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Large‐scale weather forecasting and climate models are beginning to reach horizontal resolutions of kilometers, at which common assumptions made in existing parameterization schemes of subgrid‐scale turbulence and convection—such as that they adjust instantaneously to changes in resolved‐scale dynamics—cease to be justifiable. Additionally, the common practice of representing boundary‐layer turbulence, shallow convection, and deep convection by discontinuously different parameterizations schemes, each with its own set of parameters, has contributed to the proliferation of adjustable parameters in large‐scale models. Here we lay the theoretical foundations for an extended eddy‐diffusivity mass‐flux (EDMF) scheme that has explicit time‐dependence and memory of subgrid‐scale variables and is designed to represent all subgrid‐scale turbulence and convection, from boundary layer dynamics to deep convection, in a unified manner. Coherent up and downdrafts in the scheme are represented as prognostic plumes that interact with their environment and potentially with each other through entrainment and detrainment. The more isotropic turbulence in their environment is represented through diffusive fluxes, with diffusivities obtained from a turbulence kinetic energy budget that consistently partitions turbulence kinetic energy between plumes and environment. The cross‐sectional area of up and downdrafts satisfies a prognostic continuity equation, which allows the plumes to cover variable and arbitrarily large fractions of a large‐scale grid box and to have life cycles governed by their own internal dynamics. Relatively simple preliminary proposals for closure parameters are presented and are shown to lead to a successful simulation of shallow convection, including a time‐dependent life cycle., Key Points An extended eddy‐diffusivity mass‐flux (EDMF) scheme is presented that is prognostic and has variable plume area fractionsThe new EDMF scheme consistently partitions flow variables (including turbulence kinetic energy) between plumes and the environmentIn first tests, it successfully reproduces the average condition and transient life cycles of shallow convection

Shipboard radiosonde surveys were conducted during the 2003-04 winter east of Japan to study atmospheric boundary layer (ABL) structure over the Kuroshio Extension. ABL displayed large variations in vertical structure, most of which are attributable to changes in atmospheric surface stability. Where the surface atmosphere was unstable (neutral) as measured by the sea-air temperature difference, surface turbulent heat flux increased (decreased) and a mixed-layer developed (undeveloped) with weakened (intensified) vertical wind shear. A linear regression analysis indicates that ABL height tends to increase by 1km as the sea-air temperature difference increases by 7°C or surface turbulent heat flux by 500 Wm−2. While meridional thermal advection by weather disturbances seems to cause much of atmospheric stability variability during the 43-day surveys, the strong sensitivity of vertical mixing and wind shear to stability is consistent with the observed in-phase co-variability of SST and surface wind from satellite on monthly and longer timescales.