Hovmöller diagram in the context of "Tropical wave"

The Madden–Julian oscillation (MJO) is the largest element of the intraseasonal (30- to 90-day) variability in the tropical atmosphere. It was discovered in 1971 by Roland Madden and Paul Julian of the American National Center for Atmospheric Research (NCAR). It is a large-scale coupling between atmospheric circulation and tropical deep atmospheric convection. Unlike a standing pattern like the El Niño–Southern Oscillation (ENSO), the Madden–Julian oscillation is a traveling pattern that propagates eastward, at approximately 4 to 8 m/s (14 to 29 km/h; 9 to 18 mph), through the atmosphere above the warm parts of the Indian and Pacific oceans. This overall circulation pattern manifests itself most clearly as anomalous rainfall.

The Madden–Julian oscillation is characterized by an eastward progression of large regions of both enhanced and suppressed tropical rainfall, observed mainly over the Indian and Pacific Ocean. The anomalous rainfall is usually first evident over the western Indian Ocean, and remains evident as it propagates over the very warm ocean waters of the western and central tropical Pacific. This pattern of tropical rainfall generally becomes nondescript as it moves over the primarily cooler ocean waters of the eastern Pacific, but reappears when passing over the warmer waters over the Pacific Coast of Central America. The pattern may also occasionally reappear at low amplitude over the tropical Atlantic and higher amplitude over the Indian Ocean. The wet phase of enhanced convection and precipitation is followed by a dry phase where thunderstorm activity is suppressed. Each cycle lasts approximately 30–60 days. Because of this pattern, the Madden–Julian oscillation is also known as the 30- to 60-day oscillation, 30- to 60-day wave, or intraseasonal oscillation.