Fractional Entrainment Rate Research Articles

A new approach for estimating entrainment rate in cumulus clouds

A new approach is presented to estimate entrainment rate in cumulus clouds. The new approach is directly derived from the definition of fractional entrainment rate and relates it to mixing fraction and the height above cloud base. The results derived from the new approach compare favorably with those obtained with a commonly used approach, and have smaller uncertainty. This new approach has several advantages: it eliminates the need for in‐cloud measurements of temperature and water vapor content, which are often problematic in current aircraft observations; it has the potential for straightforwardly connecting the estimation of entrainment rate and the microphysical effects of entrainment‐mixing processes; it also has the potential for developing a remote sensing technique to infer entrainment rate.

Statistical analysis of an LES shallow cumulus cloud ensemble using a cloud tracking algorithm

Abstract. A technique for the tracking of individual clouds in a Large Eddy Simulation (LES) is presented. We use this technique on an LES of a shallow cumulus cloud field based upon the Barbados Oceanographic and Meteorological Experiment (BOMEX) to calculate statistics of cloud height, lifetime, and other physical properties for individual clouds in the model. We also examine the question of nature versus nurture in shallow cumulus clouds: do properties at cloud base determine the upper-level properties of the clouds (nature), or are cloud properties determined by the environmental conditions they encounter (nurture). We find that clouds which ascend through an environment that has been pre-moistened by previous cloud activity are no more likely to reach the inversion than clouds that ascend through a drier environment. Cloud base thermodynamic properties are uncorrelated with upper-level cloud properties, while mean fractional entrainment and detrainment rates display moderate correlations with cloud properties up to the inversion. Conversely, cloud base area correlates well with upper-level cloud area and maximum cloud height. We conclude that cloud thermodynamic properties are primarily influenced by entrainment and detrainment processes, cloud area and height are primarily influenced by cloud base area, and thus nature and nurture both play roles in the dynamics of BOMEX shallow cumulus clouds.

A bulk mass flux convection scheme for climate model: description and moisture sensitivity

A convection scheme for climate model is developed based on Tiedtke’s (Mon Weather Rev 117:1779–1800, 1989) bulk mass flux framework and is evaluated with observational data and cloud resolving model simulation data. The main differences between the present parameterization and Tiedtke’s parameterization are the convection trigger, fractional entrainment and detrainment rate formulations, and closure method. Convection is triggered if the vertical velocity of a rising parcel is positive at the level at which the parcel is saturated. The fractional entrainment rate depends on the vertical velocity and buoyancy of the parcel as well as the environmental relative humidity. For the fractional detrainment rate, a linear decrease in the updraft mass flux above maximum buoyancy level is assumed. In the closure method, the cloud base mass flux is determined by considering both cloud layer instability and subcloud layer turbulent kinetic energy as controlling factors in the strength of the convection. The convection scheme is examined in a single column framework as well as using a general circulation model. The present bulk mass flux (BMF) scheme is compared with a simplified Relaxed Arakawa-Schubert (RAS) scheme. In contrast to the RAS, which specifies the cloud top, cloud top height in BMF depends on environmental properties, by considering the conditions of both the parcel and its environment in a fractional entrainment and detrainment rate formulations. As a result, BMF shows improved sensitivity in depth and strength of convection on environmental humidity compared to RAS, by strengthening coupling between cloud and environment. When the mid to lower troposphere is dry, the cloud resolving model and BMF produce cloud top around the dry layer and moisten the layer. In the framework of general circulation model, enhanced coupling between convection and environmental humidity in BMF results in improved representation of eastward propagating intraseasonal variability in the tropics—the Madden-Julian oscillation.

Resolved Versus Parametrized Boundary-Layer Plumes. Part II: Continuous Formulations of Mixing Rates for Mass-Flux Schemes

The conditional sampling of coherent structures in large-eddy simulations of the convective boundary layer (Couvreux et al. Boundary-layer Meteorol 134:441–458, 2010) is used to propose and evaluate formulations of fractional entrainment and detrainment rates for mass-flux schemes. The proposed formulations are physically-based and continuous from the surface to the top of clouds. Entrainment is related to the updraft vertical velocity divergence, while detrainment depends on the thermal vertical velocity, on buoyancy and on the moisture contrast between the mean plume and its environment. The proposed formulations are first directly evaluated in simulations of shallow clouds. They are then tested in single-column simulations with the thermal plume model, a mass-flux representation of boundary-layer thermals.

Evaluating deep updraft formulation in NCAR CAM3 with high‐resolution WRF simulations during ARM TWP‐ICE

The updraft formulation used in NCAR CAM3 deep convection parameterization assumes that the mass flux for a single updraft increases exponentially with height to its top and detrainment is confined only to a thin layer at the updraft top. These assumptions are evaluated against three‐dimensional high‐resolution simulations from the Weather Research and Forecast (WRF) model during the monsoon period of the DOE Atmospheric Radiation Measurement (ARM) Program Tropical Warm Pool–International Cloud Experiment (TWP‐ICE). Analyses of the WRF‐generated updrafts suggest that the mass flux for a single updraft increases with height below the top of the conditionally unstable layer and decreases above. Detrainment may dominate above the conditionally unstable layer rather than only over a thin layer at the updraft top. It is argued that the assumed updraft mass flux profile in CAM3 might be unrealistic in many cases because the updraft acceleration is affected by other drag processes in addition to entrainment. Our analyses suggest that the CAM3‐parameterized convection could be too active and, as a result, excess moisture and heat could be transported to the upper troposphere by the parameterized convection. Future improvement is envisioned.

A Simple Parameterization for Detrainment in Shallow Cumulus

Abstract For a wide range of shallow cumulus convection cases, large-eddy simulation (LES) model results have been used to investigate lateral mixing as expressed by the fractional entrainment and fractional detrainment rates. It appears that the fractional entrainment rates show much less variation from hour to hour and case to case than the fractional detrainment rates. Therefore, in the parameterization proposed here, the fractional entrainment rates are assumed to be described as a fixed function of height, roughly following the LES results. Based on the LES results a new, more flexible parameterization for the detrainment process is developed that contains two important dependencies. First, based on cloud ensemble principles it can be understood that deeper cloud layers call for smaller detrainment rates. All current mass flux schemes ignore this cloud-height dependence, which evidently leads to large discrepancies with observed mass flux profiles. The new detrainment formulation deals with this dependence by considering the mass flux profile in a nondimensionalized way. Second, both relative humidity of the environmental air and the buoyancy excess of the updraft influence the detrainment rates and, therefore, the mass flux profiles. This influence can be taken into account by borrowing a parameter from the buoyancy-sorting concept and using it in a bulk sense. LES results show that with this bulk parameter, the effect of environmental conditions on the fractional detrainment rate can be accurately described. A simple, practical but flexible parameterization for the fractional detrainment rate is derived and evaluated in a single-column model (SCM) for three different shallow cumulus cases, which shows the clear potential of this parameterization. The proposed parameterization is an attractive and more robust alternative for existing, more complex, buoyancy-sorting-based mixing schemes, and can be easily incorporated in current mass flux schemes.

An Integrated Turbulence Scheme for Boundary Layers with Shallow Cumulus Applied to Pollutant Transport

Abstract A scheme is described that provides an integrated description of turbulent transport in free convective boundary layers with shallow cumulus. The scheme uses a mass-flux formulation, as is commonly found in cumulus schemes, and a 1.5-order closure, involving turbulent kinetic energy and eddy diffusivity. Both components are active in both the subcloud and cloud layers. The scheme is called “mass flux–diffusion.” In the subcloud layer, the mass-flux component provides nonlocal transport. The scheme combines elements from schemes that are conceptually similar but differ in detail. An entraining plume model is used to find the mass flux. The mass flux is continuous through the cloud base. The lateral fractional entrainment rate is constant with height, while the detrainment-rate profile reduces the mass flux smoothly to zero at the cloud top. The eddy diffusivity comes from a turbulent kinetic energy–length scale formulation. The scheme has been implemented in a simple one-dimensional (single column) model. Results of simulations of a standard case that has been used for other model intercomparisons [Atmospheric Radiation Measurement (ARM), 21 June 1997] are shown and indicate that the scheme provides good results. The model also simulates the profile of a conserved scalar; this capability is applied to a case from the 1999 Southern Oxidants Study Nashville (Tennessee) experiment, where it produces good simulations of vertical profiles of carbon monoxide in a cloud-topped boundary layer.

The Vertical Profile of Entrainment Rate Simulated by a Cloud-Resolving Model and Application to a Cumulus Parameterization

To investigate the vertical profiles of fractional entrainment rate as to cumulus convection, numerical simulations of a tropical cyclone rainband are conducted, using a high-resolution three-dimensional cloud-resolving model (CRM), with the 200-m horizontal resolution. On the basis of the results of CRM simulations, venically variable entrainment rate is applied to the Arakawa-Schubert (AS) cumulus parameterization. Fractional entrainment rate, derived from the calculation based on the vertical gradient of cloud mass flux, clearly shows larger near cloud base and top. Between the heights of cloud base and top, entrainment rate is smaller, and even negative in many cases, suggesting laterally detrained air from a cumulus into the environment. From the analyses where entrainment rate is divided into three terms, it is found that the contributions of updraft is relatively large near the cloud base and top, compared to that in between. The cloud amount contribution depends on whether cloudy areas expand or shrink accompanying cloud growth or decay, respectively.On the basis of the result of the CRM simulations, vertically variable entrainment rate is applied to the AS scheme. For investigating the effect of the modifications of the scheme, simulations of typhoon Saomai (2000) are conducted. The simulations show significant improvements: underestimates of moisture in the mid- to upper troposphere are reduced. The result is predominantly attributed to cloud mass flux, greatly influenced by lateral detrainment. The peak height of the mass flux corresponds to that in the moisture tendency.

A similarity hypothesis for shallow‐cumulus transports

AbstractA similarity theory for cumulus convection is proposed, and applied to the problem of cumulus transports, using data from several large‐eddy simulations to test the theory. the parameters in the similarity hypothesis include the cloud‐base mass flux, the buoyancy of a parcel undergoing reversible ascent, through the cloud layer and the depth of the cloud layer. Using arguments based on the turbulence kinetic‐energy budget a velocity‐scale is derived, in addition to the conventional Convective Available Potential Energy scale. This new scale is analogous to the convective velocity‐scale used in boundary‐layer theories, but incorporates the effects of latent‐heat release. the ratio between the cloud‐base mass flux and the velocity‐scale is found to be a key parameter in describing cumulus convection.It is shown that the similarity hypothesis can be applied to mass‐flux schemes to determine the fractional entrainment rate. For this the entrainment rate is assumed to be related to the rate of generation of turbulent kinetic energy in the cloud ensemble. the resulting scaling is tested against fractional entrainment rates diagnosed from the large‐eddy simulations.

Analysis of Astex-Stratocumulus Observational Data Using a Mass-Flux Approach

A mass-flux approach is applied to observational data obtained in a convective boundary layer topped with stratocumulus clouds. The observational data were obtained from aircraft measurements during the Atlantic Stratocumulus Transition Experiment (ASTEX). A conditional sampling method is used to calculate average updraft and downdraft values. The vertical fluxes calculated with the mass-flux approach are found to be proportional to the real (measured) fluxes, with a proportionality factor being about 0.6. This value is predicted by theory for two variables having a joint Gaussian distribution function; proportionality factor = 2π-1 ≈ 0.637. The horizontal fractional entrainment and detrainment rates calculated from the data (e ≈ 1–2 × 10-2 m-1) are an order of magnitude higher than the rates obtained by large eddy simulations for cumulus convection (e ≈ 2–3 × 10-3 m-1) and two orders of magnitude higher than those used in modelling cumulus convection with a mass-flux scheme in an operational weather forecast model (e ≈ 3 × 10-4 m-1). A numerical mass-flux model for the thermodynamics was developed and showed that results are in good agreement when compared with measured profiles of the liquid water content.

The components of fractional transport rate

Fractional transport rates are defined as the product of spatial grain entrainment, displacement length, and displacement frequency. Grain entrainment is defined relative to the population of grains on the bed surface at an initial time in order to account for partial transport, a condition in which only a portion of the exposed grains of a single size Di are mobilized over the duration of a transport event. A relation for grain displacement frequency is calculated from an assumed relation for displacement length and observed values of fractional transport rate, bed surface size distribution, and spatial entrainment in flume experiments. Fractional transport rates are independent of Di for fully mobilized fractions and decrease rapidly with Di for partially mobile fractions; the latter results from a decrease in both the displacement frequency and the mobilized proportion of each fraction. These two terms, which together determine the fractional entrainment rate, have different relations with flow strength and Di and should be independently included in a general fractional transport model. Grain‐size similarity in fractional transport rates does not hold for conditions of partial transport. Partial transport is a grain‐scale representation of incipient motion and can be directly related to the reference shear stress τri a surrogate for the critical shear stress for incipient motion based on transport rate rather than grain mobility. Fractional mobilization at different flows may be predicted from τri, and partial transport appears to be the general condition at the reference transport rate. Using τri as input, the transport component relations are used to predict the bed mobilization and fractional transport rates for a field case.

Evaluation of Parametric Assumptions for Shallow Cumulus Convection

Abstract A large-eddy simulation (LES) model has been utilized to study nonprecipitating Shallow Convective clouds such as observed during the undisturbed BOMEX period in the trade wind areas. By choosing a realistic large-scale forcing the authors have been able to simulate shallow convective clouds under quasi-steady-state conditions over a long period of 7 hours. This is a necessary condition to investigate diagnostic cumulus parameterization schemes since such schemes usually assume steady-state conditions. The response of the model to the applied large-scale forcing compares well with budget study results of BOMEX. In addition, the LES model delivers detailed information concerning the dynamics of shallow convective clouds. This is used to verify basic parameterizations of turbulent fluxes and entrainment and detrainment rates used in large-scale models. The most important conclusions are (i) the fractional entrainment and detrainment rates used in present large-scale atmospheric models are one order...

Entrainment and Detrainment in a Simple Cumulus Cloud Model

A cumulus cloud model, analogous to the mixed-layer models of the planetary boundary layer and the upper ocean, is developed using a single, unitary entrainment process in which the motion of the cloud boundary relative to the mean flow is permitted, produced, and controlled by turbulent processes. An alternate theory to the mixing-length theory of Asai and Kasahara (1967) is proposed which completely removes the strong scale-dependence of the Asai-Kasahara model. The model reintroduces scale-dependence by introducing including the pe5turbation pressure term of the equation of vertical motion. It is shown that the model predicts deeper clouds than the Asai-Kasahara model for a given sounding, due to the entrainment assumption and the effects of the perturbation pressure. Lateral entrainment dominates cloud-top entrainment, although finite-difference errors increase the cloud-top entrainment rate from zero to a positive value in actual situations. The fractional entrainment rate for updrafts is determined to vary only slightly with height and to decrease only slowly as the cloud radius increases, while the fractional detrainment rate for updrafts increases with height.

Interaction of a Cumulus Cloud Ensemble with the Large-Scale Environment, Part I

A theory of the interaction of a cumulus cloud ensemble with the large-scale environment is developed. In this theory, the large-scale environment is divided into the subcloud mixed layer and the region above. The time changes of the environment are governed by the heat and moisture budget equations for the subcloud mixed layer and for the region above, and by a prognostic equation for the depth of the mixed layer. In the environment above the mixed layer, the cumulus convection affects the temperature and moisture fields through cumulus-induced subsidence and detrainment of saturated air containing liquid water which evaporates in the environment. In the subcloud mixed layer, the cumulus convection does not act directly on the temperature and moisture fields, but it affects the depth of the mixed layer through cumulus-induced subsidence. Under these conditions the problem of parameterization of cumulus convection reduces to the determination of the vertical distributions of the total vertical mass flux by the ensemble, the total detrainment of mass from the ensemble, and the thermodynamical properties of the detraining air. The cumulus ensemble is spectrally divided into sub-ensembles according to the fractional entrainment rate, given by the ratio of the entrainment per unit height to the vertical mass flux in the cloud. For these sub-ensembles, the budget equations for mass, moist static energy, and total water content are obtained. The solutions of these equations give the temperature excess, the water vapor excess, and the liquid water content of each sub-ensemble, and further reduce the problem of parameterization to the determination of the mass flux distribution function, which is the sub-ensemble vertical mass flux at the top of the mixed layer. The cloud work function, which is an integral measure of the buoyancy force in the clouds, is defined for each sub-ensemble; and, under the assumption that it is in quasi-equilibrium, an integral equation for the mass flux distribution function is derived. This equation describes how a cumulus ensemble is forced by large-scale advection, radiation, and surface turbulent fluxes, and it provides a closed parameterization of cumulus convection for use in prognostic models of large-scale atmospheric motion.