central India and the west coast of India. In contrast, positive anomalies are seen over the southeast and some parts of the northeast region of the country, which is the canonical structure of rainfall associated with break monsoon conditions. In phase 2 composite of MISO (phase 3 for MJO), we can notice the weakening of negative anomalies over the central India region and elongation of positive anomalies from southern parts towards the north. As we move from phase 3 towards phase 5 for MISO (phases 4-5 for MJO), the composite structure shows a systematic northward movement of rain band similar to that of active monsoon conditions (positive anomalies over core monsoon zone and negative anomalies over northeast and southeast part of India). The magnitude of rainfall anomalies is much stronger in the MISO phase composite than in the MJO phase composite. Composite structure during phases 6-8 for MISO shows a sudden change in the pattern. Mainly negative anomalies prevail over most of the central India region, resembling the canonical structure of monsoon break. However, for MJO, we do not see such a sudden change in the rainfall pattern during phases 6-8, and changes are prominently seen during phase 1. Therefore, it could be contemplated that MJO phases 6-8 is the phase during which active to break transition happens; during this, both active and break occur over India. The same is consistent with Fig. 2. In Fig. 4, we show the Hovmoller plot (phase vs latitude) of rainfall anomalies averaged over 65-90°E for MISO (Fig. 4a) and MJO (Fig. 4b) composite. In the Hovmoller diagram, along the abscissa phases 5-8 (to the left of phases 1-8) and phases 1-4 (to the right of phases 1-8) are repeated for the display of continuity. Although the Hovmoller plot for MISO and MJO phase composite indicates a precise northward movement of the rain band, the signal is much more robust for MISO composite compared to MJO composite.

Composite of unfiltered convection and circulation anomalies for eight MISO and MJO phases
In the last section, patterns of the rainfall anomalies for various MJO and MISO phases are discussed. Now we examine how these changes are linked with the low-level circulation and convection patterns. We show phase composites of OLR anomalies (shaded; W/m 2 ) and wind anomalies at 850 hPa (vector; m/s) for eight different MISO and MJO phases in Fig. 5a and Fig. 5b, respectively. Like rainfall composite, here also we notice a lag in the MISO phase composite compared to the MJO phase composite. By and large, OLR and wind composite structures during phases 2-4 for MISO (phases 3-5 for MJO) look like active monsoon condition, whereas during phases 5-8 and 1 for MISO (phases 6-8, 1 and 2 for MJO) resemble like break monsoon condition. In Fig. 6, we show the Hovmoller diagram of the OLR anomalies (shaded; W/m 2 ) and vorticity anomalies at 850 hPa (contour; positive solid and negative dashed; contour interval 1 × 10 −6 s −1 ) averaged over 65-90°E for MISO and MJO composite. From Fig. 6, it may be noted that the centre of cyclonic (anticyclonic) vorticity at the low level is located to the north of negative (positive) OLR anomalies for both MISO and MJO. This result is persistent with the previous study ( Fig. 2.15a of Goswami (2005)) and confirms that both these intraseasonal oscillations progress and sustain as a convectively coupled system. MJO reconstructed field, obtained from Fig. 7a and Fig. 7b, respectively. Phases are repeated like Fig. 4

MISO and MJO phase composite of the reconstructed field
We use a regression-based reconstruction technique for rebuilding the MISO/MJO filtered field. The leading pair of PCs are utilised to regress any variable to be reconstructed at every grid location. We regress the principal components (PCs) time series of MISO and MJO separately with a pool of past data of the required variables during the JJAS season. This way, we obtain the regression coefficients during the JJAS season for any particular variable. These coefficients are then used for reconstructing any specific field (X) as follows: where b0, b1 and b2 are the regression coefficients during the JJAS season, and PC1 and PC2 are the pair of leading PCs of MISO/MJO. In Fig. 7, we show the regression-based reconstructed rainfall anomalies (mm/day) for eight phases of MISO (Fig. 7a) and MJO (Fig. 7b). Phase composite of the reconstructed rainfall looks more robust and organised compared to the unfiltered composite. For MISO, the composite structure for phases 6-8 and 1 looks like break composite, and that of phases 2-5 looks like active composite. For MJO, the composite for phases 1-2 and 8 seems like a break, and for phases 3-6 resembles an active composite. The northward propagation of the rain band is very prominent. The magnitude of the MISO reconstructed field is much more robust compared to the MJO reconstructed field. Figure 8 displays the Hovmoller plot (averaged over 65-90°E) of reconstructed rainfall for MISO (Fig. 8a) and MJO (Fig. 8b). Phases are repeated for the ease of visualisation, like Fig. 4. Figure 8 shows the relatively intense and organised northward propagation in the reconstructed field compared to the unfiltered field (refer to Fig. 4).
In Fig. 9, we plot the percentage of variance explained by the MISO reconstructed rainfall, MJO reconstructed rainfall and jointly by both the oscillations with respect to the 20-90-day Lanczos filtered variance. The MISO reconstructed field explains a much better percentage of variance and spatial extend compared to the MJO reconstructed field.

MJO and MISO during long active and break phase
The active and break spells of relatively shorter duration (< 7 days) might be more related to synoptic-scale than the intraseasonal scale. Therefore, from the identified active and break spells (Table 1), we selected the spells with a minimum duration of 7 days or more. We call them as long active or long break spells. We got eight (fourteen) such long active (break) spells during the study period. We have plotted MISO and MJO PCs in the phase space for that long active and long break spells; the same is shown in Fig. 10 (1) X(x, y, yr, t) = b0(x, y, t) + b1(x, y, t) * PC1(yr, t) + b2(x, y, t) * PC2(yr, t)  Fig. 11, respectively. It is clear from Fig. 10 that long active may occur when both MISO and MJO are strong, or either one of them is strong and associated signals are mainly somewhere in between phases 2 and 5. Figure 11 indicates that the long break may occur when either one or both of them are weak; otherwise, even though associated signals are strong, they are primarily located in phases 1, 6, 7 and 8.

Summary and conclusions
In the current study, we analyse the relationship of active/break spells of the Indian summer monsoon with the phases of MISO and MJO. A strong relationship between active and break spells with the MISO phases is evident (Fig. 1). The active (break) days mainly occur during MISO phases 2-5 (6-8), whereas the frequency of active (break) days is high during MJO phases 3-6 (6-8 and 1). However, the relationship between active and break days with the MJO phase is not quite prominent. The MISO phase composite structure for unfiltered rainfall during phases 2-5 shows systematic northward propagation (as we move from phase 2 towards phase 5) and resembles the canonical structure of active monsoon condition, and phases 6-8 resembles with break monsoon condition (Fig. 3a). The MJO phase composite structure for unfiltered rainfall during phases 3-5 looks like the canonical structure of active monsoon condition, and during phases 6-8, active to break transition happens and phase 1 composite looks like break monsoon condition. Hovmoller plot of unfiltered rainfall for MISO and MJO phases shows northward propagation; however, the signal is much strong for MISO compared to MJO (Fig. 4) MISO and MJO phase composite for unfiltered low-level circulation and convection anomalies are also consistent with the above findings, except there is a lag compared to the rainfall phase composite. The MISO and MJO phase composite of the regression-based reconstructed field also show similar features like unfiltered fields, but the signal is well organised. Spatial extent and percentage variance explained by MISO reconstructed rainfall with respect to 20-90-day filtered rainfall is much more compared to MJO reconstructed rainfall (Fig. 9). It is found that a long active (> 7 days) mainly occurs when both MISO and MJO are active or at least one of them is active, and the associated signal is somewhere in between phases 2 and 5 (Fig. 10).
On the other hand, a long break occurs when either one or both of them (MISO and MJO) are weak; even though associated signals are strong, they are primarily located in phases 1, 6, 7 and 8 (Fig. 11).