OBSERVATIONS AND NUMERICAL MODELING OF ENTRAINMENT

OBSERVATIONS AND NUMERICAL MODELING OF ENTRAINMENT AND MIXING NEAR THE TOP OF MARINE STRATOCUMULUS Marcin J. Kurowski1, Krzysztof E. Haman1, Wojciech W. Grabowski2, Szymon P. Malinowski1 1 Institute of Geophysics, University of Warsaw, Warsaw, Poland 2 National Center for Atmospheric Research, Boulder, Colorado, USA 1. INTRODUCTION Entrainment of free-tropospheric air into stratocumulus-topped boundary layer (STBL) is of crucial importance for dynamical, microphysical, and radiative processes within STBL. The second Dynamics and Chemistry of Marine Stratocumulus field program (DYCOMSII, Stevens et al. 2003) yielded, among other things, new data concerning the morphology of the stratocumuls (Sc) top. Gerber et al. (2005) presented detailed analysis of narrow in-cloud regions near the Sc top with lower liquid water content and cooler temperatures than averaged background values, the so-called "cloud holes". Using high resolution aircraft data, Haman et al. (2007) illustrated various ways the freetropospheric air from above the inversion mixes with the cloudy STBL air. Their discussion illustrates the existence of a finite-thickness transition layer separating STBL from the free troposphere, the entrainment interface layer (EIL), postulated on theoretical grounds by Randall (1980) and suggested by airborne measurements discussed in Caughey et al. (1982) and Lenshow et al. (2000), among others. This layer is characterized by strong gradients of thermodynamic properties and substantial changes in the intensity of turbulence. The exchange of mass between wet and cold STBL, and dry and warm (in the potential temperature sense) free atmosphere may produce air parcels with negative buoyancy, and thus affect the dynamics of Sc top. Early studies (e.g., Lilly 1968) formulated thermodynamic conditions for such a production and a concept of cloud-top entrainment instability was introduced. The key idea is that the negative buoyancy produced through the mixing between the STBL air and the air from above the inversion can lead to a positive feedback, where the entrainment leads to buoyancy reversal and subsequently to more entrainment, and eventually to cloud dissipation. In the present study we compare the observations from the DYCOMS-II campaign and the results from numerical simulations investigating entrainment and mixing near the top of STBL, especially concerning the EIL formation process. 2. ENTRAINMENT INTERFACE LAYER

EIL can be identified in observations and in model results as a region between the cloud top and the height of the temperature inversion. In a nutshell, EIL is a mixing zone that separates the cloudy and cold (in the potential temperature sense) boundary layer air from the dry and warm free-tropospheric air aloft. In the observations, EIL often features filaments of cloudy and clear air at different stages of stirring, mixing, and homogenization. Typical thickness of EIL is about 20m, but it varies from almost 0 to 70m. Observational results are supported by numerical modeling using the large-eddy simulations (LES) model. The model used in this study is the 3D anelastic semiLagrangian/Eulerian finite-difference model EULAG documented in Smolarkiewicz and Margolin (1997; model dynamics), Grabowski and Smolarkiewicz (1996; model thermodynamics) and Margolin et al.~(1999; subgrid-scale turbulent mixing). Model setup is based on RF-01 flight of the DYCOMS-II experiment, previously used in the model intercomparison study (Stevens et al. 2005). The depth of EIL is estimated as a distance between the material top of STBL and the surface of maximum static stability. The former is defined as the interface where total water mixing ratio falls below about 90% of its STBL value, i.e. 8 g/kg. The latter is simply the height of the maximum virtual potential temperature gradient. The distance between them, the EIL thickness, is shown in Fig. 1 for both model simulations and observations.

Fig.1. Histogram of the distance between material top of STBL and the inversion level in the model simulation (upper panel) and DYCOMS observations (Haman et al. 2007; lower panel).

3. ENTRAINMENT AND MIXING WITHIN STBL In order to explain processes leading to the formation of EIL, we focus on the stability of the flow in the cloud-top region using the local gradient Richardson number at the surface of maximum static stability (maximum temperature gradient) and at the material top of STBL, defined by a threshold value of the total water mixing ratio. Boundary-layer updrafts, spanning entire depth of the STBL, impinge upon the inversion and produce a diverging horizontal flows in the upper part of the STBL. Despite the strong static stability near the cloud top, the horizontal flow is characterized by vertical shears that are strong enough to produce small-scale turbulence. This is manifested by values of the gradient Richardson number falling below the value typically associated with the onset of flow instabilities (cf. Fig. 2). Resulting turbulent mixing is responsible for the formation of the EIL and for entrainment of freetropospheric air into the STBL.

corresponds to the density temperature lower than the free-tropospheric air and the STBL air. These parcels descend into STBL through "cloud holes" - trenches of cloud-free air surrounding areas of cloudy updrafts. Those cloud-free downward currents may be partially recirculated into the cloud, increasing the local cloud base height. The rest of the sinking air provides systematic dilution of the STBL.

Fig.3. Vertical cross-sections of the freetropospheric air fraction (cloud water contours shown by white lines) at t=6hrs (i.e. 3 hours after injection of the passive scalar into the free troposphere. The position of the cross-section was selected to illustrate relevant features.

Fig.2. The gradient Richardson number Ri on the TS (a) and QS (b), as well as the enstrophy on TS (c) and QS (d) at t=3~hr. Note that the darkest shading in (a) and (b) corresponds to values of Ri suggesting flow instability. TS is a temperature inversion surface and QS is a surface defined with use of total water mixing ratio threshold (see text for details).

Mixing processes near the cloud top create finite-thickness interface layer with smoothed gradients of the temperature and humidity. The EIL is also a zone where negative buoyancy is produced and downdrafts are initiated. Injection of a passive scalar above the surface of maximum static stability after 3 hours of the model spin-up time allowed marking the free-tropospheric air that is subsequently involved in mixing with the STBL air. As expected, mixed parcels descending into STBL are characterized by the mixing proportion (i.e., the fraction of the free-tropospheric air) that

An important issue is to what extent entrainment and mixing processes are driven by resolved model physics, and what effects are purely due to numerical aspects, e.g., the grid resolution. To answer this question, sensitivity simulations were performed with finer vertical resolution and modified subgrid-scale parameterizations. Results of the higherresolution simulation show a clear dependence of main STBL characteristics on the choice of the vertical resolution, in agreement with previous results of Stevens and Bretherton (1999). Finer vertical resolution leads to smaller cloud holes (i.e., higher cloud cover) and a thicker cloud (i.e., larger liquid water path). The simulation in which the subgrid-scale mixing was switched off, similarly to one of the simulations discussed in Stevens et al. (2005), resulted in an unrealistically thick cloud, void of cloud holes, and continuously deepening without reaching the steady state. Sensitivity simulations, perhaps in agreement with previous studies, indicate that LES modeling a Sc cloud is quite intricate. Fine model tuning is necessary to obtain results that agree with observations, arguably due to subtle interactions between resolved and subgridscale energy, mass, and momentum fluxes, as

well as fluxes resulting from radiation parameterization. Novel representations of subgrid-scale mixing, focusing on the interactions between turbulent transport and microphysical processes, are necessary to overcome this problem. In consequence, conclusions summarized in the next section are subject of further verification. On the other hand, the agreement between modeled and measured statistical properties of EIL strongly suggests that the mechanism of entrainment and mixing described in this paper is close to the one existing in nature. 4. SUMMARY EIL can be defined as a layer between the level of a threshold total water content and the level of the maximum static stability. Its depth is typically between of few meters and a few tens of meters, with occasional deviations close to a hundred meters. The entrainment and mixing near the STBL top occurs at upper parts of updrafts associated with convective cells spanning the entire STBL depth. The moist air rising within convective cells reaches the boundary layer top and is forced to diverge under strong capping inversion. The divergence produces significant vertical shears at the level of maximum stability, which is illustrated by the model-resolved enstrophy. Despite strong stability across the inversion, the shear can be large enough to initiate turbulent mixing as illustrated by the small Richardson number, often smaller than Ri=0.25. Small mixing fraction of the air entrained from above the inversion results in a weakly negative buoyancy of the mixture. Mixed air sinks into STBL forming cloud holes, areas void of cloud water in shape of trenches or lines, surrounding regions of diverging updraft circulations. Part of the descending air can be wrapped around the cloud edge and mixed into the updraft. The latter leads to a locally elevated cloud base and thinner cloud, as illustrated in Fig. 3. The entrained free-tropospheric air spreads across the STB relatively slowly: typical velocity of sinking motions is a few tenths of 1 m/s, with a few percent of free-tropospheric air in the downdraft. 5. BIBLIOGRAPHY Caughey, S. J., B. A. Crease, and W. T. Roach, 1982: A field study of nocturnal stratocumulus: II. Turbulence structure and entrainment. Quart. J. Roy. Meteor. Soc., 108, 125–144. Gerber, H., S. P. Malinowski, J.-L. Brenguier, and F. Burnet, 2005: Holes and entrainment in Stratocumulus. J. Atmos.

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ACKNOWLEDGEMENT This work was partially supported by Polish MNiSW grant N N307 2649 33 . The National Center for Atmospheric Research is

operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation.