1 Introduction

The intraseasonal oscillation is one of the dominant modes of variability of the tropical atmosphere–ocean system. It exhibits substantial seasonality in propagation, amplitude and spatio-temporal characteristics (Zhang and Dong 2004; Kikuchi et al. 2012). While the eastward propagating Madden-Julian oscillation (MJO, Madden and Julian 1971, 1972, 1994) dominates in boreal winter, it considerably weakens in boreal summer. Unlike boreal winter, the boreal summer intraseasonal oscillation (BSISO) exhibits a pronounced northward propagation over Indian summer monsoon (ISM) region with a periodicity of 30–60 days (Goswami 2011 and reference therein). In addition to the eastward and northward propagating modes, the off-equatorial westward and northwestward propagations are also evident over the Indian Ocean (IO) and western Pacific (WP) region (Murakami 1980; Lau and Chan 1986; Wang and Xu 1997). The similarity in the temporal scales of eastward and northward propagating modes may indicate the coherent characteristics of these two components of BSISO (Lau and Chan 1986; Madden and Julian 1994). Observational evidences suggest that about 78 % northward propagating modes are linked with the eastward propagating equatorial convection (Wang and Rui 1990; Lawrence and Webster 2002). Nevertheless, the quasi-periodic northward propagation, one of the principal features of the BSISO, is considered to be associated with active/break cycle of the ISM (Goswami 2011 and reference therein) and thus has received considerable attention in last few decades. However, the inherent complexity of the BSISO makes it a challenging issue for the climate modeling community (Demott et al. 2011; Jiang et al. 2011).

A series of theories have been proposed towards understanding the complex characteristics of BSISO, including convection-thermal relaxation (Goswami and Shukla 1984), unstable Rossby wave response from eastward propagating equatorial wave packets (Lau and Peng 1990; Wang and Xie 1997), vertical wind-shear mechanism and moisture convection feedback (Jiang et al. 2004), air-sea interaction (Fu and Wang 2004), convective feedback (Jiang et al. 2011; Abhik et al. 2013). Despite these attempts in understanding of BSISO, the ability of the current general circulation models (GCMs) to simulate the realistic spatio-temporal structure of BSISO remains limited (Waliser et al. 2003; Kim et al. 2008; Sperber and Annamalai 2008). The prediction skill of current GCMs is limited only up to 2–3 pentads, while the potential predictability of the BSISO is about 25–30 days (Waliser 2011). Kang et al. (2002) and Waliser et al. (2003) showed that atmospheric GCMs (AGCMs) could simulate weak intraseasonal variability but mostly failed to capture the eastward propagating mode and tilted rain band structure. Although it is argued that the internal dynamics is crucial for realistic representation of BSISO (Seo et al. 2005; Ajayamohan et al. 2011; Abhik et al. 2014), many recent studies have suggested that atmosphere–ocean coupling is essential for better representation of the BSISO characteristics (Krishnamurti et al. 1988; Fu et al. 2003; Wang et al. 2009). Analyzing 14 ocean–atmosphere coupled GCMs (CGCM) participated in the Fourth Assessment Report (AR4) of Intergovernmental Panel on Climate Change (IPCC), Lin et al. (2008) indicated that most of the models overestimate the near-equatorial precipitation and underestimate the variability of northward propagating BSISO and westward propagating 12–24-day mode. One of the chief difficulties to simulate realistic BSISO is the inadequate simulation of eastward propagating convection across the Maritime Continent that causes unusual tilting of the rain-band in present CGCMs (Sperber and Annamalai 2008; Demott et al. 2011). However, the simulation of BSISO is found to be improved with the implementation of air-sea interaction and the explicit representation of the convective processes in the models (Demott et al. 2011; Goswami et al. 2013).

In recent times, the National Centers for Environmental Prediction (NCEP) coupled Climate Forecast System (CFS) has showed an improved representation of northward propagating BSISO (Sharmila et al. 2013, hereafter S13). But the model at T126 resolution exhibits significant dry (wet) bias over the Indian subcontinent (ocean). Goswami et al. (2014; hereafter G14) further analyzed the same coarse resolution of CFS and indicated that the limitation of subgrid scale processes could be responsible for the model inadequacy. They argued that the improper interaction between large-scale circulation and subgrid-scale processes might lead to underestimation of the high frequency modes of BSISO in CFS T126. Despite the limitations in simulating realistic BSISO modes, CFS T126 shows some skills in simulating the salient features of the BSISO (S13, G14). Both the atmosphere-only and coupled versions of the model are being used operationally at NCEP since 2004 (Saha et al. 2006, 2010) and recently the latest version (version 2) of CFS (CFSv2, Saha et al. 2014) is implemented for the dynamical ISM prediction under the National Monsoon Mission, Ministry of Earth Sciences (MoES), Govt. of India. The high resolution (T382) of CFSv2 (CFS T382) is presently being used for dynamical seasonal and extended range monsoon prediction (Sahai et al. 2014; Joseph et al. 2015). However, the identification of systematic biases of the CFS T382 is yet to be evaluated. Therefore, the identification of the systematic biases in CFS T382 would be the first-step towards further development of the model to improve its fidelity in operational forecast.

Keeping these in background, the present study attempts to examine the simulation of BSISO in CFS T382 and identifies the biases in reproducing the observed BSISO characteristics. Recent studies (e.g. Kinter et al. 2013; Sahai et al. 2014; Joseph et al. 2015) indicated that the forecast skill of GCMs enhances with increase in horizontal resolution. It remains in question whether CFS T382 can resolve the earlier reported (e.g. S13, G14) biases in relatively coarser resolution of CFS (CFS T126). Moreover, the systematic biases present in CFS T382 are thoroughly evaluated and their possible sources are also identified in this study. The model details and the dataset used for validation of the simulation are described in Sect. 2. In Sect. 3, the results obtained by analyzing the simulation are discussed. The major conclusions and important findings of the study are summarized in Sect. 4.

2 Model details, datasets and methodology

The CFSv2 is the latest version of NCEP’s fully coupled ocean–land–atmosphere modeling system (Saha et al. 2014) combined with the atmospheric component NCEP Global Forecast System (GFS) AGCM (Moorthi et al. 2001) and the ocean component Modular Ocean Model version 4 (MOM4P0) (Griffies et al. 2004). In this study, the simulation is performed using spectral triangular truncation of 382 waves (T382) for the atmosphere (equivalent to about 38-km grid spacing) with 64 sigma-pressure hybrid vertical layers. The details of the model physics and schemes are available in Saha et al. (2014 and references therein). The ocean model MOM4P0 from the Geophysical Fluid Dynamics Laboratory (GFDL) has horizontal resolution of 0.25° × 0.25° between 10°S and 10°N and 0.5° × 0.5° resolution elsewhere. The coupled model is integrated for 20 years using 2 February 1999 initial condition but only last 15 years of simulation is analyzed in the present study.

The Tropical Rainfall Measuring Mission (TRMM) 3B42 rainfall observations (Huffman et al. 2007) during boreal summer (June to September, JJAS) from 1998 to 2010 based on multi-satellite and rain-gauge analysis are used to validate the simulation. This dataset provides 3 hourly gridded precipitation estimates at 0.25° × 0.25° spatial resolutions over the global tropics (180°W–180°E, 50°S–50°N). Additionally, observed BSISO phases are defined based on extended empirical orthogonal function (EEOF) analysis on Global Precipitation Climatology Project (GPCP) daily rainfall data (Huffman et al. 2001) at 1° × 1° resolution during JJAS from 1998 to 2010. Daily wind and temperature dataset for the same period are derived from 6-hourly analysis of the National Oceanic and Atmospheric Administration (NOAA) Climate Forecast System Reanalysis (CFSR; Saha et al. 2010) dataset and treated as the observation in this study. These dataset have a horizontal resolution of 1° × 1° and are on 37 pressure levels between 1000 and 1 hPa. The Advanced Very High Resolution Radiometer (AVHRR) Outgoing longwave Radiation (OLR) dataset from the NOAA polar orbiting satellite for the period of 1998–2010 is utilized in this study. This daily averaged dataset is processed on to a 2.5° × 2.5° latitude-longitude grid with missing values filled by interpolation (Liebmann and Smith 1996). Additionally, TRMM Microwave Imager (TMI) daily sea surface temperature (SST) at 0.25° × 0.25° resolution (Gentemann et al. 2004) is used for the period of 2000–2010.

The daily anomalies of each meteorological field for both the observed dataset and model output are computed by subtracting the annual cycle (defined by the sum of annual mean and the first three harmonics) of each year. Further, a 20–100-day band-pass filter (Duchon 1979) is applied to extract the BSISO signal. An EEOF analysis is performed on 60.5°–95.5°E averaged GPCP rainfall anomalies over 12.5°S–30.5°N during JJAS following Suhas et al. (2013). The first two principal components (PC1 and PC2) from EEOF analysis are considered to represent the spatio-temporal evolution of observed BSISO. The model dataset are projected onto the observed EEOF to obtain the corresponding PCs. It may be noted that this methodology is operationally being used for real-time monitoring of the intraseasonal variability over the ISM region. Other than the band-pass filter, daily OLR anomalies are filtered in wavenumber-frequency space to retain the signals associated with the Kelvin and n = 1 westward propagating equatorial Rossby (ER) wave (Wheeler and Kiladis 1999). It may be noted that each of the wavenumber-frequency filtered convectively coupled equatorial waves (CCEWs) are either symmetric or anti-symmetric with respect to the equator. In the present study, the Kelvin wave filter spans eastward propagating periods of 2.5–17 days and zonal wavenumbers 1–14, and is bounded by the dispersion curves having equivalent depth of 8 and 90 m. The n = 1 ER filter spans westward propagating periods of 10–45 days and zonal wavenumbers 1–10, and is bounded by the 8 and 90 m ER wave dispersion curves.

3 Results and discussion

3.1 Seasonal mean state

The capability of a model to simulate the realistic intraseasonal variability is intimately associated with its ability to simulate the mean climate (Slingo et al. 1996; Waliser et al. 2003; Yang et al. 2012). In view of such importance, an assessment of the simulated seasonal mean state is provided in this subsection. Figure 1 shows the seasonal (JJAS) mean precipitation (shaded, mm day−1) and SST (contour, °C) for observations (TRMM and TMI respectively, top panel) and CFS T382 (bottom panel). In observation, the summer monsoon precipitation maxima are located over the Western Ghats, along the eastern shore of the Bay of Bengal (BoB) and over the western Pacific, near the Philippines (Fig. 1a). A secondary precipitation maximum is also evident over the EEIO. TMI based seasonal mean SST displays the maxima (~29 °C) over EEIO, head BoB and WP warm pool region (Fig. 1a). Although CFS T382 simulates the locations of the observed precipitation maxima (Fig. 1b) reasonably well, it considerably overestimates (underestimates) the rainfall amount over the oceanic region (Indian landmass). Additionally, the simulated rain-band is zonally oriented and its southern branch is extended up to central Pacific, forming a spurious double Inter Tropical Convergence Zone (ITCZ) over the WP. The rainfall distribution of the present resolution appears to be largely similar to CFS T126, as reported in S13 and G14. However, CFS T382 simulates relatively higher SST signals over the tropical oceans compared to the observation and the SST isotherm at 29 °C is extended up to the eastern Pacific.

Fig. 1
figure 1

Seasonal (June–September) mean precipitation (shaded, mm day−1) and SST (contour, °C) for a observation and b CFS T382 model

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The model biases in the seasonal mean simulation relative to the observation are displayed in Fig. 2. CFS T382 produces positive precipitation bias over the tropical oceans (Fig. 2a), but it exhibits dry biases over the Indian land and the Head BoB. S13 and G14 also identified similar precipitation bias in CFS T126. The cold SST bias and the simulation of weak ascending branch of seasonal Hadley circulation over the Indian latitudes in CFS T126 were argued to be responsible for the dry bias over the Indian region. Interestingly, the dry bias over Indian land appears to be present in CFS T382 also, despite the simulation of warmer SST over the tropical Oceans (Fig. 2b). As a consequence, the horizontal SST gradient over the tropical Pacific and IO is weak in CFS T382. Moreover, a prominent wet bias is also evident over the EEIO and tropical Pacific that might be associated with the local seasonal mean warmer SST and strong anomalous ascending branch of Hadley circulation (Figure not shown) in CFS T382. Consistent with the positive SST bias, the seasonal mean lower level (850 hPa) zonal wind (U850) appears to be weaker in the model relative to the observation (Fig. 2c). The weaker low level easterlies (westerlies) in CFS T382 over the Pacific and southern IO (western IO) could be associated with the weakening of observed horizontal SST gradient over the tropical oceans in the model (Chung and Ramanathan 2006; Ohba and Ueda 2006). In addition to that, CFS T382 simulates weaker vertical easterly shear over the global tropics (Figure not shown). Furthermore, the simulated tropospheric temperature (TT, average atmospheric temperature between 600 and 200 hPa) is examined in Fig. 2d, as TT is one of the important metrics for ISM (Xavier et al. 2007). Interestingly, CFS T382 exhibits warm TT bias over the tropics instead of cold TT bias in CFS T126.

Fig. 2
figure 2

Seasonal mean bias in a precipitation (mm day−1), b SST (°C), c zonal wind at 850 hPa (m s−1) and d tropospheric temperature (TT, K) relative to TRMM, TMI and CFSR

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The performance of CFS T382 in simulating the seasonal mean is summarized in the Taylor diagram (Taylor 2001) (Fig. 3a). It assesses the JJAS mean spatial pattern correlation, root-mean square difference (RMSE) and the simulated to observed ratio of the variances of rainfall, wind, temperature and humidity over broad ISM region (40°–120°E, 15°S–30°N), highlighed by red box in Fig. 3b. In Taylor diagram, the distance from the origin indicates the normalized standard deviation of each variable, while the cosine of the angle swept out by the position vector from the origin indicates the pattern correlation between observed and the simulated variable. The distance from the reference point (marked by solid red dot) to the plotted point denotes the RMSE. The isocircles (grey concentric circles) of RMSE are drawn based on the skill score calculation using normalized standard deviation and the correlation coefficient. An accurately simulated variable that has least RMSE, highest correlation and normalized standard deviation close to the unity, should be placed close to the reference point. Figure 3 indicates that the model reasonably produces the zonal winds (at 850 and 200 hPa, U850 and U200 respectively) over the region. However, as shown in Fig. 2, CFS T382 shows considerably poor skill in simulating precipitation, SST and TT. As a consequence, a scientific question may be posed why the rainfall bias in the model appears to be similar in both the resolutions, even though the SST and TT biases are different in CFS T382 and CFS T126.

Fig. 3
figure 3

a Taylor diagram for CFS T382 model to summarize the relative skill to simulate the mean meteorological fields over broad ISM region (40°–120°E, 15°S–30°N) during JJAS. Red dot denotes the reference point. b The red box represents the area (40°–120°E, 15°S–30°N) over which Taylor diagram is computed and the white boxes show the regions those are used in Fig. 4

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To get further insights into the rainfall bias, the probability distribution function (PDF) of daily rainfall during JJAS periods with a bin width of 5 mm day−1 over four different regions is shown in Fig. 4. These four regions, Central India (CI), BoB, Arabian Sea (AS) and EEIO, are chosen following G14 for direct comparison with CFS T126. These regions are highlighted by white boxes in Fig. 3b. The rain rates are classified into three categories, lighter: <10 mm day−1; moderate: 10–40 mm day−1 and heavy: >40 mm day−1 (Mukhopadhyay et al. 2010; Abhik et al. 2014). It may be argued that the biases in different rainfall categories may eventually contribute to the bias in the daily rainfall. In CFS T382, the lighter rain rate is found to be overestimated and moderate and high rain rates are underestimated over all four regions relative to the observation. This bias appears to be associated with the model’s inability to represent adequate amount of deep convection in CFS T382, consistent with the results of Ganai et al. (2014). It may be noted that G14 also reported the simulation of shallow diabatic heating profile and overestimation of lighter rainfall in CFS T126. However, compared to its lower resolution version, CFS T382 shows some improvements in simulating lighter rain rate over these four regions.

Fig. 4
figure 4

Probability distribution function (PDF) of daily rainfall (mm day−1) during all JJAS seasons with a bin width of 5 mm day−1 in percentage over a central India (CI), b Bay of Bengal (BoB), c Arabian Sea (AS) and eastern equatorial Indian Ocean (EEIO). The regions are marked by white boxes in Fig. 3b

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3.2 Boreal summer intraseasonal variability

The fidelity of the model in simulating the boreal summer intraseasonal variability is examined in this section. The assessment of the simulated BSISO begins with an evaluation of the wavenumber-frequency analysis (Hayashi 1982; Teng and Wang 2003) in meridional direction over Indian region (65°–95°E, 15°S–30°N) (Fig. 5). This analysis provides a qualitative estimation of the northward propagating modes, the dominant component of the BSISO. The spectra are calculated using Fourier transformation of 184-day segments centered on boreal summer, and then averaging over all the boreal summer seasons. The seasonal cycle is removed from precipitation and U850 dataset before computing the spectra. The dominant spectral peak in observed precipitation and U850 is evident at wavenumber 1 with 45–50-day periodicity (Fig. 5a). These scales distinguish the low-frequency northward propagating BSISO mode from other high-frequency convective disturbances. In CFS T382, the power of the northward propagating BSISO mode is overestimated and the peak is slightly shifted towards the lower frequencies, around 60 days (Fig. 5b). It may be noted that CFS T126 also exhibits similar meridional spectra (S13, G14). However, unlike most of the current GCMs (Kim et al. 2009), both precipitation and U850 show similar spectral characteristics in CFS T382. This feature indicates the coherent characteristics between the simulated wind and precipitation at intraseasonal timescales, at least over the ISM domain.

Fig. 5
figure 5

Meridional wavenumber-frequency spectra during boreal summer over 15°S–30°N using precipitation (shaded, mm2 day−2) and U850 (contour, m2 s−2) data averaged between 60° and 95°E for a TRMM 3B42 and CFSR, b CFS T382

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The intraseasonal variability of simulated precipitation and U850 compared to observation during boreal summer is shown in Fig. 6. The variability of the dataset is estimated by the corresponding standard deviation (SD). The SD of observed rainfall shows the maxima at three different locations over south Asia: Western Ghats, BoB and WP warm pool region (Fig. 6a). Additionally, another secondary maximum associated with the eastward propagation of BSISO is also evident over the EEIO. Both precipitation and U850 variability over the tropics are concentrated in the summer hemisphere. CFS T382 reasonably captures the salient features of observed distribution in both the precipitation and U850 SD (Fig. 6b). However, compared to observations, the model produces excessive intraseasonal variability over the south Asian monsoon domain. Note that, similar overestimation of intraseasonal precipitation variability is also noted in CFS T126 over IO and WP (S13, G14).

Fig. 6
figure 6

Boreal summer (JJAS) 20–100-day filtered precipitation (shaded, mm day−1) and U850 (contour, m s−1) standard deviation for a TRMM 3B42 and CFSR, b CFS T382

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To understand the spatial distribution of the rainfall associated with BSISO, Fig. 7 shows the JJAS composite precipitation anomalies for observation and CFS T382 based on the EEOF analysis (Suhas et al. 2013, see Sect. 2 for details). In observation (Fig. 7a), the enhanced rainfall anomalies first appear over western equatorial IO at phase 1 and slowly propagate eastward. At phase 3, the BSISO signal further intensifies and reaches to the EEIO. It further bifurcates in meridional directions, while another branch continues its eastward progression across the Maritime Continent up to the WP. The southern branch of the convection rapidly decays, but the northern component slowly propagates towards Indian subcontinent. The combination of eastward and northward movement of the BSISO convection results a northwest-southeast tilting structure of rainfall anomalies (phase 4–5), one of the characteristic features of the BSISO. During phase 5–6, the northward propagating enhanced convective anomalies reside over the central India, leads to the “active” spell of the ISM. The enhanced convective signal is further replaced by the suppressed convection in subsequent phases. CFS T382 reasonably reproduces the salient features of the observed BSISO (Fig. 7b). However, amplitude of the simulated BSISO is stronger and the rain-band of the model is zonally oriented rather than tilted. The weak eastward propagation over the WP could eventually affect the zonal orientation of the rain-band in CFS T382.

Fig. 7
figure 7

Composite evolution of 20–100-day filtered anomalous precipitation (shaded, mm day−1) constructed with the PCs of EEOF analysis for a observation and b CFS T382. Number of days in each of eight phases (marked by P1 and so) is indicated at the lower right box of each panel

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To illustrate the spatio-temporal characteristics of eastward and northward propagating BSISO, Fig. 8 shows the lag correlation analysis of 20–100-day filtered precipitation (shaded) and U850 (contour) against a base time series of 20–100-day filtered precipitation averaged over the EEIO (10°S–5°N, 75°–100°E) during boreal summer. The correlation based on such time series implicitly selects the eastward propagating mode of BSISO (top panels, Fig. 8a, b) and the northward propagating BSISO events (bottom panels, Fig. 8c, d) associated with the eastward propagations (CLIVAR Madden-Julian Oscillation Working Group 2009). The observed eastward propagating mode first appears over the western Indian Ocean and propagates eastward across the Maritime Continent up to the WP before decaying near the date line (Fig. 8a). The easterly (westerly) U850 leads (lags) the precipitation anomaly by about 5–7 days and the zonal wind anomaly shows faster eastward propagation after the decay of precipitation anomaly near the date line. CFS T382 simulates slower eastward movement of BSISO convection over the IO and the correlation between the precipitation anomalies and the base time series rapidly decays over the Maritime Continent (Fig. 8b). Surprisingly, the CFS T126 simulates slightly better eastward propagation across the Maritime Continent (Figure not shown) relative to CFS T382. However, the U850 anomalies show prominent eastward movement across the WP in CFS T382. This may indicate the lack of coherence between moist convective processes and internal atmospheric dynamics over WP in the model.

Fig. 8
figure 8

a, b Longitude versus lag correlation and c, d latitude versus lag correlation of 20–100-day filtered precipitation (shaded) and U850 (contour) with base 20–100-day filtered precipitation time series over EEIO (10°S–5°N, 75°–100°E) for observation and CFS T382. For longitude-lag (latitude-lag) plot data are averaged between 70°E and 90°E (10°S and 10°N)

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Similar phase relationship between precipitation and U850 is also observed for the northward propagating mode of BSISO (Fig. 8c). The precipitation anomalies propagate poleward from the equatorial region. The northward moving component appears to be stronger, slower and of longer duration relative to the southward component. Unlike the eastward propagating mode, the northward propagating BSISOs are reasonably well simulated in CFS T382 (Fig. 8d). Interestingly, although the phase speed of the simulated northward propagation is slightly lower than the observation, the amplitude of CFS T382 simulated northward propagation is more realistic compared to CFS T126 (figure not shown). In contrast, the southward propagating signal is considerably underestimated in simulated precipitation anomalies, while the U850 anomalies show some of the southward propagating mode in the model. These results indicate the lack of coherence between simulated moist convection and wind field over southern IO at the intraseasonal timescale. It is noteworthy that the model reasonably simulates this coherency during northward propagation over northern IO.

Similar to Fig. 8, the phase relationship between SST and precipitation is further investigated. Figure 9 shows the lag correlation analysis for 20–100-day filtered precipitation (contour) and SST (shaded) against precipitation time series over EEIO. The SST dataset is only available over the oceanic regions, while both the land and ocean points are considered for precipitation correlation. A coherent relationship between SST and precipitation is evident for observed eastward propagation, especially over the IO (Fig. 9a). The warm SST anomalies lead the positive rainfall anomalies by 7–10 days. However, such coherent phase relationship is not prominent over WP, where the SST anomalies show relatively faster propagation characteristics. The model reasonably captures the SST-rainfall phase relationship over IO, but the correlation rapidly decays across the Maritime Continent (Fig. 9b). CFS T382 simulates excess rainfall and warm SST bias over the WP warm pool region. This does not rule out the possibility that the warm SST and wet bias of the model over WP warm pool region further be amplified through the coupled feedbacks with the barrier layer below shallow mixed layer (Lukas and Lindstrom 1991). Excess convection over the warm pool is likely to play a role in the suppression of the eastward propagation of the BSISO from the IO into the WP warm pool. However, a prominent phase relationship between precipitation and SST is evident both in observation (Fig. 9c) and CFS T382 (Fig. 9d) during northward propagation of BSISO. Notably, this performance of CFS T382 is largely similar to the earlier reported (e.g. S13, Roxy et al. 2013) aspect of CFS T126.

Fig. 9
figure 9

Same as Fig. 8, but for SST (shaded) and precipitation (contour)

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To discuss the discrepancy in the simulated BSISO modes in CFS T382, the percentage precipitation variance accounted for low-frequency intraseasonal (20–100-day) band and high frequency (2–20-day) band relative to total daily variance is shown in Fig. 10. The intraseasonal band strongly modulates the high frequency variability over the IO and WP regions (Straub and Kiladis 2003; Goswami 2011). In observation (Fig. 10a), the intraseasonal variance accounts about 20 % of the total daily variance and it peaks over the Western Ghats, BoB, WP and eastern Pacific. But in CFS T382, the contribution of intraseasonal band exceeds 50 % over the tropical oceans, especially over the IO and WP regions (Fig. 10b). Compared to intraseasonal component, observed high frequency variance explains a significant amount of the total daily observed precipitation variance (Fig. 10c). However, CFS T382 severely underestimates the high frequency variance over the entire tropics, especially over the equatorial IO, WP and Indian land. This possibly indicates inadequate interaction between simulated intraseasonal mode and the high frequency CCEWs in the model. It is worth mentioning that G14 also reported similar disagreement between observation and CFS T126. Although the choice of intraseasonal and high frequency bands in present study slightly differs from G14, the results are largely similar in both the resolutions of the model. To further investigate such bias of the model, the simulated CCEWs in CFS T382 are analyzed in the next subsection.

Fig. 10
figure 10

Percentage of total daily precipitation variance explained by 20–100-day mode (top panels, a, b) and 2–20-day mode (bottom panels, c, d) for observation (a, c) and CFS T382  (b, d)

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3.3 Convectively coupled equatorial waves

The low-frequency BSISO is a large-scale wave envelope of high frequency CCEWs (Nakazawa 1988; Straub and Kiladis 2003). The complex interaction between the planetary-scale convection and the high-frequency waves is crucial for BSISO simulation (Majda and Biello 2004; Demott et al. 2011). Previous studies indicate that the westward propagating n = 1 equatorial Rossby (ER) waves are associated with the northward movement of the BSISO (Wang and Xie 1997; Demott et al. 2011). In addition to that, the westward moving mixed Rossby-gravity (MRG) wave and the tropical depression activity are enhanced during active BSISO convection, while the eastward propagating Kelvin wave activity (super cloud cluster) increases at the leading edge of the BSISO convection (Straub and Kiladis 2003). Details on the interactions between BSISO and CCEWs are available in Straub and Kiladis (2003).

Figure 11 shows the distribution of the equatorially symmetric wavenumber-frequency spectra of observed and simulated OLR dataset during boreal summer following Wheeler and Kiladis (1999). The black solid curves in Fig. 11 represent the shallow water dispersion relationship for equivalent depths of 12, 25 and 50 m respectively. In observation (Fig. 11a), significant spectral peaks are evident for MJO (wavenumber 1–3 and periodicity about 45-day), the Kelvin waves, the westward propagating n = 1 ER waves, n = 1 inertio-gravity (WIG) waves and Tropical Depression (TD) type disturbances. However, the peak around wavenumber 14 and periodicity ~10-day is an artifact of the satellite sampling (Wheeler and Kiladis 1999). In CFS T382, both the MJO and Kelvin wave peaks are weaker (Fig. 11b), while n = 1 ER wave peak appears to be stronger than the observed. Additionally, n = 1 WIG waves and TD-type disturbances are underestimated in the model. However, the simulated dispersion characteristics of the convectively coupled waves agree well with the observation. The underestimation of the high frequency waves is consistent with the result in Fig. 10.

Fig. 11
figure 11

Wavenumber versus frequency distribution of spectral-power divided by estimate background spectra for equatorially symmetric OLR anomalies. Shallow water dispersion relationships for equivalent depths of h = 12, 25, and 50 m are shown for the n = 1 equatorial Rossby, Kelvin, and n = 1 inertio-gravity waves for a observation, b CFS T382

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Figure 12 shows the distribution of boreal summer equatorially anti-symmetric wavenumber-frequency spectra of observed and simulated OLR dataset. Both the westward propagating MRG and eastward propagating n = 0 inertio-gravity (EIG) waves are evident in observation (Fig. 12a). The TD-type disturbances appear as a weaker peak around wavenumber −5 and periodicity of 4-day. Similar to Fig. 11a, same artifact of the data sampling is also present around wavenumber 14. Consistent with the results in Fig. 10, the MRG/EIG waves and TD disturbances are severely underestimated in CFS T382 (Fig. 12b). Only some weak and disorganized peaks are present near the dispersion curves. Earlier, Straub and Kiladis (2003) suggested that the low frequency BSISO convection favours the MRG wave activity over the WP. However, the simulated MRG variance is considerably underestimated in CFS T382. Surprisingly, the anti-symmetric MJO peak appears to be stronger in CFS, indicating the presence of asymmetric heating induced propagation in the model.

Fig. 12
figure 12

Same as Fig. 11, but for equatorially antisymmetric OLR anomalies. Shallow water dispersion relationships for equivalent depths of h = 12, 25, and 50 m are shown for the mixed Rossby-gravity (MRG) and n = 0 eastward inertio-gravity (EIG) waves

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The spatial distributions of Kelvin, n = 1 ER and MRG wave variability during boreal summer for observation and CFS T382 are examined in Fig. 13. The Kelvin wave variance is mostly confined to the equator and the maximum variability is observed over EEIO, extending towards WP (Fig. 13a). Although the simulated Kelvin wave variance maximizes over the EEIO (Fig. 13b), the magnitude is considerably underestimated all over the global tropics and the distribution differs from observation over WP. The observed ER wave distribution is symmetric about the equator, with maximum variance spanning over IO and WP (Fig. 13c). In addition to the equatorial maxima, two off-equatorial maxima over northern and southern IO also appear in the observed OLR variance. The simulated ER variance pattern agrees well with the observation (Fig. 13d), but the magnitude is stronger than that of observation. As reported in earlier studies (e.g. Demott et al. 2011), the excessive ER wave magnitude may influence the northward propagating BSISO in CFS T382.

Fig. 13
figure 13

Distribution of boreal summer time OLR variance (W2 m−4) of a, b Kelvin and c, d n = 1 ER for AVHRR and CFS T382 respectively

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The model underestimates the Kelvin and MRG variance, but the ER wave variance is excessive in CFS T382, as shown in Fig. 13. It is also shown in previous subsection that the model reasonably simulates the northward propagating BSISO, although the eastward propagating mode is underestimated across the Maritime Continent and WP. To address the contribution of the CCEWs on the BSISO propagation, Fig. 14 shows the lag-autocorrelation analysis for observed and simulated longitudinal propagation of Kelvin and ER waves as well as meridional propagation of ER wave. The Kelvin and ER waves are correlated with their own base time series around the equator (2.5°S–2.5°N) and 5°N (2.5°–7.5°N) respectively for longitudinal propagation and likewise ER wave envelope are auto-correlated against base time series at 10°N (7.5°–12.5°N) for latitudinal propagation. In observation, the Kelvin wave shows prominent eastward propagation across the date line (Fig. 14a). The magnitude of the simulated Kelvin wave is relatively weaker and its eastward movement ceases before crossing the date line (Fig. 14b).

Fig. 14
figure 14

a–d Longitude versus lag autocorrelation and e–f latitude versus lag autocorrelation of eastern Indian Ocean Kelvinand n = 1 ER wave filtered OLR anomalies. Base time series are computed as (first column, a, b) Kelvin wave over 75°–85°E and 2.5°S–2.5°N, (second column, c, d) n = 1 ER wave over 75°–85°E and 2.5°–7.5°N, (third column, e, f) n = 1 ER wave over 75°–85°E and 7.5°–12.5°N. For longitude versus lag autocorrelation (latitude vs lag autocorrelation) dataset are averaged between 2.5°S–2.5°N for Kelvin wave and 2.5°–5°N for n = 1 ER wave (75°–85°E). The top panels are for AVHRR and bottom panels are for CFS T382

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Figure 14c shows the westward movement of the observed ER wave at 5°N. CFS T382 reasonably simulates the observed features of the westward propagating ER wave at 5°N, except over the west-central Pacific (Fig. 14d). As suggested in previous studies (e.g. Straub and Kiladis 2003; Demott et al. 2011), the unrealistic distribution of the eastward and westward propagating modes may be, at least partially, responsible for the poor simulation of the eastward propagating BSISO in CFS T382.

The meridional propagation of observed ER wave is shown in Fig. 14e. In observation, ER wave propagates northward from the equator to 20°N. Earlier studies (e.g. Kemball-Cook and Wang 2001; Demott et al. 2011) showed how the observed ER waves promote the northward propagating BSISO over the ISM region. In CFS T382, the simulated ER wave also shows similar northward movement with stronger amplitude and low phase-speed (Fig. 14f). The stronger ER wave may reinforce the northward propagating BSISO in CFS T382. This result partially addresses why the low frequency northward propagation is reasonably simulated in CFS T382, even though other BSISO modes are weak in the model.

4 Summary and conclusions

This study evaluates the fidelity of NCEP CFS T382 in simulating boreal summer mean climate and intraseasonal variability over the south Asia. The assessment of the model is important for detail understanding of the physical processes associated with the tropical atmosphere–ocean coupled system which influences the BSISO characteristics. Earlier studies (e.g. S13, G14) reported the dry bias over the Indian land and cold temperature bias over the tropics in CFS T126. One might wonder whether such biases are resolved or still present in CFS T382. Moreover, identification of CFS T382 biases and its possible sources would provide a guideline for further development of the model. This in turn will benefit the present prediction system.

CFS T382 exhibits certain skill to reproduce the salient features of the observed mean climate and intraseasonal variability during boreal summer. However, the detailed analysis reveals that CFS T382 overestimates the precipitation over the oceanic region, while the precipitation over Indian land points is considerably underestimated in the simulation. Seasonal mean vertical easterly wind-shear, one of the key elements of the internal dynamics, is also weakly simulated in the model. Additionally, the model systematically simulates warmer SST and TT over the global tropics relative to the observation. Earlier studies (e.g. S13, G14) argued that the simulation of colder SST and TT in CFS T126 may be responsible for the dry bias over the Indian land. Unlike the lower resolution of the model, CFS T382 simulates warmer TT and SST over the global tropics. But the dry bias over the Indian land still remains similar to the lower resolution of the model. This study suggests that temperature bias may not only be responsible for the dry bias in precipitation distribution over Indian subcontinent. It may be argued that the precipitation biases could be associated with the large scale atmospheric circulation and associated the convective processes in the model.

Sperber and Annamalai (2008) identified five important BSISO characteristics: (a) eastward propagation over eastern equatorial Indian Ocean (EEIO), (b) extension of the equatorial convective mode across the Maritime Continent, (c) northward propagation near India, (d) north-westward propagation over the west Pacific and (e) the tilted rain-band. It is argued that proper representation of these features ensures realistic simulation of BSISO in a model. CFS T382 well reproduces the westward and northward propagating modes of BSISO. Although the phase speed of the simulated northward propagation is slightly slower than the observation, the convection smoothly propagates from the equatorial region to the northern latitudes with observed magnitude. It may be noted that CFS T382 simulates better northward propagating BSISO relative to its coarser resolution. In contrast, the simulated eastward propagation of the convection decays rapidly across the Maritime Continent. As a consequence, extension of the BSISO convection is found to be zonally oriented across the Maritime Continent rather than exhibiting northwest-southeast tilted structure. It is interesting to note that CFS T126 exhibits slightly better eastward propagation across the Maritime Continent. The warmer SST and heavy precipitation biases over WP may lead to strong density stratification and shallow mixed layer depth in CFS T382. This could play a vital role in weak intraseasonal SST variability and reduced eastward propagation of BSISO over WP.

The simulated synoptic variability appears to be underestimated in CFS T382. In contrast, the intraseasonal variability of CFS T382 is found to be stronger than that of observation. It may be noted that, G14 also reported similar deficiency in CFS T126. Although CFS T382, unlike CFS T126, exhibits a positive bias in mean SST and TT distributions, the biases in simulated mean precipitation as well as the BSISO characteristics are broadly similar in both the resolutions of the model. In light of the inconsistency, the present study attempts to put forward some new insights on the simulated CCEWs in CFS T382. The analysis indicates that the simulated ER wave variability is underestimated over WP, while it dominates over IO region. In contrast, both the Kelvin and MRG waves are underestimated over the global tropics in the model. The simulated northward propagation is facilitated by strong westward propagating gravest ER wave in the model. It could be responsible for the slow northward propagation in CFS T382. The weak easterlies over WP may be responsible for the underestimation of the simulated Kelvin wave. It possibly indicates the inadequate interaction between convective processes and large-scale circulation in CFS T382. The ratio between eastward and westward propagating modes is crucial for the propagation of intraseasonal convection. The weak ratio between simulated Kelvin and ER wave variability may be responsible for the reduced eastward propagation in the model.

A qualitative comparison of CFS T382 with earlier reported CFS T126 indicates that the spatio-tempotal distribution of the simulated BSISO remains largely similar in both the resolutions of the model. The high frequency variability is underestimated both in CFS T126 and CFS T382. As a consequence, difficulty remains in realistic representation of the organization and propagation characteristics of the BSISO. Thus, it may be argued that the change in resolution alone is not sufficient to improve the convectively coupled high-frequency variability in the model. Convectively coupled processes play an important role on the development of the observed high frequency disturbances. Therefore, the representation of cloud processes in the model needs to be improved for better simulation of the internal dynamics. Further attempts to improve the physical parameterization of CFS will be addressed in the future work.