Temporal clustering of tropical cyclone occurrence on intraseasonal time scales

Over the global tropics, the Madden-Julian Oscillation (MJO) explains a significant amount of the variability in circulation and convection on intraseasonal time scales. However, significant variation exists in the spatial extent and seasonal occurrence of the MJO. While the upper-level divergent flow associated with MJO is often traced around the globe, the low-level wind circulations and regions of enhanced and reduced deep convection have maximum amplitudes over the Indian and Pacific Oceans. Furthermore, the MJO appears to be stronger during the Northern Hemisphere winter.

Over each tropical ocean basin in which tropical cyclones form, the potential for tropical cyclone formation has been linked to several dynamic and thermodynamic conditions. Many of the characteristics associated with the MJO are similar to the dynamic and thermodynamic factors that govern the potential for tropical cyclone formation. Therefore, several studies have examined the physical relationship between the MJO and tropical cyclone activity over the Southern Indian and Pacific Oceans (Hall et al. 2001), the western North Pacific (Liebmann et al. 1994), the eastern North Pacific (Maloney and Hartmann 2001) and the Atlantic Ocean (Mo 2000). Statistically, Hall et al. (2001) illustrated that there was a significant increase (decrease) in the probability of a tropical cyclone occurrence relative to a climatological value in the South Indian Ocean and South Pacific Ocean when the enhanced (reduced) convection phase of the MJO propagated through the region of the Australian monsoon trough.

While the MJO may impact the daily probability of tropical cyclone formation, there has not been a strict statistical examination of temporal variability as it relates to clustering of tropical cyclone activity in time due to the quasi-periodic nature of the MJO. In this context, a cluster is defined as a temporally bound group of tropical cyclone occurrences of sufficient size and concentration to be unlikely to have occurred by chance. Furthermore, the cluster of tropical cyclone activity is defined such that the individual occurrences in the cluster are related through a common physical mechanism (i.e., the MJO).

The study of Hall et al. (2001) was based on a count of tropical cyclone formations on days associated with each phase of the MJO. The hypothesis test for a significant change in probability of formation due to the MJO was examined using a normal approximation to the binomial distribution for the count of tropical cyclone formations. To examine temporal clustering, a Bernoulli random variable is used to identify all days when a tropical cyclone formed. For each tropical cyclone season, a uniform multinomial probability distribution is estimated in which the distribution parameter is defined as the relative frequency of formation for that year. A cluster index (Tango 1984, 1990) is based on a measure of the temporal interval between each formation. The significance of the index is based on the degree of departure from the underlying uniform multinomial distribution. The procedure is applied to examine the clustering of tropical cyclone occurrences during 1979-2004 over several ocean basins during each basin's tropical cyclone season. This clustering algorithm was chosen as it is capable of examining the cyclic occurrence of a phenomenon and is associated in an asymptotic sense to the chi-square distribution such that a level of significance may be identified.

A particular interesting result was found for the western North Pacific in which the cluster methodology is applied to tropical cyclone occurrence during May-October, 1979-2004. The MJO characteristics during this period are defined by the MJO index of Wheeler and Hendon (2004). Ten of the 26 periods are labeled as MJO years since more than 40% of the days contained significant MJO activity. Based on the cluster methodology, eight of the 26 years contained significant temporal clustering of tropical cyclone activity over the period range of 30-60 days. Five (three) of the eight years with temporal clusters were (not) MJO years. Furthermore, five of the ten MJO years did not contain significant temporal clustering. To compare with previous studies of the impact on the probability of tropical cyclone formation due to the MJO, the probabilities due to the MJO are examined for all years, years with temporal clusters during MJO years, years with temporal clusters in non-MJO years, years without temporal clusters during MJO years, and years without temporal clusters in non-MJO years. Results for the western North Pacific indicate that the inactive convection portion of the MJO is more effective in producing temporal clusters via forcing of periods of anomalous low tropical cyclone activity. This differs from other basins in which there is a statistically significant increase in the probability during the enhanced convection portion of the MJO. Temporal clustering in five of the ten MJO years did not occur due to more tropical cyclone formations than expected during the inactive convection portion of the MJO.

Comparisons of the temporal clustering of tropical cyclones associated with the MJO in several ocean basins will be presented.