1. Introduction
The Madden–Julian oscillation (MJO; Madden and Julian 1971, 1972a, 2011) is the dominant component of intraseasonal variability in the tropical atmosphere. It is characterized by eastward-propagating convective centers and associated baroclinic oscillations in the tropical wind field. These anomalies propagate eastward at an average speed of 5 m s−1 across the equatorial Indian and western and central Pacific Oceans, with a local intraseasonal period of roughly 30–90 days. The convection anomalies associated with the MJO are most intense over the central and eastern Indian Ocean and western Pacific Ocean, with a weaker signal over the Maritime Continent. However, even after the convective anomaly ceases in the cooler waters of the central Pacific, the MJO’s dynamical signal can still be traced as a dry Kelvin wave, often completing a global circuit (Hendon and Salby 1994; Matthews 2000; Sperber 2003; Kiladis et al. 2005). The properties of the MJO tend to be strongest during boreal winter, during which the Indo-Pacific warm pool is centered on the equator (Zhang and Dong 2004). Extensive reviews of the MJO can be found in Madden and Julian (1994), Zhang (2005), and Lau and Waliser (2011).
Recently, the MJO has been the subject of intense study because of its extensive interactions with other components of the climate system and its modulation of weather around the globe (Zhang et al. 2001; Schubert et al. 2002; Waliser et al. 2003; Yoneyama et al. 2008; Waliser et al. 2009; Roundy et al. 2010). Some of its interactions include a close relation to onsets and breaks in the Asian–Australian monsoon (Yasunari 1980; Goswami 2005; Wheeler and McBride 2005; Straub et al. 2006) and to the onset and evolution of the El Niño–Southern Oscillation (ENSO) (Lau and Chan 1988; Kessler and Kleeman 2000; Straub et al. 2006; Hendon et al. 2007). The MJO modulates weather activity on a global scale, including tropical cyclone activity (Liebmann et al. 2001; Maloney and Hartmann 2000a,b; Hall et al. 2001; Bessafi and Wheeler 2006), the diurnal cycle (Chen et al. 2004; Tian et al. 2006), and precipitation events at different latitudes (Bond and Vecchi 2003; Vecchi and Bond 2004; Jones 2000; Jones et al. 2004; Weickmann and Berry 2007; Martin and Schumacher 2011; Guan et al. 2011; Jones and Carvalho 2012). It has also been recently shown that the MJO modulates the concentration of atmospheric chemicals (Wong and Dessler 2007; Tian et al. 2007) and aerosols (Tian et al. 2008, 2011).
Despite a growing list of impacts associated with the MJO, our current understanding of its mechanisms remains limited. There are many gaps in our understanding of its initiation and propagation processes (Hendon and Salby 1994; Matthews 2000; Sperber 2003; Kiladis et al. 2005; Matthews 2008; Seo and Kumar 2008), and climate models continue to struggle to represent MJO events correctly (Waliser et al. 2009; Kim et al. 2009; Monier et al. 2010; Thayer-Calder and Randall 2009; Hannah and Maloney 2011; Ray et al. 2009). Often models reproduce MJO events that have a realistic structure but a phase speed closer to that of a convectively coupled Kelvin wave (Slingo et al. 1996). Other modeling studies fail to reproduce a strong-enough signal (Sperber 2004) or can accurately reproduce MJO events at the cost of a degraded atmospheric mean state (Kim et al. 2012). Deficiencies in modeling have been thought to be attributed to erroneous convective parameterization, misrepresentation of surface fluxes (Maloney and Sobel 2004) or ocean–atmosphere coupling (Kemball-Cook and Weare 2001; Sperber et al. 2005), and an inadequate understanding of the interactions of the multiple spatiotemporal scales of organized tropical convection (Majda and Stechmann 2009; Khouider et al. 2012).
The initiation and structure of the MJO is potentially influenced by extratropical motions (Lau and Peng 1987). Hsu et al. (1990) showed that anomalous extratropical potential vorticity (PV) could intrude into the tropics and generate upward motion within the area and argue that this mechanism was responsible for the initiation of an MJO event during the 1985/86 boreal winter season. Moore et al. (2010) suggest that the MJO influences the extratropical flow and then in turn is modulated by it, in addition to disturbing the equatorial waveguide and modulating wave activity downstream. Recent studies by Ray et al. (2009) and Ray and Zhang (2010) showed, by using a tropical channel model, that MJO signals develop in the equatorial atmosphere when forced by reanalysis fields at poleward boundaries during periods when an MJO was known to develop. However, the signal did not develop when the applied forcing was just the climatological winds. They conclude that the meridional transport of westerly momentum from the extratropics into the tropics is crucial in the generation of the intraseasonal anomaly in their model. In agreement with these results, Vitart and Jung (2010) found that the tropical intraseasonal oscillation predictive skill (measured as a bivariate correlation above the threshold of 0.5) of the European Centre for Medium-Range Weather Forecasts (ECMWF) forecast system improved by 15 days when extratropical activity was taken into account.
In this paper we seek a method that can capture the different dynamical components of the MJO. A partitioning technique is proposed that can separate the wind field within the tropics into an irrotational component, a nondivergent component, and a third harmonic component associated with vorticity and divergence elements from higher latitudes (>30°). We make use of the four-times-daily Interim ECMWF Re-Analysis (ERA-Interim; Dee et al. 2011) dataset for this purpose. The dataset is created by assimilating global, historical climate observations into a numerical weather prediction model, forecasting a series of fields 6 h later, optimally matching the forecast with the next set of observations, and interpolating the output onto a 1.5° latitude × 1.5° longitude grid. All pressure levels from 1000 to 100 hPa are used in this study. In particular, we make use of the zonal (u) and meridional (υ) components of the wind field to describe the convectively driven circulation of the MJO and the patterns associated with it. The geopotential height (Z) and specific humidity (q) fields are also used extensively.
The remaining sections of this paper are organized as follows. Section 2 describes the kinematic wind-partitioning technique applied to the ERA-Interim dataset. The wavenumber–frequency characteristics of the partitioned winds are shown in section 3. Section 4 further explores the three wind components within the context of the MJO through a composite analysis. A discussion of these results is offered in section 5. Finally, concluding remarks on the use of the wind-partitioning technique in the tropics are given in section 6.
2. Wind partitioning
Because it is of interest to study the contribution of vorticity and divergence elements to the different tropical dynamical modes, it is desirable to partition the wind field into nondivergent and irrotational components and to analyze each resulting wind field as an individual component of the propagation of the MJO. One approach involves a Helmholtz decomposition into rotational and divergent flow components with piecewise attribution to flow elements associated with the local dynamical features and the environment. Although this is straightforward across the entire sphere, results for a limited-area domain, such as those we consider here, can be sensitive to boundary conditions (Lynch 1989). This issue motivated Bishop (1996a,b) to develop an attribution technique using free-space (boundary free) Green’s functions to extract local features from their environment and to study the influence of the environmental flow on these features. This method was used in several studies of the influence of the environmental flow on the development of fronts and frontal waves (Renfrew et al. 1997; Rivals et al. 1998; Patoux et al. 2005). Here, we extend the method to separate the rotational (uψ) and divergent (uχ) components of the flow in the tropics and to investigate the characteristics of the environmental flow during MJO events. We do this by adapting the technique to a zonal channel centered on the equator in spherical coordinates. Because the meridional extent of the MJO increases with height, we choose partition boundaries that change with height, with the chosen ranges being from 30°S to 30°N in the lower troposphere (850 hPa), rising monotonically to 35°S–35°N in the upper troposphere (200 hPa). Via this method, uψ and uχ essentially capture the winds from vorticity and divergence elements within the annulus, respectively. Thus, uψ captures the rotational aspect of waves while uχ captures the divergent aspect of waves, in addition to other vortical and divergent features within the channel (e.g., the subtropical highs and the intertropical convergence zone). We can think of the final component as a pure deformation field associated with vorticity and divergence elements outside the channel.
We will briefly summarize the method here and will refer the reader to Bishop (1996a), Kimura and Okamoto (1987), and the appendix for more detail. The method consists of identifying the local flow with elements of vorticity and divergence and reconstructing the corresponding uψ and uχ components. By subtraction from the total wind, the environmental flow uθ is calculated.
An example of wind partitioning in the Indian Ocean. (a) Total wind with sea level pressure. (b) Nondivergent component with corresponding vorticity. (c) Irrotational component with corresponding divergence. (d) Background flow. Pressure and wind fields are both ECMWF surface analyses.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
It must be noted, however, that the attribution technique loses accuracy toward the edges of the annulus due to the presence of rotational and divergent features in the vicinity of the boundaries (Bishop 1996a). Therefore, we exclude the last few grid points and only analyze a subdomain of the annulus.
3. Space–time spectral analysis
The space–time power and cross-power spectra are obtained via fast Fourier transforms (FFTs). We follow a procedure similar to that used in previous studies (Yasunaga and Mapes 2012; Hendon and Wheeler 2008; Yang et al. 2007; Masunaga 2007; Masunaga et al. 2006; Roundy and Frank 2004; Wheeler and Kiladis 1999). To obtain the anomalies of each variable Φ, we subtract the climatological seasonal cycle, defined as the mean and the first three harmonics of the annual cycle. We partition each variable into equatorially symmetric and antisymmetric components, defined by Yanai and Murakami (1970) as ΦS = [Φ(NH) + Φ(SH)]/2 and ΦA = [Φ(NH) − Φ(SH)]/2, where ΦS and ΦA denote the symmetric and antisymmetric components of the variable, and NH and SH stand for the Northern and Southern Hemisphere, respectively. Third, the time series of each anomaly is divided into 128-day segments that overlap by 64 days, similar to Masunaga et al. (2006). Then, the space–time mean and linear trends are removed by least squares fits and the ends of the series are tapered to zero. After tapering, the complex FFTs are computed, first in longitude and then in time, to obtain the wavenumber–frequency spectrum for each latitude. Finally, the power and cross spectra are averaged over all segments and latitudes, defined as 15°N–15°S. For ERA-Interim variables, the number of degrees of freedom is calculated to be 188 [≈2 (amplitude and phase) × 33 yr × 365 days/128 (segment length)].
a. Power spectra of the partitioned winds
The signal strength [defined as the fraction of the power spectrum that stands above a red background spectrum (Hendon and Wheeler 2008)] of the equatorially symmetric and antisymmetric components of the partitioned winds are shown in Fig. 2. For uψ (Fig. 2, top), a pronounced peak in the antisymmetric spectrum is observed between westward wavenumbers 1–7 and a period of about 5 days, corresponding to the mixed Rossby–gravity (MRG) wave. Peaks are also seen to closely follow the dashed lines in both the symmetric and antisymmetric spectra, in particular the 7 m s−1 line, to periods of about 3 days, which correspond to easterly waves. Easterly waves are structurally very similar to the equatorial Rossby (ER1) waves, so their strong signal in the uψ power spectra is expected. Significant peaks are observed over periods of 3–10 days and westward wavenumbers 1–6. These peaks correspond to external Rossby–Haurtwitz waves, which are the gravest planetary wave modes that correspond to solutions of Laplace’s tidal equations (Madden and Julian 1972b; Misra 1975; Madden 2007). The dispersion curves presented for these wave modes are calculated in the same way as in Hendon and Wheeler (2008). At the lowest frequencies, peaks are observed over eastward wavenumbers 1–4, in both the symmetric and antisymmetric components, which correspond to the MJO.
Signal strength of the (left) symmetric and (right) antisymmetric components (top) uψ, (middle) uχ, and (bottom) uθ over 15°S–15°N. Shading interval is 0.1 with the first contour beginning at 0.2, which is significant at the 99% interval (based on 188 degrees of freedom). Dispersion curves are also plotted for Kelvin, ER1, n = 1 and n = 2 westward inertia–gravity (WIGn1 and WIGn2), n = 1 and n = 2 eastward inertia–gravity (EIGn1 and EIGn2), n = 0 inertia–gravity (EIGn0), and mixed Rossby–gravity (MRG) waves, with equivalent depths of 8, 12, 25 50, and 90 m, respectively. Dashed lines indicate constant phase speeds of 7.0, 9.0, and 11.0 m s−1, which are representative of westward-propagating easterly waves. Dash–dotted lines represent external Rossby–Haurwitz waves for equivalent depth of 10 km. The meridional mode n = 1 and n = 3 in the symmetric component, and n = 2 and n = 4 in the antisymmetric component. Contour interval is every 0.1 signal strength fraction.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
For uχ (Fig. 2, middle), the strongest signal corresponds to the Kelvin wave at zonal wavenumbers 4–7 and a period of about 5 days and the westward-propagating n = 1 inertia–gravity waves at wavenumbers 4–12 and a period of about 2 days. The MRG and eastward-propagating n = 0 inertia–gravity waves dominate the antisymmetric spectrum. Significant signals are also seen for n = 2 inertia–gravity waves and easterly waves. A strong signature at wavenumbers 1 and 2, corresponding to the MJO, is also seen, particularly in the antisymmetric spectrum. It is worth noting that uχ has larger signal strength values than uψ over intraseasonal time scales.
For uθ (Fig. 2, bottom), the strongest and most coherent signal appears in what would be the Kelvin wave band but is visible in both the symmetric and antisymmetric spectra. The maximum strength is not as high as in the irrotational wind component, but values as high as 0.6 are seen over periods of 3–10 days. This signature likely corresponds to extratropical Rossby waves that are superimposed over a region of westerly winds (Pratt 1977; Hayashi and Golder 1977, 1983). This is further supported by the signal strength of the geopotential height anomalies over the 30°–35° region in both the Northern and Southern Hemispheres, which is depicted in Fig. 3. The signal strength of the height anomalies in that latitude band is similar to the signal of the background flow. In particular, a strong Kelvin wave–like signal is evident, indicating extratropical Rossby waves.
Signal strength of the (left) Northern and (right) Southern Hemisphere Z from 30° to 35° at 850 hPa. Solid and dashed lines are as in Fig. 2. Dash–dotted lines represent external Rossby–Haurwitz waves for equivalent depth of 10 km. The meridional mode n = 1 and n = 3. Unlike Fig. 2, the anomalies are not decomposed into equatorially symmetric and antisymmetric components.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
b. Coherence of uθ with geopotential heights
To further analyze the nature of the background flow, we perform a cross-spectral analysis with ERA-Interim geopotential heights and analyze the coherence and phase spectra. The latitudes chosen for comparison are in the 30°–45° band, in both the Northern and Southern Hemispheres, for the geopotential heights, and 15°S–15°N for uθ. The coherence value at the 99% confidence interval is calculated to be 0.03. However, for the following figures, we opted for a higher minimum interval of 0.05 in order to emphasize the signals that are most strongly related to fluctuations in extratropical geopotential height anomalies.
Symmetric and antisymmetric spectra are shown in Fig. 4. For both the symmetric (Fig. 4a) and antisymmetric (Fig. 4b) coherence spectra, the highest coherences agree with the dispersion curve of extratropical Rossby waves, with coherence values as high as 0.7 in both spectra, dominant in wavenumbers 3–6 in the lowest frequencies and in higher wavenumbers at higher frequencies. These results are consistent with observations of extratropical wave activity (Blackmon 1976; Simmons et al. 1983; Branstator 2002). A westward-moving component is also seen with high coherence values. This is likely due to standing waves in the extratropical atmosphere affecting the tropical flow (Hayashi 1979; Wallace 1983). Additionally, high coherence values in westward-propagating waves over the highest frequencies are likely due to Rossby–Haurtwitz waves (Blackmon 1976; Blackmon et al. 1984; Hendon and Wheeler 2008). The phase spectra (Figs. 4c and 4d) show that the winds are nearly 180° out of phase with the extratropical heights. This indicates that westerly flow is associated with lower heights while easterlies are associated with positive heights. In other words, westerly flow is associated with cyclonic-vorticity sources and easterly flow is associated with anticyclonic sources outside the partition domain. The higher-frequency, eastward-propagating disturbances show a slight lag of the winds with respect to the height anomalies. This lag is due to higher-frequency momentum-transporting waves having a tilt with latitude (Starr 1948; Lau 1979). These plots were calculated for different pressure levels, and nearly identical coherence and phase spectra were obtained. These results indicate that uθ indeed captures the winds that are associated with extratropical motions. The similarities between the signals of uθ, and extratropical Z along with the high coherence between the two variables, evidences that uθ is indeed able to influence extratropical motions on the tropical annulus.
Coherence squared and phase spectrum for (a),(c) symmetric and (b),(d) antisymmetric components of uθ (850 hPa) within the latitude band 15°S–15°N with Z at 850 hPa within the latitude band 30°–45°N/S. The dispersion curves are as in Fig. 2.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
4. Composites
The characteristics of the partitioned winds in relation to the MJO are shown through compositing with the real-time multivariate MJO index (Wheeler and Hendon 2004). For this study, we focus on MJO events that occurred during the months of November–March (NDJFM), when MJO activity is strongest. Results discussed in this section are shown to be statistically significant at the 95% confidence interval with a Student’s t test of each composite.
a. Irrotational and nondivergent winds
Figure 5 shows a composite of uχ with 850-hPa humidity anomalies overlaid as shading. The corresponding velocity potential (χ) anomalies are contoured, with gray contours denoting negative (divergent) anomalies and black contours denoting positive (convergent) anomalies. The minimum in OLR and the maximum in convergence are denoted in Fig. 5 by a magenta circle and a red star, respectively.
Composite of uχ at 850 hPa for MJO phases 1–8 [based on real-time multivariate MJO (RMM) PCs] during the months of November–March. Overlaid are colored contours of anomalies in specific humidity at the same pressure level. Red (blue) dots depict positive (negative) humidity anomalies that are statistically significant at the 95% confidence interval. Positive velocity potential anomalies are denoted with black contours while negative velocity potential anomalies are denoted with gray contours. Contour interval is 5 × 105 m2 s−1. The magenta circle denotes the location of minimum OLR and the red star represents the location of maximum convergence associated with the MJO. MJO phases (a)–(d) 1–4 and (e)–(h) 5–8. Only wind vectors that are statistically significant at the 95% level are shown.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
The irrotational winds and the positive moisture anomalies track the convective envelope associated with the MJO during phases 2–6. Areas of dry anomalies and divergent winds tend to flank the regions of convergence and enhanced moisture. Beginning in phase 2 and most clearly during phases 3–6, a narrow zone of convergence and positive moisture anomalies over the latitudes of the climatological ITCZ is seen advancing ahead of the center of maximum convergence. This area of convergence gives a kink to the χ contours that lie east of the center of convection. Convergence reaches the Western Hemisphere at about phase 4, and enhanced moisture can be seen over the Amazon region and parts of the Atlantic ITCZ in phase 5.
An elongation in the χ anomaly appears in phase 7. The minima in OLR and maximum in convergence are now located along the western edge of the velocity potential anomaly. The elongation becomes more apparent in phase 8, as the OLR minimum remains in the central Pacific while the center of convergence is now over South America. Additionally, new convergent features strengthen over Africa. This is consistent with the Kelvin wave–signature decoupling from the weakening convective envelope, as discussed in previous studies (Matthews 2000; Sperber 2003).
Figure 6 is a similar composite for uψ. Streamfunction (ψ) anomalies are contoured with positive anomalies depicted in black and negative anomalies depicted in gray. A noticeable feature in phases 1–5 is a Southern Hemisphere anticyclonic circulation pattern, which during phase 1 extends from about 50° to 170°E. The eastern edge of this anticyclonic circulation is associated with drier moisture anomalies and easterly winds near the equator. This dry anomaly is particularly strong during phase 1 and weakens during subsequent phases. The western edge of this circulation is associated with positive moisture anomalies and poleward flow. Beginning in phase 3, a cyclonic circulation that enhances the westerlies behind the MJO’s convective envelope is seen trailing the anticyclone in the Southern Hemisphere. The western edge of the cyclonic circulation is associated with equatorward flow and dry anomalies. The eastern edge is associated with poleward flow and moist anomalies. The Southern Hemisphere pattern is best defined when convection is centered over the Maritime Continent (phases 4 and 5), and the circulation anomalies quickly dissipate after they cross the date line.
Composite of uψ winds at 850 hPa for MJO phases 1–8 (based on RMM PCs) during the months of November–March. Overlaid are colored contours of anomalies in specific humidity at the same pressure level. Red (blue) dots depict positive (negative) humidity anomalies that are statistically significant at the 95% confidence interval. Positive streamfunction anomalies are denoted with black contours while negative streamfunction anomalies are denoted with gray contours. Contour interval is 1 × 106 m2 s−1. The magenta circle denotes the location of minimum OLR. Only wind vectors that are statistically significant at the 95% level are shown.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
The streamfunction anomalies and corresponding nondivergent winds are weaker and less defined in the Northern Hemisphere. An anticyclone is observed over Southeast Asia in phase 1, propagating eastward toward the Pacific, where it dissipates in phase 4. The Northern Hemisphere circulation feature is then followed by a reverse pattern. A cyclonic vortex is seen developing over the northern Indian Ocean in phase 3, which then strengthens as it propagates eastward, enhancing equatorial westerly wind anomalies. Unlike the anticyclonic feature, the pattern does not quickly dissipate as it enters the northwestern Pacific.
Another noteworthy circulation pattern is observed near the Amazon, where an anticyclone is seen in phases 4–6 in association with a dry anomaly east of it, which then reverses to a cyclonic pattern in phases 8 and 1, with a slight enhancement of moisture over the region. The observed flow patterns in this section agree with previous studies (Sperber 2003; Kiladis et al. 2005; Benedict and Randall 2007; Kiranmayi and Maloney 2011).
b. The background flow uθ
As described in previous sections, the background flow is the third component obtained from the wind partitioning and can be calculated by subtracting uχ and uψ from the total wind field. It is irrotational and nondivergent and is induced by vorticity and divergence elements outside the partitioned domain. Figure 7 shows an eight-phase composite of the background flow and the geopotential height anomalies at 850 hPa for the months of November–March. Similar to the procedure undertaken in the previous sections, the space–time mean and first three harmonics of the seasonal cycle are removed from each variable to best extract the signal of the intraseasonal anomaly. Dashed contours of the geopotential height anomalies denote troughs and solid contours denote ridge anomalies. The maximum in 850-hPa convergence and the minimum equatorial (10°S–10°N) stretching deformation contribution by uθ are denoted in Fig. 7 by a red star and a green circle, respectively. Stretching deformation is defined as the difference between the zonal gradient of zonal wind minus the meridional gradient of meridional wind (i.e., ∂uθ/∂x − ∂υθ/∂y). The shaded zonal wind anomalies of the background flow are clearly related to the troughs and ridges along and near the tropical annulus. A cycle in the zonal winds, which appears to be in phase with the extratropical height anomalies, can clearly be seen in the eight phases of the MJO. These height anomalies agree with results found by Roundy et al. (2010) and other general circulation studies (Matthews et al. 2004; Seo and Son 2011). For example, an anomalous ridge can be seen off the coast of Japan in phase 1, along with anomalous easterlies on its southern flank. The ridge propagates eastward while strengthening during subsequent phases. A poleward propagation of the pattern is also evident. The ridge peaks in intensity in phase 5 near the central North Pacific, when a trough pattern develops where the ridge was located during phase 1 (i.e., off the coast of Japan). The ridging pattern continues northward in phases 6 and 7 as the trough propagates eastward. Near-equatorial westerlies are seen to accompany this trough anomaly. By phase 8, the pattern looks remarkably similar to the Pacific–North America pattern described in several studies (Wallace and Gutzler 1981; Rennert and Wallace 2009) and described within the context of the MJO (Matthews et al. 2004). The overall zonal winds are weak, with a maximum anomaly of about 1 m s−1 in the western and central Pacific, but cover a substantial area of the tropical belt. The areas of strong stretching deformation, as marked in Fig. 7 by the green circle, are confined to the Pacific basin. This area appears to also propagate eastward with different MJO phases.
Composite of the background flow at 850 hPa for MJO phases 1–8 during the months of November–March. Shading denotes the zonal component of the background flow. Solid contours denote positive geopotential height anomalies while dashed contours denote negative anomalies. Contour interval is 2.5 m. Red dots denote geopotential height anomalies poleward of 30°N/S that are statistically significant at the 95% confidence interval. The red star represents the location of maximum convergence at 850 hPa associated with the MJO, while the green circle denotes the area of strongest stretching deformation associated with the background flow at 850 hPa. Only wind vectors that are statistically significant at the 95% level are shown.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
It is important to note that during phases 4–6 the ridges are closer to the equator and significantly stronger; thus, the tropical belt is more uniformly easterly. The opposite is also true for phases 1, 2, and 8. The overall wind pattern resembles an oscillation in the zonal mean zonal wind field (wavenumber 0) with a superposition of propagating waves with zonal wavenumbers 1–5. The compositing was also done for the 500-hPa level, and the pattern looks similar, although higher in the troposphere the height anomalies and the corresponding winds are stronger. Composite plots for the boreal summer months (not shown) display a similar pattern, although the stronger anomalies are instead located in the Southern Hemisphere.
In comparison, the background flow at 200 hPa (Fig. 8) shows a different pattern. In phase 1, the strong trough in the extratropical north-central Pacific is present, and westerly flow is seen over the equatorial central Pacific, similar to but stronger than that seen in Fig. 7. However, strong ridges in the northern and southern Indian and Atlantic Oceans are seen to influence uθ significantly more than at 850 hPa. In particular, an elongated ridge is seen in phase 1 and propagates eastward; it is replaced by an elongated trough by phase 3. Strengthening of the central Pacific wave train, which consists of a ridge near Japan, a north-central Pacific trough, and a second ridge over North America during phase 3, is now accompanied by a strengthening of a north-to-south trough–ridge–trough pattern over the equatorial Asian region. This pattern also propagates eastward. Phase 4 is a nearly complete reversal of the global pattern seen in phase 1. This eastward propagation is further evidenced by the stretching deformation minimum, as depicted by the green circle. In contrast to Fig. 7, where deformation is confined to the Pacific Ocean, the deformation anomaly in the upper levels is seen over the Indian Ocean sector in phases 1 and 2 and propagates toward the Pacific basin as the active phase of the MJO propagates into the Maritime Continent. Figures 7 and 8 show that the zonal mean of the zonal component of uθ oscillates between easterlies and westerlies over the eight phases of the MJO. This suggests an extratropical influence on oscillations in tropical angular momentum (Weickmann and Sardeshmukh 1994; Weickmann et al. 2000; Weickmann and Berry 2009). The following section investigates the relationship of the zonal means of uθ to the zonally averaged fluctuations in geopotential heights.
As in Fig. 7, but at 200 hPa. Contour interval is 5 m. The red star represents the location of maximum convergence at 850 hPa, associated with the MJO, while the green circle denotes the area of strongest stretching deformation associated with the background flow at 200 hPa.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
c. Zonal means
The zonal average of uθ superimposed on the zonal mean geopotential height anomalies is shown in Figs. 9b and 9d, for the 850- and 200-hPa heights, respectively. Black contours denote positive height anomalies and dashed gray contours denote negative height anomalies. An oscillation in the background winds is observed in the zonally averaged flow at 850 hPa (Fig. 9b), with easterlies prevailing from phases 3 to 7, when poleward pressure gradients prevail, and westerlies prevailing in phases 7, 8, and 1, when the pressure gradient is equatorward. The negative height anomaly arising in phase 2 appears to propagate poleward through phase 8. This is likely associated with the Kelvin wave response to the MJO in the Pacific basin (Matthews 2000; Sperber 2003). In comparison, the nondivergent winds at 850 hPa (Fig. 9a) show a stronger, more localized, zonal mean pattern, with prevailing easterlies during phases 1–3 and westerlies in phases 4–8. This is likely due to the anticyclonic gyres generating strong bursts of easterly winds, and the large zonal extent of the Kelvin wave response (Gill 1980) in the early phases. As the MJO progresses toward the western Pacific, the westerly winds associated with the Rossby gyres become the dominant wind feature.
Phase–latitude diagrams of uψ at (a) 850 and (c) 200 hPa and uθ at (b) 850 and (d) 200 hPa, averaged over NDJFM. Negative values (blue shading) denote easterly wind anomalies while positive values (yellow and red shading) denote westerly wind anomalies. Contours denote geopotential height anomalies, with black contours denoting positive anomalies and dashed gray contours denoting negative anomalies. Contour interval is 2 m.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
At 200 hPa, a nearly inverse pattern is seen in uθ (Fig. 9d), with westerlies dominating the zonal pattern. This is likely due to the presence of the troughs in Asia and the Atlantic observed in Fig. 8, which are the dominant extratropical features as opposed to the central Pacific ridge that dominates at 850 hPa. In contrast, the zonal wind pattern in uψ at 200 hPa (Fig. 9c) is qualitatively similar to the 850-hPa pattern. Height anomalies near 30°N and 30°S correspond to the Rossby gyres. The nondivergent winds at the edges of the tropical annulus closely correspond to the height anomalies. Thus, the zonal wind at the edge of the domain is dominated by the Rossby wave response of the MJO. Near the equator, the Kelvin wave response is much larger in extent and shows a nearly circumglobal pattern, with intensity comparable to the Rossby wave response (Kiladis et al. 2005); thus, it is the dominant pattern in the zonal mean closer to the equator. A zonal mean of the irrotational winds (not shown) does not show any significant patterns at either level.
d. Vertical cross sections
Figure 10 shows vertical cross-section composites of the zonal components of the partitioned winds for the different MJO phases during NDJFM. The local wind components, uχ and uψ, are averaged over 0°–10°S while uθ is averaged over 15°S–15°N. Overlaid are contours of geopotential height anomalies, averaged over 0°–10°S for uχ and uψ, and over the 35°– 50° latitude band, in both the Northern and Southern Hemispheres, for uθ.
Composite of vertical cross sections of (left) uχ, (middle) uψ, and (right) uθ for MJO phases 1–8 during the months of November–March. Winds are averaged from 5°N to 15°S. Contours denote Z anomalies averaged from 5°N to 15°S for uχ and uψ. Contour interval is every 2 m. For uθ, the contours are Z anomalies averaged from 35° to 50°N/S. Contour interval is every 4 m. The MJO phases are arranged from (a) phase 1 to (h) phase 8. Areas where the positive (negative) zonal wind anomalies are statistically significant at the 95% confidence interval are depicted by a red (blue) dotted contour.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
The irrotational flow anomalies (Fig. 10, left) follow the classic MJO pattern, with both the easterly and westerly anomalies strongest when the convective signal is over the Maritime Continent. Anomalous easterlies near the surface reverse to stronger westerlies in the 500–300-hPa layer, reaching a maximum of 1.5 m s−1. The near-surface convergence over the Indian Ocean seen in phase 3 is slightly east of the surface low. This surface convergence follows the low pressure through phase 7. In the upper levels, positive height anomalies appear to slightly lag the westerly winds during early phases of the MJO. The westerly wind signal decays by phase 7, although the height anomaly continues to strengthen. It is worth noticing that the suppressed phase shows stronger irrotational winds and geopotential height anomalies.
The nondivergent winds (Fig. 10, middle) show a similar pattern, though it is much stronger higher in the troposphere when compared to the irrotational winds. There is a clear difference in strength between the surface winds and the upper-level winds, with the upper-level pattern being more global compared to the lower levels. The lower-level winds appear to maximize between 850 and 700 hPa while the upper-level winds maximize between 150 and 100 hPa. The relationship between the nondivergent winds and the height anomalies is evident, but it is likely due to more than one dynamical process. For example, during phase 6, the upper-level westerly winds and ridging to the east of the date line closely resemble an idealized Kelvin wave pattern, whereas the easterlies over the Maritime Continent more closely resemble a Rossby wave pattern (Matsuno 1966; Kiladis et al. 2005, 2009).
The strongest signal in uθ (Fig. 10, right) develops over the western Pacific, near 180°, during phase 4. The areas of anomalous winds strengthen up to about 300 hPa and appear nearly vertically stacked. The corresponding extratropical geopotential height anomalies show a slight westward tilt with height near the central Pacific. This signal is strongest in phase 4, when the active phase of the MJO is located over the Maritime Continent. This is the typical signature of baroclinic wave disturbances, suggesting that the height anomalies see in Fig. 7 indeed correspond to Rossby wave trains, potentially a response to the localized heating and the redistribution of mass by convection within the MJO (Jin and Hoskins 1995; Matthews et al. 2004).
e. Angular momentum
The contribution to the total atmospheric angular momentum (M = ρua cosφ; ρ is the atmospheric density, u is the total zonal wind, a is the radius of the Earth, and φ is latitude) of the partitioned winds is analyzed. This is done by integrating each component of the partitioned winds zonally and vertically, from 1000 to 100 hPa. For the purpose of comparing with other studies, the resulting angular momentum components are multiplied by an additional a cosφ. Results for the nondivergent (Mψ) and background (Mθ) angular momentum contributions are shown in Fig. 11. It can clearly be seen that modulations in atmospheric angular momentum are dominated by the local nondivergent elements, with an overall structure similar to that is observed in Fig. 9c, indicating that upper levels dominate angular momentum changes associated with the MJO. These results are consistent with previous studies (Weickmann and Sardeshmukh 1994; Weickmann et al. 1997, 2000; Weickmann and Berry 2009). Higher-latitude elements of vorticity and divergence do not seem to significantly influence equatorial changes in angular momentum, with Mθ being about 4 times smaller, and lacking the structure that is observed in Mψ. In contrast to Mψ, the structure observed in Mθ is more similar to that in Fig. 9b, indicating that the lower troposphere contributes more to Mθ. The contribution of Mψ and Mθ to M is shown in Fig. 12. While Mψ clearly dominates M, the smaller contribution from Mθ seems to reduce the amplitude of the total angular momentum anomaly, while also causing a slight phase shift in the sign of M.
Zonally and vertically integrated angular momentum as a function of latitude and MJO phase. Angular momentum for the (left) nondivergent winds and (right) background flow. Contour interval is 1 kg m−2 s−1 × 1026. The zero contour is denoted by a red dashed line.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
Angular momentum averaged from 15°S to 15°N as a function of MJO phase. The dashed line depicts the contribution by the nondivergent winds, the dotted line denotes the contribution from the background flow, and the solid line is the total angular momentum.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
5. Discussion
An attribution technique making use of free-space Green’s functions has been applied to the 33-yr record of ERA-Interim winds at different pressure levels. This technique efficiently partitions the wind field into nondivergent and irrotational components within the partition region and a third harmonic component associated with vorticity and divergence elements outside this domain. In this study, the partitioning domain is the entire tropical grid. Because the partition encompasses all longitudes across the tropics, the background flow is induced by extratropical vorticity and divergence elements. The analysis shows that the local (uψ and uχ) components of the flow have high coherence with the local geopotential height field while uθ has low coherence with the local height field and is not directly related to equatorial wave modes, but shows a strong coherence with the height anomalies in the extratropics. While previous studies have shown the existence of a relationship between the local rotational and divergent elements of the MJO and midlatitude wave trains, the wind-partitioning technique used in this study has the advantage of quantitatively attributing the contribution of these extratropical features to the near-equatorial wind field.
A composite analysis of the MJO shows that the partitioned winds capture the Rossby gyres and the convergence regions of the MJO. Additionally, the overlaid humidity anomalies correspond well with both wind components, with cyclonic gyres north and south of the equator advecting drier air from higher latitudes and then advecting it eastward via the equatorial westerly winds. An opposite relationship is seen with the anticyclones, with easterlies advecting moist air from the Maritime Continent into the Indian Ocean, and then spreading it meridionally, away from the equator. Additionally, a broad area of enhanced moisture is associated with converging winds while an area of suppressed moisture is associated with divergence. These results are in good agreement with previous studies on the horizontal structure of the MJO (Sperber 2003; Kiladis et al. 2005; Benedict and Randall 2007; Kiranmayi and Maloney 2011; Hsu and Li 2012).
The background flow shows an oscillation with phases of the MJO, closely following changes in the extratropical geopotential height field, resembling results found by Roundy et al. (2010). The winds are relatively weak but cover a significant area of the tropics. Additionally, the wind anomalies strengthen with height, showing a signature typical of extratropical wave motions (Holton 2004). The other wind components do not show such behavior, peaking in strength around 700 hPa and weakening in the midtroposphere, following a typical dynamical response to near-equatorial heating (Gill 1980). The zonally averaged oscillation in the background flow hints at a small modulation of the Hadley cell due to the orientation of the extratropical troughs and ridges, with enhanced easterlies in one phase and suppressed easterlies in another.
Based on results obtained by partitioning the wind field, as discussed in the previous sections, we show a schematic of the atmospheric circulation in the lower troposphere in Fig. 13 (top). During an active phase of the MJO that is centered close to the Maritime Continent, we can expect to have near-equatorial low pressure from the Kelvin wave response over the Pacific basin. Rossby gyres with associated westerly winds along the equatorial flanks can be found over the east-central Indian Ocean. At higher latitudes we can expect a train of Rossby waves emanating from the region of the MJO. The high-pressure regions that are centered on the central Pacific enhance the near-equatorial easterly flow from the Kelvin response and contribute to stronger easterlies away from the equator, as is seen in Kiladis et al. (2005). The trough centered at about 60°N near the Gulf of Alaska does not contribute much to the tropical flow. However, the second ridge arising from the Rossby wave pattern adds to the easterly flow over the area. Results from zonal averaging suggest that the extratropical height anomalies add an eastward torque when the active MJO is centered near the Maritime Continent and a westward torque when the suppressed phase is centered over this region. A more complex scenario is seen in the upper levels (Fig. 13, bottom). As depicted in Fig. 8, a trough now appears poleward of the Rossby anticyclones, and the Rossby wave train appears to propagate farther downstream than in the lower troposphere. The Kelvin wave pattern circumnavigates the globe and is accompanied by a pair of cyclones. Because of the equivalent barotropic structure of the Rossby wave train in the central Pacific, the easterlies associated with this pattern now oppose the winds associated with the local MJO structure.
Schematic of the global geopotential height field during an active MJO over the Maritime Continent. The L denotes negative height anomalies and the H denotes positive height anomalies at (top) 850 and (bottom) 200 hPa.
Citation: Journal of the Atmospheric Sciences 71, 1; 10.1175/JAS-D-13-084.1
It is likely that the background flow changes with varying atmospheric conditions [i.e., North Atlantic Oscillation (NAO), ENSO]. This implies that different background states can indirectly affect the structure and propagation of organized tropical deep convection, such as convectively coupled equatorial waves and the MJO. Future work will include a study of how the background flow changes with different modes of tropical convection, different global atmospheric states (ENSO phase, NAO phase), and the two-way interaction between the tropics and extratropics.
6. Conclusions
The use of free-space Green’s functions on a tropical grid provides several advantages:
It allows us to evaluate the contributions to the flow from local vorticity and divergence elements within the tropical channel. The component wind fields reveal details of the tropical circulation that are not as easily seen in the total wind field.
It allows a quantitative analysis of the contribution of sources outside the domain to the tropical circulation, (i.e., nonintruding extratropical systems), thereby providing a new perspective on the role of lateral forcing in tropical dynamics (Hoskins and Yang 2000), as well as on tropical–extratropical interactions. Thus, it allows for the determination of the significance of higher-latitude features in the dynamics of equatorial disturbances.
However, the technique is not without its caveats. The different wind components obtained by partitioning are not as meaningful near the edge of the channel. Additionally, large errors can exist where the gradients of vorticity and divergence are poorly resolved, and inaccuracies within such localized regions can be significant.
However, these results, which were obtained through analyzing a large dataset, agree well with previous studies (Sperber 2003; Kiladis et al. 2005; Roundy et al. 2010). We believe that this technique allows us to investigate the potential for the extratropically forced environmental flow to modulate the propagation of the MJO (or other convective systems). The partitioning provides a detailed view of the environmental flow structure, its interaction with higher-latitude waves, and the possibility for two-way feedback that could be a factor in the initiation or modulation of intraseasonal interactions.
Acknowledgments
This research was supported by NASA OVWST Grant NNX10AO87G and by the National Science Foundation’s Graduate Fellowship Program (NSF-GRFP) Grant DGE-0718124. The first author would like to thank Chris Bretherton and Elizabeth Maroon for comments that helped improve the manuscript. The authors would also like to thank three anonymous reviewers for their valuable feedback.
APPENDIX
Attribution Technique on the Surface of a Sphere
We seek to derive a set of equations that can partition the wind field into its irrotational, nondivergent, and background components over a large region of the globe. While previous studies derive the free-space Green’s functions assuming an infinite plane (Bishop 1996a,b), a solution on a sphere is likely better suited to study motions that cover a significant area of the globe. Here, we obtain the free-space Green’s function for the surface of the earth following a procedure similar to those in Bogomolov (1977) and Kimura and Okamoto (1987).
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