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A new version of the stochastic multiplume Jet Propulsion Laboratory Eddy‐Diffusivity/Mass‐Flux (JPL‐EDMF) parameterization which consistently couples the simplified Khairoutdinov and Kogan (2000),https://doi.org/10.1175/1520-0493(2000)128<0229:ANCPPI>2.0.CO;2, warm phase cloud microphysical parameterization with the parameterization of cloud macrophysical and subgrid scale dynamical processes is described. The new parameterization combines the EDMF approach with an assumed shape of a joint probability density function of thermodynamic and kinematic variables which provide the basis for the computation of all parameterized processes. As far as we are aware this is the first attempt to consistently couple all of these parameterized processes in the EDMF framework. This paper is part one of a two paper series. Here, the JPL‐EDMF parameterization is described and benchmark simulations of precipitating stratocumulus and cumulus convection are performed in a single‐column‐model framework. The parameterization results compare favorably to the reference large‐eddy‐simulation results. In the second part (Smalley et al., 2022,https://doi.org/10.1029/2021MS002729) the JPL‐EDMF parameterization is validated for a wide range of observation‐based scenarios covering the continuous transition from subtropical stratocumulus to cumulus convection derived from global reanalysis, and parameterization uncertainties are studied in detail.