scholarly journals A PDF-Based Formulation of Microphysical Variability in Cumulus Congestus Clouds*

2015 ◽  
Vol 73 (1) ◽  
pp. 167-184 ◽  
Author(s):  
Yefim L. Kogan ◽  
David B. Mechem
Keyword(s):  
Mesoscale Model ◽  
Distribution Functions ◽  
Cumulus Clouds ◽  
Atmospheric Sciences ◽  
Microphysical Process ◽  
Eddy Simulation ◽  
Shallow Cumulus ◽  
Toga Coare ◽  
Accretion Rates ◽  
Cumulus Congestus

Abstract Calculating unbiased microphysical process rates over mesoscale model grid volumes necessitates knowledge of the subgrid-scale (SGS) distribution of variables, typically represented as probability distribution functions (PDFs) of the prognostic variables. In the 2014 Journal of the Atmospheric Sciences paper by Kogan and Mechem, they employed large-eddy simulation of Rain in Cumulus over the Ocean (RICO) trade cumulus to develop PDFs and joint PDFs of cloud water, rainwater, and droplet concentration. In this paper, the approach of Kogan and Mechem is extended to deeper, precipitating cumulus congestus clouds as represented by a simulation based on conditions from the TOGA COARE field campaign. The fidelity of various PDF approximations was assessed by evaluating errors in estimating autoconversion and accretion rates. The dependence of the PDF shape on grid-mean variables is much stronger in congestus clouds than in shallow cumulus. The PDFs obtained from the TOGA COARE simulations for the calculation of accretion rates may be applied to both shallow and congestus cumulus clouds. However, applying the TOGA COARE PDFs to calculate autoconversion rates introduces unacceptably large errors in shallow cumulus clouds, thus precluding the use of a “universal” PDF formulation for both cloud types.

scholarly journals A PDF-Based Microphysics Parameterization for Shallow Cumulus Clouds

2014 ◽  
Vol 71 (3) ◽  
pp. 1070-1089 ◽  
Author(s):  
Yefim L. Kogan ◽  
David B. Mechem
Keyword(s):  
Prediction Models ◽  
Weather Prediction ◽  
Distribution Functions ◽  
Cumulus Clouds ◽  
Microphysical Process ◽  
Eddy Simulation ◽  
Droplet Concentration ◽  
Accretion Rates ◽  
Order Of Magnitude ◽  
Les Model

Abstract Unbiased calculations of microphysical process rates such as autoconversion and accretion in mesoscale numerical weather prediction models require that subgrid-scale (SGS) variability over the model grid volume be taken into account. This variability can be expressed as probability distribution functions (PDFs) of microphysical variables. Using dynamically balanced large-eddy simulation (LES) model results from a case of marine trade cumulus, the authors develop PDFs of the cloud water, droplet concentration, and rainwater variables (qc, Nc, and qr). Both 1D and 2D joint PDFs (JPDFs) are presented. The authors demonstrate that accounting for the JPDFs results in more accurate process rates for a regional-model grid size. Bias in autoconversion and accretion rates are presented, assuming different formulations of the JPDFs. Approximating the 2D PDF using a product of individual 1D PDFs overestimates the autoconversion rates by an order of magnitude, whereas neglecting the SGS variability altogether results in a drastic underestimate of the grid-mean autoconversion rate. PDF assumptions have a much smaller impact on accretion, largely because of the near-linear dependence of the variables in the accretion rate formula and the relatively weak correlation between qc and qr over the small LES grid volumes. The latter is attributed to the spatial decorrelation in the vertical between the two fields. Although the full PDFs are both height and time dependent, results suggest that fixed-in-time and fixed-in-height PDFs give an acceptable level of accuracy, especially for the crucial autoconversion calculation.

scholarly journals A Cloud Microphysics Parameterization for Shallow Cumulus Clouds Based on Lagrangian Cloud Model Simulations

2018 ◽  
Vol 75 (11) ◽  
pp. 4031-4047 ◽  
Author(s):  
Yign Noh ◽  
Donggun Oh ◽  
Fabian Hoffmann ◽  
Siegfried Raasch
Keyword(s):  
Cloud Model ◽  
Cloud Microphysics ◽  
Heaviside Function ◽  
Mixing Ratio ◽  
Cumulus Clouds ◽  
Cloud Droplets ◽  
Shallow Cumulus ◽  
Initial Stage ◽  
Accretion Rates ◽  
The Moment

Abstract Cloud microphysics parameterizations for shallow cumulus clouds are analyzed based on Lagrangian cloud model (LCM) data, focusing on autoconversion and accretion. The autoconversion and accretion rates, A and C, respectively, are calculated directly by capturing the moment of the conversion of individual Lagrangian droplets from cloud droplets to raindrops, and it results in the reproduction of the formulas of A and C for the first time. Comparison with various parameterizations reveals the closest agreement with Tripoli and Cotton, such as and , where and are the mixing ratio and the number concentration of cloud droplets, is the mixing ratio of raindrops, is the threshold volume radius, and H is the Heaviside function. Furthermore, it is found that increases linearly with the dissipation rate and the standard deviation of radius and that decreases rapidly with while disappearing at > 3.5 μm. The LCM also reveals that and increase with time during the period of autoconversion, which helps to suppress the early precipitation by reducing A with smaller and larger in the initial stage. Finally, is found to be affected by the accumulated collisional growth, which determines the drop size distribution.

scholarly journals Investigating the Scale Adaptivity of a Size-Filtered Mass Flux Parameterization in the Gray Zone of Shallow Cumulus Convection

2018 ◽  
Vol 75 (4) ◽  
pp. 1195-1214 ◽  
Author(s):  
Maren Brast ◽  
Vera Schemann ◽  
Roel A. J. Neggers
Keyword(s):  
Mass Flux ◽  
Turbulent Transport ◽  
Eddy Diffusivity ◽  
Coarse Grained ◽  
Parameterization Scheme ◽  
Quasi Equilibrium ◽  
Gray Zone ◽  
Cumulus Clouds ◽  
Eddy Simulation ◽  
Shallow Cumulus

Abstract In this study, the scale adaptivity of a new parameterization scheme for shallow cumulus clouds in the gray zone is investigated. The eddy diffusivity/multiple mass flux [ED(MF)n] scheme is a bin-macrophysics scheme in which subgrid transport is formulated in terms of discretized size densities. While scale adaptivity in the ED component is achieved using a pragmatic blending approach, the MF component is filtered such that only the transport by plumes smaller than the grid size is maintained. For testing, ED(MF)n is implemented into a large-eddy simulation (LES) model, replacing the original subgrid scheme for turbulent transport. LES thus plays the role of a nonhydrostatic testing ground, which can be run at different resolutions to study the behavior of the parameterization scheme in the boundary layer gray zone. In this range, convective cumulus clouds are partially resolved. The authors find that for quasi-equilibrium marine subtropical conditions at high resolutions, the clouds and the turbulent transport are predominantly resolved by the LES. This partitioning changes toward coarser resolutions, with the representation of shallow cumulus clouds gradually becoming completely carried by the ED(MF)n. The way the partitioning changes with grid spacing matches the behavior diagnosed in coarse-grained LES fields, suggesting that some scale adaptivity is captured. Sensitivity studies show that the scale adaptivity of the ED closure is important and that the location of the gray zone is found to be moderately sensitive to some model constants.

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

2012 ◽  
Vol 12 (2) ◽  
pp. 1101-1119 ◽  
Author(s):  
J. T. Dawe ◽  
P. H. Austin
Keyword(s):  
Thermodynamic Properties ◽  
Cloud Base ◽  
Cumulus Cloud ◽  
Cumulus Clouds ◽  
Base Area ◽  
Eddy Simulation ◽  
Cloud Properties ◽  
Shallow Cumulus ◽  
Cloud Height ◽  
Upper Level

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.

An efficient method to account for microphysical inhomogeneity in mesoscale models by using one-dimensional variability factor.

2020 ◽  
Author(s):  
Yefim Kogan
Keyword(s):  
Joint Probability ◽  
Distribution Functions ◽  
Joint Probability Distribution ◽  
Ambient Conditions ◽  
Cloud Type ◽  
Mesoscale Models ◽  
One Dimensional ◽  
Microphysical Process ◽  
Surface Precipitation ◽  
Eddy Simulation

<p>Neglecting subgrid-scale (SGS) variability can lead to substantial bias in calculations of microphysical process rates. The solution to the SGS variability bias problem lies in representing the variability using two-dimensional joint probability distribution functions (JPDFs) for the pairs of different microphysical variables. The JPDFs have also been shown to vary in the vertical: as a result their implementation in mesoscale models presents a challenging task.</p><p>We developed a more efficient formulation of cloud inhomogeneity by using a concept of “generic” JPDF. Using Large Eddy Simulation (LES) studies of shallow cumulus and cumulus congestus clouds we showed that JPDFs calculated based on datasets representing “typical” cloud types (“generic” JPDFs) provide good approximation of microphysical process rates. The generic JPDF, therefore, represent the cloud type in general, i.e. they do not depend on changing ambient conditions. The advantage of generic JPDFs is that they can be a-priory integrated and yield a one-dimensional variability factor (<strong><em>V-facto</em></strong>r) specific for each cloud type. A quite accurate approximation of V-factors by an analytical function in the form of a 3<sup>rd</sup> order polynomial was obtained and can be easily implemented in mesoscale models.</p><p><strong>How big is the effect of cloud inhomogeneity on precipitation</strong>? To answer this question we evaluated the effect of accounting for cloud inhomogeneity on precipitation in sensitivity simulations. In the shallow Cu case over the 24 hr simulation the surface precipitation increased by about 40% when inhomogeneity was accounted. In the congestus Cu case the increase in precipitation was even more significant: by more than 75% over only 8 hours since rain first appeared at the surface. The sensitivity experiments also revealed that most of the increase resulted from the augmented autoconversion process. The effect of modified by the <em><strong>V-factor</strong></em> accretion rates was much less significant, primarily, because of the nearly linear dependence of accretion on its parameters.  This shows importance of the most accurate formulation of the autoconversion process.</p><p> </p><p> </p>

scholarly journals LES study of microphysical variability bias in shallow cumulus

2017 ◽  
Vol 14 ◽  
pp. 103-107 ◽  
Author(s):  
Yefim Kogan
Keyword(s):  
Weather Prediction ◽  
Joint Probability ◽  
Distribution Functions ◽  
Rain Water ◽  
Joint Probability Distribution ◽  
Negative Bias ◽  
Eddy Simulation ◽  
Long Run ◽  
Accretion Rates ◽  
Nwp Model

Abstract. Subgrid-scale (SGS) variability of cloud microphysical variables over the mesoscale numerical weather prediction (NWP) model has been evaluated by means of joint probability distribution functions (JPDFs). The latter were obtained using dynamically balanced Large Eddy Simulation (LES) model dataset from a case of marine trade cumulus initialized with soundings from Rain in Cumulus Over the Ocean (RICO) field project. Bias in autoconversion and accretion rates from different formulations of the JPDFs was analyzed. Approximating the 2-D PDF using a generic (fixed-in-time), but variable-in-height JPDFs give an acceptable level of accuracy, whereas neglecting the SGS variability altogether results in a substantial underestimate of the grid-mean total conversion rate and producing negative bias in rain water. Nevertheless the total effect on rain formation may be uncertain in the long run due to the fact that the negative bias in rain water may be counterbalanced by the positive bias in cloud water. Consequently, the overall effect of SGS neglect needs to be investigated in direct simulations with a NWP model.

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

2011 ◽  
Vol 11 (8) ◽  
pp. 23231-23273 ◽  
Author(s):  
J. T. Dawe ◽  
P. H. Austin
Keyword(s):  
Thermodynamic Properties ◽  
Cloud Base ◽  
Cumulus Cloud ◽  
Cumulus Clouds ◽  
Base Area ◽  
Eddy Simulation ◽  
Cloud Properties ◽  
Shallow Cumulus ◽  
Cloud Height ◽  
Upper Level

Abstract. A technique for the tracking of individual clouds in a Large Eddy Simulation (LES) is presented. We use this technique on a 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 rate displays 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.

scholarly journals Direct entrainment and detrainment rate distributions of individual shallow cumulus clouds in an LES

2013 ◽  
Vol 13 (2) ◽  
pp. 5365-5410 ◽  
Author(s):  
J. T. Dawe ◽  
P. H. Austin
Keyword(s):  
Distribution Functions ◽  
Lapse Rate ◽  
Entrainment Rate ◽  
Cumulus Clouds ◽  
Core Mass ◽  
Cross Sectional ◽  
Shallow Cumulus ◽  
The Mean ◽  
Cloud Core ◽  
Critical Mixing

Abstract. Probability distribution functions of shallow cumulus cloud core entrainment and detrainment rates are calculated using 4362 individual cumulus clouds isolated from LES using a cloud tracking algorithm. Calculation of the mutual information between fractional entrainment/detrainment and a variety of mean cloud core properties suggests that fractional entrainment rate is best predicted by the mean cloud buoyancy B and the environmental buoyancy lapse rate dθρdz at that level, while fractional detrainment is best predicted by the mean vertical velocity w and the critical mixing fraction χc. Fractional entrainment and detrainment rates are relatively insensitive to cloud core horizontal area, and the circumference of horizontal cloud core sections display an a0.69 dependence. This implies that cloud core mass entrainment flux E is proportional to cloud core cross-sectional area instead of cloud core surface area, as is generally assumed. Empirical best-fit relations for ε(B, dθρdz and δ(w, χc) are found for both individual shallow cumulus clouds and cloud ensembles. It is found that clouds with high buoyancy in strong stratification experience low entrainment rates, while clouds with high vertical velocities and critical mixing fractions experience low detrainment rates.

scholarly journals Using a Variability Factor to Account for Cloud Microphysical Inhomogeneity in Mesoscale Models

2018 ◽  
Vol 75 (8) ◽  
pp. 2549-2561
Author(s):  
Yefim Kogan
Keyword(s):  
A Priori ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Factor V ◽  
Mesoscale Models ◽  
Surface Precipitation ◽  
Eddy Simulation ◽  
Shallow Cumulus ◽  
Conversion Rates ◽  
Cumulus Congestus

Abstract Different formulations of the joint probability distribution function (JPDF) based on large-eddy simulation (LES) studies of shallow cumulus and cumulus congestus clouds were evaluated. It was shown that inhomogeneity in both cloud types can be quantified by their respective JPDFs calculated using datasets from the entire simulation time period (“generic” JPDFs). The generic JPDF can be a priori integrated and yield a one-dimensional variability factor (V factor) specific for each cloud type. A quite accurate approximation of V factors by an analytical function in the form of a third-order polynomial was obtained and can be easily implemented in mesoscale models. The effect on precipitation of conversion rates modified by V factors was also evaluated in LES sensitivity studies of shallow cumulus (Cu) and congestus Cu clouds. The surface precipitation increased significantly when V factors were taken into account. The sensitivity experiments revealed that most of the increase resulted from the modified autoconversion process. The effect of accretion rates modified by V factors was much less significant, primarily because of the nearly linear dependence of accretion on its parameters. This fact shows the importance of the most accurate formulation of the autoconversion process.

scholarly journals Life Cycle of Numerically Simulated Shallow Cumulus Clouds. Part II: Mixing Dynamics

2005 ◽  
Vol 62 (5) ◽  
pp. 1291-1310 ◽  
Author(s):  
Ming Zhao ◽  
Philip H. Austin
Keyword(s):  
Dynamic Structure ◽  
Low Pressure ◽  
Life Cycles ◽  
Maximum Height ◽  
Low Velocity ◽  
Cumulus Clouds ◽  
Eddy Simulation ◽  
Shallow Cumulus ◽  
Single Realization ◽  
Mixing Dynamics

Abstract This paper is the second in a two-part series in which life cycles of six numerically simulated shallow cumulus clouds are systematically examined. The six clouds, selected from a single realization of a large-eddy simulation, grow as a series of pulses/thermals detached from the subcloud layer. All six clouds exhibit a coherent vortical circulation and a low buoyancy, low velocity trailing wake. The ascending cloud top (ACT), which contains this vortical circulation, is associated with a dynamic perturbation pressure field with high pressure located at the ascending frontal cap and low pressure below and on the downshear side of the maximum updrafts. Examination of the thermodynamic and kinematic structure, together with passive tracer experiments, suggests that this vortical circulation is primarily responsible for mixing between cloud and environment. As the cloud ACTs rise through the sheared environment, the low pressure, vortical circulation, and mixing are all strongly enhanced on the downshear side and weakened on the upshear side. Collapse of the ACT also occurs on the downshear side, with subsequent thermals ascending on the upshear side of their predecessors. The coherent core structure is maintained throughout the ACT ascent; mixing begins to gradually dilute the ACT core only in the upper half of the cloud's depth. The characteristic kinematic and dynamic structure of these simulated ACTs, together with their mixing behavior, corresponds closely to that of shedding thermals. These shallow simulated clouds, however, reach a maximum height of only about four ACT diameters so that ACT mixing differs from predictions of self-similar laboratory thermals.

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