Abstract

A set of atmospheric general circulation model (GCM) experiments is designed to explore the relative roles of the circumnavigating waves and the extratropics on the Madden–Julian oscillation (MJO). In a “control” simulation, the model is forced by the climatological monthly sea surface temperature for 20 yr. In the first sensitivity experiment, model prognostic variables are relaxed in the tropical Atlantic region (20°S–20°N, 80°W–0°) toward the “controlled” climatological annual cycle to suppress the influences from the circumnavigating waves. In the second sensitivity experiment, model prognostic variables are relaxed in the 20°–30° latitude zones toward the controlled climatological annual cycle to suppress the influences from the extratropics (or the tropics–extratropics interactions). The numerical results demonstrate that the extratropics play a more important role in maintaining the MJO variance than the circumnavigating waves.

The simulations further show that both the tropical mean precipitation and the intraseasonal precipitation variability are reduced when the extratropical influences are suppressed. The in-phase relationship is primarily attributed to the effect of the mean state on perturbations. A moisture budget analysis indicates that a positive feedback to the mean precipitation by the anomalous moisture convergence is offset by a negative feedback due to the anomalous moisture advection. The change in the mean precipitation in the absence of extratropical influences is primarily determined by the change in the mean moisture convergence, which in turn is due to the change in circulation. This study is the first attempt to quantitatively separate the effects of the circumnavigating waves and the extratropics on the MJO. Implications and limitations of this study are discussed.

1. Introduction

The Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972) is a dominant component of intraseasonal (20–100 days) variability in the tropics. It affects the medium- and extended-range weather forecasts around the globe (Ferranti et al. 1990; Mo and Higgins 1998; Jones and Schemn 2000) and works as a barrier in our pursuit toward seamless prediction (Hurrell et al. 2009). Therefore, understanding the MJO mechanisms is of utmost importance. The challenges, prospects, and opportunities toward understanding and forecasting the MJO are documented in detail by Lau and Waliser (2005) and Zhang (2005).

Proposed mechanisms to understand the MJO and its initiation include (i) local discharge–recharge processes (i.e., tropical internal dynamics; Bladé and Hartmann 1993; Hu and Randall 1994, 1995; Salby et al. 1994; Kemball-Cook and Weare 2001), (ii) influences by the circumnavigating waves (i.e., previous MJO events; Knutson et al. 1986; Knutson and Weickmann 1987; Lau and Peng 1987; Chang and Lim 1988; Wang and Li 1994), and (iii) influences by the extratropics (Yanai and Lu 1983; Liebmann and Hartmann 1984; Hsu et al. 1990; Lin et al. 2007; Pan and Li 2008; Ray and Zhang 2010). Note that the extratropical influences in reality represent the influences from the tropics–extratropics interactions because of the inseparability of the tropics and extratropics at multiple scales (Weickmann and Berry 2009; Roundy 2012). For brevity, however, we will refer this as extratropical influence.

Given the fact that more than 50% of the MJO events are “successive” (with preceding event; Matthews 2008) and they are possibly influenced by both the extratropics and the circumnavigating waves, it is natural to investigate the roles of extratropics and circumnavigating waves on the MJO. However, no quantitative estimates have been reported in this regard primarily because of the difficulty to separate the tropical and extratropical effects from any observational data; and from a modeling perspective, so far there is no systematic effort undertaken in isolating their influences.

Regional models were used previously to study the external influences on the MJO by modifying the model boundary conditions (Gustafson and Weare 2004a). For example, any prior MJO signal can be removed from the boundary conditions to find their influences on the MJO (Gustafson and Weare 2004b). However, the simulated MJO in a standard regional model is influenced by the zonal (owing to circumnavigating waves) and the meridional (from the extratropics) boundary conditions simultaneously (see Fig. 1a). As a result, their individual influences on the MJO cannot be separated. This problem was overcome by utilizing a tropical channel model (Ray et al. 2009, 2011, 2012), which is global in the zonal direction (i.e., no east–west boundaries), but confined in the meridional direction, thereby isolating the effects that arrive solely from the extratropics.

Fig. 1.

(a) Schematic diagram showing the influences of the circumnavigating waves and the extratropics on the MJO. Gray area indicates the MJO convective region. (b) Schematic of the numerical experiment in which the model prognostic variables are relaxed toward the controlled climatological annual cycle in the tropical Atlantic region (20°S–20°N, 80°W–0°). This is our experiment EW. Note that, although there are MJO-associated circumnavigating waves, they do not propagate to the west of the MJO convective region. (c) Schematic of the experiment NS in which the relaxation zone was placed in the 20°–30° latitudes. See text in section 2 for further details.

Fig. 1.

(a) Schematic diagram showing the influences of the circumnavigating waves and the extratropics on the MJO. Gray area indicates the MJO convective region. (b) Schematic of the numerical experiment in which the model prognostic variables are relaxed toward the controlled climatological annual cycle in the tropical Atlantic region (20°S–20°N, 80°W–0°). This is our experiment EW. Note that, although there are MJO-associated circumnavigating waves, they do not propagate to the west of the MJO convective region. (c) Schematic of the experiment NS in which the relaxation zone was placed in the 20°–30° latitudes. See text in section 2 for further details.

A disadvantage in using a tropical channel model (or a regular regional model) is that a global view of the intraseasonal oscillation is not possible. This can be overcome by using a general circulation model (GCM) forced at the selected latitudes by the reanalysis boundary conditions (Vitart and Jung 2010). However, in all these approaches (Gustafson and Weare 2004a,b; Ray et al. 2009, 2011; Vitart and Jung 2010), the boundary conditions come from a different dataset (reanalysis or other model output), and the intraseasonal variability present in the boundary conditions may be different from the model’s intrinsic intraseasonal variability. To overcome this problem, we introduce a GCM-based framework, in which the boundary conditions come from a parallel simulation (“control”) of the same model, thereby allowing a consistent comparison between the control and the sensitivity simulations. We believe that the present study is the first attempt to make a systematic effort in quantifying the relative roles played by the circumnavigating waves and the extratropics on the simulated MJO.

The modeling framework and the data are described in section 2. Results are presented in sections 3 and 4, which include the relationship between the MJO and the mean state (section 3), followed by a diagnosis of the moisture budget (section 4) to elucidate the mechanism through which model variability is influenced by the simulated mean state and vice versa. Summary and further discussion are presented in section 5.

2. Model and data

The GCM used is atmosphere-only ECHAM4 (Roeckner et al. 1996) since this model is found to be one of the better models for the MJO simulation (Fu et al. 2003; Jiang et al. 2004; Sperber et al. 2005; Zhang et al. 2006; Kim et al. 2009). The horizontal resolution is about 2.8° × 2.8° (T42). Model top is set at 10 hPa. A modified Tiedtke (1989) convection scheme (Nordeng 1994) is used.

In the control simulation, the model is integrated for 20 yr (1972–91) using the climatological monthly mean sea surface temperature (SST). In the first sensitivity experiment [East–West (EW)], the model prognostic variables are relaxed toward the “controlled” climatological annual cycle over the tropical Atlantic Ocean region (20°S–20°N, 80°W–0°; green area in Fig. 1b) to remove the influences from the MJO associated circumnavigating waves. This zone is chosen for relaxation because it is far from the active MJO convection region. Note that the influences from the extratropics are not affected in the EW experiment. Also, since the SST used did not have interannual variation, the time period of simulation (1972–91) is not quite important.

In the second sensitivity experiment [North–South (NS)], the model prognostic variables (e.g., u, υ, T, q) are relaxed toward the controlled annual cycle over the 20°–30° latitude zones (red area in Fig. 1c) to prevent the propagation of midlatitude Rossby waves or baroclinic eddies into the tropics (i.e., removing the extratropical influences), but without interfering the influences from the circumnavigating waves. This is an ideal modeling setup, given that the MJO has a global scale in the zonal direction (Madden and Julian 1971; Li and Zhou 2009) and most of its variance is confined within the 20° latitudes (Zhang and Dong 2004; also see section 3). Note that the high-frequency eddy variability and its role in maintaining the mean circulation are much greater in midlatitudes than in tropics (Peixoto and Oort 1992). As a result, our relaxation zone was bounded within 30° latitudes.

In all the previous observational studies of MJO cases (Hsu et al. 1990; Ray and Zhang 2010) and MJO statistics (Matthews 2008; Zhao et al. 2013) the initial perturbation in the extratropics that eventually influenced the MJO was found to be originated beyond 30° latitudes. So a relaxation zone beyond 30° latitude for the NS experiment may not be appropriate since the purpose of the NS experiment is to remove the extratropical influences. By comparing the simulated MJO in the control and the two sensitivity experiments EW and NS, the relative roles of the circumnavigating waves and the extratropics on the MJO can be estimated.

For model validation, we utilize National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) reanalysis wind data (Kalnay et al. 1996), the Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP; Xie and Arkin 1997), and the National Oceanic and Atmospheric Administration (NOAA) interpolated outgoing longwave radiation (OLR; Liebmann and Smith 1996) at the top of the atmosphere.

3. Relationship between the simulated mean state and MJO

The possible role of the mean state on the MJO has been studied extensively using observations (Zhang and Dong 2004), models (Slingo et al. 1996; Inness et al. 2003; Maloney and Hartmann 2001; Ajayamohan and Goswami 2007; Ray et al. 2011), and model–observations comparison (Zhang et al. 2006; Kim et al. 2011; Ray 2012). It was found that the realistic time-mean distributions of lower-tropospheric zonal winds and humidity, moisture convergence in the boundary layer, and precipitation in models were necessary for them to reproduce realistic MJO. Therefore, we will first examine the tropical mean state and the MJO variance in the simulations, followed by a diagnosis of the relationship between them, if any.

Figure 2 shows the mean wind vectors at 850 and 200 hPa averaged over 20 yr. The control and the EW simulate the mean winds reasonably well although it is underestimated near the equator. However, with respect to the control, the NS simulation winds are underestimated in the southern Indian Ocean at 850 hPa (Fig. 2d) and are overestimated near 20°S at 200 hPa (Fig. 2h). We further look at the mean zonal winds at 850 hPa (U850) and 200 hPa (U200) in Fig. 3. The reanalysis (Fig. 3a) has lower (upper)-tropospheric westerlies (easterlies) over the equatorial Indian Ocean. The control (Fig. 3b) captures the observed mean flow field well. The EW (Fig. 3c) simulation is almost identical to the control. However, in the NS (Fig. 3d), westerlies (easterlies) at the lower (upper) troposphere are underestimated. As a result, vertical shear defined as U200 − U850 is reduced in the NS (Fig. 3h), particularly over the equatorial Indian Ocean (IO) and western Pacific (WP). Such a reduction in the mean easterly shear may have a great impact on the development of tropical perturbations, as demonstrated by previous theoretical and modeling studies (e.g., Wang and Xie 1996; Li 2006, Ge et al. 2007; Sooraj et al. 2009; Li et al. 2010).

Fig. 2.

Mean winds at 850 hPa from the (a) reanalysis, (b) control, (c) test run EW where circumnavigating waves are suppressed, and (d) test run NS where extratropical influences are suppressed. (e)–(h) As in (a)–(d), respectively, but for the 200-hPa level.

Fig. 2.

Mean winds at 850 hPa from the (a) reanalysis, (b) control, (c) test run EW where circumnavigating waves are suppressed, and (d) test run NS where extratropical influences are suppressed. (e)–(h) As in (a)–(d), respectively, but for the 200-hPa level.

Fig. 3.

Mean U850 (shaded) and U200 (contoured) from the (a) reanalysis, (b) control, (c) test run EW where circumnavigating waves are suppressed, and (d) test run NS where extratropical influences are suppressed. (e)–(h) As in (a)–(d), respectively, but for vertical shear (U200 − U850). Contour interval for U200 is 3 m s−1. All units are m s−1.

Fig. 3.

Mean U850 (shaded) and U200 (contoured) from the (a) reanalysis, (b) control, (c) test run EW where circumnavigating waves are suppressed, and (d) test run NS where extratropical influences are suppressed. (e)–(h) As in (a)–(d), respectively, but for vertical shear (U200 − U850). Contour interval for U200 is 3 m s−1. All units are m s−1.

As the easterly shear is closely linked to precipitation strength in the monsoon region (Li 2010), we examine associated mean precipitation (shaded) and OLR (contoured) in Fig. 4. Observed precipitation (Fig. 4a) in the equatorial region is captured well by the control (Fig. 4b) and EW (Fig. 4c) experiments, whereas most GCMs perform poorly in the equatorial Indian Ocean and western Pacific (Lin et al. 2006). In the sensitivity experiment NS (in which extratropical influences are suppressed), mean precipitation is underestimated over the tropical oceans. This is consistent with the reduction of the mean easterly shear over this region (Fig. 3, right panels). The SPCZ region in the NS simulation seems to have a larger change compared to the control possibly because this region experiences stronger tropical–extratropical interactions (Kiladis et al. 1989; Vincent 1994). We consider the control simulation using ECHAM4 to be good enough to be treated as the benchmark for the remaining figures and discussions. The ability of ECHAM4 model to capture the tropical mean state and the MJO can be found in a number of papers (Jiang et al. 2004; Sperber et al. 2005; Zhang et al. 2006; Lin et al. 2006; Kim et al. 2011).

Fig. 4.

Mean precipitation (shaded; mm day−1) and OLR (contoured; W m−2) from the (a) observation, (b) control, (c) EW, and (d) NS.

Fig. 4.

Mean precipitation (shaded; mm day−1) and OLR (contoured; W m−2) from the (a) observation, (b) control, (c) EW, and (d) NS.

The reduction in the annual mean precipitation in the NS as seen in Fig. 4 is true at all longitudes (Fig. 5a). The EW simulation is almost identical to the control simulation. The reduction of precipitation in the NS occurs not only in the annual mean but also over all seasons. Examples for northern summer [June–September (JJAS)] and winter [December–March (DJFM)] are shown in Figs. 5b and 5c, respectively. And in both seasons, the precipitation is reduced in the NS compared to that in control and EW. However, the longitudinal variations are similar for all these simulations. Is the mean-state change associated with the change in MJO? We will address this question by examining the simulated MJO at each of the experiments above and their upscale feedback to the mean state (see section 4).

Fig. 5.

Simulated precipitation (mm day−1) during (a) all season, (b) JJAS, and (c) DJFM averaged over 10°S–10°N.

Fig. 5.

Simulated precipitation (mm day−1) during (a) all season, (b) JJAS, and (c) DJFM averaged over 10°S–10°N.

A space–time spectrum analysis (Hayashi 1979) using the filtered (20–100 day; CLIVAR MJO Working Group 2009) time series of precipitation (P) is shown in Fig. 6. In the control (Fig. 6a) and EW (Fig. 6b), the spectral powers show a maximum around zonal wavenumber 1, but are reduced substantially in the NS simulation (Fig. 6c). A good indicator for the MJO is the dominance of the eastward-propagating power over its westward-propagating counterpart at the intraseasonal and planetary scales. Averaged over zonal wavenumbers 1 and 2, and period of 20–100 days, this ratio for P in EW (1.7) is same to that in control (1.7). However, in the NS, this ratio is much weaker (1.0) and seems like a standing oscillation. Overall, the MJO spectrum in the NS is not well captured compared to the control, indicating possible influences from the extratropics on the simulated MJO. On the other hand, MJO spectrum in EW is almost identical to that in the control, indicating little to no influence by the circumnavigating waves on the MJO. The results hold for other variables including the OLR, U850, and U200 (not shown). The control simulation also captures the seasonality of the MJO (Zhang and Dong 2004; Kikuchi et al. 2012) reasonably well.

Fig. 6.

Time–space spectra for precipitation from the (a) control, (b) sensitivity test EW, and (c) sensitivity test NS. All are averaged over 10°S–10°N. Twenty and 100 days are marked by dashed lines.

Fig. 6.

Time–space spectra for precipitation from the (a) control, (b) sensitivity test EW, and (c) sensitivity test NS. All are averaged over 10°S–10°N. Twenty and 100 days are marked by dashed lines.

To further explore the relative influences of the circumnavigating waves and the extratropics, geographic distribution of MJO variance associated with the 20–100-day bandpass filtered U850 (MJOU850) and P (MJOP) is shown in Fig. 7. The control simulation resembles well with respect to the observations (not shown). The variance in MJOU850 in the NS (Fig. 7c) over the Indian Ocean is reduced substantially compared to the other simulations (Figs. 7a,b). For example, the averaged value of MJOU850 over the equatorial IO (10°S–10°N, 60°–100°E) is 12.5 and 12.6 mm2 day−2 for the control and EW but only 7.8 mm2 day−2 for the NS. Note that the Indian Ocean is the region where MJO initiation occurs. Over the western Pacific, MJO variances in the NS are in general weaker and appear farther from the equator. Variance in MJOP is similar for control (Fig. 7d) and EW (Fig. 7e), indicating little influence from the circumnavigating waves. Similar to the variance in MJOU850, the MJOP variance in the equatorial Indian Ocean and western Pacific regions is also reduced in the NS (Fig. 7f) compared to that in the control and EW.

Fig. 7.

Variance of MJOU850 (m2 s−2) from the (a) control, (b) EW, and (c) NS. (d)–(f) As in (a)–(c), respectively, but for variance of MJOP (mm2 day−2).

Fig. 7.

Variance of MJOU850 (m2 s−2) from the (a) control, (b) EW, and (c) NS. (d)–(f) As in (a)–(c), respectively, but for variance of MJOP (mm2 day−2).

To explore the MJO variance further, Fig. 8 shows the differences in the precipitation variance. For the EW experiment (Fig. 8a), the difference in general is small with overestimation in the Southern Hemisphere. However, for NS (Fig. 8b), the difference is much larger. The variance in MJOP is underestimated in the equatorial region, but is overestimated near the 20° latitudes.

Fig. 8.

Precipitation variance of MJOP (mm2 day−2) for (a) EW − control and (b) NS − control.

Fig. 8.

Precipitation variance of MJOP (mm2 day−2) for (a) EW − control and (b) NS − control.

Is there a close relationship between the mean state and MJO? That is, the smaller the mean precipitation and the mean easterly shear are, the weaker the MJO variability is. The longitudinal distribution of the mean precipitation and MJO variance differences (NS − control; Fig. 9) shows that the reduction in P is well correlated with the reduction in the variance of MJOP in ECHAM4. For instance, the mean precipitation difference increases with increased longitude over the Indian Ocean, and so does the MJO variance difference. A similar feature is found in the western Pacific. This indicates that the MJO variability depends greatly on the mean precipitation (Zhang and Dong 2004). The results are summarized in Table 1. For example, in the NS, over the Indian Ocean, a mean precipitation reduction of 36% corresponds to a variance reduction of 45%. Over the western Pacific, a 25% reduction in the mean precipitation corresponds to a 34% reduction in the variance. Considering the entire tropical Indo-Pacific Oceans (10°S–10°N, 40°E–180°), a mean precipitation reduction of 29% corresponds to a 36% reduction in the MJO variance.

Fig. 9.

Longitudinal distribution of difference between the sensitivity simulation and control for mean precipitation (solid) and variance of MJOP (dashed). All are averaged over 10°S–10°N. Units are mm day−1 for P and 0.2 mm2 day−2 for variance of MJOP.

Fig. 9.

Longitudinal distribution of difference between the sensitivity simulation and control for mean precipitation (solid) and variance of MJOP (dashed). All are averaged over 10°S–10°N. Units are mm day−1 for P and 0.2 mm2 day−2 for variance of MJOP.

Table 1.

NS − control for mean precipitation (%) and MJO variance (%). All are averaged over 10°S–10°N.

NS − control for mean precipitation (%) and MJO variance (%). All are averaged over 10°S–10°N.
NS − control for mean precipitation (%) and MJO variance (%). All are averaged over 10°S–10°N.

This mean-state-dependent feature is also true for the EW − control case, but the amplitude is much smaller (Table 2). Note that there is an increase in the mean and variance when the circumnavigating waves are suppressed, further indicating that the circumnavigating waves play a minor role compared to the extratropics in modulating the MJO in the ECHAM4.

Table 2.

As in Table 1, but for EW − control.

As in Table 1, but for EW − control.
As in Table 1, but for EW − control.

An interesting question is what causes the reduction of the mean precipitation in the NS experiment. One possible factor is due to the change of the atmospheric static stability. Mean vertical profiles of potential temperature and equivalent potential temperature remain unchanged in EW and NS compared to the control irrespective of the locations considered (not shown). Therefore, atmospheric stability cannot explain the observed rainfall changes in the NS.

Another possibility is due to the eddy–mean flow interaction. Because of the blocking of equatorward propagation of midlatitude waves, tropical eddy activity (including MJO and higher-frequency variability) may be reduced in the NS experiment. The reduced eddy activity due to the cutoff of midlatitude influence may further decrease the mean rainfall through nonlinear rectification of diabatic heating and moisture convergence (Hsu and Li 2011). The decrease of the mean precipitation may further suppress the tropical perturbations through reduced background easterly shear (Wang and Xie 1996; Li 2006; Sooraj et al. 2009). For example, GCM experiments by Sooraj et al. (2009) showed that the eddy activity at the equator is strengthened under an easterly shear background flow.

To demonstrate whether or not the tropical perturbations can feed back to the mean state, in the next section we conduct a moisture budget analysis to reveal the possible role of perturbations on the mean precipitation.

4. Diagnosis of upscale feedback of perturbations to the mean precipitation

A time-averaged vertically integrated moisture budget equation may be written as

 
formula

where P is the precipitation, E is the evaporation, V is the horizontal component of the wind, q is the specific humidity, R is the residual, is the advection of moisture, and is the moisture convergence. The overbar denotes the 20-yr time mean. The angle brackets the vertical integration and is given by

 
formula

where Pt is the pressure at top of the troposphere (10 hPa), Ps is 1000 hPa, and g is the acceleration due to gravity. The advection term can be further separated into two terms (Adv1 and Adv2):

 
formula

where a prime denotes the perturbation from the mean and includes all resolvable time scales including MJO and higher-frequency perturbations. Adv1 denotes the advection of the mean moisture by mean flow, and Adv2 denotes the mean advection of the anomalous moisture by anomalous flow. Similarly, the convergence term can be separated into two terms (Conv1 and Conv2):

 
formula

where Conv1 represents convergence of mean moisture by the mean flow, and Conv2 represents the mean convergence of the anomalous moisture by the anomalous flow.

Fig. 10 shows the moisture budget terms based on Eq. (1) from the control and NS. We do not show the results from the EW since they are almost identical to the control. Compared to large spatial variations of the mean precipitation (Figs. 10a,f), the evaporation fields look more uniformly distributed (Figs. 10b,g). The moisture advection contributes negatively to the mean precipitation (Figs. 10c,h). The moisture convergence is the largest term that resembles well the overall structure of the precipitation (Figs. 10d,i). This is expected since the mean precipitation is typically dominated by the mean moisture convergence in the tropics. The moisture divergence is found over part of the northern Indian Ocean (Arabian Sea), northern parts of Australia and the surrounding oceans, and near the equator east of the date line. Residual (Figs. 10e,j) is more noisy and small over the entire region, which gives confidence on the moisture budget analysis.

Fig. 10.

The terms of the moisture budget from (a)–(e) the control and (f)–(j) NS. The units are 10−5 kg m−2 s−1.

Fig. 10.

The terms of the moisture budget from (a)–(e) the control and (f)–(j) NS. The units are 10−5 kg m−2 s−1.

The differences between the NS and control (as shown in Fig. 11) may provide clues on the relative importance of the terms that lead to the differences in the mean precipitation. Compared to the precipitation difference pattern (Fig. 11a), evaporation (Fig. 11b), advection (Fig. 11c), and residual (Fig. 11e) differences are generally small. On the other hand, the moisture convergence difference pattern (Fig. 11d) is very similar to the precipitation pattern (Fig. 11a), indicating that this term is crucial in explaining the rainfall difference. This is consistent with Seo and Kumar (2008), who found that the strength of the low-level convergence plays a key role in the MJO variability.

Fig. 11.

Moisture budget terms for NS − control. The units are 10−5 kg m−2 s−1. The rectangles indicate where the differences are higher over the tropical Indian Ocean (10°S–0°, 60°–100°E) and western Pacific (0°–10°N, 140°E–180°). The results are further described in Table 3.

Fig. 11.

Moisture budget terms for NS − control. The units are 10−5 kg m−2 s−1. The rectangles indicate where the differences are higher over the tropical Indian Ocean (10°S–0°, 60°–100°E) and western Pacific (0°–10°N, 140°E–180°). The results are further described in Table 3.

The latitudinal distribution of precipitation and Conv1 for NS − control over the Indian Ocean and western Pacific was plotted in Fig. 12. There is increased convergence and precipitation near 20° over both hemispheres. The increase in the extratropics may lead to a decrease in the moisture convergence near the equator. We will later show that this decrease in moisture convergence near the equator in the IO and WP is primarily due to the changes in winds and not due to the humidity difference.

Fig. 12.

Latitudinal distribution of mean precipitation and mean moisture convergence for NS − control over the (a) Indian Ocean and (b) western Pacific. The units are 10−5 kg m−2 s−1.

Fig. 12.

Latitudinal distribution of mean precipitation and mean moisture convergence for NS − control over the (a) Indian Ocean and (b) western Pacific. The units are 10−5 kg m−2 s−1.

The results of moisture budget analysis for NS are summarized in Table 3. The amplitude of the terms for EW (not shown) is much smaller compared to those in NS. For example, over the Indian Ocean, precipitation difference for EW (i.e., EW − control) is 0.38 compared to −4.60 for NS (Table 3). Note that the two convergence terms [Conv1 and Conv2; see Eq. (4)] that constitute the total moisture convergence always have the same sign as precipitation, suggesting that the nonlinear rectification of the moisture convergence through the eddy–eddy interaction contributes positively to the mean precipitation. Over the tropical Indian Ocean (10°S–0°N, 60°–100°E; rectangular box in Fig. 11), the Conv2 term (i.e., convergence of the perturbation moisture by perturbation winds) contributes about 10% of the difference in total precipitation, which represents a positive feedback of the perturbations (that include MJO) on the mean state.

Table 3.

Moisture budget terms for NS − control over IO (10°S–0°, 60°–100°E) and WP (0°–10°N, 140°E–180°). Units are in 10−5 kg m−2 s−1.

Moisture budget terms for NS − control over IO (10°S–0°, 60°–100°E) and WP (0°–10°N, 140°E–180°). Units are in 10−5 kg m−2 s−1.
Moisture budget terms for NS − control over IO (10°S–0°, 60°–100°E) and WP (0°–10°N, 140°E–180°). Units are in 10−5 kg m−2 s−1.

Physically how does the Conv2 affect the mean precipitation? Consider an MJO perturbation in the western North Pacific as an example. Observations show that there is an in-phase relationship between perturbation moisture and perturbation convergence at low level (Hsu and Li 2012). As we know, precipitation is proportional to column-integrated moisture convergence. For example, during an active (suppressed) phase of MJO, the low-level convergence (divergence) anomaly is often associated with the increased (decreased) specific humidity (Maloney and Hartmann 1998; Hsu and Li 2012). As a result, the time average of Conv2 will attain a greater (smaller) value during the active (suppressed) phase of MJO.

To illustrate this point, we calculated the correlation coefficients (Fig. 13) for perturbation moisture and convergence fields at 850 hPa for all the simulations. It is noted that the correlation coefficient between the two variables is greater in the experiment when the MJO is stronger. This is most prominent over the Indian and western Pacific Oceans where the mean precipitation and convergence were reduced substantially for the NS experiment (see Fig. 11). In particular, note that the weaker MJO variance in the NS compared to the control (Table 1) is reflected well in smaller correlation in the NS than control. Also, the mean Conv2 in the control are greater than those in the NS experiment, indicating a greater feedback of MJO to the mean state. The percentage change of Conv2 in NS with respect to control averaged over the tropical Indian Ocean is 30%. At 850-hPa level, the anomalous motion contributes 25% of the total moisture convergence, while the mean flow contributes about 75%.

Fig. 13.

Correlation between the anomalous moisture and anomalous convergence at 850 hPa from the control, EW, and NS for the Indian Ocean and the western Pacific.

Fig. 13.

Correlation between the anomalous moisture and anomalous convergence at 850 hPa from the control, EW, and NS for the Indian Ocean and the western Pacific.

It is interesting to note that the anomalous advection (Adv2) has a negative feedback to the precipitation, and its amplitude is larger than the anomalous convergence (Conv2). As a result, the combination of anomalous advection and anomalous convergence tends to reduce the mean precipitation. Given the fact that the analysis above is based on all resolvable time scales, we cannot claim whether the weakening of the MJO variability in the NS run would increase or decrease the mean rainfall.

The vertical structures of moisture convergence for NS − control are examined over the Indian Ocean (Fig. 14a) and western Pacific (Fig. 14d). As expected, the largest moisture convergence difference is confined in the lower troposphere below 600 hPa. Above 700 hPa, Conv2 is similar or larger than Conv1. To examine whether the mean moisture convergence (Conv1) is contributed by the mean humidity or the mean wind, we isolate the influences of the two factors. For a perfect q scenario (i.e., replace the q in NS by the q in control), we see that the modified Conv1 matches almost perfectly with the Conv1 from the NS simulation (Figs. 14b,e). This suggests that the contribution from changes in q is negligible. This is consistent with the fact that the static stability remains unchanged for all three simulations.

Fig. 14.

Vertical structures of (a) the convergence terms Conv1 (solid) and Conv2 (dashed) for the Indian Ocean for NS − control, (b) Conv1 (solid) and Conv1 with perfect q (dashed), and (c) Conv1 (solid) and Conv1 with perfect divergence (dashed). (d)–(f) As in (a)–(c), but for the western Pacific. Note that Conv1 is the same over all of the left (right) panels. All are for NS − control. The units are 10−5 kg m−2 s−1.

Fig. 14.

Vertical structures of (a) the convergence terms Conv1 (solid) and Conv2 (dashed) for the Indian Ocean for NS − control, (b) Conv1 (solid) and Conv1 with perfect q (dashed), and (c) Conv1 (solid) and Conv1 with perfect divergence (dashed). (d)–(f) As in (a)–(c), but for the western Pacific. Note that Conv1 is the same over all of the left (right) panels. All are for NS − control. The units are 10−5 kg m−2 s−1.

In the perfect divergence scenario (i.e., replace the divergence in NS by the divergence in control), the modified Conv1 is close to zero at all levels (Figs. 14c,f). This indicates that the change in divergence in NS from the control is primarily responsible for the change in mean precipitation. This is consistent with the reduction in U850 over the equatorial region as seen in Fig. 3. Therefore, in the absence of extratropical influences in the NS, the reduction of mean precipitation further modulates the background wind, which in turn decreases mean moisture convergence and thus mean precipitation.

5. Summary and discussion

A set of idealized atmospheric GCM experiments is designed to explore the relative roles of the circumnavigating waves and the extratropics on the MJO. A “control” simulation and two sensitivity experiments are conducted, and each of them is run for 20 years. In the control experiment, the model (ECHAM4) is forced by the observed climatological monthly SST field and is able to reproduce quite realistic mean-state and MJO variability in the tropics. In the first sensitivity experiment (named EW), the model prognostic variables are relaxed in the tropical Atlantic region (20°S–20°N, 80°W–0°) toward the “controlled” climatological annual cycle to remove the influences from the circumnavigating waves. In the second sensitivity experiment (named NS), the model prognostic variables are relaxed in the 20°–30° latitude zones toward the controlled climatological annual cycle so that the extratropical influence (such as wave propagation into the tropics) is suppressed. The numerical model results show that the circumnavigating waves do not play a major role on the simulated MJO. However, in the absence of the extratropical influences, the simulated MJO variance in the Indian Ocean (where MJO initiation occurs) is weakened by 45% with a corresponding reduction in mean precipitation of 36% (Table 1).

To explore the possible feedback of tropical perturbations to the mean precipitation, we conducted a column-integrated moisture budget analysis. Because of the blocking of equatorward propagation of midlatitude Rossby waves and baroclinic eddies in the NS experiment, the mean moisture convergence is reduced (Figs. 11 and 12). This is mainly due to the reduction in the winds because the humidity remains practically same in the NS experiment compared to the control (Fig. 14). This reduction in the moisture convergence causes the weakening of the mean precipitation, which further reduces the MJO variance.

It is noted that the anomalous moisture convergence term (i.e., convergence of anomalous moisture by anomalous wind; Conv2 in Table 3) has a positive feedback on the mean precipitation. However, advection of anomalous moisture by anomalous winds (Adv2 terms in Table 3) provides a negative feedback to the mean precipitation. As a result, the overall influence of the anomalous moisture convergence and advection on the mean precipitation is small in the tropical Indo-Pacific region. The decrease of the mean precipitation in the equatorial region is primarily associated with the extratropical effect (Fig. 12). The decrease of the mean precipitation in the tropics further suppresses the activity of synoptic waves and MJO through reduced background easterly shear (Wang and Xie 1996; Li 2006; Sooraj et al. 2009). The distinctive roles of the anomalous moisture convergence and the anomalous advection on the mean precipitation warrant a further in-depth study.

The extratropical influences on the MJO have been shown previously through analytical (e.g., Frederiksen and Frederiksen 1997; Hoskins and Yang 2000; Wedi and Smolarkiewicz 2010), observational (e.g., Hsu et al. 1990; Ray and Zhang 2010; Wang et al. 2013; Zhao et al. 2013), and numerical modeling (e.g., Lin et al. 2000; Pan and Li 2008; Ray et al. 2009; Vitart and Jung 2010) studies. However, the present study perhaps is the first study to present quantitative estimates of the relative roles of the circumnavigating waves and extratropics on the MJO and the tropical mean state.

One can easily notice that the reduction of precipitation appears south of the equator over Indian Ocean and north of the equator over western Pacific (Fig. 11). Why the reduction in mean precipitation is asymmetrical even though midlatitude blocking zones are symmetrical? This is due to the following reason: In the Northern Hemisphere, there is evidence of extratropical waves penetrating to the North Pacific from the midlatitudes (Matthews and Kiladis 1999; Hsu et al. 1990). However, such consistent wave penetration to the equatorial Indian Ocean in the Northern Hemisphere has not been documented. On the other hand, in the Southern Hemisphere, extratropical disturbances that penetrate into the tropics are prominent in the southern Indian Ocean (Zhao et al. 2013). As a result, mean precipitation reduction is asymmetrical over the Indian Ocean and western Pacific.

There are other issues, limitations, and implications that need further discussion:

  • Our atmosphere-only model lacks any coupled interactions that have been previously shown to strengthen the MJO variance. Kemball-Cook et al. (2002) and Fu et al. (2003) demonstrated that ECHAM4 coupled to an intermediate 2.5-layer ocean model better captured the MJO evolution compared to its atmosphere-only counterpart. Oceanic Rossby waves were also found to play an important role in triggering certain MJO events (Webber et al. 2012). However, a preliminary analysis with ECHAM4 being coupled to a slab ocean model shows that the conclusion drawn in this paper does not change. It would also be interesting to find if the control simulation would improve when the model is forced by the SST with interannual variation since ENSO is the most energetic and predictable mode in the global climate system. As a result, the possibility that the mean state effect on the MJO has been magnified owing to the use of climatological SSTs cannot be ruled out.

  • We have described the reduction of MJO variance in the NS experiment as a result of removal of extratropical influences. In reality, it is practically impossible to completely separate the influence of the extratropics from that of the tropics and vice versa (Frederiksen and Frederiksen 1997; Frederiksen 2002; Hoskins and Yang 2000; Roundy 2012). As a result, the implied role of the extratropics on the MJO should be treated with caution. In contrast, we have more confidence on the implied role of circumnavigating waves on the MJO, as this is consistent with a recent observational analysis (Zhao et al. 2013). It is evident from our results that apart from the tropical processes, better representation of the extratropical processes in the GCMs may improve the MJO simulation and prediction.

  • We have not looked at individual MJO events in the ECHAM4 simulation. The detailed diagnosis of individual MJO events at their different stages of life cycle may reveal about the nature of the extratropical influences. In particular, what specific triggering processes lead to MJO initiation needs to be investigated. Such efforts are undergoing at present and will be documented later. Similarly, the influences from the circumnavigating waves on individual events, if any, may be revealed as well. Note that the circumnavigating signals might be able to propagate along the northern and southern peripheries in our EW experiment. However, moving the edges farther away from the tropics (e.g., 30°S–30°N, 40°S–40°N, and so on) would influence the eddy momentum and heat transport and thus the mean state in the midlatitudes, thereby affecting the tropics–extratropics interactions also. Such limitations highlight the difficulties in separating the influences from the circumnavigating waves and the extratropics on the MJO.

  • Note that the damping area in the EW experiment is much farther away from the MJO convective region, whereas the damping areas in the NS experiment directly border the MJO convective region. Could this explain why the results are more sensitive to the NS experiment than the EW experiment? We cannot be definitive in answering this; however, some previous studies may help address this issue. Specifying a damping zone over the eastern Pacific in their model (E. Maloney 2012, personal communication) did not influence the MJO variability, which supports our EW results. Similarly, using a tropical channel model based on fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5), Ray et al. (2009) showed that moving the model boundaries from 21°S–21°N to 28°S–28°N and 38°S–38°N did not change the simulated MJO behavior or the mean state in the tropics. Vitart and Jung (2010) also concluded the same by moving the damping zone at different latitudes in their ECMWF model simulations. Having said that, we cannot rule out the model dependence in this regard.

  • We have not conducted any experiments by restricting the relaxation zone to a smaller width (say, Indian Ocean region, 40°–100°E) or by restricting the relaxation zone to one hemisphere only. Vitart and Jung (2010), using ECMWF model during the boreal winter, found that the North Pacific region was more sensitive to tropics–extratropics interactions. This is consistent with our results, where we have also seen the North Pacific region to be more sensitive to the tropics–extratropics interactions than the northern Indian Ocean (see Figs. 4 and 8). Zhao et al. (2013) compared the relative importance of the hemispheric tropics–extratropics interactions on the MJO. They conducted two experiments. In the first (second), tropics–extratropics interactions were suppressed only in the NH (SH). They concluded that the tropics–extratropics interactions in the SH (over the Indian Ocean region) plays a dominant role for the MJO initiation compared to its counterpart in the NH.

In essence, by adopting a problem-oriented modeling strategy, we have shown that the extratropical influences are important ingredients of the MJO dynamics. Therefore, further research attention toward understanding the extratropical processes and their representations in the model is needed. This GCM-based framework also allows a global view of the intraseasonal oscillation and can be used for research and forecast of real-time MJO cases. In particular, this framework can be utilized for the MJO events during field experiment Dynamics of the MJO (DYNAMO; from October 2011 to March 2012; http://www.eol.ucar.edu/projects/dynamo) and during the Year of Tropical Convection (YOTC; Moncrieff et al. 2012; http://www.ucar.edu/yotc) to further understand the tropics–extratropics interactions and the MJO.

Acknowledgments

This work was supported by NSF Grant AGS-1106536, ONR Grant N000141210450, and by the International Pacific Research Center, which is sponsored by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), NASA (NNX07AG53G), and NOAA (NA17RJ1230). We also thank three anonymous reviewers for their thorough and insightful comments.

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Footnotes

*

School of Ocean and Earth Science and Technology Contribution Number 8774 and International Pacific Research Center Contribution Number 925.

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Current affiliation: Department of Marine and Environmental Systems, Florida Institute of Technology, Melbourne, Florida.