Cloud-top Mixing Layer Research Articles

Estimating Turbulence Kinetic Energy Dissipation Rates in the Numerically Simulated Stratocumulus Cloud-Top Mixing Layer: Evaluation of Different Methods

AbstractIn this work, direct numerical simulation (DNS) of the stratocumulus cloud-top mixing layer is used to test various approaches to estimate the turbulence kinetic energy (TKE) dissipation rate ε from one-dimensional (1D) intersections that resemble experimental series. Results of these estimates are compared with “true” (DNS) values of ε in buoyant and inhomogeneous atmospheric flows. We focus on recently proposed methods of the TKE dissipation-rate retrievals based on zero crossings and recovering the missing part of the spectrum. These methods are tested on fully resolved turbulence fields and compared to standard retrievals from power spectra and structure functions. Anisotropy of turbulence due to buoyancy is shown to influence retrievals based on the vertical velocity component. TKE dissipation-rate estimates from the number of crossings correspond well to spectral estimates. The method based on the recovery of the missing part of the spectrum works best for Pope’s model of the dissipation spectrum and is sensitive to external intermittency. This allows for characterization of external intermittency by the Taylor-to-Liepmann scale ratio. Further improvements of this method are possible when the variance of the velocity derivative is used instead of the number of zero crossings per unit length. In conclusion, the new methods of TKE dissipation-rate retrieval from 1D series provide a valuable complement to standard approaches.

Reduction of the Entrainment Velocity by Cloud Droplet Sedimentation in Stratocumulus

Abstract The effect of sedimentation on stratocumulus entrainment is investigated using direct numerical simulations of a cloud-top mixing layer driven by radiative and evaporative cooling. The simulations focus on the meter and submeter scales that are expected to be relevant for entrainment, and the finest grid spacing is Δx = 26 cm. The entrainment velocity is investigated from the analysis of the integrated-buoyancy evolution equation, which is exactly derived from the flow evolution equations. The analysis shows that sedimentation interacts with entrainment through two different mechanisms. As previously reported, sedimentation prevents droplets from evaporating in the entrainment zone, which in turn reduces the entrainment velocity. Here it is shown that sedimentation also promotes a positive buoyancy flux that directly opposes entrainment. The strengths of both mechanisms are characterized by two different settling numbers, which allow for predicting which meteorological conditions favor the reduction of entrainment by sedimentation. These new insights allow for including sedimentation in a parameterization of the entrainment velocity. The reduction of the entrainment velocity by sedimentation predicted by the parameterization and observed in the simulations is 3 times larger than previously reported in large-eddy simulations, which implies that meter- and submeter-scale turbulence plays an important role in the interaction of entrainment with sedimentation. On the whole, analysis and simulations indicate that stratocumulus entrainment is more sensitive to the cloud droplet number density due to sedimentation than previously thought.

Mixing Driven by Radiative and Evaporative Cooling at the Stratocumulus Top

Abstract The stratocumulus-top mixing process is investigated using direct numerical simulations of a shear-free cloud-top mixing layer driven by evaporative and radiative cooling. An extension of previous linear formulations allows for quantifying radiative cooling, evaporative cooling, and the diffusive effects that artificially enhance mixing and evaporative cooling in high-viscosity direct numerical simulations (DNS) and many atmospheric simulations. The diffusive cooling accounts for 20% of the total evaporative cooling for the highest resolution (grid spacing ~14 cm), but this can be much larger (~100%) for lower resolutions that are commonly used in large-eddy simulations (grid spacing ~5 m). This result implies that the κ scaling for cloud cover might be strongly influenced by diffusive effects. Furthermore, the definition of the inversion point as the point of neutral buoyancy allows the derivation of two scaling laws. The in-cloud scaling law relates the velocity and buoyancy integral scales to a buoyancy flux defined by the inversion point. The entrainment-zone scaling law provides a relationship between the entrainment velocity and the liquid evaporation rate. By using this inversion point, it is shown that the radiative-cooling contribution to the entrainment velocity decouples from the evaporative-cooling contribution and behaves very similarly as in the smoke cloud. Finally, evaporative and radiative cooling have similar strengths, when this strength is measured by the integrated buoyancy source. This result partially explains why current entrainment parameterizations are not accurate enough, given that most of them implicitly assume that only one of the two mechanisms rules the entrainment.

Evaporative cooling amplification of the entrainment velocity in radiatively driven stratocumulus

AbstractEvaporative cooling monotonically increases as the thermodynamical properties of the inversion allow for more evaporation in shear‐free radiatively driven stratocumulus. However, the entrainment velocity can deviate from the evaporative cooling trend and even become insensitive to variations in the inversion properties. Here the efficiency of evaporative cooling at amplifying the entrainment velocity is quantified by means of direct numerical simulations of a cloud top mixing layer. We demonstrate that variations in the efficiency modulate the effect of evaporative cooling on entrainment, explaining the different trends. These variations are associated with the evaporation of droplets in cloud holes below the inversion point. The parametrization of the efficiency provides the evaporative amplification of the entrainment velocity as a function of a single parameter that characterizes the inversion. The resulting entrainment velocities match our experiments and previous measurements to within ±25%. The parametrization also predicts the transition to a broken‐cloud field consistently with observations.

Direct Numerical Simulations of a Smoke Cloud–Top Mixing Layer as a Model for Stratocumuli

Abstract A radiatively driven cloud-top mixing layer is investigated using direct numerical simulations. This configuration mimics the mixing process across the inversion that bounds the stratocumulus-topped boundary layer. The main focus of this paper is on small-scale turbulence. The finest resolution (7.4 cm) is about two orders of magnitude finer than that in cloud large-eddy simulations (LES). A one-dimensional horizontally averaged model is employed for the radiation. The results show that the definition of the inversion point with the mean buoyancy of 〈b〉(zi) = 0 leads to convective turbulent scalings in the cloud bulk consistent with the Deardorff theory. Three mechanisms contribute to the entrainment by cooling the inversion layer: a molecular flux, a turbulent flux, and the direct radiative cooling by the smoke inside the inversion layer. In the simulations the molecular flux is negligible, but the direct cooling reaches values comparable to the turbulent flux as the inversion layer thickens. The results suggest that the direct cooling might be overestimated in less-resolved models like LES, resulting in an excessive entrainment. The scaled turbulent flux is independent of the stratification for the range of Richardson numbers studied here. As suggested by earlier studies, the turbulent entrainment only occurs at the small scales and eddies larger than approximately four optical lengths (60 m in a typical stratocumulus cloud) perform little or no entrainment. Based on those results, a parameterization is proposed that accounts for a large part (50%–100%) of the entrainment velocities measured in the Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS II) campaign.

Study of low-order numerical effects in the two-dimensional cloud-top mixing layer

Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES.

Probability density functions in the cloud-top mixing layer

The cloud-top mixing layer is an idealized configuration often employed in the literature to study local aspects (over length scales of the order of 10 m) of the top of stratocumulus-topped mixed layers. Latent heat effects are further investigated here by means of direct numerical simulations, discussing the probability density functions of the horizontal and vertical velocities, as well as the mixture fraction (equal to a normalized enthalpy and total water-specific humidity). The focus is on the turbulent convection layer that develops from the buoyancy reversal instability as a consequence of the evaporative cooling at the upper cloud boundary. An approximately self-similar behavior is found, where the convection scales based on the molecular buoyancy flux at the cloud top characterize the distributions at different times, at least to leading order and within the statistical convergence achieved in the simulations. However, a very strong vertical variation in the density functions across the turbulent convection layer is found, which is of relevance to possible models. Non-Gaussian behavior is often observed, even in the horizontal component of the velocity vector. In particular, large values of skewness and flatness are measured at the lower end of the turbulent zone, where external intermittency is very strong.

The evaporatively driven cloud-top mixing layer

Direct numerical simulations of the turbulent temporally evolving cloud-top mixing layer are used to investigate the role of evaporative cooling by isobaric mixing locally at the stratocumulus top. It is shown that the system develops a horizontal layered structure whose evolution is determined by molecular transport. A relatively thin inversion with a constant thickness h = κ/we is formed on top and travels upwards at a mean velocity we ≃ 0.1(κ |bs|χc2)1/3, where κ is the mixture-fraction diffusivity, bs < 0 is the buoyancy anomaly at saturation conditions χs and χc is the cross-over mixture fraction defining the interval of buoyancy reversing mixtures. A turbulent convection layer develops below and continuously broadens into the cloud (the lower saturated fluid). This turbulent layer approaches a self-preserving state that is characterized by the convection scales constructed from a constant reference buoyancy flux Bs = |bs|we/χs. Right underneath the inversion base, a transition or buffer zone is defined based on a strong local conversion of vertical to horizontal motion that leads to a cellular pattern and sheet-like plumes, as observed in cloud measurements and reported in other free-convection problems. The fluctuating saturation surface (instantaneous cloud top) is contained inside this intermediate region. Results show that the inversion is not broken due to the turbulent convection generated by the evaporative cooling, and the upward mean entrainment velocity we is negligibly small compared to the convection velocity scale w* of the turbulent layer and the corresponding growth rate into the cloud.

Two-fluid formulation of the cloud-top mixing layer for direct numerical simulation

A mixture fraction formulation to perform direct numerical simulations of a disperse and dilute two-phase system consisting of water liquid and vapor in air in local thermodynamic equilibrium using a two-fluid model is derived and discussed. The goal is to understand the assumptions intrinsic to this simplified but commonly employed approach for the study of two-layer buoyancy reversing systems like the cloud-top mixing layer. Emphasis is placed on molecular transport phenomena. In particular, a formulation is proposed that recovers the actual nondiffusive liquid-phase continuum as a limiting case of differential diffusion. High-order numerical schemes suitable for direct numerical simulations in the compressible and Boussinesq limits are described, and simulations are presented to validate the incompressible approach. As expected, the Boussinesq approximation provides an accurate and efficient description of the flow on the scales (of the order of meters) that are considered.

Response of a Subtropical Stratocumulus-Capped Mixed Layer to Climate and Aerosol Changes

Abstract In this paper, an idealized framework based on a cloud-topped mixed layer model is developed for investigating feedbacks between subtropical stratocumulus (Sc) and global warming. The two principal control parameters are Sc-region sea surface temperature (SST) and intertropical convergence zone (ITCZ) SST (which controls the temperature and mean subsidence profiles above the Sc). The direct effect of CO2 doubling (leaving all other parameters fixed) is tested and found to somewhat reduce liquid water path; discussion of this effect on the SST-change simulations is included. The presence of a cold boundary layer is found to significantly affect the temperature and subsidence rate just above cloud top by enhancing lower-tropospheric diabatic cooling in this region. A simple representation of this effect (easily generalizable to a more realistic boundary layer model) is developed. Steady-state solutions are analyzed as a function of local and ITCZ SST. Two climate change scenarios are considered. The first scenario is an equal increase of local and ITCZ SSTs. In this case, predicted boundary layer depth and cloud thickness increase. This is found in a simplified context to result from subsidence and entrainment decreases due to increased static stability in a warmer climate. In the second case, local SST change is diagnosed from a surface energy balance under the assumption that ocean heat transport remains unchanged. In this case, predicted boundary layer depth decreases. Cloud continues to thicken with rising ITCZ SST, but at a rate much reduced in comparison to the equal-warming scenario. This cloud shading feedback keeps SST in the Sc region nearly constant as the ITCZ SST increases. Model sensitivity to aerosol indirect effects is also considered by varying the assumed droplet concentration. The resulting change in liquid water path is small, suggesting a weaker dependence on second indirect effect than found in previous studies.

Continental Stratus Clouds: A Case Study Using Coordinated Remote Sensing and Aircraft Measurements

Abstract A continental stratus cloud layer was studied by advanced ground-based remote sensing instruments and aircraft probes on 30 April 1994 from the Cloud and Radiation Testbed site in north-central Oklahoma. The boundary layer structure clearly resembled that of a cloud-topped mixed layer, and the cloud content is shown to be near adiabatic up to the cloud-top entrainment zone. A cloud retrieval algorithm using the radar reflectivity and cloud droplet concentration (either measured in situ or deduced using dual-channel microwave radiometer data) is applied to construct uniquely high-resolution cross sections of liquid water content and mean droplet radius. The combined evidence indicates that the 350–600 m deep, slightly supercooled (2.0° to −2.0°C) cloud, which failed to produce any detectable ice or drizzle particles, contained an average droplet concentration of 347 cm−3, and a maximum liquid water content of 0.8 g m−3 and mean droplet radius of 9 μm near cloud top. Lidar data indicate that the Ka...

Autumnal Mixed-Phase Cloudy Boundary Layers in the Arctic

Abstract Two mixed-phase cloudy boundary layer events observed over the Arctic ice pack in autumn are extensively analyzed. The local dynamic and thermodynamic structure of the boundary layers is determined from aircraft measurements including analysis of turbulence, longwave radiative transfer, and cloud microphysics. The large-scale forcing is determined from the National Centers for Environmental Prediction reanalysis fields while mesoscale forcing is estimated from 40-km aircraft box patterns. The two cases differed somewhat in their local static stability, surface characteristics, and large-scale forcing. One case was characterized by a stably stratified cloudy boundary layer over a heterogeneous surface containing numerous open leads. The other case occurred over a fairly homogenous surface of multiyear ice and consisted of a surface-based stable layer surmounted by a low-level jet and a cloud-topped mixed layer. An important large-scale factor in the development of low clouds appears to have been w...

Parametric representation of heat and moisture fluxes in cloud-topped mixed layers

Aircraft measurements were made from the NCAR Electra in stratus and stratocumulus clouds off the coast of California in June 1976. Several types of cloud conditions were observed, including (1) a broken layer less than 100 m thick, capped by an inversion at ~1000 m, (2) a broken stratocumulus layer ~300 m thick with an inversion at ~500 m, and (3) a ‘solid’ stratocumulus layer ~250 m thick with an inversion at ~500 m. Although these observations indicate that a variety of cloud conditions may exist in mixed layers, simple one-dimensional mixed-layer models implicitly assume a solid cloud layer with no unsaturated region within the cloud. In order to generalize these simple models, a parametric representation of the heat and moisture fluxes is considered. In this scheme, the fluxes are parameterized in terms of the product of a cloud mass flux and the characteristic difference between the thermodynamic properties of an updraft-downdraft circulation. This representation allows for an explicit representation of the buoyancy flux when the downdraft has no liquid water.

An Observational Study of Cloud-Topped Mixed Layers

Abstract The turbulence and mean structure of oceanic stratocumulus was studied using aircraft data collected during the summer of 1976 off the coast of California. Three cloud-topped mixed layers were studied in detail. They consisted of 1) a thin cloud capped by an inversion at a height of ∼1000 m, 2) a relatively thick but broken cloud layer capped by a weak inversion at ∼600 m and 3) a solid cloud capped by a strong inversion at ∼600 m. The mean temperature, moisture, liquid water and radiative characteristics obtained for these three cases were compared. Heat and moisture fluxes were also calculated and compared. Although there was considerable variation in the characteristics of the three cloud-topped mixed layers studied, all indicated the validity of the general approach used in simple mixed-layer models of stratocumulus. But for these models to be useful, they should be generalized to allow clouds other than solid clouds to be modeled. The measurements indicate that cloud microphysics may be impo...

Buoyant Production and Consumption of Turbulence Kinetic Energy in Cloud-Topped Mixed Layers

Entrainment closure theories for mixed-layer models entail assumptions about how the net rate of buoyant production of turbulence kinetic energy is partitioned into gross production and consumption. Three alternative partitioning theories are examined in this paper: Eulerian partitioning, process partitioning and Lagrangian partitioning. Lagrangian partitioning provides a definition of the gross production rate, but is difficult to implement directly. Eulerian and process partitioning are attempts to implement Lagrangian partitioning indirectly. For the buoyancy fluxes due to a single family of plumes, Eulerian and Lagrangian partitioning are shown to be equivalent. Recent observations reported by Wilczak and Businger rule out such a model. However, it serves as a useful conceptual link between Eulerian and Lagrangian partitioning. Process partitioning can be formulated in a variety of ways. Examples show that mixed-layer model results are very sensitive to the way in which radiative cooling is assumed to influence the production and consumption rates. A quantitative relationship between process partitioning and Lagrangian partitioning has yet to be established. The observations of Wilczak and Businger show that consumption and entrainment are not as closely linked as current versions of process partitioning suggest.

The Mesoscale Stability of Entrainment into Cloud-Topped Mixed Layers

The Lilly-type models for stratocumulus-capped mixed layers are shown to allow for a mesoscale instability in which mesoscale fluctuations of buoyancy and humidity are reinforced in phase by entrainment. In a model of an AMTEX mixed layer, this mesoscale instability has a maximum growth rate of about 0.00002 per sec at wavelengths 30 times the depth of the mixed layer. The instability is able to account for the existence and broad scale of the stratiform cloud patterns known as mesoscale cellular convection.

Cloud-Top Entrainment Instability Observed in AMTEX

Abstract Aircraft data collected at the top of a cloud-topped mixed layer during the Air Mass Transformation Experiment are analyzed. Entrainment instability due to evaporation of liquid water is found to occur intermittently. This instability and upward heat flux occur frequently at the downstream edge of cloudy mixed-layer motions which have penetrated upward into the faster moving dry air of the inversion layer. Such circulations appear to occur mainly on scales of the order of 100 or 200 m. At the level of the aircraft at the mixed-layer top, the net heat flux is upward in cloudy regions and downward in the driest regions.

Note on Mixed-Layer Entrainment Closure

Abstract The entrainment closure for the turbulence energy budgetcommonly used in unsaturated mixed layer models is re-derivedfrom the perspective of potential energy changes, and it isconcluded that the correct physical interpretation of theenergetics based on experimental evidence is that the turbulenceform entrainment at about the 20% efficiency level(not the 4% level). In the case of a cloud-toppedmixed layer, this physical interpretation leads to are-examination of the condition for stratocumulus cloud-topentrainment instability and the conclusion that recentcorrections for liquid water loading may yet be toorestrictive.

The Effects of Radiative Cooling in a Cloud-Topped Mixed Layer

Abstract The sensitivity of models of cloud-topped mixed layers to various specifications of the radiative cooling rate near the cloud top is investigated. It is found that for the “dry cloud” case an assumed distributed cooling rate leads to a shallower mixed layer and more positive surface turbulent heat flux than does a discontinuous radiative flux model.

Experiments with Lilly's Cloud-Topped Mixed Layer Model

Abstract Lilly's model of a horizontally homogeneous cloud-topped mixed layer is studied. The model is closed by taking a weighted (weighting factor or entrainment parameter k) average of Lilly's maximum and minimum entrainment cases. The dependence of steady-state solutions on large-scale divergence, sea surface temperature and entrainment parameter k is investigated. By numerical integration the response of the mixed layer to a diurnally varying radiative flux is investigated. Significant variations in the state of the mixed layer and in the convective fluxes are found.