Discretization problem in modeling cloudy boundary layer growth using diffusion of conservative variables

Many numerical weather prediction and atmospheric general cirlution models use vertical diffusion to represent boundary layer (BL) processes. In such a context we use conservative variables, i.e. total water content and liquid water temperature, to model saturated as well as unsaturated air in and above the boundary layer. Vertical diffusion coefficents are calculated using turbulent energy and/or local stability functions that take into account the extra buoyancy in cloudy air. In these simple models growth of the BL is accomplished by gradually destabilizing the layer above its top, eventually incorporating this layer into the BL. Though this process is working resonably well, it is characterized by uneven growth: when the upper layer is completely above the BL, it has maximum (compared to its later stages) static stability and allows minimal exchanges with the BL air. At this stage the growth of the BL is small. As the layer mixes with the underlying BL, it destabilizes and permits more and more transfer. This process repeats itself for each new layer and creates a pulsation in the growth rate that is completely artificial. This model behavior occurs in unsaturated as well as in saturated air, but its effect is more dramatic in saturated air. At the time of maximum growth, drier and warmer air is ingulfed into the BL and causes part of the cloud to disappear, especially the bottom part, which contains less liquid water.

Mechanisms to prevent or minimize this undesirable phenomenon will bepresented. They involve a special treatment of the top layer and the introduction of an explicit growth rate for the BL.