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\begin{document}

\title{A dimensionless parameter for predicting convective self-aggregation
onset in a stochastic reaction-diffusion model of tropical
radiative-convective equilibrium.}



\author[1]{Giovanni Biagioli}%
\author[2]{Adrian Mark Tompkins}%
\affil[1]{University of Trieste}%
\affil[2]{Abdus Salam International Centre for Theoretical Physics (ICTP)}%


\vspace{-1em}



  
  \date{June 10, 2024}


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\begin{abstract}
We introduce a minimal stochastic lattice model for the column relative
humidity (\$R\$) in the tropics, which incorporates convective
moistening, lateral mixing and subsidence drying. The probability of
convection occurring in a location increases with \$R\$, based on TRMM
observations, providing a positive feedback that could lead to
aggregation. We show that the simple model reproduces many aspects of
full-physics cloud resolving model experiments. Depending on model
parameter settings and domain size and resolution choices, it can
produce both random or aggregated equilibrium states. Clustering occurs
more readily with larger domains and coarser resolutions, in agreement
with full physics models. Using dimensional arguments and fits from
empirical data, we derive a dimensionless parameter we call the
aggregation number, \$N\_\{ag\}\$, that predicts whether a specific
model and experiment setup will result in an aggregated or random state.
The parameter includes the moistening feedback strength, the diffusion,
the subsidence timescale, the domain size and spatial resolution. Using
large ensembles of experiments, we show that the transition between
random and aggregated states occurs at a critical value of
\$N\_\{ag\}\$. We argue that \$N\_\{ag\}\$ could help to understand the
differences in aggregation states between full physics, cloud resolving
models.%
\end{abstract}%



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