Formulation of a bulk boundary layer model with partial mixing and cloudiness - Randall, David A. (David Allan), 1948-, author; Shao, Qingqiu, author; Department of Atmospheric Science, Colorado State University, publisher (Colorado State University. Libraries, 1990)
The classical cloud-topped mixed-layer model is generalized to allow for arbitrary fractional cloudiness and incomplete mixing. The boundary-layer depth and turbulence kinetic energy (TKE) are prognostically determined. The large turbulent eddies that contain most of the TKE and are primarily responsible for the fluxes are modeled as convective circulations, with ascending and descending branches. By assuming that the ventilation and entrainment layers at the lower and upper edges of the PBL are dominated by small-scale turbulence in quasicquilibrium, boundary conditions are developed for the rising and sinking branches of the convective circulations, and also for the scalar variances associated with the convective circulations. The convective mass flux and the fractional area covered by updrafts arc diagnosed by the model. Fractional cloudiness occurs when the ascending branches are saturated and the descending branches are not. We use a modified bulk formula in which the square root of the TKE takes the place of the wind speed. The advantages of this approach are discussed. The entrainment rate is also assumed to be proportional to the square root of the TKE; the proportionality factor depends on the inversion Richardson number, and also on an additional parameter that represents the effects of evaporative cooling when clouds are present. The ventilation mass flux is similarly parameterized. Instead of using a conventional bulk formula in which the wind speed is multiplied by a transfer coefficient, we use a modified bulk formula in which the square root of the TKE takes the place of the wind speed. The advantages of this approach are discussed. Large-eddy simulations arc used to validate several aspects of the model's formulation. For the special case of a well-mixed layer, the model predicts that the fractional area covered by rising motion is near 1/2, and that dissipation in the interior of the layer is weak. When the dissipation is weak and the fractional area covered by rising motion is small, the model gives the "compensating subsidence -- detrainment" relationship that has become familiar in cumulus parameterization theories. When the dissipation is strong and the fractional area covered by rising motion is near 1/2, the model gives downgradient diffusion. For the shallow cumulus regime, the model predicts that the fractional area covered by rising motion is smaller for the case of large-scale rising motion than for that of large-scale sinking motion. A number of idealized dry cases are simulated to illustrate the model's ability to predict the development and evolution of partially mixed states. More extensive results, including both overcast and partly cloudy cases, are presented in a companion paper.
Keywords: Boundary layer (Meteorology); Clouds; Convection (Meteorology); Atmospheric circulation