Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloudresolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss-Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloudresolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.C onvection in the tropics has a profound impact on short-term climate. Observational data indicate that tropical deep convection is organized on a hierarchy of scales ranging from cumulus clouds over a few kilometers to interseasonal oscillations over planetary scales of order 40,000 km (1-3). The mechanisms for this behavior present a major unsolved problem, despite the fact that there has been extensive research over the last few decades on these topics through parameterization of convection in general circulation models (4) as well as theory (refs. 5 and 6 and refs. therein). A particularly promising emerging approach to address these issues is cloud-resolving modeling (CRM), where idealized highly resolved two-dimensional simulations of clouds are coupled to largerscale dynamics in a variety of ways (7-9), utilizing massively parallel computer architecture. Nevertheless, only very crude resolution of the large-scale interaction is possible with the current generation of computers. Here a hierarchy of numerical models is introduced specifically to model the feedback of small-scale deep convection on the tropical planetary waves and tropical circulation in a highly efficient manner compatible with the CRM approach. Besides its efficiency, this numerical strategy also makes a direct link with many of the observed larger-scale patterns in the equatorial wave guide such as Kelvin, Yanai, and equatorial Rossby waves (3, 10, 11), so that observations, theory, and CRM simulations can be compared in an interactive fashion.The basic idea in the approach is to use low-order truncation in the meriodonal direction through Hermite polynomials combined with Gauss-Hermite quadrature in a meriodonal Galerkin approximation projected onto a simple discrete radiation condition. In this fashion, for example, ...