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.