A Higher-Order Closure Model with an Explicit PBL Top

Abstract

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.