An analysis of bulk parameterizations of stably-stratified atmospheric boundary layers using large-eddy simulations

An important application of large-eddy simulations (LES) is in the validation and improvement of atmospheric boundary layer (ABL) models used in large-scale models, from mesoscale models to general circulation models (GCM). The simple parameterizations of boundary layers often used in GCM's are based on bulk parameters of boundary layers such as the drag coefficient,heat flux coefficient, boundary layer height, bulk Richardson number, etc.

We use our extensive LES database to study bulk parameterizations for stably-stratified boundary layers (SBLs), point out inherent limitations of such parameterizations, and attempt to propose improvements. We first study a bulk Richardson number and show that that its behavior critically depends on the definition of the SBL height. We show that as the ABL approaches quasi-steady state, the bulk Richardson number increases without limit if the SBL height is defined as a level where turbulent flux vanishes. However, the bulk Richardson number approaches a constant value when the SBL height is defined as a level where turbulent kinetic energy vanishes.

We also examine a similarity approach to modeling the SBL, which provides the possibility of directly relating the conditions above the boundary layer (i.e. geostrophic wind, potential temperature) to the surface quantities (i.e. surface stress, surface flux). Such an approach requires that universal resistance law functions be determined empirically. However, experimentally determined 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.

We also conduct a high-resolution (160^3 grid points), long-term (12 hours) LES of a stable ABL over a sufficiently large domain that enables us to simultaneously resolve small-scale as well as internal gravity waves and study their interaction.