Introduction to the MJO

The tropical atmosphere-ocean system varies on many time scales, including:

• The diurnal or daily cycle, forced by the daily cycle of the sun due to the rotation of the Earth about its axis
• Synoptic weather systems (e.g., tropical cyclones, hurricanes, typhoons, and others) that last up to a few days
• Intraseasonal or month-to-month variability (the Madden-Julian oscillation).
• The seasonal/annual cycle, forced by the annual cycle of the sun due to the rotation of the Earth about the sun.
• Interannual or year-to-year variability, such as El Nino.

Accurate forecasting of this variability will benefit people living in the tropical regions, and also over the rest of the Earth due to remote 'teleconnections' between the weather in the tropics and the weather elsewhere around the globe. Here, we focus on variability on the intraseasonal time scale, which is dominated by the Madden-Julian oscillation (MJO). This was discovered by Madden and Julian (1971, 1972) who called it the '40-50-day oscillation' because of its preferred time scale. Since then it has been called the '30-60-day oscillation' and the 'intraseasonal oscillation', but the term 'MJO' has now emerged as a favourite. Zhang (2005) gives a comprehensive review of the MJO. Further information can be found in research papers on the MJO.

MJO rainfall cycle

The MJO is characterised by an eastward propagation of rainfall over the 'warm pool' region from the Indian Ocean to the western Pacific. A composite mean MJO cycle, calculated by averaging over many individual MJO events, is shown in the animation in Fig. 1. The animation is on an endless loop, showing maps every day through the MJO cycle, which is given a nominal period here of 48 days. The maps show 'anomalies' of rainfall, where the climatological mean rainfall map has been subtracted to leave the remainder. Where this remainder, or anomaly, is positive (blue shading), there is more rainfall than usual, i.e., conditions are wetter than normal. Where it is negative (red shading), there is less rainfall than usual, and conditions are drier than normal.

The MJO cycle presented here is as defined by Wheeler and Hendon (2004). Back in the day, there was no universally accepted definition of the MJO, and each MJO paper spent its first section defining its own, slightly different definition of the MJO, which made comparison of results rather difficult. However, the real-time multivariate (RMM) MJO index of Wheeler and Hendon is now the accepted standard definition. So thanks guys. The MJO cycle, as defined by the RMM index, is split up into 8 phases, for convenience. Each phase corresponds to 1/8 of the full cycle. An individual MJO event can last anywhere between 30 and 60 days (the MJO is a 'broadband' phenomenon). In the animation here, a typical period of 48 days is assumed, which conveniently means that each of the 8 RMM phases lasts 48/8=6 days. At the top right of Figure 1, an 'MJO clock' sweeps round showing the current RMM phase, and the actual values of the current RMM phase and day are shown to the left.

An MJO cycle can be considered to start in RMM phase 1. In phase 1, enhanced rainfall (blue shading) develops over the western Indian Ocean. This region of enhanced rainfall (wet conditions) then moves slowly eastward over the Indian Ocean in phase 2 and 3. By phase 4, it has reached the 'maritime continent' (the archipelago of islands and shallow seas of Indonesia and surrounding countries). In phase 6, 7 and 8, it propagates further eastward over the western Pacific, eventually dying out in the central Pacific. The next MJO cycle then starts, with enhanced rainfall over the western Indian Ocean in phase 1. Behind the region of enhanced rainfall is a region of suppressed rainfall (negative anomalies, red shading). Hence, at certain times during the MJO cycle there is a 'dipole' of rainfall anomalies. For example, in phase 6 there is enhanced rainfall over the western Pacific and suppressed rainfall over the Indian Ocean. In phase 2, the dipole is in the opposite sense (dry over the western Pacific and wet over the Indian Ocean).

Figure 1. MJO cycle of precipitation anomalies (CMAP data set). The life cycle is calculated from MJO events in the November-April (northern hemisphere winter) season only. Composite maps were calculated for each of the 8 RMM phases, and linearly interpolated for the intermediate days to give a smooth cycle. In addition to the colour shading, a thick solid contour at 1 mm day^-1 outlines the region of enhanced rainfall, and a thick dashed contour at -1 mm day^-1 outlines the region of suppressed rainfall. These contours are reproduced in subsequent animations below to indicate the main regions of MJO precipitation.

The rainfall anomalies shown above are calculated using the CMAP precipitation data set. This is a global data set, mainly based on satellite measurements of cloud top temperatures, and calibrated against ground based rain gauges. Although the data set has a relatively low horizontal resolution (grid length of 2.5 degrees, or approximately 250 km), its length (it begins in 1979) makes it very useful for defining the coarse-grained features of the MJO, as in Figure 1.

An alternative rainfall data set is available from the TRMM (Tropical Rainfall Measuring Mission) satellite. This has a much higher horizontal resolution (0.25 degrees, approximately 25 km). An animation of MJO rainfall anomalies from the TRMM data set is shown in Figure 2. The basic structure of the TRMM rainfall anomalies in Figure 2 agrees with the CMAP rainfall anomalies in Figure 1. However, much finer scale behaviour can be seen in the TRMM data set, especially around the islands of the maritime continent.

Figure 2. MJO cycle of precipitation anomalies (TRMM data set). The thick solid and dashed contours outline the main regions of enhanced and suppressed MJO rainfall from the CMAP data set, respectively, as in Figure 1.

Further reading:

Matthews AJ, Pickup G, Peatman SC, Clews P, Martin J, 2013: The effect of the Madden-Julian Oscillation on station rainfall and river level in the Fly River system, Papua New Guinea. J. Geophys. Res., 118, 10926-10935.	Abstract
Matthews AJ, Li HYY, 2005: Modulation of station rainfall over the western Pacific by the Madden-Julian Oscillation. Geophys. Res. Lett., 32, L14827, doi: 10.1029/2005GL023595.	Abstract

MJO tropical dynamics

In addition to strongly modulating the rainfall in the tropics, the MJO has a signal in other meteorological variables. For example, a clear MJO cycle in sea level pressure can also be seen (Figure 3). The negative sea level pressure anomalies (where the pressure is lower than usual) are coloured blue, and the positive sea level pressure anomalies (where the pressure is higher than usual) are coloured red (see the legend for exact values). The sea level pressure signal is clearly related to the cycle in rainfall; the thick solid contour outlines the area of enhanced rainfall that was shown in detail in Fig. 1, and the thick dashed contour outlines the area of suppressed rainfall.

The negative pressure anomalies appear to emanate out of the region of enhanced rainfall. One signal propagates eastward along the equator. This is an equatorial Kelvin wave. When it reaches the Andes mountain range along the eastern coast of the Pacific it is momentarily blocked, before continuing on eastward across the Atlantic, completing a circuit of the equator in one MJO cycle, about 48 days.

An equatorial Rossby wave signal is also forced by the MJO rainfall anomalies. This can be seen as a pair of negative sea level pressure anomalies, one either side of the equator, that lie slightly to the west of the enhanced rainfall.

In the 'other half' of the MJO cycle, the reduced rainfall triggers equatorial Kelvin and Rossby waves of the opposite sign (positive sea level pressure anomalies).

Figure 3. MJO cycle of sea level pressure anomalies (NCEP-DOE reanalysis data set). The thick solid and dashed contours outline the main regions of enhanced and suppressed MJO rainfall, respectively, as in Figure 1.

These equatorial Kelvin and Rossby waves are well understood theoretically through the Matsuno-Gill model of tropical dynamics (Matsuno, 1966; Gill, 1980). In the many individual cumulonimbus and other clouds that produce rain in the tropics, water vapour condenses to form liquid water or ice, that eventually falls out as rain. This condensation releases (latent) heat into the atmosphere, and this heat source can then drive the tropical circulation. An animation of the equatorial Kelvin-Rossby wave response to a heat source on the equator in a numerical model of the atmosphere (Figure 4) simulates many of the aspects of the observed MJO sea level pressure cycle in Figure 3.

Figure 4. Equatorial Kelvin-Rossby wave response to fixed equatorial heating in a shallow water model of the atmosphere. The upper panel represents the pressure and wind distribution in the upper atmosphere. The middle panel represents the vertical and zonal circulation in an equatorial plane. The lower panel represents the pressure and wind distribution in the lowerr atmosphere.

The MJO also affects other meteorological systems in the tropics:

• Monsoons. The MJO modulates the active/break cycles that occur within the Asian and West African monsoons.
• Tropical cyclones/hurricanes. The MJO modulates tropical cyclone numbers.
• El Nino - Southern Oscillation (ENSO). The MJO has been instrumental in triggering recent El Nino episodes.
• South Pacific Convergence Zone (SPCZ). The MJO affects the route taken by extratropical cyclones that propagate into the tropics and trigger convection along the SPCZ.

Further reading:

Birch CE, Webster S, Peatman SC, Parker DJ, Matthews AJ, Li Y, Hassim ME, 2016: Scale interactions between the MJO and the western Maritime Continent. J. Climate, 29, 2471-2492.	Abstract
Peatman SC, Matthews AJ, Stevens DP, 2015: Propagation of the Madden-Julian Oscillation and scale interaction with the diurnal cycle in a high-resolution GCM. Climate Dyn., 45, 2901-2918.	Abstract
Peatman SC, Matthews AJ, Stevens DP, 2014: Propagation of the Madden-Julian Oscillation through the Maritime Continent and scale interaction with the diurnal cycle of precipitation. Quart. J. Roy. Meteorol. Soc., 140, 814-825.	Abstract
Matthews AJ, 2012: A multiscale framework for the origin and variability of the South Pacific Convergence Zone. Quart. J. Roy. Meteorol. Soc., 138, 1165-1178.	Abstract
Lavender SL, Taylor CM, Matthews AJ, 2010: Coupled land-atmosphere intraseasonal variability of the West African monsoon in a GCM. J. Climate, 23, 5557-5571.	Abstract
Love BS, Matthews AJ, 2009: Real-time localised forecasting of the Madden-Julian Oscillation using neural network models. Quart. J. Roy. Meteorol. Soc., 135, 1471-1483.	Abstract
Lavender SL, Matthews AJ, 2009: Response of the West African monsoon to the Madden-Julian Oscillation. J. Climate, 22, 4097-4116.	Abstract
Love BS, Matthews AJ, Janacek GJ, 2008: Real-time extraction of the Madden-Julian Oscillation using empirical mode decomposition and statistical forecasting with a VARMA model. J. Climate, 21, 5318-5335.	Abstract
Matthews AJ, 2008: Primary and successive events in the Madden-Julian Oscillation. Quart. J. Roy. Meteorol. Soc., 134, 439-453.	Abstract
Pohl B, Matthews AJ, 2007: Observed changes in the lifetime and amplitude of the Madden-Julian Oscillation associated with interannual ENSO sea surface temperature anomalies. J. Climate, 20, 2659-2674.	Abstract
Matthews AJ, 2004: Intraseasonal variability over tropical Africa during northern summer. J. Climate, 17, 2427-2440.	Abstract
Hall JD, Matthews AJ, Karoly DJ, 2001: The modulation of tropical cyclone activity in the Australian region by the Madden-Julian Oscillation. Mon. Wea. Rev., 129, 2970-2982.	Abstract
Matthews AJ, 2000: Propagation mechanisms for the Madden-Julian Oscillation. Quart. J. Roy. Meteorol. Soc., 126, 2637-2652.	Abstract
Matthews AJ, Kiladis GN, 2000: A model of Rossby waves linked to submonthly convection over the eastern tropical Pacific. J. Atmos. Sci., 57, 3785-3798.	Abstract
Matthews AJ, Kiladis GN, 1999: Interactions between ENSO, transient circulation and tropical convection over the Pacific. J. Climate, 12, 3062-3086.	Abstract
Matthews AJ, Kiladis GN, 1999: The tropical-extratropical interaction between high-frequency transients and the Madden-Julian Oscillation. Mon. Wea. Rev., 127, 661-677.	Abstract
Matthews AJ, Slingo JM, Hoskins BJ, Inness PM, 1999: Fast and slow Kelvin waves in the Madden-Julian Oscillation of a GCM. Quart. J. Roy. Meteorol. Soc., 125, 1473-1498.	Abstract
Matthews AJ, Lander J, 1999: Physical and numerical contributions to the structure of Kelvin wave-CISK modes in a spectral transform model. J. Atmos. Sci., 56, 4050-4058.	Abstract
Slingo JM, Sperber KR, Boyle JS, Ceron JP, Dix M, Dugas B, Ebisuzaki W, Fyfe J, Gregory D, Gueremy JF, Hack J, Harzallah A, Inness P, Kitoh A, Lau WKM, McAvaney B, Madden R, Matthews AJ, Palmer TN, Park CK, Randall D, Renno N, 1996: Intraseasonal oscillations in 15 atmospheric general circulation models: results from an AMIP diagnostic subproject. Climate Dyn., 12, 325-358.	Abstract
Matthews AJ, Hoskins BJ, Slingo JM, Blackburn M, 1996: Development of convection along the SPCZ within a Madden-Julian Oscillation. Quart. J. Roy. Meteorol. Soc., 122, 669-688.	Abstract

Global structure of the MJO

The MJO is not just confined to the tropics. Figure 5 shows an animation of the MJO cycle in 200-hPa streamfunction anomalies. Streamfunction is a measure of the circulation in the atmosphere. The wind blows parallel to streamfunction contours: clockwise around positive streamfunction anomalies (red shading), and anticlockwise around negative streamfunction anomalies (blue shading). 200 hPa is a pressure level in the upper troposphere, about 8 km above the Earth's surface. It is the level at which the jet streams are strongest, and the MJO streamfunction anomalies in Figure 5 represent changes to the position and strength of the jet streams. The animation in Figure 5 shows that the MJO signal is truly global, with planetary-scale Rossby wave trains reaching out from the tropical core region out into the extratopics and high latitudes.

Figure 5. MJO cycle of 200-hPa streamfunction anomalies (NCEP-DOE reanalysis data set).

Further reading:

Matthews AJ, Hoskins BJ, Masutani M, 2004: The global response to tropical heating in the Madden-Julian Oscillation during northern winter. Quart. J. Roy. Meteorol. Soc., 130, 1991-2011.

Abstract

Ocean component of the MJO

The MJO is not just confined to the atmosphere. It has a strong signal in the ocean, with warm sea surface temperatures (SSTs) leading the enhanced rainfall, and cool SSTs leading the reduced rainfall (Figure 6). This has lead to theories of the MJO based on coupled ocean-atmosphere interactions.

Figure 6. MJO cycle of sea surface temperature anomalies (NOAA OI v2 data set).

Further reading:

Baranowski DB, Flatau MK, Flatau PJ, Matthews AJ, 2016: Impact of atmospheric convectively-coupled Kelvin waves on upper ocean variability. J. Geophys. Res., 121, 2045-2059.	Abstract
Matthews AJ, Baranowski DB, Heywood KJ, Flatau PJ, Schmidtko S, 2014: The surface diurnal warm layer in the Indian Ocean during CINDY/DYNAMO. J. Climate, 27, 9101-9122.	Abstract
Webber BGM, Matthews AJ, Heywood KJ, Kaiser J, Schmidtko S, 2014: Seaglider observations of equatorial Indian Ocean Rossby waves associated with the Madden-Julian Oscillation. J. Geophys. Res., 119, 3714-3731.	Abstract
Webber BGM, Stevens DP, Matthews AJ, Heywood KJ, 2012: Dynamical ocean forcing of the Madden-Julian Oscillation at lead times of up to five months. J. Climate, 25, 2824-2842.	Abstract
Webber BGM, Matthews AJ, Heywood KJ, Stevens DP, 2012: Ocean Rossby waves as a triggering mechanism for primary Madden-Julian events. Quart. J. Roy. Meteorol. Soc., 138, 514-527.	Abstract
Matthews AJ, Singhruck P, Heywood KJ, 2010: Ocean temperature and salinity components of the Madden-Julian Oscillation observed by Argo floats. Climate Dyn., 35, 1149-1168.	Abstract
Webber BGM, Matthews AJ, Heywood KJ, 2010: A dynamical ocean feedback mechanism for the Madden-Julian Oscillation. Quart. J. Roy. Meteorol. Soc., 136, 740-754.	Abstract
Matthews AJ, Singhruck P, Heywood KJ, 2007: Deep ocean impact of a Madden-Julian Oscillation observed by Argo floats. Science, 318, 1765-1769.	Abstract
Batstone CP, Matthews AJ, Stevens DP, 2005: Coupled ocean-atmosphere interactions between the Madden-Julian Oscillation and synoptic-scale variability over the warm pool. J. Climate, 18, 2004-2020.	Abstract
Matthews AJ, Meredith MP, 2004: Variability of Antarctic circumpolar transport and the southern annular mode associated with the Madden-Julian Oscillation. Geophys. Res. Lett., 31, L24312, doi: 10.1029/2004GL021666.	Abstract
Matthews AJ, 2004: The atmospheric response to observed intraseasonal tropical sea surface temperature anomalies. Geophys. Res. Lett., 31, L14107, doi: 10.1029/2004GL020474.	Abstract