Parametric representation of heat and moisture fluxes in cloud-topped mixed layers

Aircraft measurements were made from the NCAR Electra in stratus and stratocumulus clouds off the coast of California in June 1976. Several types of cloud conditions were observed, including (1) a broken layer less than 100 m thick, capped by an inversion at ~1000 m, (2) a broken stratocumulus layer ~300 m thick with an inversion at ~500 m, and (3) a solid stratocumulus layer ~250 m thick with an inversion at ~500 m. Although these observations indicate that a variety of cloud conditions may exist in mixed layers, simple one-dimensional mixed-layer models implicitly assume a solid cloud layer with no unsaturated region within the cloud. In order to generalize these simple models, a parametric representation of the heat and moisture fluxes is considered. In this scheme, the fluxes are parameterized in terms of the product of a cloud mass flux and the characteristic difference between the thermodynamic properties of an updraft-downdraft circulation. This representation allows for an explicit representation of the buoyancy flux when the downdraft has no liquid water.Data collected during these flights were used to calculate heat and moisture fluxes and to obtain the mean difference in the thermodynamic properties of the updrafts and downdrafts at a given level. The mass flux was calculated using updraft-downdraft differences and the fluxes. The mass fluxes obtained using various thermodynamic quantities are examined for consistency. The vertical distribution of the mass flux is determined. These results indicate that a mass flux formulation could prove to be useful in modeling applications where cloud conditions may vary between solid and broken.