PBL-LIB Technical Page

Technical Synopsis

Very briefly, in the 1960's it was shown that the Ekman solution (1905) is unstable to infinitesimal perturbations (the inflection point instability). A weakly non-linear finite perturbation analysis by R.A. Brown yielded an analytic solution for boundary layer flow in a rotating frame of reference. The fastest growing mode of the initial instability was used to define the shape of the finite perturbation. Conditions for an energy balance were found, resulting in a solution for the modified Ekman layer plus Organized Large Eddies (OLE or rolls). This solution was used to parameterize the OLE effect according to various stratification conditions. In 1974 the modified Ekman layer solution was matched to a surface layer solution (the Businger-Dyer log-layer) to yield a model for PBL flow.

PBL-LIB's main program is called BWIND and is an implementation of Brown's PBL model. When the solution for the outer PBL (Ekman plus OLE) is patched to the surface layer (log layer), a two-layer similarity model with one similarity parameter (lamda, the ratio of the height of the surface layer to the Ekman scale height) results. This ratio was found to be 0.15 from observations. The model is insensitive to its exact value. The traditional similarity parameters A and B can be derived from this work. The end result is that given a geostrophic wind speed G (an analogue for the horizontal pressure gradient), the model calculates a friction velocity (u-star):

u*/G = function(Pressure gradient, Stratification, Thermal wind, Humidity)

That is, the model includes corrections for stratification, thermal wind, and rolls (OLE). Fluxes are obtained from bulk aerodynamic calculations. Input humidity is used to correct for the latent heat effect on stratification and to calculate the latent heat flux. Horizontal fields of surface and air temperatures are used to calculate stratification corrections, sensible heat flux and thermal winds. The Liu, Katsaros and Businger (LKB) formulation for the molecular sub-layer is used.

For steady-state fields, the model yields state-of-the-art surface winds, surface fluxes and wind profiles at a points. Resonable synoptic-scale surface wind and stress fields can be found with only surface pressure as in input. A better solution with stratification corrections is found with the surface and air temperatures and surface humidity as inputs.

Some articles to learn more about this model are:

Brown, R.A.: 1970, 'A Secondary Flow Model for the Planetary Boundary Layer', J. Atmos. Sci. 27(5), 742-757
Brown, R.A.: 1981, 'Modeling the Geostrophic Drag Coefficient for AIDJEX', J. Geophys Research , 86(C3), 1989-1994
Brown, R.A. and Liu, W.T.: 1982, 'An Operational Large Scale Marine PBL Model', J. Applied Meteorol., 21(3), 261-269
Brown, R.A.: 1982, 'On Two-Layer Models and the Similarity Functions for the PBL', Boundary-Layer Meteorol., 24, 451-463
Foster, R.C. and Brown, R.A.: (1994), 'On Large-Scale PBL Modelling: Surface Layer Models', The Global Atmosphere and Ocean System, 2, 185-198
Foster, R.C. and Brown, R.A.: (1994), 'On Large-Scale PBL Modelling: Surface Wind and Latent Heat Flux Comparisons', The Global Atmosphere and Ocean System, 2, 199-219

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