  Tropical cyclones are affected by a large number of climatic factors, which
translates into complex patterns of occurrence. The variability of annual
metrics of tropical-cyclone activity has been intensively studied, in
particular since the sudden activation of the N Atl in the mid 1990's. We
provide first a swift overview on previous work by diverse authors about these
annual metrics for the NAtl basin, where the natural variability of the
phenomenon, the existence of trends, the drawbacks of the records, and the
influence of global warming have been the subject of interesting debates. Next,
we present an alternative approach that does not focus on seasonal features but
on the characteristics of single events [Corral et al Nature Phys 6, 693,
2010]. It is argued that the individual-storm power dissipation index (PDI)
constitutes a natural way to describe each event, and further, that the PDI
statistics yields a robust law for the occurrence of tropical cyclones in terms
of a power law. In this context, methods of fitting these distributions are
discussed. As an important extension to this work we introduce a distribution
function that models the whole range of the PDI density (excluding
incompleteness effects at the smallest values), the gamma distribution,
consisting in a power-law with an exponential decay at the tail. The
characteristic scale of this decay, represented by the cutoff parameter,
provides very valuable information on the finiteness size of the basin, via the
largest values of the PDIs that the basin can sustain. We use the gamma fit to
evaluate the influence of sea surface temperature (SST) on the occurrence of
extreme PDI values, for which we find an increase around 50 % in the values of
these basin-wide events for a 0.49 degC SST average difference. ...
