Bulk Models of the Atmospheric Convective Boundary Layer

The paper presents an overview of modeling the atmospheric convective boundary layer (CBL) using bulk parameterizations for the vertical structure of the layer. Such parameterizations are constructed based on empirical knowledge about vertical distributions of meteorological variables in the CBL. Two main types of CBL bulk models are presented and discussed. The first model considered is the so-called zero-order jump model, which implies a vertical homogeneity of meteorological variables in the bulk of the CBL, and zero-order discontinuities of variables at the interfaces of the layer. Integral budgets of momentum and heat in the zero-order jump model of the dry atmospheric CBL are considered. A general version of the equation describing the CBL growth rate (the entrainment rate equation) is obtained through integration of the turbulence kinetic energy balance equation, evoking basic assumptions of the zero-order representation of the CBL vertical structure. The developed theory is generalized for the case of the CBL over an irregular terrain. The second model considered is the general-structure CBL bulk model, which incorporates a self-similar representation of the buoyancy profile within the capping inversion layer. This representation has been examined against the data from atmospheric measurements, laboratory experiments with buoyancy agitated turbulence, and large eddy simulations. The growth rate equations for mixed and inversion layers are derived using the turbulence kinetic energy balance equation and the Deardorff scaling hypothesis refined to account for the inversion-layer structure. The model is found to be able to reproduce transition regimes of the CBL development affected by nonstationarity of the entrainment zone.