Comparison of Eulerian bin and Lagrangian particle-based schemes in simulations of Pi Chamber dynamics and microphysics

2020 ◽  
Author(s):  
Wojciech W. Grabowski
Keyword(s):  
Cloud Droplet ◽  
Spectral Width ◽  
Spectral Density Function ◽  
Lagrangian Approach ◽  
Droplet Growth ◽  
Growth Equation ◽  
Lagrangian Particle ◽  
Droplet Concentration ◽  
The Mean ◽  
Bin Microphysics

<p>This paper discusses a comparison of simulations applying either a traditional Eulerian bin microphysics or a novel particle-based Lagrangian approach to represent CCN activation and cloud droplet growth. The Eulerian microphysics solve the evolution equation for the spectral density function, whereas the Lagrangian approach follows computational particles referred to as super-droplets. Each super-droplet represents a multiplicity of natural droplets that makes the Lagrangian approach computationally feasible. The two schemes apply identical representation of CCN activation and use the same droplet growth equation; these make direct comparison between the two schemes practical. The comparison, the first of its kind, applies an idealized simulation setup motivated by laboratory experiments with the Pi Chamber and previous model simulations of the Pi Chamber dynamics and microphysics. The Pi Chamber laboratory apparatus considers interactions between turbulence, CCN activation, and cloud droplet growth in moist Rayleigh-Bénard convection. Simulated steady-state droplet spectra averaged over the entire chamber are similar, with the mean droplet concentration, mean radius, and spectral width close in Eulerian and Lagrangian simulations. Small differences that do exist are explained by the inherent differences between the two schemes and their numerical implementation. The local droplet spectra differ substantially, again in agreement with the inherent limitations of the theoretical foundation behind each approach. There is a general agreement between simulations and Pi Chamber observations, with simplifications of the CCN activation and droplet growth equation used in the simulations likely explaining specific differences.</p>

Comparison of Eulerian Bin and Lagrangian Particle-Based Schemes in Simulations of Pi Chamber Dynamics and Microphysics

2019 ◽  
Vol 77 (3) ◽  
pp. 1151-1165 ◽  
Author(s):  
Wojciech W. Grabowski
Keyword(s):  
Cloud Droplet ◽  
Spectral Width ◽  
Spectral Density Function ◽  
Lagrangian Approach ◽  
Droplet Growth ◽  
Growth Equation ◽  
Droplet Concentration ◽  
Bin Microphysics ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract This paper presents a comparison of simulations applying either a traditional Eulerian bin microphysics or a novel particle-based Lagrangian approach to represent CCN activation and cloud droplet growth. The Eulerian microphysics solve the evolution equation for the spectral density function, whereas the Lagrangian approach follows computational particles referred to as superdroplets. Each superdroplet represents a multiplicity of natural droplets that makes the Lagrangian approach computationally feasible. The two schemes apply identical representation of CCN activation and use the same droplet growth equation; these make direct comparison between the two schemes practical. The comparison, the first of its kind, applies an idealized simulation setup motivated by laboratory experiments with the Pi Chamber and previous model simulations of the Pi Chamber dynamics and microphysics. The Pi Chamber laboratory apparatus considers interactions between turbulence, CCN activation, and cloud droplet growth in moist Rayleigh–Bénard convection. Simulated steady-state droplet spectra averaged over the entire chamber are similar, with the mean droplet concentration, mean radius, and spectral width close in Eulerian and Lagrangian simulations. Small differences that do exist are explained by the inherent differences between the two schemes and their numerical implementation. The local droplet spectra differ substantially, again in agreement with the inherent limitations of the theoretical foundation behind each approach. There is a general agreement between simulations and Pi Chamber observations, with simplifications of the CCN activation and droplet growth equation used in the simulations likely explaining specific differences.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian super-droplet simulations

2021 ◽  
Vol 21 (5) ◽  
pp. 4059-4077
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Isotropic Turbulence ◽  
Cloud Droplet ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. The increase in the spectral width of an initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated by applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or a Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase in the spectral width. We apply a large computational domain (643 m3), one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence integral timescale is much larger than the droplet phase relaxation timescale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 µm is only sufficient for the lowest droplet concentration (26 cm−3). For the highest droplet concentration (650 cm−3), an order of magnitude smaller bin size is barely sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high-TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and a relatively small number of Lagrangian particles that are used in the particle-based microphysics.

scholarly journals Broadening of Cloud Droplet Spectra through Eddy Hopping: Turbulent Entraining Parcel Simulations

2018 ◽  
Vol 75 (10) ◽  
pp. 3365-3379 ◽  
Author(s):  
Gustavo C. Abade ◽  
Wojciech W. Grabowski ◽  
Hanna Pawlowska
Keyword(s):  
Droplet Size ◽  
Turbulent Mixing ◽  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Cloud Microphysics ◽  
Droplet Growth ◽  
Size Spectrum ◽  
Entrainment Rate ◽  
The Mean ◽  
The Impact

This paper discusses the effects of cloud turbulence, turbulent entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet size spectrum. We simulate an ensemble of idealized turbulent cloud parcels that are subject to entrainment events modeled as a random process. Entrainment events, subsequent turbulent mixing inside the parcel, supersaturation fluctuations, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. Quantities characterizing the turbulence intensity, entrainment rate, CCN concentration, and the mean fraction of environmental air entrained in an event are all specified as independent external parameters. Cloud microphysics is described by applying Lagrangian particles, the so-called superdroplets. These are either unactivated CCN or cloud droplets that grow from activated CCN. The model accounts for the addition of environmental CCN into the cloud by entraining eddies at the cloud edge. Turbulent mixing of the entrained dry air with cloudy air is described using the classical linear relaxation to the mean model. We show that turbulence plays an important role in aiding entrained CCN to activate, and thus broadening the droplet size distribution. These findings are consistent with previous large-eddy simulations (LESs) that consider the impact of variable droplet growth histories on the droplet size spectra in small cumuli. The scheme developed in this work is ready to be used as a stochastic subgrid-scale scheme in LESs of natural clouds.

scholarly journals Cloud droplet diffusional growth in homogeneous isotropic turbulence: bin microphysics versus Lagrangian superdroplet simulations

2020 ◽  
Author(s):  
Wojciech W. Grabowski ◽  
Lois Thomas
Keyword(s):  
Fluid Flow ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Spectral Width ◽  
Small Scale ◽  
Computational Domain ◽  
Homogeneous Isotropic Turbulence ◽  
Diffusional Growth ◽  
Droplet Concentration ◽  
Bin Microphysics

Abstract. Increase of the spectral width of initially monodisperse population of cloud droplets in homogeneous isotropic turbulence is investigated applying a finite-difference fluid flow model combined with either Eulerian bin microphysics or Lagrangian particle-based scheme. The turbulence is forced applying a variant of the so-called linear forcing method that maintains the mean turbulent kinetic energy (TKE) and the TKE partitioning between velocity components. The latter is important for maintaining the quasi-steady forcing of the supersaturation fluctuations that drive the increase of the spectral width. We apply a large computational domain, 643 m3, one of the domains considered in Thomas et al. (2020). The simulations apply 1 m grid length and are in the spirit of the implicit large eddy simulation (ILES), that is, with explicit small-scale dissipation provided by the model numerics. This is in contrast to the scaled-up direct numerical simulation (DNS) applied in Thomas et al. (2020). Two TKE intensities and three different droplet concentrations are considered. Analytic solutions derived in Sardina et al. (2015), valid for the case when the turbulence time scale is much larger than the droplet phase relaxation time scale, are used to guide the comparison between the two microphysics simulation techniques. The Lagrangian approach reproduces the scalings relatively well. Representing the spectral width increase in time is more challenging for the bin microphysics because appropriately high resolution in the bin space is needed. The bin width of 0.5 μm is only sufficient for the lowest droplet concentration, 26 cm−3. For the highest droplet concentration, 650 cm−3, even an order of magnitude smaller bin size is not sufficient. The scalings are not expected to be valid for the lowest droplet concentration and the high TKE case, and the two microphysics schemes represent similar departures. Finally, because the fluid flow is the same for all simulations featuring either low or high TKE, one can compare point-by-point simulation results. Such a comparison shows very close temperature and water vapor point-by-point values across the computational domain, and larger differences between simulated mean droplet radii and spectral width. The latter are explained by fundamental differences in the two simulation methodologies, numerical diffusion in the Eulerian bin approach and relatively small number of Lagrangian particles that are used in the particle-based microphysics.

On the droplet spectral broadening numerics

2020 ◽  
Author(s):  
Michael Olesik ◽  
Piotr Bartman ◽  
Sylwester Arabas ◽  
Gustavo Abade ◽  
Manuel Baumgartner ◽  
...  
Keyword(s):  
Ostwald Ripening ◽  
Spectral Width ◽  
Cloud Microphysics ◽  
Lagrangian Approach ◽  
Size Spectrum ◽  
Advective Transport ◽  
Spectrum Width ◽  
Modelling Studies ◽  
Bin Microphysics ◽  
Condensational Growth

<p>Owing to its key role in determining both the droplet collision probabilities and the radiative-transfer-relevant spectrum characteristics, the evolution of droplet spectral width has long been the focus of cloud modelling studies. Cloud simulations with detailed treatment of droplet microphysics face a twofold challenge in prognosing the droplet spectrum width. First, it is challenging to model and numerically represent the subtleties of condensational growth, even more so when considering the interplay between particle population dynamics and supersaturation fluctuations. Second, the discretisation strategies employed in representing the particle size spectrum and its evolution are characterised by inherent limitations. </p><p>In the poster, we will present results of both Eulerian and Lagrangian numerical representations of spectrum width evolution. In the case of Lagrangian approach, we will discuss the differences in numerical integration procedures between (a) the sophisticated solvers typically used in parcel-model frameworks with moving-sectional spectrum representation and (b) the simpler solvers typically used in mathematically-analogous particle-based (super-droplet) microphysics representations used in multi-dimensional models.</p><p>In the case of Eulerian (bin microphysics) approach, we will present condensational growth simulations performed with the MPDATA numerical scheme using the newly developed MPyDATA package (http://github.com/atmos-cloud-sim-uj/MPyDATA/). The MPDATA family of numerical schemes for solving advective transport problems has been in continuous development for almost four decades. MPDATA features a variety of options allowing to pick an algorithm variant appropriate to the problem at hand. We will focus on the importance the MPDATA algorithm variant choice and the grid setup for the resultant numerical diffusion.</p><p>In the case of Lagrangian approach, we will present simulations performed using the newly developed PySDM package (https://github.com/atmos-cloud-sim-uj/PySDM) that features a set of cloud microphysics algorithms including condensational growth solvers. In the discussion, we will focus on: (a) the numerical realisability of the Ostwald ripening process (i.e. the growth of larger particles at the expense of water content of the smaller ones) and (b) the numerical approaches available for integrating stochastic fluctuations of ambient thermodynamic properties that drive the water vapour saturation.</p>

scholarly journals Conditions for super-adiabatic droplet growth after entrainment mixing

2016 ◽  
Vol 16 (14) ◽  
pp. 9421-9433 ◽  
Author(s):  
Fan Yang ◽  
Raymond Shaw ◽  
Huiwen Xue
Keyword(s):  
Cloud Model ◽  
Cloud Droplet ◽  
Droplet Radius ◽  
Droplet Growth ◽  
Critical Height ◽  
Growth Region ◽  
Cloud Droplets ◽  
Environmental Air ◽  
Bin Microphysics ◽  
Entrainment Mixing

Abstract. Cloud droplet response to entrainment and mixing between a cloud and its environment is considered, accounting for subsequent droplet growth during adiabatic ascent following a mixing event. The vertical profile for liquid water mixing ratio after a mixing event is derived analytically, allowing the reduction to be predicted from the mixing fraction and from the temperature and humidity for both the cloud and environment. It is derived for the limit of homogeneous mixing. The expression leads to a critical height above the mixing level: at the critical height the cloud droplet radius is the same for both mixed and unmixed parcels, and the critical height is independent of the updraft velocity and mixing fraction. Cloud droplets in a mixed parcel are larger than in an unmixed parcel above the critical height, which we refer to as the “super-adiabatic” growth region. Analytical results are confirmed with a bin microphysics cloud model. Using the model, we explore the effects of updraft velocity, aerosol source in the environmental air, and polydisperse cloud droplets. Results show that the mixed parcel is more likely to reach the super-adiabatic growth region when the environmental air is humid and clean. It is also confirmed that the analytical predictions are matched by the volume-mean cloud droplet radius for polydisperse size distributions. The findings have implications for the origin of large cloud droplets that may contribute to onset of collision–coalescence in warm clouds.

scholarly journals Evaluation of a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

2021 ◽  
Author(s):  
Hengqi Wang ◽  
Yiran Peng ◽  
Knut von Salzen ◽  
Yan Yang ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Steady State ◽  
Cloud Droplet ◽  
Droplet Growth ◽  
Pollution Level ◽  
Growth Equation ◽  
Quasi Steady State ◽  
Mean Relative Error ◽  
State Approximation ◽  
Steady State Approximation ◽  
Aerosol Activation

Abstract. This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. We evaluate the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the Maximum Information Coefficient (MIC) between the mean relative error (MRE) and input variables for the individual campaigns and all cloud cases. MIC values are then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE . Based on the error analysis we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

Evaluation of a numerically efficient aerosol activation scheme by using worldwide cloud data from multiple field campaigns in continental and marine regions

2021 ◽  
Author(s):  
Hengqi Wang ◽  
Yiran Peng ◽  
Knut von Salzen ◽  
Yan Yang ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Dynamic Condition ◽  
Cloud Droplet ◽  
Cloud Base ◽  
Droplet Growth ◽  
Growth Equation ◽  
Maximum Information ◽  
Cloud Data ◽  
Wide Range ◽  
Aerosol Activation ◽  
Aerosol Properties

<p>This research summarizes a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in China, Canada, Brazil, and Chile. The scheme employs a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) to efficiently simulate aerosol activation and vertical profiles of supersaturation and cloud droplet number concentration (CDNC) near the cloud base. We evaluated the scheme by specifying observed environmental thermodynamic variables and aerosol properties from 36 cloud cases as input and comparing the simulated CDNC and other simulated variables with cloud microphysical observations. The relative error (RE) of the mean simulated CDNC ranges from 15.27 % for Chile to 23.97 % for China, with an average of 19.69 %, indicating that the scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Subsequently, we carried out an error analysis by calculating the Maximum Information Coefficient (MIC) values between RE and individual input variables and sorted them by aerosol properties, pollution degree, environmental humidity, and dynamic condition according to their importance. Based on this analysis we find that the magnitude of the RE is sensitive to the specification of aerosol chemical composition and updraft velocity in the simulation, which can partly explain differences between simulated and observed CDNC in some of the regions.</p>

Comparison of Eulerian Bin and Lagrangian Particle-Based Microphysics in Simulations of Nonprecipitating Cumulus

2020 ◽  
Vol 77 (11) ◽  
pp. 3951-3970
Author(s):  
Wojciech W. Grabowski
Keyword(s):  
Cloud Condensation Nuclei ◽  
Cloud Droplet ◽  
Spectral Width ◽  
Diffusional Growth ◽  
Spectral Evolution ◽  
Numerical Diffusion ◽  
Fourfold Increase ◽  
Bin Microphysics ◽  
The Impact ◽  
Lagrangian Scheme

AbstractA single nonprecipitating cumulus congestus setup is applied to compare droplet spectra grown by the diffusion of water vapor in Eulerian bin and particle-based Lagrangian microphysics schemes. Bin microphysics represent droplet spectral evolution applying the spectral density function. In the Lagrangian microphysics, computational particles referred to as superdroplets are followed in time and space with each superdroplet representing a multiplicity of natural cloud droplets. The same cloud condensation nuclei (CCN) activation and identical representation of the droplet diffusional growth allow the comparison. The piggybacking method is used with the two schemes operating in a single simulation, one scheme driving the dynamics and the other one piggybacking the simulated flow. Piggybacking allows point-by-point comparison of droplet spectra predicted by the two schemes. The results show the impact of inherent limitations of the two microphysics simulation methods, numerical diffusion in the Eulerian scheme and a limited number of superdroplets in the Lagrangian scheme. Numerical diffusion in the Eulerian scheme results in a more dilution of the cloud upper half and thus smaller cloud droplet mean radius. The Lagrangian scheme typically has larger spatial fluctuations of droplet spectral properties. A significantly larger mean spectral width in the bin microphysics across the entire cloud depth is the largest difference between the two schemes. A fourfold increase of the number of superdroplets per grid volume and a twofold increase of the spectral resolution and thus the number of bins have small impact on the results and provide only minor changes to the comparison between simulated cloud properties.

scholarly journals The Importance of the Shape of Cloud Droplet Size Distributions in Shallow Cumulus Clouds. Part I: Bin Microphysics Simulations

2017 ◽  
Vol 74 (1) ◽  
pp. 249-258 ◽  
Author(s):  
Adele L. Igel ◽  
Susan C. van den Heever
Keyword(s):  
Droplet Size ◽  
Cloud Droplet ◽  
Relative Width ◽  
Size Distributions ◽  
Cumulus Clouds ◽  
Microphysics Scheme ◽  
Droplet Concentration ◽  
Shallow Cumulus ◽  
Bin Microphysics ◽  
Droplet Size Distributions

Abstract In this two-part study, the relationships between the width of the cloud droplet size distribution and the microphysical processes and cloud characteristics of nonprecipitating shallow cumulus clouds are investigated using large-eddy simulations. In Part I, simulations are run with a bin microphysics scheme and the relative widths (standard deviation divided by mean diameter) of the simulated cloud droplet size distributions are calculated. They reveal that the value of the relative width is higher and less variable in the subsaturated regions of the cloud than in the supersaturated regions owing to both the evaporation process itself and enhanced mixing and entrainment of environmental air. Unlike in some previous studies, the relative width is not found to depend strongly on the initial aerosol concentration or mean droplet concentration. Nonetheless, local values of the relative width are found to positively correlate with local values of the droplet concentrations, particularly in the supersaturated regions of clouds. In general, the distributions become narrower as the local droplet concentration increases, which is consistent with the difference in relative width between the supersaturated and subsaturated cloud regions and with physically based expectations. Traditional parameterizations for the relative width (or shape parameter, a related quantity) of cloud droplet size distributions in bulk microphysics schemes are based on cloud mean values, but the bin simulation results shown here demonstrate that more appropriate parameterizations should be based on the relationship between the local values of the relative width and the cloud droplet concentration.

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