  The Madden-Julian oscillation (MJO) is a tropical weather system having
important influence in the tropics and beyond; however, many of its
characteristics are poorly understood, including their initiation and
completion. Here we define Madden-Julian events as the contiguous time periods
with an active MJO, and we show that both the durations and the sizes of these
events are well described by a double power-law distribution. Thus, small
events have no characteristic scale, and the same for large events;
nevertheless, both types of events are separated by a characteristic duration
of about 27 days (this corresponds to half a cycle, roughly). Thus, after 27
days, there is a sharp increase in the probability that an event gets extinct.
We find that this effect is independent of the starting and ending phases of
the events, which seems to point to an internal mechanism of exhaustion rather
than to the effect of an external barrier. Our results would imply an important
limitation of the MJO as a driver of sub-seasonal predictability.
