  Tropical precipitation clusters exhibit power-law frequency distributions in
area and volume (integrated precipitation), implying a lack of characteristic
scale in tropical convective organization. However, it remains unknown what
gives rise to the power laws and how the power-law exponents for area and
volume are related to one another. Here, we explore the perspective that
precipitation clusters are islands above a convective threshold on a rough
column-water-vapor (CWV) topography. This perspective is supported by the
agreement between the precipitation clusters and CWV islands in their frequency
distributions as well as fractal dimensions. Power laws exist for CWV islands
at different thresholds through the CWV topography, suggesting that the
existence of power-laws is not specifically related to local precipitation
dynamics, but is rather a general feature of CWV islands. Furthermore, the
frequency distributions and fractal dimensions of the clusters can be
reproduced when the CWV field is modeled to be self-affine with a roughness
exponent of 0.3. Self-affine scaling theory relates the statistics of
precipitation clusters to the roughness exponent; it also relates the power-law
slopes for area and volume without involving the roughness exponent. Thus, the
perspective of precipitation clusters as CWV islands provides a useful
framework to consider many statistical properties of the precipitation
clusters, particularly given that CWV is well-observed over a wide range of
length scales in the tropics. However, the statistics of CWV islands at the
convective threshold imply a smaller roughness than is inferred from the power
spectrum of the bulk CWV field, and further work is needed to understand the
scaling of the CWV field.
