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The Neutral, Barotropic Planetary Boundary Layer, Capped by a Low-Level Inversion

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Abstract

The presence of a low-level, capping inversion layer will affect the height and structure of the planetary boundary layer (PBL). Results from models of varying levels of sophistication, including analytical, turbulent kinetic energy (TKE), second-order closure (SOC), large-eddy simulation (LES) and direct numerical simulation (DNS) models, are used to investigate this influence for the neutral, barotropic PBL. Predicted and observed profiles of stress and geostrophic departure components, and integral measures, such as the parameters of Rossby-number similarity theory, are compared for the KONTUR, Marine Stratocumulus, JASIN, Leipzig, Pre-Wangara and Upavon field experiments.

Analytical models of the equilibrium value of inversion height zi, which depend on the surface friction velocity u*, and both the Coriolis parameter f and the free-flow Brunt-Väisälä frequency N, are found to give reasonable estimates of the PBL height. They also indicate that only the KONTUR and Marine Stratocumulus experiments were strongly influenced by N. More quantitative comparisons would require larger, more comprehensive datasets. The effects of the presence of a capping inversion on the profile structure were found to be insignificant for h* = |f|zi/u* > 0.15.

The simple analytical model performed quite well over all values of h*; it predicted the profiles of the longitudinal stress component (in the direction of the surface stress) better than the lateral component. The more advanced models performed well for small values of h* (for flow over the sea), but systematically underestimated the cross-isobaric angle for flow over land. These models predicted the profiles of the lateral stress component better than the longitudinal component. The profiles of the analytical model agreed with those of the advanced models when the constant eddy viscosity of the outer layer was increased.Agreement with DNS was achieved by increasing the eddyviscosity of the analytical model by a factor of 5.

Zilitinkevich and Esau(2002, Boundary-Layer Meteorology, 104, 371–379)suggest that the neutral, barotropic values of A and B of Rossby-numbersimilarity theory are not universal constants, but depend on the ratio N/|f|. The dependence for A and B is calculated using the analytical model and TKE models. Over the sea (h* ≅ 0.1; N/|f| ∼ 100, where we have used the Zilitinkevich-Esau relation to convert between h* and N/|f|) there is agreement between the model predictions and observations; however over land where the equilibrium boundary-layer height is greater (h* ≅ 0.35; N/|f| ∼ 10) the inconsistency between the advanced model predictions (TKE, SOC, LES, and DNS) and observations, as noted previously by Hess and Garratt, still exists. We attribute this disagreement to violations of the strict assumptions of steady, horizontally homogeneous, neutral, barotropic conditions implicit in the observations. At small values of zi and a strongly stable background stratification (h* ≅ 0.04; N/|f| ∼ 1000) both the TKE and analytical models predict that A and B depend significantly on h*, however observations are unavailable to confirm these predictions. Zilitinkevich and Esau call this case the `long-lived near-neutral PBL', and state that it is found in cold weather at high latitudes.

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    G. D. Hess

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Hess, G.D. The Neutral, Barotropic Planetary Boundary Layer, Capped by a Low-Level Inversion. Boundary-Layer Meteorology 110, 319–355 (2004). https://doi.org/10.1023/B:BOUN.0000007248.42321.d5

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