Mixing line parameterizations for cloudy boundary layers.
It has been almost 25 years since I started work on the topic of cloudy boundary layers (CBL); so I thought I would attempt an overview of some basic issues in parametrizing CBL's. We are seeing at this workshop a wide range of approaches, which illustrate the importance and complexity of the topic. It is important, however, in GCM parametrization to frequently step back, and ask whether we have modelled the key processes in the simplest possible way, and whether these processes are interacting correctly. I hope this paper will serve as an introduction to this session.
My framework is this. From a modelling and observational perspective, the key issue for the CBL is (I believe) whether we can predict the correct equilibrium thermodynamic state (which I shall represent by potential temperature theta, and mixing ratio q) in situations over land and sea that are changing slowly; and the correct rates of change for CBL's forced from the surface; such as the diurnal cycle over land, or the advection of cold air over a warmer ocean. In this verbal definition, we immediately see the essential issue of timescale, so I shall first discuss the internal and external timescales ( tauI`, tauE) for the CBL. This separation is for conceptual convenience. The external or boundary timescales are those which determine the fluxes at the surface (surface wind, roughness, vegetation etc) and at CBL top (entrainment of air from above). The radiative process also has a comparable timescale to entrainment (Betts, 1989). The internal timescale is the timescale of mixing within the CBL. There may be different values for the cloud and subcloud layers. If tauI~<~<~tauE, then the CBL will have a nearly well-mixed structure, and correspondingly mixed layer models are useful simplifications. However even if a CBL is nearly well-mixed, its equilibrium state or time-change will not be correctly predicted in a model, if the boundary fluxes are wrong. Superficially the surface flux problem over the oceans is easier than over land (but still a problem at low wind speeds (eg Miller et al, 1992)). Over land, the surface fluxes during the daytime depend on the vegetation and soil moisture (and their time history) and the net radiation (which is controlled on a short time-scale by CBL cloud). The entrainment fluxes are not well-known, either for cloud-free BL's (Betts et al 1992), or for cloudy CBL's, which many papers here address. This is because entrainment is not really external at all. It is driven by the circulations within the BL, and may well differ significantly for circulations driven by surface fluxes, or radiative processes interacting with the cloud layer.
Betts, A.K., 1993: Mixing line parameterizations for cloudy boundary layers. ECMWF/GCSS Workshop on the parameterization of cloud topped BL's, June 8-11, 1993. http://www.ecmwf.int/publications/library/ecpublications/_pdf/workshop/1993/Parametrization/betts.pdf