Ocean Surface Stress

Surface stress is available from the PBL-LIB output and is also amongst the ECMWF data.

PBL_LIB is derived by patching the analytic PBL with OLE solution to a state of the art surface layer solution. The patching is enabled by the fact that the nonlinear equilibrium solution provides a compatible velocity profile for patching to the surface layer wind profile. This is made possible by the fact that the OLE vary with wind speed, surface roughness feedback, stratification and thermal wind.

A similarity relation results with a single similarity parameter (l) that is nearly constant with stratification (l= 0.15). A similarity equation relates the characteristic velocity ratio (u*/U_G) to the characteristic height scale ratio (h_p/d = l) producing a drag law or stress equation, u*(U_G,l).

Here h_p is the patch height (surface layer height), and d is Ekman's depth of frictional resistance. {d = sqrt [2K/f], K is the eddy coefficient for SMALL eddies and f is the Coriolis parameter}.

The surface analysis of the numerical model (ECMWF) gives a u* from a similar surface stress relation taken from the model's lowest level, about 50m. In comparison studies (Foster and Brown, 1994a,b,c) this agrees with PBL_LIB when the OLE are surpressed. When OLE are included, higher U₁₀, u* and fluxes are predicted. In addition, a physically realistic variation in stress with roughness and stratification changes is included in the model. This is because the Rolls are explicitely represented and not simply approximated with an average in a diffusion coefficient.