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2001a: Toward a unified parameterization of the boundary layer and moist convection. Part II: Lateral mass exchanges and subplumescale fluxes
 J. Atmos. Sci
"... Higherorder closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higherorder moments (e.g., fourth moments in thirdorder closure models), for pressure terms, and for dissipation terms. Massflux closure ..."
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Cited by 25 (2 self)
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Higherorder closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higherorder moments (e.g., fourth moments in thirdorder closure models), for pressure terms, and for dissipation terms. Massflux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called AssumedDistribution HigherOrder Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments; thereafter the joint
C.: Using probability density functions to derive consistent closure relationships among higherorder moments
 Weather Rev
"... Parameterizations of turbulence often predict several lowerorder moments and make closure assumptions for higherorder moments. In principle, the low and highorder moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When t ..."
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Cited by 16 (5 self)
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Parameterizations of turbulence often predict several lowerorder moments and make closure assumptions for higherorder moments. In principle, the low and highorder moments share the same probability density function (PDF). One closure assumption, then, is the shape of this family of PDFs. When the higherorder moments involve both velocity and thermodynamic scalars, often the PDF shape has been assumed to be a double or triple delta function. This is equivalent to assuming a massflux model with no subplume variability. However, PDF families other than delta functions can be assumed. This is because the assumed PDF methodology is fairly general. This paper proposes closures for several third and fourthorder moments. To derive the closures, the moments are assumed to be consistent with a particular PDF family, namely, a mixture of two trivariate Gaussians. (This PDF is also called a double Gaussian or binormal PDF by some authors.) Separately from the PDF assumption, the paper also proposes a simplified relationship between scalar and velocity skewnesses. This PDF family and skewness relationship are simple enough to yield simple, analytic closure formulas relating the moments. If certain conditions hold, this set of moments is specifically realizable. By this it is meant that the set of moments corresponds to a real Gaussianmixture PDF, one that is normalized
Smallscale and mesoscale variability of scalars in cloudy boundary layers: Onedimensional probability density functions
, 2001
"... A key to parameterization of subgridscale processes is the probability density function (PDF) of conserved scalars. If the appropriate PDF is known, then grid box average cloud fraction, liquid water content, temperature, and autoconversion can be diagnosed. Despite the fundamental role of PDFs in ..."
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Cited by 11 (3 self)
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A key to parameterization of subgridscale processes is the probability density function (PDF) of conserved scalars. If the appropriate PDF is known, then grid box average cloud fraction, liquid water content, temperature, and autoconversion can be diagnosed. Despite the fundamental role of PDFs in parameterization, there have been few observational studies of conservedscalar PDFs in clouds. The present work analyzes PDFs from boundary layers containing stratocumulus, cumulus, and cumulusrisingintostratocumulus clouds. Using observational aircraft data, the authors test eight different parameterizations of PDFs, including double delta function, gamma function, Gaussian, and double Gaussian shapes. The Gaussian parameterization, which depends on two parameters, fits most observed PDFs well but fails for largescale PDFs of cumulus legs. In contrast, threeparameter parameterizations appear to be sufficiently general to model PDFs from a variety of cloudy boundary layers. If a numerical model ignores subgrid variability, the model has biases in diagnoses of grid box average liquid water content, temperature, and Kessler autoconversion, relative to the values it would obtain if subgrid variability were taken into account. The magnitude of such biases is assessed using observational data. The biases can be largely eliminated by threeparameter PDF parameterizations.
2002: Smallscale and mesoscale variability in cloudy boundary layers: Joint probability density functions
 J. Atmos. Sci
"... The joint probability density function (PDF) of vertical velocity and conserved scalars is important for at least two reasons. First, the shape of the joint PDF determines the buoyancy flux in partly cloudy layers. Second, the PDF provides a wealth of information about subgrid variability and hence ..."
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Cited by 9 (2 self)
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The joint probability density function (PDF) of vertical velocity and conserved scalars is important for at least two reasons. First, the shape of the joint PDF determines the buoyancy flux in partly cloudy layers. Second, the PDF provides a wealth of information about subgrid variability and hence can serve as the foundation of a boundary layer cloud and turbulence parameterization. This paper analyzes PDFs of stratocumulus, cumulus, and clear boundary layers obtained from both aircraft observations and large eddy simulations. The data are used to fit five families of PDFs: a double delta function, a single Gaussian, and three PDF families based on the sum of two Gaussians. Overall, the double Gaussian, that is binormal, PDFs perform better than the single Gaussian or double delta function PDFs. In cumulus layers with low cloud fraction, the improvement occurs because typical PDFs are highly skewed, and it is crucial to accurately represent the tail of the distribution, which is where cloud occurs. Since the double delta function has been shown in prior work to be the PDF underlying massflux schemes, the data analysis herein hints that massflux simulations may be improved upon by using a parameterization built upon a more realistic PDF. 1.
Vertical velocity and buoyancy characteristics of coherent echo plumes in the convective boundary layer, detected by a profiling airborne radar
 J. Appl.Meteorol. Climatol
, 2006
"... Aircraft and airborne millimeterwave radar observations are used to interpret the dynamics of radar echoes and radarinferred updrafts within the welldeveloped, weakly sheared continental convective boundary layer. Vertically pointing radar reflectivity and Doppler velocity data collected above an ..."
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Cited by 2 (1 self)
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Aircraft and airborne millimeterwave radar observations are used to interpret the dynamics of radar echoes and radarinferred updrafts within the welldeveloped, weakly sheared continental convective boundary layer. Vertically pointing radar reflectivity and Doppler velocity data collected above and below the aircraft, flying along fixed tracks in the central Great Plains during the International H2O Project (IHOP_2002), are used to define echo plumes and updraft plumes, respectively. Updraft plumes are generally narrower than echo plumes, but both types of plumes have the dynamical properties of buoyant eddies, especially at low levels. This buoyancy is driven both by temperature excess and water vapor excess over the ambient air. Plumes that are better defined in terms of reflectivity or updraft strength tend to be more buoyant. 1.
1870 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 58 Simulations of Trade Wind Cumuli under a Strong Inversion
, 2000
"... ..."
A HigherOrder Closure Model with an Explicit PBL Top
, 2009
"... In 2001, the authors presented a higherorder massflux model called ‘‘assumed distributions with higherorder closure’ ’ (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent ..."
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In 2001, the authors presented a higherorder massflux model called ‘‘assumed distributions with higherorder closure’ ’ (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higherorder closure models, are not suitable for use in largescale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higherorder closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are ‘‘hidden’ ’ in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in largescale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixedlayer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in largescale models. 1.
q 2003 American Meteorological Society MassFlux Budgets of Shallow Cumulus Clouds
, 2001
"... The vertical transport by shallow nonprecipitating cumulus clouds of conserved variables, such as the total specific humidity or the liquid water potential temperature, can be well modeled by the massflux approach, in which the cloud field is represented by a tophat distribution of clouds and its ..."
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The vertical transport by shallow nonprecipitating cumulus clouds of conserved variables, such as the total specific humidity or the liquid water potential temperature, can be well modeled by the massflux approach, in which the cloud field is represented by a tophat distribution of clouds and its environment. The massflux budget is computed by conditionally sampling the prognostic vertical velocity equation by means of a large eddy simulation of shallow cumulus clouds. The model initialization is based on observations made during the Barbados Oceanographic and Meteorological Experiment (BOMEX). Several different sampling criteria are applied. The presence of liquid water is used to select clouds, whereas additional criteria are applied to sample cloud updraft, downdraft, and core properties. A comparison between the budgets of the mass flux and the vertical velocity variance show that they appear to be qualitatively similar. The mass flux is driven by buoyancy in the lower part of the cloud layer, whereas turbulent transport is important in generating mass flux in the upper part of the cloud layer. Pressure and subgridscale effects typically act to dissipate mass flux. Entrainment and detrainment rates for the vertical velocity equation are presented. They are found to be smaller in comparison to the ones for conserved variables. It is explained that the tophat structure for the virtual potential temperature is degraded by mixing at the cloud boundaries leading to a subsequent evaporative cooling of cloud droplets that supports the formation of negatively buoyant cloud parcels. 1.
q 2001 American Meteorological Society Simulations of Trade Wind Cumuli under a Strong Inversion
, 2000
"... The fifth intercomparison of the Global Water and Energy Experiment Cloud System Studies Working Group 1 is used as a vehicle for better understanding the dynamics of trade wind cumuli capped by a strong inversion. The basis of the intercomparison is 10 simulations by 7 groups. These simulations are ..."
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The fifth intercomparison of the Global Water and Energy Experiment Cloud System Studies Working Group 1 is used as a vehicle for better understanding the dynamics of trade wind cumuli capped by a strong inversion. The basis of the intercomparison is 10 simulations by 7 groups. These simulations are supplemented by many further sensitivity studies, including some with very refined grid meshes. The simulations help illustrate the turbulent dynamics of trade cumuli in such a regime. In many respects the dynamics are similar to those found in many previous simulations of trade cumuli capped by weaker inversions. The principal differences are the extent to which the cloud layer is quasisteady in the current simulations, evidence of weak countergradient momentum transport within the cloud layer, and the development and influence of an incipient stratiform cloud layer at the top of the cloud layer. Although many elements of the turbulent structure (including the wind profiles, the evolution of cloudbase height, the statistics of the subcloud layer, and the nature of mixing in the lower and middle parts of the cloud layer) are robustly predicted, the representation of the stratiform cloud amount by the different simulations is remarkably sensitive to a number of factors. Chief