Testing the robustness of precipitation cluster scalings with an ensemble of aquaplanet simulations

Large and/or long-lived convective clusters are associated with extreme weather, drive the global circulation by forcing atmospheric waves, and affect the energy budget of the atmosphere by modulating outgoing longwave radiation in their vicinity. The majority of tropical clusters follow scale-free occurrence frequency distributions for cluster sizes and the rainfall integrated over a cluster (intensity). The relationships between intensity and area, and circumference and area also follow scaling laws. The exponents of all of these four scaling laws follow when we assume that precipitation clusters inherit their properties from the geometry of the integrated column water vapor field. Specifically, the column water vapor field would have to be a self-affine surface with a roughness exponent H=0.4. Coincidentally, H=0.4 is the prediction of the Kardar-Parisi-Zhang universality class in two dimensions.

I analyze the statistics of precipitation clusters and the column water vapor field in observations (using data from CMORPH and ERA5) and thirteen one-year global simulations performed with the ICON model at a horizontal resolution of 10 km. The simulations differ for example in their forcing (RCE or realistic forcing), in their rotation (no rotation, real rotation, constant Coriolis parameter), in their sea surface temperatures (SSTs; realistic and with land, zonal mean with land, constant without land, latitudinal gradient without land) etc. They are designed to test how robust the scaling laws of precipitation and column water vapor are.

What changes drastically between the simulations is the probability density distribution of points in the phase space of column water vapor and tropospheric bulk temperature. This distribution occupies a very narrow space in the RCE simulations, but a very wide space in the realistic simulation with land. The critical column water vapor, where precipitation starts to occur, is approximately a linear function of temperature. It turns out that the column water vapor axes and the temperatures axes can be rescaled so that the onset curves of all simulations collapse onto one line (approximately). The results show that there is a good match with the observed scaling in most simulations, with the control simulation (realistic SSTs and land) showing the closest match. I speculate what the results may imply for interpreting observed scalings based on the Kardar-Parisi-Zhang equation.