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\begin{document}

\title{A Conceptual Model for Tropical Convective Organization}



\author[1]{Ziwei Li}%
\author[1]{Paul O'Gorman}%
\affil[1]{Massachusetts Institute of Technology}%


\vspace{-1em}



  
  \date{May 04, 2024}


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\begin{abstract}
Tropical convective organization and associated clusters of
precipitation affect the global circulation and Earth's energy budget,
but many aspects such as the power-law distribution of precipitation
clusters and the relation to convective self-aggregation remain poorly
understood. Here, we present a physics-informed 2D conceptual model for
tropical convective organization. The model is based on the budget
equation of column moist static energy (CMSE) with terms that are
parameterized based on diagnosing them in a high-resolution simulation
with explicit convection. The conceptual model combines a
reaction-diffusion equation, where the reaction term has memory, with a
temporal red noise. We find that vertical advection has a strengthening
effect on CMSE perturbations, whereas horizontal advection has a
mitigating effect on CMSE perturbations. The CMSE tendencies from
vertical and horizontal advection terms are larger in magnitude than
those from radiation and surface fluxes. The strengthening effect of
vertical advection corresponds to a negative gross moist stability (GMS)
at short spatiotemporal scales, but the GMS becomes positive when the
convection changes from shallow to deep, killing off the growth in CMSE.
The conceptual model is faithful in simulating self-aggregation in that
it shows a domain-size dependence of aggregation found in many prior
works, and its CMSE power spectrum matches that of the high-resolution
simulation except for a shallowing of the slope at high wavenumbers.
Through analyzing the conceptual model equation, we show that 1) the
domain-size dependence of self-aggregation is due to a competition
between the strengthening effect of vertical advection and the smoothing
effect of horizontal advection, and 2) the combination of temporal red
noise and diffusive horizontal advection sets the shape of the CMSE
power spectrum. Furthermore, the conceptual model also reproduces
power-law distributions of precipitation clusters when precipitation
clusters are viewed as thresholded islands on the CMSE topography. Thus,
the simple conceptual model captures and helps to explain important
aspects of convective self-aggregation and tropical convective
organization.%
\end{abstract}%



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