Momentum Transport in Shallow Cumulus Clouds and Its Parameterization by Higher‐Order Closure

It is challenging to parameterize subgrid vertical momentum fluxes in marine shallow cumulus layers that contain a jet in the profile of horizontal wind. In a large‐eddy simulation of such a layer, it is found that the momentum flux in the direction of strongest wind magnitude has a three‐layer structure. The lowest layer, from the ocean surface up to the jet maximum, has downgradient momentum flux. The middle layer, from the jet maximum up to an altitude several hundred meters above, has upgradient (i.e., countergradient) momentum flux because of transport of low‐magnitude momentum upward through the jet maximum. In the upper layer, the layer‐average momentum flux is weak. The budget of momentum flux shows that in the middle and upper layers, both the buoyancy production term and turbulent advection (i.e., third‐order flux‐of‐flux) terms are important. To parameterize the profile of momentum flux in a single‐column model, the momentum flux is prognosed in this study. The buoyancy production and flux‐of‐flux terms are parameterized by integrating them over a subgrid probability density function with an assumed normal‐mixture shape. The resulting parameterized fluxes and mean‐wind profiles are demonstrated to be comparable to those produced in large‐eddy simulations, both for two marine shallow cumulus cases with upgradient fluxes and for a continental cumulus case and two stratocumulus cases with downgradient fluxes. In the two marine shallow cumulus cases, the parameterization is able to capture the upgradient momentum flux above the jet maximum and the weak momentum fluxes aloft.