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.
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