Evaluating models of the neutral, barotropic planetary boundary layer using integral measures: Part I. Overview

Data for the cross-isobaric angle alpha(0), the geostrophic drag coefficient C-g, and the functions A and B of Rossby number similarity theory, obtained from meteorological field experiments, are used to evaluate a range of models of the neutral, barotropic planetary boundary layer. The data give well-defined relationships for alpha(0), C-g, and the integrated dissipation rate over the boundary layer, as a function of the surface Rossby number. Lettau's first-order closure mixing-length model gives an excellent fit to the data; other simple models give reasonable agreement. However more sophisticated models, e.g., higher-order closure, large-eddy simulation, direct numerical simulation and laboratory models, give poor fits to the data. The simple models have (at least) one free parameter in their turbulence closure that is matched to atmospheric observations; the more sophisticated models either base their closure on more general flows or have no free closure parameters. It is suggested that all of the atmospheric experiments that we could locate violate the strict simplifying assumptions of steady, homogeneous, neutral, barotropic flow required by the sophisticated models. The angle alpha(0) is more sensitive to violations of the assumptions than is C-g. The behaviour of the data varies in three latitude regimes. In middle and high latitudes the observed values of A and B exhibit little latitudinal dependence; the best estimates are A = 1.3 and B = 4.4. In lower latitudes the neutral, barotropic Rossby number theory breaks down. The value of B increases towards the Equator; the determination of A is ambiguous - the trend can increase or decrease towards the Equator. Between approximately 5degrees and 30degrees latitude, the scatter in the data is thought to be primarily due to the inherent presence of baroclinicity. The presence of the trade-wind inversion, thermal instability and the horizontal component of the Earth's rotation Omega(H) also contribute. Marked changes in the values of A and B occur in the region between the Equator and approximately 5degrees latitude, as the Coriolis parameter \f\ approaches zero. Although the variation of A and B with latitude suggests some similarity to the results obtained from the direct numerical simulations, the presence of additional complexities in the real atmosphere that are not included in the numerical model, precludes a meaningful direct comparison.