scholarly journals The Grell–Freitas (GF) convection parameterization: recent developments, extensions, and applications

2021 ◽  
Vol 14 (9) ◽  
pp. 5393-5411
Author(s):  
Saulo R. Freitas ◽  
Georg A. Grell ◽  
Haiqin Li
Keyword(s):  
Wet Deposition ◽  
Chemical Constituents ◽  
Deep Convection ◽  
Cloud Microphysics ◽  
Probability Density Functions ◽  
Density Functions ◽  
Tracer Transport ◽  
Additional Heat ◽  
Recent Developments ◽  
Convection Parameterization

Abstract. Recent developments and options in the GF (Grell and Freitas, 2014; Freitas et al., 2018) convection parameterization are presented. The parameterization has been expanded to a trimodal spectral size to simulate three convection modes: shallow, congestus, and deep. In contrast to usual entrainment and detrainment assumptions, we assume that beta functions (BFs), commonly applied to represent probability density functions (PDFs), can be used to characterize the vertical mass flux profiles for the three modes and use the BFs to derive entrainment and detrainment rates. We also added a new closure for nonequilibrium convection that improved the simulation of the diurnal cycle of convection, with a better representation of the transition from shallow to deep convection regimes over land. The transport of chemical constituents (including wet deposition) can be treated inside the GF scheme. The tracer transport is handled in flux form and is mass-conserving. Finally, the cloud microphysics have been extended to include the ice phase to simulate the conversion from liquid water to ice in updrafts with resulting additional heat release and the melting from snow to rain.

scholarly journals The GF Convection Parameterization: recent developments, extensions, and applications

2020 ◽  
Author(s):  
Saulo R. Freitas ◽  
Georg A. Grell ◽  
Haiqin Li
Keyword(s):  
Chemical Constituents ◽  
Deep Convection ◽  
Cloud Microphysics ◽  
Probability Density Functions ◽  
Vertical Layer ◽  
Spatial Correlations ◽  
Recent Developments ◽  
Temporal And Spatial ◽  
New Feature ◽  
Convection Parameterization

Abstract. We detail recent developments in the GF (Grell and Freitas, 2014, Freitas et al., 2018) convection parameterization and applications. The parameterization has been extended to a trimodal spectral size to simulate the interaction and transition from shallow, congestus and deep convection regimes. Another main new feature is the inclusion of a closure for non-equilibrium convection that resulted in a substantial gain of realism in the simulation of the diurnal cycle of convection, mainly associated with boundary layer forcing over the land. Additional changes include the transport of momentum, the use of three Probability Density Functions (PDF's) to describe the normalized vertical mass flux profiles from deep, congestus, and shallow plumes (respectively) in the grid box, and the option of using temporal and spatial correlations to stochastically perturb PDF's, momentum transport and the closures. Cloud water detrainment is proportional to mass detrainment and in-cloud hydrometeor mixing ratio, and transport of chemical constituents (including wet deposition) can be treated inside the GF scheme. Transport is handled in flux form and is mass conserving. Finally, the cloud microphysics has been extended to include the ice phase to simulate the conversion from liquid water to ice in updrafts with resulting additional heating release, and the melting from snow to rain within a user-specified melting vertical layer.

scholarly journals Assumed Probability Density Functions for Shallow and Deep Convection

2010 ◽  
Vol 2 (4) ◽  
pp. n/a-n/a ◽  
Author(s):  
Peter A. Bogenschutz ◽  
Steven K. Krueger ◽  
Marat Khairoutdinov
Keyword(s):  
Probability Density ◽  
Deep Convection ◽  
Probability Density Functions ◽  
Density Functions

scholarly journals Multivariate Probability Density Functions with Dynamics in the GFDL Atmospheric General Circulation Model: Global Tests

2014 ◽  
Vol 27 (5) ◽  
pp. 2087-2108 ◽  
Author(s):  
Huan Guo ◽  
Jean-Christophe Golaz ◽  
Leo J. Donner ◽  
Paul Ginoux ◽  
Richard S. Hemler
Keyword(s):  
Probability Density ◽  
General Circulation ◽  
Atmospheric General Circulation Model ◽  
Circulation Model ◽  
Cloud Microphysics ◽  
Probability Density Functions ◽  
Density Functions ◽  
Shallow Convection ◽  
Atmospheric General Circulation ◽  
Aerosol Activation

Abstract A unified turbulence and cloud parameterization based on multivariate probability density functions (PDFs) has been incorporated into the GFDL atmospheric general circulation model (AM3). This PDF-based parameterization not only predicts subgrid variations in vertical velocity, temperature, and total water, which bridge subgrid-scale processes (e.g., aerosol activation and cloud microphysics) and grid-scale dynamic and thermodynamic fields, but also unifies the treatment of planetary boundary layer (PBL), shallow convection, and cloud macrophysics. This parameterization is called the Cloud Layers Unified by Binormals (CLUBB) parameterization. With the incorporation of CLUBB in AM3, coupled with a two-moment cloud microphysical scheme, AM3–CLUBB allows for a more physically based and self-consistent treatment of aerosol activation, cloud micro- and macrophysics, PBL, and shallow convection. The configuration and performance of AM3–CLUBB are described. Cloud and radiation fields, as well as most basic climate features, are modeled realistically. Relative to AM3, AM3–CLUBB improves the simulation of coastal stratocumulus, a longstanding deficiency in GFDL models, and their seasonal cycle, especially at higher horizontal resolution, but global skill scores deteriorate slightly. Through sensitivity experiments, it is shown that 1) the two-moment cloud microphysics helps relieve the deficiency of coastal stratocumulus, 2) using the CLUBB subgrid cloud water variability in the cloud microphysics has a considerable positive impact on global cloudiness, and 3) the impact of adjusting CLUBB parameters is to improve the overall agreement between model and observations.

scholarly journals Modeling Diameter Distributions with Six Probability Density Functions in Pinus halepensis Mill. Plantations Using Low-Density Airborne Laser Scanning Data in Aragón (Northeast Spain)

2021 ◽  
Vol 13 (12) ◽  
pp. 2307
Author(s):  
J. Javier Gorgoso-Varela ◽  
Rafael Alonso Ponce ◽  
Francisco Rodríguez-Puerta
Keyword(s):  
Probability Density ◽  
Linear Models ◽  
Pinus Halepensis ◽  
Beta Function ◽  
Probability Density Functions ◽  
Lidar Data ◽  
Density Functions ◽  
Minimum Diameter ◽  
Location Parameters ◽  
Diameter Distributions

The diameter distributions of trees in 50 temporary sample plots (TSPs) established in Pinus halepensis Mill. stands were recovered from LiDAR metrics by using six probability density functions (PDFs): the Weibull (2P and 3P), Johnson’s SB, beta, generalized beta and gamma-2P functions. The parameters were recovered from the first and the second moments of the distributions (mean and variance, respectively) by using parameter recovery models (PRM). Linear models were used to predict both moments from LiDAR data. In recovering the functions, the location parameters of the distributions were predetermined as the minimum diameter inventoried, and scale parameters were established as the maximum diameters predicted from LiDAR metrics. The Kolmogorov–Smirnov (KS) statistic (Dn), number of acceptances by the KS test, the Cramér von Misses (W2) statistic, bias and mean square error (MSE) were used to evaluate the goodness of fits. The fits for the six recovered functions were compared with the fits to all measured data from 58 TSPs (LiDAR metrics could only be extracted from 50 of the plots). In the fitting phase, the location parameters were fixed at a suitable value determined according to the forestry literature (0.75·dmin). The linear models used to recover the two moments of the distributions and the maximum diameters determined from LiDAR data were accurate, with R2 values of 0.750, 0.724 and 0.873 for dg, dmed and dmax. Reasonable results were obtained with all six recovered functions. The goodness-of-fit statistics indicated that the beta function was the most accurate, followed by the generalized beta function. The Weibull-3P function provided the poorest fits and the Weibull-2P and Johnson’s SB also yielded poor fits to the data.

scholarly journals A synergy of the velocity gradients technique and the probability density functions for identifying gravitational collapse in self-absorbing media

2021 ◽  
Vol 502 (2) ◽  
pp. 1768-1784
Author(s):  
Yue Hu ◽  
A Lazarian
Keyword(s):  
Magnetic Fields ◽  
Probability Density ◽  
Column Density ◽  
Mass Density ◽  
Probability Density Functions ◽  
Emission Lines ◽  
Density Functions ◽  
Star Forming ◽  
Velocity Gradients ◽  
Self Gravity

ABSTRACT The velocity gradients technique (VGT) and the probability density functions (PDFs) of mass density are tools to study turbulence, magnetic fields, and self-gravity in molecular clouds. However, self-absorption can significantly make the observed intensity different from the column density structures. In this work, we study the effects of self-absorption on the VGT and the intensity PDFs utilizing three synthetic emission lines of CO isotopologues 12CO (1–0), 13CO (1–0), and C18O (1–0). We confirm that the performance of VGT is insensitive to the radiative transfer effect. We numerically show the possibility of constructing 3D magnetic fields tomography through VGT. We find that the intensity PDFs change their shape from the pure lognormal to a distribution that exhibits a power-law tail depending on the optical depth for supersonic turbulence. We conclude the change of CO isotopologues’ intensity PDFs can be independent of self-gravity, which makes the intensity PDFs less reliable in identifying gravitational collapsing regions. We compute the intensity PDFs for a star-forming region NGC 1333 and find the change of intensity PDFs in observation agrees with our numerical results. The synergy of VGT and the column density PDFs confirms that the self-gravitating gas occupies a large volume in NGC 1333.

scholarly journals Modelling with star-shaped distributions

2020 ◽  
Vol 8 (1) ◽  
pp. 45-69
Author(s):  
Eckhard Liebscher ◽  
Wolf-Dieter Richter
Keyword(s):  
Probabilistic Models ◽  
Arbitrary Dimension ◽  
Probability Density Functions ◽  
Density Functions ◽  
Wide Range ◽  
Gaussian Density ◽  
Spherical Distributions ◽  
Data Points ◽  
Non Gaussian ◽  
General Method

AbstractWe prove and describe in great detail a general method for constructing a wide range of multivariate probability density functions. We introduce probabilistic models for a large variety of clouds of multivariate data points. In the present paper, the focus is on star-shaped distributions of an arbitrary dimension, where in case of spherical distributions dependence is modeled by a non-Gaussian density generating function.

scholarly journals Interactive design of probability density functions for shape grammars

2015 ◽  
Vol 34 (6) ◽  
pp. 1-13 ◽  
Author(s):  
Minh Dang ◽  
Stefan Lienhard ◽  
Duygu Ceylan ◽  
Boris Neubert ◽  
Peter Wonka ◽  
...  
Keyword(s):  
Probability Density ◽  
Probability Density Functions ◽  
Interactive Design ◽  
Density Functions ◽  
Shape Grammars

scholarly journals The Impact of Probability Density Functions Assessment on Model Performance for Slope Stability Analysis

Geosciences ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 322
Author(s):  
Evelina Volpe ◽  
Luca Ciabatta ◽  
Diana Salciarini ◽  
Stefania Camici ◽  
Elisabetta Cattoni ◽  
...  
Keyword(s):  
Probability Density ◽  
Central Italy ◽  
Model Performance ◽  
Probability Density Functions ◽  
Slope Instability ◽  
Complex Nature ◽  
Density Functions ◽  
Umbria Region ◽  
Input Variables ◽  
The Impact

The development of forecasting models for the evaluation of potential slope instability after rainfall events represents an important issue for the scientific community. This topic has received considerable impetus due to the climate change effect on territories, as several studies demonstrate that an increase in global warming can significantly influence the landslide activity and stability conditions of natural and artificial slopes. A consolidated approach in evaluating rainfall-induced landslide hazard is based on the integration of rainfall forecasts and physically based (PB) predictive models through deterministic laws. However, considering the complex nature of the processes and the high variability of the random quantities involved, probabilistic approaches are recommended in order to obtain reliable predictions. A crucial aspect of the stochastic approach is represented by the definition of appropriate probability density functions (pdfs) to model the uncertainty of the input variables as this may have an important effect on the evaluation of the probability of failure (PoF). The role of the pdf definition on reliability analysis is discussed through a comparison of PoF maps generated using Monte Carlo (MC) simulations performed over a study area located in the Umbria region of central Italy. The study revealed that the use of uniform pdfs for the random input variables, often considered when a detailed geotechnical characterization for the soil is not available, could be inappropriate.

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