1 Introduction

The Asian summer monsoon is a regular phenomenon, which brings heavy rainfall to India during the months of June through September. The summer monsoon is the lifeline for the agrarian economy of not only India but for its neighboring continent and a delayed or weak monsoon can have disastrous consequences on productivity of the crops (Swaminathan 1987). There are two main features of the summer monsoon namely intraseasonal and interannual variability and it shows pronounced variability on both these time scales. Although year-to-year variation of all India rainfall is about 10 % of its seasonal mean, the significant variability on various time scales like intraseasonal, interannual, and interdecadal affects the Indian economy and is a matter of great concern not only for the scientific community but also for the policy makers. The India meteorological department (IMD) has been providing forecasts of seasonal mean rainfall using statistical prediction method for more than 100 years (Rajeevan 2001) but these forecasts are found to be unsatisfactory with no improvement in the forecast skill over eight decades (Gadgil et al. 2005; DelSole and Shukla 2012).

The intraseasonal scale is characterized by wet (active) and dry (break) phases within a season (Goswami et al. 2006; Hoyos and Webster 2007), which also have a large agricultural impact. The intraseasonal variability of rainfall is commonly associated with an irregularly propagating large-scale Intraseasonal Oscillation (ISO) with a period of 30–60 days (Ramamurthy 1969; Yasunari 1979; Yasunari 1980; Sikka and Gadgil 1980; Lau and Chan 1986; Hartman and Michelson 1989; Krishnamurthy and Kinter 2003) which also modulate the onset and withdrawal of monsoon over India (Gadgil 2003). The observational studies by Krishnamurthy and Shukla (2007, 2008) and Krishnamurthy and Kirtman (2009) have indicated that the rainfall anomalies associated with the South Asian summer monsoon consist of two intraseasonal oscillatory modes with periods around 45 and 28 days and two non-oscillatory components which are related to El Niño–Southern oscillation (ENSO) and Indian Ocean dipole (IOD). The observed variability of Asian summer monsoon on the interannual time scale is strongly related with ENSO (Shukla and Paolino 1983; Webster and Yang 1992; Webster et al. 1998). Moreover, it has been claimed that this relationship have weakened in recent decades (Torrence and Webster 1999; Kumar et al. 1999) but this appears to have weakened due to sampling variability (DelSole and Shukla 2012).

The atmospheric general circulation models (AGCMs) has been used to simulate and predict the South Asian summer monsoon (Sumi et al. 2005; Kang and Shukla 2006) but its performance over monsoon region is not appropriate (Sperber and Palmer 1996; Gadgil and Sajani 1998; Kang et al. 2002, 2004; Wang et al. 2004; Kumar et al. 2005). It has been established during the recent years that the coupled general circulation models (CGCMs) that include ocean–atmosphere interactions are better in simulating the South Asian summer monsoon (Wang et al. 2005; Kumar et al. 2005). Sharmila et al. (2013) and Sahai et al. (2013) have established that the representation of monsoon intraseasonal oscillations in CGCM is more reasonable as compared to AGCM due to the more realistic local sea surface temperature (SST)–rainfall lead–lag relationship in CGCM. The major modeling centers of the world use the coupled models for their national seasonal forecasting system, e.g., European Centre for medium range weather forecasting (ECMWF) of the United Kingdom (UK) and the national centers of environmental prediction (NCEP) of the United States. India has also started to provide extended and long-range prediction of monsoon on experimental basis.

The first version of the NCEP CFSv1 (Saha et al. 2006) was run operationally from 2004 to 2011 which was further upgraded and version 2 of CFS (CFSv2 hereafter) was made operational in March 2011 (Saha et al. 2014). The prediction of space–time structure of intraseasonal variability of the South Asian summer monsoon rainfall in the NCEP CFSv1 was not obvious; however, oscillations were found in analogous with observation with respect to its space–time structure but with higher time period (Achuthavarier and Krishnamurthy 2011a). The dependence of non-oscillatory component on ENSO has also been obtained in accordance with observation but ENSO and IOD variability occurs in conjunction with each other in the CFS while in observations the dipole variability is somewhat independent of that of the ENSO in certain years (Achuthavarier and Krishnamurthy 2011a).

Recently, CFSv2 has been extensively used by India for operational long-range prediction (Abhilash et al. 2013) and reliable prediction was obtained (Sharmila et al. 2013). It has been found that the CFSv2 is able to reproduce SST–precipitation relationship, northward propagation and spectral characteristics of intraseasonal oscillation due to better representation of air-sea coupling (Roxy et al. 2013; Saha et al. 2014; Sahai et al. 2013; Sharmila et al. 2013).

In the present work, we have tried to investigate the space–time structures of the dominant modes of intraseasonal variability of the monsoon rainfall in CFSv2. The method of investigation in the present study is similar to a previous work done by Achuthavarier and Krishnamurthy (2011a) and is in line with the observational studies done by Krishnamurthy and Shukla (2007, 2008). We have also investigated the ability of CFSv2 to simulate the observed relationship of intraseasonal and non-oscillatory component with the SST of Indian and Pacific Ocean.

The model, data, and method used in the present work are described in Sect. 2. The dominant modes of monsoon variability and their spectra are presented in Sect. 3. Phase composites and the propagation of the oscillatory modes were described in Sect. 4. The prediction of observed relationship of Indian and Pacific Ocean SST and monsoon has been described in Sect. 5 and the summary and conclusions are given in Sect. 6.

2 Model, data, and methodology

2.1 Model

The NCEP has developed the CFSv2 fully coupled land–atmosphere–ocean model (Saha et al. 2014). This model was used by Indian Institute of Tropical Meteorology (IITM), Pune, India for operational extended range monsoon forecasting under ‘National Monsoon Mission (NMM)’ (Saha et al. 2014; Abhilash et al. 2013). The atmospheric component of the model is NCEP global forecast system (GFS) at T126 resolution (approximately 100 km) with 64 vertical levels. The ocean component is modular ocean model version 4p0d (Griffies et al. 2004) of Geophysical fluid dynamics laboratory (GFDL) at 1.0° × 1.0° grid spacing with 40 vertical layers having 27 layers in the upper 400 m with a maximum depth of approximately 4.5 km. The atmosphere and ocean models are coupled with no flux adjustment.

2.2 Data

NCEP CFSv2 runs with the initial conditions on 31st May, 30th June, 30th July, 29th August, and 28th September having 11 ensemble members and each run gives forecast for 45 days (Abhilash et al. 2013). In the present study, we have taken the first 30 days data from each forecast of 45 days from first four initial conditions and the dataset for 45 days from 5th initial condition. In this way, we get the daily continuous rainfall data from 1st June to 12th November for 13 years during 2001 to 2013. The observed precipitation data during 2001–2013 on a daily time scale from global precipitation climatology project one-degree daily precipitation observed rainfall dataset (GPCP) version 1.2 for verification (Huffman et al. 2001) was taken. We propose to study the space–time structure of oscillatory modes and northeastward propagation of convection happens towards Indian subcontinent from equatorial Indian Ocean. This study requires the observational dataset of precipitation over the Indian Ocean also so we preferred GPCP observation as compared to IMD gridded dataset which is available only at the land points of India. The SST data during the time domain discussed above on a daily time scale has been taken from tropical rainfall measurement mission (TRMM) microwave imager (TMI) version 4 (Wentz et al. 2000) for the identification of relationship between the SST and intraseasonal and seasonally persisting modes.

2.3 Methodology (MSSA)

The space–time structure of the daily modes for summer monsoon rainfall is obtained by applying the MSSA. MSSA is similar to singular-spectrum analysis (SSA) but for multivariate time series. This method is analogous to the empirical orthogonal function (EOF) and extended EOF (EEOF). The EOF gives the spatial patterns of maximum variance and their temporal behavior, whereas MSSA provides information about the propagation of these patterns as well. MSSA extracts the space–time structure of oscillatory modes and persisting modes and has been applied to study the intraseasonal variability in the climate physics (Krishnamurthy and Shukla 2007, 2008; Plaut and Vautard 1994). This method has been applied to identify and categorize the spatio-temporal structure of the intraseasonal oscillations of precipitation in China (Wang et al. 1996), North America (Ye and Cho 2001), and India (Krishnamurthy and Shukla 2007, 2008). The readers are advised to refer Plaut and Vautard (1994) and Ghil et al. (2002) and related references therein for the detailed description of MSSA.

MSSA is applied to the original dataset containing L channels (or grid points) specified at an N discrete time. The analysis involves constructing a lag-covariance matrix by choosing a certain lag window of length M for each L spatial point and a lag window length of 61 days was taken in present work. The trajectory matrix of order (LM, N − M + 1) was formed by arranging all spatial points for lag-covariance matrix. We have performed eigen analysis which yields LM eigenvalues and LM eigenvectors. The eigenvector is the space–time EOF (ST-EOF), which consists of an M sequence of spatial maps. The corresponding space–time principal components (ST-PCs), of time length N − M + 1, are obtained by projecting the data onto the corresponding ST-EOF, and the variance is determined by the eigenvalues. The part of the original time series corresponding to the each eigenmode can be reconstructed by combining the ST-PC and its respective ST-EOF in a least square sense, and referred to as reconstructed component (RC) (Ghil et al. 2002). RCs are mapped on the same spatial grid (or multi-channel) as the original field, and their time length and sequence is exactly same as the original time series. The pair of eigenmodes represents the oscillatory pair, and the amplitude A(t) and the phase angle θ(t) of the oscillation can be determined from the RC by the method provided by Moron et al. (1998).

3 Dominant daily modes

We have applied MSSA on daily anomalies of rainfall over the South Asian monsoon region (40°E–160°E, 30°S–35°N) for the period of 2001–2013 with a lag window of 61 days for June–July–August–September (JJAS) season. We have considered only the ensemble mean of the model output in the present work. This method allows the decomposition of the total variability into nonlinear oscillations, persisting signals, and trends. We can also study their space–time structures on a daily time scale basis. The percentage of variance explained by the 30 leading modes obtained from the MSSA analysis are plotted in Fig. 1a for model and Fig. 1b for observation. The maximum variance explained by the model and observation is 2.1 and 1.5 %, respectively. However, the first seven eigenmodes together explains 10.6 and 7.4 % of the total variance for model and observation, respectively. The comparatively less value of the variance explained is due to the fact that we are using daily unfiltered data which have higher variability. The power spectra of the principal components (PCs) of the dominant eigenmodes were also computed and are shown in Fig. 1c for model and Fig. 1d for observation. The modes (1, 2) from observation and (2, 3) from model may constitute oscillatory signals with broad spectra centered around 45 and 50 days, respectively. These oscillatory modes show rainfall patterns over India in depicting the active and break phases. The earlier work by Achuthavarier and Krishnamurthy (2011a) has identified three intraseasonal oscillations with periods around 106, 57, and 30 days from the earlier version of the model (CFSv1). Furthermore, identification of these modes was not obvious in the model used in the previous study and some of the modes were identified by filtering the dataset. It is pertinent to mention that the data of the model set-up which we analyzed in the present work was used by the Indian Government for operational extended range monsoon forecasting under ‘National Monsoon Mission (NMM)’ on experimental basis. The improvement in the space–time structure of the intraseasonal oscillation will certainly improve the dynamical monsoon prediction for India. The fifth mode of model and third mode of observation are non-oscillatory modes within the 61 days lag window. These non-oscillatory modes to be a seasonally persistent mode may be related to externally forced boundary forcing like ENSO and IOD, and it will be analyzed in the later sections.

Fig. 1
figure 1

MSSA of daily rainfall anomaly for 13 years. Eigenvalue spectrum with the first 30 eigenvalues plotted as percentage of the total variance, for a model (ensemble mean), b observation. The Power spectra of the ST-PCs of c eigenmodes 5 (blue), 2 and 3 (red) of MSSA analysis for model and d eigenmodes 3 (blue), 1 and 2 (red) of observation

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4 Phase composites of the oscillatory modes

The space–time propagation characteristics of the oscillatory modes will be discussed in this section. The original time series corresponding to a particular eigenmode is reconstructed from the corresponding ST-EOF and ST-PC and called as reconstructed component (RC) (Ghil et al. 2002). The RC of the oscillatory modes is the sum of the RCs of the individual eigenmodes of the pair and denoted as RC (i, j). In the present case, the RCs of 45 and 50 days oscillations in observation and model are R (1, 2) and R (2, 3), respectively. The space–time structure of the oscillatory modes is described using a phase composite which is obtained by averaging the sum of the RCs in 8 equal intervals having 45° apart. This decomposition of the original time series in terms of RCs will help in understanding the space–time structure of each eigenmode.

The phase composites of the 50- and 45-days mode have been shown in Figs. 2 and 3, respectively. The space–time structure of 50- and 45-days mode shows the precipitation anomalies over the Arabian Sea extending towards the western Pacific in all the phases but the maximum precipitation anomaly is seen in phases 2 and 6 which may be considered as peak active and break phase, respectively. The precipitation anomaly over the Indian Ocean and Bay of Bengal were seen in 45- and 50-days mode in all the phases but the maximum values of precipitation anomaly are seen in phases 2 and 6 in the oscillatory modes of model and observation both. The structure and value of precipitation anomaly over the land points of India and adjoining Western Ghat region is higher in 45-days mode corresponding to observation as compared to model in all the phases. Three centers of maxima of the precipitation anomalies are seen across the latitudinal belt 5°N–25°N during the mature phase in the observation which is simulated by the model also. The space–time structure of 106 days mode in the model of the earlier work (Achuthavarier and Krishnamurthy 2011a) was close to observation but the time period was higher as compared to observation. The improvement in the space–time structure of phase composite of the oscillatory mode in the model-produced precipitation is observed in CFSv2 as compared to CFSv1.

Fig. 2
figure 2

Phase composites of the 50-days oscillatory mode. Units are in mm days−1

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Fig. 3
figure 3

Phase composites of the 45-days oscillatory mode. Units are in mm days−1

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The robustness to predict intraseasonal oscillation is examined by plotting the corresponding RCs of oscillatory modes averaged over (60°E–140°E, 0°–35°N) with the total rainfall anomalies for the first 12 years of the simulation and is shown in Fig. 4. It is clear from Fig. 4 by comparing the total anomaly with RC (1, 2) of the observation that the MSSA is able to decompose the oscillation pattern correctly. The model is able to predict the oscillations correctly and in phase as compared to observation in the year 2004 and 2008, whereas it is out of phase in the year 2002 and 2009. The phases of the corresponding RCs of model and observations are shifted for the 7 out of 12 years. The averaged precipitation anomalies over the land points of India from the corresponding RCs of oscillatory mode from model and observation has been compared and the amplitude is underestimated from the model (Fig. not shown).

Fig. 4
figure 4

Rainfall averaged over the region 60°E–140°E, 0°–35°N for total daily anomalies for observation (black, left y axis scale), green represent the 45-day oscillatory modes for observation and red represent the 50-day oscillatory modes for model (right y axis scale) for the first 12 years. Simulation year is noted at the top right corner. Units are in mm days−1

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4.1 Propagation of the oscillatory modes

The propagation in the east and north direction of these oscillatory modes thus obtained is examined by averaging the RCs over two latitudinal and longitudinal belts and plotted against phase angle. The RCs are averaged across the two latitude belts of 10°N–25°N and 5°S–10°N for the corresponding oscillatory modes of model and observation and shown in Fig. 5. The propagation signals are not clear in the latitude belt of 10°N–25°N from the observation as well as model (Fig. 5a, c). However, the eastward propagation of the oscillatory modes in Indian and Pacific Ocean is clearly seen in observation and model captured it correctly (Fig. 5b, d). The latitude-phase cross sections of the oscillatory modes obtained from observation and model are plotted by averaging the corresponding RCs across the two longitude belts of 100°E–160°E and 60°E–100°E and are shown in Fig. 6a, b for observation and in Fig. 6c, d for model. The southward propagation to the south of equator and northward propagation to the north of equator in the longitude belt of 60°E–100°E which includes Indian Ocean and Indian subcontinent is simulated by the model (Fig. 6b, d). In the western Pacific Ocean region, northward propagation in the latitude belt of 5°S–15°N is observed from observation and is well simulated by the model (Fig. 6a, c). However, the time scale of 57 days mode which was observed in CFSv1 was close to observation but eastward prorogation of this mode was poor in the model (Achuthavarier and Krishnamurthy 2011a). This study strengthen the argument that CFSv2 simulates the northward propagating characteristic correctly (Sahai et al. 2013; Sharmila et al. 2013) and it is much better than that of CFSv1 (Seo et al. 2007; Achuthavarier and Krishnamurthy 2011a, b).

Fig. 5
figure 5

The longitude-phase cross sections of the 45- and 50-days mode by averaging its RCs across the latitudes 10°N–25°N and 5°S–10°N for observation (a, b) and model (c, d), respectively. Y axis panels represent the phase angles for a complete oscillation. Units are in mm days−1

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Fig. 6
figure 6

The latitude-phase cross sections of the 45- and 50-days mode by averaging its RC across the latitudes 100°E–160°E and 60°E–100°E for observation (a, b) and model (c, d), respectively. X axis panels represent phase angles for a complete oscillation. Units are in mm days−1

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4.2 Relation with SST

In this section, the relationship between the intraseasonal modes of the South Asian monsoon and SST are described. It is obtained by computing the daily point correlation between the RCs corresponding to oscillatory mode averaged over the Extended Indian monsoon region (EIMR) (70°E–110°E, 10°N–30°N) (Goswami et al. 1999) and the daily SST anomalies during the JJAS season for the 13 years. The Correlation values significant above 90 % confidence level are shown. The slight significant correlation in the Indian Ocean and Indonesian region is obtained from the model (Fig. 7a) as well as observation (Fig. 7b) with opposite sign which may be due to phase lag in the oscillatory pattern. However, the oscillatory modes seem to be independent of the SST in the Pacific Ocean.

Fig. 7
figure 7

Daily point correlation between the daily anomalies of SST and EIMR index of the RCs of the a 50-day, and b 45-day oscillatory modes in the JJAS season for 13 years of the simulation. The correlation values above 90 % confidence level are shown

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5 Persistent modes and its relationship with SST

Some of the eigenmodes obtained from the MSSA computation were identified as seasonally persisting modes and they may be related with ENSO and IOD. It is evident from Fig. 1c, d that the mode 5 of the model and mode 3 of the observation may be considered as non-oscillatory or seasonally persisting modes. The behavior of these modes and their dependency with the Indian and Pacific Ocean will be addressed below.

We have computed two time series by taking area-average precipitation over the EIMR region for the RC5 of the model and RC3 of the observation. The point correlation between these time series and the daily SST anomalies during the JJAS season were computed and shown in Fig. 8. The correlation coefficient above 90 % confidence level is shaded. The negative correlation observed in the central equatorial Pacific Ocean between 160°E and 150°W is reflected in RC5 and it is in agreement with the observation. The negative correlation in the Pacific Ocean extending from 30°S to 30°N in a parabolic shape is observed in the model which was absent in the observation. We further extended our study and computed the EOF of the RC3 of observation and RC5 of the model. The first mode of EOF explains a variance of 82.0 and 72.9 %, respectively for the RC3 of observation and RC5 of the model. We have computed the pointwise correlation coefficient between PC of first mode of EOF analysis with the observed daily SST anomalies during the JJAS season. The correlation pattern which we have observed (Fig. not shown) is similar to the correlation pattern observed in Fig. 8 with slight variation at few places.

Fig. 8
figure 8

Daily point correlation between SST anomalies and EIMR index of a mode 5 for Model, and b mode 3 for observation in the JJAS season for 13 years. The correlation values above the 90 % confidence level are shown

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6 Summary and conclusions

In the present work, we have applied the multichannel singular spectrum analysis (MSSA) which extracts the space–time structure of oscillatory modes and persisting modes and has been applied in many of the previous studies related to study of intraseasonal variability in the climate physics. We did the study from the latest version of the model i.e., NCEP CFS version 2 (CFSv2). We applied the MSSA on daily unfiltered data with lag window of 61 days for the June–July–August–September (JJAS) season in the present work and intraseasonal oscillation having period around 50 days was obtained from the model, which is close to observed period of 45 days. The space–time structure of the oscillatory modes identified by the model is in agreement with that of the observation except slight variation at few places. There is significant improvement in the space–time structure, period of oscillation, and propagation of oscillatory modes in the present version of the model as compared to the previous version of the model (Achuthavarier and Krishnamurthy 2011a, b). Further, it is pertinent to mention that the data of the model set-up which we analyzed in present work was used by the Government of India for operational extended range monsoon forecasting under NMM on experimental basis. These forecasts were used for providing National Agromet advisory bulletins (http://www.imdagrimet.gov.in). The improvement will certainly enhance our capability related to extended range dynamical prediction of monsoon in the context of India.

The yearwise intraseasonal variability obtained by MSSA has been compared with respect to observation for JJAS season, and it is observed that the model is able to predict the variability for some years, whereas a phase shift between model and observation is observed in few years.

The relationship of oscillatory and persistent mode with the Indian and Pacific Ocean was also done in the present study. The significant relationship of Pacific Ocean SST with the oscillatory mode was not observed in the time domain of our study which is in conformity of the earlier work (Achuthavarier and Krishnamurthy 2011a). However, a slight indication of significant correlation between EIMR of oscillatory mode and the SST in the Arabian Sea, Bay of Bengal, and Indonesian region was observed which will be further investigated. The prediction of the observed relationship between the Indian summer monsoon and the SST of Indian and Pacific Ocean has been investigated. It was found that the model is able to predict the observed ENSO–monsoon relationship from the persisting mode which was found in the earlier version of the model (Achuthavarier and Krishnamurthy 2011a) and observation. The significant negative correlation between EIMR index of persisting mode of the model and observed SST throughout the latitudinal belt of 30°S to 30°N in the Pacific Ocean was observed, but it was absent in the observation. The Indian Ocean SST and the persisting mode of observation and model show some significant correlation in the South Indian Ocean also which seems interesting and will be further investigated.