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A. Khain
and
A. Pokrovsky

Abstract

Effects of different size distributions of cloud condensational nuclei (CCN) on the evolution of deep convective clouds under dry unstable continental thermodynamic conditions are investigated using the spectral microphysics Hebrew University Cloud Model (HUCM). In particular, high supercooled water content just below the level of homogeneous freezing, as well as an extremely high concentration of ice crystals above the level, observed recently by Rosenfeld and Woodley at the tops of growing clouds in Texas, were successfully reproduced.

Numerical experiments indicate a significant decrease in accumulated precipitation in smoky air. The fraction of warm rain in the total precipitation amount increases with a decrease in the CCN concentration. The fraction is low in smoky continental air and is dominating in clean maritime air. As warm rain is a smaller fraction of total precipitation, the decrease in the accumulated rain amount in smoky air results mainly from the reduction of melted precipitation.

It is shown that aerosols significantly influence cloud dynamics leading to the elevation of the level of precipitating particle formation. The falling down of these particles through dry air leads to a loss in precipitation. Thus, close coupling of microphysical and dynamical aerosol effects leads to the rain suppression from clouds arising in dry smoky air.

The roles of freezing, CCN penetration through lateral cloud boundaries, and turbulent effects on cloud particles collisions are evaluated.

Results, obtained using spectral microphysics, were compared with those obtained using two well-known schemes of bulk parameterization. The results indicate that the bulk parameterization schemes do not reproduce well the observed cloud microstructure.

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M. Pinsky
and
A. Khain

Abstract

A new feature of cloud structure has been discovered while analyzing the measurements obtained in situ in 57 clouds by the Fast Forward-Scattering Spectrometer Probe (FSSP). By means of a novel technique of statistical analysis, it is shown that droplets form distinct “communities” of about 1-cm scale that differ in concentration, thus creating a highly inhomogeneous cloud microstructure (inch clouds). Those droplet clusters can be found all over the cloud volume and appear to be induced by droplet inertia within a turbulent flow. An increase in turbulence intensity and droplet inertia results in an increase of concentration fluctuations. The authors believe that this finding is the first direct evidence of turbulence–inertia impact on droplet motion in clouds that leads to formation of microstructure conductive to precipitation formation.

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M. Pinsky
and
A. Khain

Abstract

A minimalistic analytical model allowing analysis of the dissolving stage of nonprecipitating convective clouds is proposed. The model takes into account two mechanisms: turbulent mixing with a dry environment and cloud volume settling. The temporal changes in the spatial structure of a cloud and in its immediate environment in the course of cloud dissolving are analyzed. The comparison of the effects of a temperature increase in the course of cloud descent and mixing with dry surrounding air shows that the descent is a dominating factor determining a decrease in the liquid water content (LWC), while mixing has a stronger effect on the cloud shape. Narrowing/broadening of clouds due to lateral mixing with dry air during cloud dissolving is determined by the potential evaporation parameter proportional to the ratio of the saturation deficit in the cloud environment to LWC. An equation for cloud dissolving time is obtained. After a cloud totally dissolves, it leaves behind an area with humidity exceeding that of the environment. The main parameter determining the dissolving time is the downdraft velocity. It should exceed 50 cm s−1 in order to provide reasonable dissolving time. The turbulent intensity, LWC, and humidity of the environment air also have an impact on dissolving time: the lower the LWC and the humidity of environment air, the faster cloud dissolving is. The simple solution presented in this paper can be useful for evaluation of cloud characteristics at the dissolving stage and can be included in procedures of parameterization of cloud cover formed by nonprecipitating or slightly precipitating cumulus clouds (Cu). Values of the environment humidity and temperature, LWC at cloud top, cloud width, vertical velocity of downdraft, and the turbulent coefficient should be parameters of this parameterization.

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M. Pinsky
and
A. Khain

Abstract

Evolution of nonprecipitating cumulus clouds (Cu) at the developing stage under the influence of lateral entrainment and mixing is studied analytically using a minimalistic analytical model. We present a model of an ascending cloud volume (a model of developing Cu) whose structure is determined by the processes of droplet diffusion growth/evaporation and entrainment mixing in the horizontal direction. Spatial and time changes of liquid water content, the adiabatic fraction, droplet concentration, and the mean volume droplet radius are calculated. It is shown that the existence of a nondiluted core in a growing cumulus cloud significantly depends on the cloud width and vertical velocity. While at the updraft velocity of 2 m s−1 the core of a 400-m-wide cloud becomes diluted at distances of a few hundred meters above cloud base, the core of a cloud of 1000-m width remains nondiluted at distances up to 1500 m above cloud base. The explanation of this result is simple: the increase in cloud width and the decrease in the updraft velocity increase the time during which the cloud is diluted due to mixing. Since lateral mixing synchronously decreases both the cloud water content and droplet concentration, the variation of the mean volume droplet radius is low inside the cloud. The approximate quantitative condition for cloud formation in updraft is derived. It is shown that a cloud can arise when its vertical velocity exceeds a critical value. To produce clouds, narrow turbulent plumes should ascend at higher velocity as compared to wider plumes. High humidity of the environment air is favorable for formation of clouds from plumes. The comparison of the obtained results with previously published observational data indicates a reasonable agreement. The results can be useful for parameterization purposes.

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M. Pinsky
,
A. Khain
, and
A. Korolev

Abstract

Glaciation in mixed-phase adiabatic cloudy parcels is investigated analytically using two new equations: the equation for coexistence of liquid water and ice and the mass balance equation. The analysis of glaciation time is performed for a vertically moving adiabatic mixed-phase cloud parcel. The effects of vertical velocity, liquid water content, and concentrations of ice particles, liquid droplets, temperature, and other parameters on the glaciation process are discussed. It is shown analytically that, for a certain envelope of vertical velocities, the glaciation time depends only on the vertical displacement of the parcel and does not depend on the trajectory along which the cloud parcel travels toward the glaciation point. Analytical dependencies of the glaciation time and of the altitude of glaciation on vertical velocity are presented. The results demonstrate a good agreement with those obtained using the corresponding parcel model. The limitations of the newly proposed approach are discussed as well, and it is shown that implementation of a simple correction factor allows one to calculate the glaciation time within a wide range of temperatures, from 0° down to −30°C.

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M. Pinsky
,
A. Khain
, and
A. Korolev

Abstract

The process of ice–liquid water interaction in the unsaturated environment is explored both analytically and with the help of a numerical simulation. Ice–liquid water interaction via the condensation–evaporation mechanism is considered in relation to the problem of homogeneous mixing in an unmovable air volume. The process is separated into three stages: the homogenization stage, during which the rapid alignment of thermodynamic and microphysical parameters in the mixing volume takes place; the glaciation stage, during which the liquid droplets evaporate; and the ice stage, which leads to attaining a thermodynamic equilibrium. Depending on the initial temperature, humidity, and mixing ratios of liquid water and of ice water, the third stage may result in two outcomes: existence of ice particles under zero supersaturation with respect to ice or a complete disappearance of ice particles.

Three characteristic times are associated with the microphysical stages: the phase relaxation time associated with droplets, the glaciation time determined by the Wegener–Bergeron–Findeisen process, and the phase relaxation time associated with ice. Since the duration of the second and third microphysical stages may be of the same order as the homogenization time or even longer, the homogeneous mixing scenario is more probable in mixed-phase clouds than in liquid clouds.

It is shown that mixing of a mixed-phase cloud with a dry environment accelerates cloud glaciation, leading to a decrease in the glaciation time by more than 2 times. The conditions of fast ice particles’ disappearance due to sublimation are analyzed as well.

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A. Ryzhkov
,
M. Pinsky
,
A. Pokrovsky
, and
A. Khain

Abstract

The radar observation operator for computation of polarimetric radar variables from the output of numerical cloud models is described in its most generic form. This operator is combined with the Hebrew University of Jerusalem cloud model with spectral microphysics. The model contains 7 classes of hydrometeors and each class is represented by size distribution functions in 43 size bins. The performance of the cloud model and radar observation operator has been evaluated for the case of a hailstorm in Oklahoma on 2 February 2009. It is shown that the retrieved fields of polarimetric radar variables at C and S microwave bands are generally consistent with results of observations. The relationship between microphysical and polarimetric signatures is illustrated.

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M. Pinsky
and
A. P. Khain

Abstract

A statistical analysis of a series of droplet arrival times measured by the Fast Forward-Scattering Spectrometer Probe (FSSP) during aircraft flights in cumulus clouds was conducted. The main purpose of the analysis was to determine whether droplet concentration fluctuates at small scales on the order of a few centimeters or whether these fluctuations are negligible as compared with the mean concentration.

In the analysis, the series of droplet arrival times is regarded as a generalized Poisson random process with time-dependent (or space dependent) parameters. The method developed is based on the representation of droplet concentration in a cloud along the aircraft track as the sum of three components: average droplet concentration in a cloud, large-scale fluctuations of droplet concentrations described by the Fourier series, and a small-scale noncoherent fraction of concentration fluctuation characterized by the energy spectrum and the correlation function. The efficiency of the method to estimate the amplitude and spatial characteristics of small-scale droplet concentration fluctuations and to calculate the profile of large-scale components of droplet concentration along the aircraft track was carefully tested using model-simulated series of droplet arrival times.

The method was used to analyze a measurement sample in a cumulus cloud on a 350-m segment. The properties of droplet concentration were calculated both over the whole cloud traverse and within the adiabatic core.

The results of the calculations show the existence of pronounced small-scale droplet concentration fluctuations in the case study. The rms of small-scale droplet concentration fluctuations was estimated to be about 31% of the mean values of droplet concentration both over the whole cloud and in a more homogeneous adiabatic core. The power spectrum shows that fluctuations with spatial scales within the 0.5–5-cm range contain over 80% of the energy of small-scale fluctuations.

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A. P. Khain
and
M. B. Pinsky

Abstract

The results of simulated drop fall in horizontal flows with the vertical shear of different kinds (constant linear, periodic, and with random velocity distribution) are presented. It is shown that the inertia of drops is significant enough to lead to substantial drop velocity deviations from the velocity of the flow and to the generation of relative velocity between drops of different sizes. For small droplet the velocity difference caused by turbulence is of the same order as the difference in terminal fall velocities. The results of calculations of drop fall through the horizontal flow with the random Kolmogorov spectrum distribution of velocity indicate that a comparable impact of turbulence in this flow is significant for the whole spectrum of drop sizes and that it even increases for small droplets. The increase of the relative velocity between interacting drops is interpreted as an increase in the swept volume and an increase of a number of drop collisions per unit of times. Thus, in the commonly used expression for the collision kernel, the difference between terminal velocities was replaced by the mean square root relative velocity difference. Simulation of drop spectrum evolution using the stochastic coalescence equation indicates that cloud turbulence significantly influences warm rain initiation and development even when the collision efficiencies obtained in still air are used. The results also show that the difference in the horizontal components of drop velocities in a turbulent cloud can contribute significantly to the rain formation process. Hence, we have to keep in mind the “horizontal” coalescence in convective clouds along with the commonly considered “vertical” coalescence.

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M. Pinsky
,
A. Khain
, and
M. Shapiro

Abstract

A mathematical approach to the calculation of the collision efficiency between droplets within a turbulent flow is suggested. The problem of drops’ hydrodynamic interaction is reconsidered taking into account additional inertia-induced relative velocities between droplets of different sizes moving within a turbulent flow. The relative velocities are determined at different points of a turbulent flow using a model of homogeneous and isotropic turbulent flow.

The collision efficiencies of Stokesian droplets are calculated using the superposition method. Two important results have been obtained: 1) the droplet collision efficiencies in a turbulent flow are usually greater than those in calm atmosphere and 2) in a turbulent flow the collision efficiency between droplets is a random value with significant dispersion. The maximum values of the collision efficiency can be several times as much as the mean values.

Variation of the collision efficiency in a turbulent flow is attributed to the variations of drop–drop relative velocities and the angles of drop approach. The velocities stem from the differential response of droplets of different inertia to flow velocity shears and flow accelerations. Specific features of drop approach geometry in a turbulent flow can also contribute to the increase of the collision efficiency.

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