Propagation of the MJO As a Kelvin Wave over the Western Hemisphere

Over the Western Hemisphere, the Madden-Julian Oscillation (MJO) maintains a structure in zonal wind and vertical velocity similar to that of a first baroclinic wavenumber 1 Kelvin wave. Despite the absence of equatorial convection over the eastern Pacific cold tongue, the wave propagates slower than a free Kelvin wave (~45 m s^-1). The present work explains how the propagation speed of the MJO, particularly outside of the tropical warm pool, can be depicted as that of an equatorial Kelvin wave coupled to equatorial and off-equatorial convection within ~15º latitude of the equator. MERRA2 reanalysis is used to quantify total diabatic heating and vertical motion associated with a variety of wavenumber 1 MJO signals present during 1981–2011 throughout the tropics by filtering reanalysis fields as done in Powell and Houze (2015).

Generally, diabatic heating within convection occurring on the wave-scale does not completely offset the adiabatic cooling associated with wave-scale vertical motion. The degree to which the two cancel each other determines the theoretical phase speed of the wave by way of reducing the effective static stability of the environment (as described by Neelin and Held [1987] or Emanuel et al. [1994]). The magnitude of the offset is shown to have a longitudinal dependence. The theoretical phase speed of a composite of several MJO signals is largest (20–25 m s^-1) relative to mean zonal flow over the eastern Pacific and eastern Atlantic/equatorial Africa. It is smaller (18–20 m s^-1) over the Amazon, and the least over the TWP (12–18 m s^-1). When the mean equatorial zonal flow is added, the phase speed is reduced at all longitudes outside the eastern Pacific and reaches a minimum of 5 m s^-1 over the Maritime Continent, where equatorial convection is most prevalent. The theoretically derived phase speeds match closely to the propagation speeds of the actual circulation signal (derived using zonal wind or velocity potential anomalies) as depicted in reanalysis throughout the tropics. Theoretical and actual phase speeds of low-frequency Kelvin waves within several individual series of successive MJO events will be illustrated to show robustness of the relationship between wave heating and phase speed.

As the wave approaches the Indian Ocean, it supports widespread deep convective development by reducing the temperature above the boundary layer, allowing convective updrafts to more frequently penetrate the stable layer located at 700–850 hPa and grow into deeper and wider convective elements. An understanding of what controls the propagation speed of the wave as it circumnavigates will eventually be important for predicting the timing of successive MJO events. Thus, the relationship proposed by Powell and Houze (2015) and Powell (2016) between the large-scale circulation dynamics in the wave and convective development over the Indian Ocean will also be briefly reviewed.