  Convective self-aggregation is a modelling paradigm for thunderstorm
organisation over a constant-temperature tropical sea surface. This setup can
give rise to cloud clusters over timescales of weeks. In reality, sea surface
temperatures do oscillate diurnally, affecting the atmospheric state. Over
land, surface temperatures vary more strongly, and rain rate is significantly
influenced. Here, we carry out a substantial suite of cloud-resolving numerical
experiments, and find that even weak surface temperature oscillations enable
qualitatively different dynamics to emerge: the spatial distribution of
rainfall is only homogeneous during the first day. Already on the second day,
the rain field is firmly structured. In later days, the clustering becomes
stronger and alternates from day-to-day. We show that these features are robust
to changes in resolution, domain size, and surface temperature, but can be
removed by a reduction of the amplitude of oscillation, suggesting a transition
to a clustered state. Maximal clustering occurs at a scale of
$\mathbf{l_{max}\approx 180\;km}$, a scale we relate to the emergence of
mesoscale convective systems. At $\mathbf{l_{max}}$ rainfall is strongly
enhanced and far exceeds the rainfall expected at random. We explain the
transition to clustering using simple conceptual modelling. Our results may
help clarify how continental extremes build up and how cloud clustering over
the tropical ocean could emerge much faster than through conventional
self-aggregation alone.
