Mixing at a stratocumulus cloud top driven by radiative and evaporative cooling

Mixing at a stratocumulus cloud top driven by radiative and evaporative cooling

Alberto de Lozar and Juan Pedro Mellado

Max Planck Institute for Meteorology. Bundesstr. 53, D-20146 Hamburg, Germany

Overview

Marine planetary boundary layers topped by stratocumulus clouds (STBL) cover 20% of the earth and are thus key for the planetary radiative balance. Turbulence in STBL is driven at the cloud top by radiative and evaporative cooling. Modeling these apparently simple clouds presents two important challenges. First, the interaction of turbulence and strong stratification that results in mixing is not yet well understood and therefore it is poorly parametrized. Second, both driving mechanism operate on a thin layer (around 20 meters) in the mixing region. 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 simulations, in which we have investigated the interplay between evaporative and radiative cooling and the role of the buoyancy reversal instability.

Methods

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.

Results

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 [1], based on the BRI. For our highest resolution this instability causes a 25% 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.

Using DYCOMS-II as a reference, we perform different simulations which are stable and unstable for the BRI. Our results do not show a large increase in the evaporative cooling strength due to the BRI. We conclude that future mixing parameterizations should consider evaporative and radiative cooling in detail, but also be insensitive to the BRI criterion

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[1] Mellado JP. 2010. The evaporatively driven cloud--top mixing layer. J. Fluid Mech. 660: 5--36. DOI: 10.1017/S0022112010002831.

[2] 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.