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Unification of mass flux and higher-order closure in the simulation of boundary layer turbulence




Lappen, Cara-Lyn, author

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Typically, in large-scale models, cloud schemes vary depending on the type of convection. Separate schemes are used for planetary boundary layer (PBL) processes, shallow and deep cumulus convection, and stratiform clouds. Individually, these schemes may work well in their respective regimes. However, these regimes are not always distinct. Often, two or more of the regimes coexist (e.g., the "stratocumulus-to-cumulus" transition region, "cumulus-under-stratus", and stratocumulus "decoupling"). Large-scale models tend to poorly represent the total effect of clouds in these multiple-cloud regimes. (Randall et al., 1998). The conventional distinction between the boundary layer and the cumulus layer is based on the assumption that they are physically distinct layers. However, this is not always the case. For example, shallow cumulus clouds may be considered to exist completely within the planetary boundary layer (PBL), or they may be regarded as starting in the PBL but terminating above it. Deeper cumulus clouds often originate within the PBL but also can originate aloft. Thus, the distinction between the two layers clearly reflects holes in our understanding. In order to realistically simulate the global hydrologic cycle, energy budget and large-scale circulation, it is imperative that large-scale models accurately represent clouds. Thus, there is a need to unify the approaches that these models take towards representing clouds and the boundary layer. This study is the first attempt to overcome the dependence of cloud and boundary-layer parameterizations on the type of convection. I present a method to combine the concepts of mass­ flux closure (MFC) and "standard" higher-order closure (HOC) into one unified theory which is consistent with both formulations. The model that I will describe combines the two approaches in such a manner that the MFC equations are term-by-term consistent with the terms of "conventional" HOC equations. For this new closure method, the only prognostic variables are the second and third moments of the vertical velocity, all second-order vertical fluxes, and mean quantities. Variances and all other higher-order moments are diagnosed in terms of an updraft area fraction, a convective mass flux and the differences in properties between the updraft and downdraft. This new closure method is called ''Assumed Distribution Higher-Order Closure" (ADHOC). The name is directly reflective of the approach. I assume a "tophat" distribution similar to that used in current mass-flux models (the "assumed distribution"), in which all mean quantities and higher-moment statistics are written in terms of an updraft-downdraft decomposition. I then take plume equations describing the updraft and downdraft mean states and derive higher-order closure "plume" equations (the "higher-order closure" part). Some new things are discovered and some new techniques are introduced in this model. For example, an interesting result of the term­ by-term analogy between the two systems (MFC and HOC) is that the lateral mass exchange terms in ADHOC are directly related to the dissipation terms of the HOC equations. I provide a new "ADHOC-specific" parameterization for these lateral mass exchange terms in the spirit of this discovery. In addition, I add a subplume-scale turbulence scheme to the model to directly address the issue of the inherent "scale-inconsistency" between HOC and MFC closure equations. Results from this model are compared with observations and with those obtained using large­eddy simulation models. The model is run with a variety of tropical, sub-tropical, and high-latitude cases. These cases include cloud-free convection, stratocumulus, two types of shallow non­precipitating cumulus, and Arctic stratus. These results are discussed in detail and conclusions are drawn as to the strengths and weaknesses of this new closure method when applied to the various regimes.


July 1999.
Also issued as author's dissertation (Ph.D.) -- Colorado State University, 1999.

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Atmospheric turbulence
Boundary layer (Meteorology)


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