Our purpose is to evaluate Large-Eddy Simulation of Stratocumulus using a case-study approach. The case study is chosen from the first flight of DYCOMS-II and is an elaboration of simulations performed in support of initial analyses of this flight (Stevens et al., 2003), which provides essential background for this case. The basic questions which this and previous analyses have posed, and which we will attempt to answer in this study, are the following:
- Can LES produce the observed cloud evolution?
- Can LES maintain the observed mixing line structure at cloud top?
- Does the satisfaction of the Randall-Deardorff criterion for CTEI imprint itself on the cloud evolution in any noticeable way?
- To what extent is boundary projection a proper way to cast the forcing?
- To what extent do detailed radiative processes in the clear air above cloud top (cf., Siems et al., 1993) determine the subsequent cloud evolution?
- Can LES capture the higher order turbulent statistics (specifically third order velocity statistics and cloud top interfacial statistics) at the cloud top interface?
These questions are elaborated on in turn below. The stratocumulus deck observed during RF01 of DYCOMS-II provides an interesting case study because its evolution was one of gradual deepening through the course of the flight, within a large-scale environment which was remarkably constant in time. The basic structure of the cloud deck is illustrated with sounding data in Fig. 1. The variability in cloud thickness apparent in the sounding is due mostly to the fact that the aircraft sampled the deck in a quasi-Lagrangian sense, where cloud base appeared to be lower to the north. Correcting for these biases leads to an estimate of cloud evolution during the course of the flight which is illustrated in the left panel of Fig. 2. Note that there is no apparent cloud thinning, and although the correlation of the best fit line for the evolution of cloud base is rather low, this is due to compensation between moistening and warming tendencies within the layer (cf. Stevens et al. (2003)). Mixing line analysis of all the cloud penetrations does however indicate that the clod-top interface was on the unstable side of the Randall-Deardorff CTEI criterion (right panel, Fig. 2). Hence our first three motivating questions above.
The fourth motivating question, called boundary projection, has to do with how to count the forcings in estimating the work done on cloud layers by diabatic processes, namely radiative fluxes (but also drizzle), which in actuality act throughout the cloud and boundary layer. For instance, in (Stevens, 2002) and in (Stevens et al. 2003) the radiative driving of the boundary layer is taken as the net radiative flux divergence acting across the boundary layer as a whole. This driving is then modeled as if it were only acting on a boundary. While this might seem reasonable for the cloud top radiative cooling, is it correct to count the cloud base warming in this fashion? During RF01, the former was approximately 70Wm-2 while the latter was roughly 20Wm-2, thus how one counts the latter’s energetic contribution can be crucial. This issue also comes to the fore when we consider strategies for modeling the effect of drizzle on stratocumulus energetics. By having separate models of the cloud base warming and cloud top cooling radiative tendencies, a case study of RF01 seems like an excellent way to address this question. Because of its explicit representation of the large-eddies, LES is an ideal tool in this respect. The fifth question arises from the observation that sl above the cloud layer increases roughly as (z - zi)1/3. This implies a change in sl of 2K (equivalent to a 20% increase in the inversion strength over a distance of only 8m. To formulate jump conditions from the perspective of a mixed layer model, one needs to know the depth of the interfacial layer, and hence the effective stratification felt by the turbulent eddies as they push upward on the inversion. Thus it becomes interesting to investigate how enhanced cooling just above the cloud layer (which is thought to be responsible for the curvature in the sl there) interacts with dynamical processes, and helps determine the effective stability of the entrainment interface. To address this question we will specify a radiative flux profile which depends on the distance from cloud top in a way which produces the correct profile of sl in the limit of constant divergence with height.
The sixth question is motivated by Fig. 3 which shows the vertical velocity statistics from an exploratory simulation (e.g., Stevens et al. 2003) and those observed using in situ measurements and cloud radar. The main point of this figure is that despite reasonable agreement in the cloud variance statistics there is a marked departure between the simulation and the data in the vertical velocity skewness in the upper part of the cloud layer. This result is a more forceful statement of previous findings (e.g., Moeng and Rotunno, 1990; Moyer and Young, 1991), which suggests that LES does not represent the higher order turbulent statistics in the vicinity of the cloud top interface with great
