Quantifying radiative cooling, evaporative cooling and diffusion at the stratocumulus cloud top
Alberto de Lozar and Juan Pedro Mellado
Max Planck Institute for Meteorology. Bundesstr. 53, D-20146 Hamburg, Germany
Modeling stratocumulus topped boundary layers (STBL) presents two important challenges. First, the main turbulence-driving mechanisms, radiative and evaporative cooling, operate on a thin layer (around 20 meters) at the cloud top. Second, the interaction of turbulence and strong stratification that results in mixing is not yet well understood and therefore it is poorly parametrized. The consequence is that most simulations of STBL do not capture the relevant mixing scales and tend to be too diffusive, dissipating the clouds too quickly.
We investigate the mechanisms that drive turbulence and mixing in mixed layer configurations that mimics the stratocumulus cloud top. In our recent investigations we have focused on configurations which are driven either by evaporative or by radiative cooling alone. We found that evaporative alone cannot explain field measurements; that radiative cooling alone provides the correct level of turbulence although insufficient mixing; and that the scales relevant for the mixing are probably in the range between 20 cm and 60 m [1,2].
In this presentation we will show results of recent direct numerical simulations, in which we have investigated the interplay between evaporative and radiative cooling and the role of the buoyancy reversal instability (BRI). In our simulations we explicitly resolve scales from a few centimeters to several hundred meters. We find that the BRI triggers a diffusive instability that increases the mixing with the free atmosphere. This extra mixing is a function on the viscosity and it should be negligible for atmospheric conditions, but in our highest resolution it does increase evaporative cooling by 20%. Our results suggest that the extra mixing in STBL simulations with standard resolutions (dz = 5m) might be of the same order than the real mixing. When removing this diffusive contribution our results become independent of viscosity and can be extrapolated to cloud scales. The strength of the evaporative and radiative cooling are then almost equal.
We use direct numerical simulations which are free of the uncertainty of turbulent models. The length scales that characterize mixing and radiation are properly resolved by adjusting the viscosity to a value well above the air viscosity. In the highest resolution, our simulation captures scales from from 7 cm (Kolmogorov) to 360 m (the domain size). This scale separation is large enough for many statistics to show Reynolds-number independence, a necessary condition to extrapolate our results to atmospheric conditions.
A simplified formulation is used, in which the thermodynamics equations are linearized around a reference state. This simplified formulation deviates only by 3% from the full calculations for typical cloud-top conditions, while gaining 40% speed in the calculations. Besides, the simplified equations reduce the number of independent parameters to only on five, opening the possibility for a systematic study of the stratocumulus physics.
Our first experiment is based on the measurements from the flight RF-01 in the DYCOMS-II campaign. This flight was characterized by a very dry free atmosphere, with high potential for evaporative cooling, and the cloud top is unstable according to the buoyancy reversal instability (BRI). We find that our results are not independent of diffusive effects, even for the lowest viscosities. We quantify the diffusive effects by the instability explained in , based on the BRI. For our highest resolution this instability causes a 20% increase in the evaporative cooling, but this increase is expected to be much larger for standard resolutions. We demonstrate that the diffusive instability can explain the kappa quasi scaling for cloud fraction that it is often shown in the literature, suggesting that this scaling might be just an artifact due to low resolution.
When the extra cooling by the diffusive instability is removed, our results for different viscosities collapse. Moreover, many mixing statistics seem to reach an asymptotic state when plotted as a function of the integral length scale (in our case a fraction of the boundary layer depth). Both observations confirm that the flow scales that are relevant for mixing are captured in our simulations and that our corrected results can be extrapolated to atmospheric scales. We quantify the strength of evaporative and radiative cooling by the integrated buoyancy source associated to each of these processes. This measure is the equivalent of quantifying the strength of a dry convective boundary layer by the surface buoyancy flux. We show that evaporative and radiative cooling have almost the same strength for the DYCOMS-II case. We conclude that future mixing parameterizations should consider evaporative and radiative cooling in detail, but also be insensitive to the BRI criterion.
 Mellado JP. 2010. The evaporatively driven cloud--top mixing layer. J. Fluid Mech. 660: 5--36. DOI: 10.1017/S0022112010002831.
 De Lozar A, Mellado JP. 2013. Direct numerical simulations of a smoke cloud- top mixing layer as a model for stratocumuli. J. Atmos. Sci. 70: 2356--2375. DOI: 10.1175/JAS-D-12-0333.1.