The Steady Local Turbulence Closure Model

A fundamental problem in boundary-layer physics is extrapolating limited measurements to a general description of the mean velocity and scalar properties, along with their Reynolds fluxes including values at the immediate boundary. For the atmospheric surface layer, extensive research has been devoted to methods relating relatively simple measurements to fluxes. Central to this approach is characterizing surface roughness for momentum and scalar variables. Typically, a tower is deployed with two or more levels of instrumentation and the surface fluxes are estimated either from the mean measurements across the tower using some form of the Monin-Obukhov dimensionless gradients (e.g., Businger et al. 1971; Andreas and Claffey 1995), or from a combination of mean gradients and fluxes, determined either by direct covariance or by spectral techniques (e.g., Edson et al. 1991).

In the IOBL, this is much less straightforward for a variety of reasons. First, in contrast to the upper sea-ice surface, variation in the underice morphology often occupies a significant fraction of the entire boundary layer. If the IOBL scales with about 1/30 of the atmospheric boundary layer, a pressure ridge with a 1-m sail and 5-6-m keel presents completely different aspects to the respective boundary layers. In general, for the IOBL parameterization problem, many of the surface-layer assumptions (constant stress, stress and mean velocity collinear with no direction change, etc.) are clearly inappropriate.

As illustrated in Chapter 8, it is sometimes possible to solve a time-dependent numerical PBL model with given initial conditions, letting it evolve in time as the forcing fields change. Given a suitable time series of observations at a particular location, to the extent that the model can reproduce the observed characteristics (say mixed layer temperature, salinity, depth), the model will provide a reasonably accurate description of the overall exchanges across the OBL. This depends on both having realistic initial conditions and a reasonably accurate time series of forcing fields (e.g., wind or ice velocity, conductive heat flux in the ice, etc.). In many cases, observations are scattered in both time and location (for example, stations taken from a ship or airplane during a regional survey), and one would like to produce a “snapshot” of the OBL structure, to estimate fluxes at the surface or near the base of the mixed layer.