We study stably-stratified atmospheric boundary layers, their evolution and parameterizations using large-eddy simulations (LES) and observations made during SHEBA experiment. Observations of clear-air stably-stratified ABL made between May 20 and 24, 1998 are used to initialize and monitor (LES). We create an LES database to study bulk parameterizations of stably-stratified boundary layers (SBLs). The simple parameterizations of boundary layers often used in general circulation models are based on bulk parameters of boundary layers such as the drag coefficient, heat flux coefficient, boundary layer height, bulk Richardson number, etc.

We first study the variation of a bulk Richardson number and show that that it critically depends on the definition of the SBL height. If the SBL height is defined as a level where turbulent flux vanishes then the bulk Richardson number increases without limit. However, when the SBL height is defined as a level where turbulent kinetic energy vanishes, Richardson number is well defined and approaches a constant value as SBL approaches a quasi-steady state.

Using LES we also analyze a similarity approach to modeling SBLs. In this approach the conditions above the boundary layer (i.e. geostrophic wind, potential temperature) are directly related to the surface quantities (i.e. surface stress, surface flux). Universal resistance law functions can be determined empirically, however, their values for stable conditions are characterized by a large scatter. Our LES results indicate that similarity functions converge to universal values only as the SBL approaches a quasi-steady state. This result suggest that the scatter in experimentally determined values may be attributed to the fact that the SBLs under consideration did not reach a quasi-steady state.