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This study attempts a new identification of mechanisms of secondary ice production (SIP) based on the observation of small faceted ice crystals (hexagonal plates or columns) with typical sizes smaller than 100 µm. Due to their young age, such small ice crystals can be used as tracers for identifying the conditions for SIP. Observations reported here were conducted in oceanic tropical mesoscale convective systems (MCSs) and midlatitude frontal clouds in the temperature range from 0 to −15 ∘C and heavily seeded by aged ice particles. It was found that in both MCSs and frontal clouds, SIP was observed right above the melting layer and extended to higher altitudes with colder temperatures. The roles of six possible mechanisms to generate the SIP particles are assessed using additional observations. In most observed SIP cases, small secondary ice particles spatially correlated with liquid-phase, vertical updrafts and aged rimed ice particles. However, in many cases, neither graupel nor liquid drops were observed in the SIP regions, and therefore, the conditions for an active Hallett–Mossop process were not met. In many cases, large concentrations of small pristine ice particles were observed right above the melting layer, starting at temperatures as warm as −0.5 ∘C. It is proposed that the initiation of SIP above the melting layer is stimulated by the recirculation of large liquid drops through the melting layer with convective turbulent updrafts. After re-entering a supercooled environment above the melting layer, they impact with aged ice, freeze, and shatter. The size of the splinters generated during SIP was estimated as 10 µm or less. A principal conclusion of this work is that only the freezing-drop-shattering mechanism could be clearly supported by the airborne in situ observations.

High Ice Water Content (HIWC) regions above tropical mesoscale convective systems are investigated using data from the second collaboration of the High Altitude Ice Crystals and High Ice Water Content projects (HAIC-HIWC) based in Cayenne, French Guiana in 2015. Observations from in-situ cloud probes on the French Falcon 20 determine the microphysical and thermodynamic properties of such regions. Data from a 2-D stereo probe and precipitation imaging probe show how statistical distributions of ice crystal mass median diameter (MMD), ice water content (IWC), and total number concentration (Nt) for particles with maximum dimension (Dmax) > 55 μm vary with environmental conditions, temperature (T), and convective properties such as vertical velocity (w), MCS age, distance away from convective peak (L), and surface characteristics. IWC is significantly correlated with w, whereas MMD decreases and Nt increases with decreasing T consistent with aggregation, sedimentation and vapor deposition processes at lower altitudes. MMD typically increases with IWC when IWC < 0.5 g m-3, but decreases with IWC when IWC > 0.5 g m-3 for -15 °C ≤ T ≤ -5 °C. Trends also depend on environmental conditions, such as presence of convective updrafts that are the ice crystal source, MMD being larger in older MCSs consistent with aggregation and less injection of small crystals into anvils, and IWCs decrease with increasing L at lower T. The relationship between IWC and MMD depends on environmental conditions, with correlations decreasing with decreasing T. The strength of correlation between IWC and Nt increases as T decreases.

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.

Regimes of liquid-ice coexistence that may form in an adiabatic parcel ascending at constant velocity at freezing temperatures are investigated. Four zones with different microphysical structures succeeding one another along the vertical direction have been established. On the basis of a novel balance equation, analytical expressions are derived to determine the conditions specific for each of these zones. In particular, the necessary and sufficient conditions for formation of liquid water phase within an ascending parcel containing only ice particles are determined. The results are compared to findings reported in earlier studies. The role of the Wegener-Bergeron-Findeisen mechanism in the phase transformation is analyzed. The dependence of the phase relaxation time on height in the four zones is investigated on the basis of a novel analytical expression. The results obtained in the study can be instrumental for analysis and interpretation of observed mixed-phase clouds.

The process of collective diffusional growth of droplets in an adiabatic parcel ascending or descending with the constant vertical velocity is analyzed in the frame of the regular condensation approach. Closed equations for the evolution of liquid water content, droplet radius, and supersaturation are derived from the mass balance equation centered with respect to the adiabatic water content. The analytical expression for the maximum supersaturation formed near the cloud base is obtained here. Similar analytical expressions for the height and liquid water mixing ratio corresponding to the level where occurs have also been obtained. It is shown that all three variables , , and are linearly related to each other and all are proportional to , where w is the vertical velocity and N is the droplet number concentration. Universal solutions for supersaturation and liquid water mixing ratio are found here, which incorporates the dependence on vertical velocity, droplet concentration, temperature, and pressure into one dimensionless parameter. The actual solutions for and can be obtained from the universal solutions with the help of appropriate scaling factors described in this study. The results obtained in the frame of this study provide a new look at the nature of supersaturation formation in liquid clouds. Despite the fact that the study does not include a detailed treatment of the activation process, it is shown that this work can be useful for the parameterization of cloud microphysical processes in cloud models, especially for the parameterization of cloud condensation nuclei (CCN) activation.

A new mechanism has been developed for size distribution broadening toward large droplet sizes. This mechanism may explain the rapid formation of large cloud droplets, which may subsequently trigger precipitation formation through the collision–coalescence process. The essence of the new mechanism consists of a sequence of mixing events between ascending and descending parcels. When adiabatically ascending and descending parcels having the same initial conditions at the cloud base arrive at the same level, they will have different droplet sizes and temperatures, as well as different supersaturations. Isobaric mixing between such parcels followed by further ascents and descents enables the enhanced growth of large droplets. The numerical simulation of this process suggests that the formation of large 30–40-μm droplets may occur within 20–30 min inside a shallow adiabatic stratiform layer. The dependencies of the rate of the droplet size distribution broadening on the intensity of the vertical fluctuations, their spatial amplitude, rate of mixing, droplet concentration, and other parameters are considered here. The effectiveness of this mechanism in different types of clouds is discussed.

This paper presents a theoretical framework describing the thermodynamics and phase transformations of a three phase component system consisting of ice particles, liquid droplets and water vapour. The instant rates of change of water (qw), ice (qi) and vapour (qv) mixing ratios are described based on the quasi-steady approximation. The local thermodynamic conditions required for the equilibrium of liquid (qw = 0), ice (qi = 0) and vapour (qv = 0) phases are analysed. It is shown that there are four different regimes of the partitioning of water between liquid, ice, and gaseous phases in mixed clouds. The Wegener–Bergeron–Findeisen (WBF) process is identified as being relevant to two of those regimes. The efficiency of the WBF process in characterizing the capability of ice crystals to deplete the water evaporated from liquid droplets is introduced here. It is shown that the WBF process has maximum efficiency at approximately zero vertical velocity. The analysis of the dependences of qw, qi and qv on the vertical velocity, temperature, pressure and the integral radii of the cloud particles is presented. It is shown that the maximum rates of ice growth and droplet evaporation do not necessarily occur at T = − 12 °C where the maximum difference between saturation vapour pressure over ice and that over liquid is observed. Copyright © 2008 Crown in the right of Canada. Published by John Wiley & Sons, Ltd

Phase transformation and precipitation formation in mixed-phase clouds are usually associated with the Wegener–Bergeron–Findeisen (WBF) process in which ice crystals grow at the expense of liquid droplets. The evolution of mixed-phase clouds, however, is closely related to local thermodynamical conditions, and the WBF process is just one of three possible scenarios. The other two scenarios involve simultaneous growth or evaporation of liquid droplets and ice particles. Particle evolution in the other two scenarios differs significantly from that associated with the WBF process. Thus, during simultaneous growth, liquid droplets compete for the water vapor with the ice particle, which slows down the depositional growth of ice particles instead of promoting their growth at the expense of the liquid as in the WBF process. It is shown that the WBF process is expected to occur under a limited range of conditions and that ice particles and liquid droplets in mixed-phase clouds are not always processed in accordance with the WBF mechanism.

The data on cloud particle sizes and concentrations collected with the help of aircraft imaging probes [optical array probes OAP-2DC, OAP-2DP, and the High Volume Precipitation Spectrometer (HVPS)] are widely used for cloud parameterization and validation of remote sensing. The goal of the present work is to study the effect of shattering of ice particles during sampling. The shattering of ice particles may occur due to 1) mechanical impact with the probe arms prior to their entering the sample volume, and 2) fragmentation due to interaction with turbulence and wind shear generated by the probe housing. The effect of shattering is characterized by the shattering efficiency that is equal to the ratio of counts of disintegrated particles, to all counts. The shattering efficiency depends on the habit, size, and density of ice particles, probe inlet design, and airspeed. For the case of aggregates, the shattering efficiency may reach 10% or even more. The shattering of ice particles results in an overcounting of small particles and an undercounting of large ones. The number of fragments in the images of shattered particles may reach several hundreds. It was found that particles as small as 600 μm may shatter after impact with the probe arms. The effect of particle shattering should be taken into account during data analysis and carefully considered in future designs of airborne cloud particle size spectrometers.

The water vapor deposition growth of frozen drops with diameter greater than 100 mm has been studied in a thermal diffusion chamber. For varying periods of time, it was found that frozen drops experience spherical growth. The characteristic time of spherical growth depends on supersaturation, temperature, and drop size, and it varies from minutes to tens of minutes. The average rate of frozen drop growth agrees well with that predicted by the Maxwellian growth equation for ice spheres. Observations in natural clouds conducted with a cloud particle imager probe has yielded evidence that frozen drops may retain spheroidal shapes for at least 15‐20 min under conditions close to saturation over water. These observations are in agreement with the laboratory experiments. The observation of frozen drops in natural clouds may be correlated to freezing drizzle generated by overlying cloud layers that may lead to hazardous in-flight icing.

A theoretical framework is developed to estimate the supersaturation in liquid, ice, and mixed-phase clouds. An equation describing supersaturation in mixed-phase clouds in general form is considered here. The solution for this equation is obtained for the case of quasi-steady approximation, that is, when particle sizes stay constant. It is shown that the supersaturation asymptotically approaches the quasi-steady supersaturation over time. This creates a basis for the estimation of the supersaturation in clouds from the quasi-steady supersaturation calculations. The quasi-steady supersaturation is a function of the vertical velocity and size distributions of liquid and ice particles, which can be obtained from in situ measurements. It is shown that, in mixed-phase clouds, the evaporating droplets maintain the water vapor pressure close to saturation over water, which enables the analytical estimation of the time of glaciation of mixed-phase clouds. The limitations of the quasi-steady approximation in clouds with different phase composition are considered here. The role of phase relaxation time, as well as the effect of the characteristic time and spatial scales of turbulent fluctuations, are also discussed.

SUMMARY A detailed study of mixed-phase clouds associated with frontal systems obtained from a large dataset collected by the Convair 580 aircraft of the National Research Council (NRC) of Canada is presented. The total length of analysed in-cloud legs having total-water content (TWC) > 0.01g m i3 was about 44 £ 10 3 km. The ice‐water fraction (π3 D ice-water content/TWC) had a minimum in the range 0:1 0:9). The concentration of particles in glaciated clouds was found to be nearly constant at 2‐5 cm i3 for temperatures i35 ± C < T < 0 ± C. The concentration of droplets in liquid clouds decreased with decreasing temperature. The mean volume diameter of particles in ice clouds varied between 20 πm and 35 πm, and in liquid clouds between 10 πm and 12 πm. Both ice- and liquid-water content decreased with decreasing temperature. The results of this study may be used for validation of remote-sensing retrievals, and for weather- and climate-models.

Evolution of droplet size distribution (DSD) due to the water vapor diffusion in a vertically moving adiabatic parcels is investigated. Analytical expressions for height dependences of the main DSD parameters and DSD moments are obtained. The asymptotic behavior of the DSD parameters at large heights above cloud base is determined. It is shown that during diffusion growth, the width and the relative dispersion of the DSD decrease with height as z− 1/3 and z− 2/3, respectively. The paper presents examples of DSD evolution in cases DSD forms on aerosols with a three-mode lognormal distribution. The aerosol distribution parameters used in the study correspond to four aerosol types: “Marine,” “Clean continental,” “Background,” and extremely polluted “Urban.” The vertical profiles of DSD parameters are compared with the asymptotic profiles. It is shown that in case of polydisperse DSD evolution, the vertical profile of supersaturation within several hundred meters above the cloud base can be approximated by a supersaturation profile corresponding to the “equivalent” monodisperse DSD. The initial radius of this equivalent DSD is equal to the mean radius of polydisperse DSD (haze size distribution) at cloud base, which is estimated using the Kohler theory. This result of the relation between the polydisperse and monodisperse solutions is universal. A new equation for estimation of supersaturation maximum for polydisperse case is obtained. The obtained analytical expressions and numerical results are useful for understanding the mechanisms of DSD formation in clouds and for parameterization of warm microphysical processes in cloud models.

In situ microphysics measurements made during the First and Third Canadian Freezing Drizzle Experiments (CFDE I and III, respectively) have been used to assess the relative responses to ice and liquid hydrometeors for several common instruments. These included the Rosemount icing detector, 2D-C monoscale and 2D-C grayscale probes, forward-scattering spectrometer probes (FSSP) on three measurement ranges, Nevzorov liquid water content (LWC) and total water content probes, and King LWC probes. The Nevzorov LWC and King LWC probes responded to between 5% and 30% of the ice water content, with an average response of approximately 20%. The average FSSP measurements of droplet spectra were dominated by ice particles for sizes greater than 35 μm, independent of the measurement range used, when the ice-crystal concentrations exceeded approximately 1 L−1. In contrast, the FSSP measurements of the droplet spectra less than 30 μm appeared free of ice-crystal contamination, independent of the ice-crystal con...

Laboratory measurements of the response of the Particle Measuring Systems, Inc., 2DC probe have been conducted to characterize counting and sizing errors of the probe for spherical particles. Measurements of the shadow threshold intensity of a Meteorological Service of Canada (MSC) 2DC probe varied from approximately 30% to 51%, depending on the photodiode, and averaged 46% for the central 16 photodiodes. Depth-of-field and sizing measurements are quite sensitive to this threshold, which is nominally considered as 50% for the 2DC probe. Response times also varied significantly, from 0.44 to 0.90 ms. Measurements of the depth of field for known particle sizes at low velocity agreed well with published calculations at zero velocity. For particles smaller than 100 mm, the depth of field decreased significantly with increasing airspeed due to the nonzero response time of the sensing photodiodes. The average particle size also decreased with increasing airspeed but did so in such a manner as to counteract oversizing due to out-of-focus images. At 100 m s 21, the average measured sizing error of a 100-mm particle was close to negligible, rising to approximately 5% at 500 mm. The application of measured depth-of-field values and sizing calibrations at specific sizes to improve 2DC size distribution accuracy is nontrivial because measurement errors cause particles to be redistributed to other sizes in a complicated manner. However, when hypothetical true particle distributions were redistributed according to a distortion matrix approximated by the results of this study, the average error of uncorrected size distributions measured by the MSC 2DC probe, expressed as a sizing error, was found to be 610% for particles larger than 125 mm. Although these results are not strictly transferable to other 2DC probes, the methods described can be used to derive similar results for other probes.

The Rosemount Icing Detector (RICE) has been used extensively over the last three decades for aircraft measurements of the rate of ice riming in supercooled liquid and mixed clouds. Because of difficulties related to calibration and postprocessing, the RICE probe was mainly used as an indicator of the presence of supercooled liquid water. The accuracy of the RICE probe for measurements of supercooled liquid water content is studied here. The theory of ice accretion on an unheated cylinder is applied to the RICE probe. A steady-state heat balance on the surface of a riming cylinder is considered in detail. It is shown that the threshold sensitivity of the RICE probe is limited by the rate of sublimation of ice and it may exceed 0.01 g m−3 at airspeed 200 m s−1. The rate of ice sublimation limits the use of the RICE probe for measurements of low liquid water contents in clouds. The maximum possible measured liquid water content is restricted by the Ludlam limit. A new calibration technique of the R...

A new conceptual model is proposed for enhanced cloud droplet growth during condensation. Rapid droplet growth may occur in zones of high supersaturation resulting from isobaric mixing of saturated volumes with different temperatures. Cloud volumes having a temperature different from the general cloud environment may form due to turbulent vertical motions in a temperature lapse rate that is not pseudoadiabatic. This mechanism is most effective in the vicinity of cloud-top inversions. It is also shown that the isobaric mixing of saturated and dry volumes with different temperatures may also lead to high supersaturations. The high supersaturations are associated with zones of molecular mixing, and they have a characteristic size of the order of millimeters with a characteristic lifetime near tenths of a second. Some small proportion of cloud droplets, over many supersaturation events, may grow large enough to grow effectively through collision–coalescence. This hypothesis of isobaric mixing may hel...

The effective diameter of cloud droplets is usually derived from measurements of droplet size distribution measured by Particle Measuring Systems (PMS) probes. The disadvantage of this method is that PMS probes have a truncated size range. During the RACE project, an alternative method to measure the effective diameter used a cloud extinction meter and King and Nevzorov hot wire liquid water content and total water content (LWC/TWC) probes installed on the National Research Council (NRC) Twin Otter. The effective diameter was derived from direct in situ measurements of the extinction coefficient (e) and liquid water content (W) as Deff=k1W/e. This method of calculation of Deff is free of problems related to deriving Deff from the truncated particle size distribution. Since measurements of e and W cover the whole size range of cloud particles, this method gives an accurate value of Deff. This method can also be successfully applied for mixed and ice phase clouds, since the Nevzorov TWC probe provides measurements of total (ice plus liquid) water content. Effective number concentration was calculated as Neff = k2ϵ3/W2. Comparisons of Deff and Neff, calculated by this method, and directly from PMS Forward Scattering Spectrometer Probe (FSSP) spectra, are favorable in the subset of conditions when the FSSP is considered to measure the spectra fully and accurately.

This paper considers the theory of diffraction image formation of spherical particles and peculiarities of particle sizing by discrete imaging probes. The diffraction images of spherical water droplets are approximated by Fresnel diffraction by an opaque disc. The approach developed in the paper is applicable to all types of array and matrix imaging probes. The analysis measurement accuracy is performed for the PMS Optical Array Prove (OAP)-2D-C and OAP-2Dgray probes. It is shown that a 25-mm resolution PMS OAP-2D-C probe can both oversize and undersize droplets smaller than approximately 100 mm in diameter, and oversize droplets larger than approximately 100 mm. The errors in droplet sizing increase with decreasing size. The discrete manner of particle image registration also leads to losses of particles with sizes smaller than 100 mm. For the ideal case with zero photodiode response time, these losses reach 70% for 25-mm droplets. A nonzero response time will increase these losses. These findings help explain discrepancies observed in the overlap region of the PMS FSSP and OAP droplet spectra. A variety of calculated digital images for PMS OAP-2D-C and OAP-2Dgray probes is presented. Different methods of particle image sizing are discussed. Several methods of size correction of individual droplets and droplet ensembles are suggested. Correction algorithms for these effects are derived, and distortion and correction retrieval matrices are calculated. Several examples of actual and measured size distributions are presented.

Airborne measurements from a new digital holographic camera are compared with PMS 2D-C measurements during the Canadian Freezing Drizzle Experiment. The digital holographic camera is not affected by drop sizing errors associated with out of focus particles in the same way as the 2D-C probe. Recent theoretical simulations of 2D-C particle sizing errors and approaches for statistically correcting the measurements are discussed. The theoretical simulations predict that in freezing drizzle with drop diameters from about 50–200 μm, uncorrected PMS 2D-C measurements can produce an artificial tail in the drop size distribution that extends out to about 325 μm. The digital holographic camera does not see the artificial tail. 2D-C measurements of drop size distribution in freezing drizzle that have been statistically corrected show an improved agreement with the digital holographic measurements. Some digital images of drizzle drops and ice crystals from a recently improved version of the instrument, called a cloud particle imager (CPI), are also shown.

The Particle Measuring System’s optical array probes have a sample volume that depends upon the diameter of the particle measured. The sample volume also depends upon the velocity of particles that pass through the probe because of the electronic response time of these instruments. This note discusses an algorithm that has been derived to calculate sample volume as a function of size and velocity, and demonstrates the need for such an algorithm by comparison of measurements from several types of optical array probes and a forward-scattering spectrometer probe. These comparisons show that the optical array probes greatly underestimate droplet concentrations of particles less than 100 μm in diameter at typical aircraft research speeds unless sample volumes are adjusted for electronic response time limitations.

Presented here are the results of studying droplet size distributions in stratiform clouds (St, Sc, As, Ac, Ns) over the USSR obtained with a FSSP-100 (PMS). The bimodal droplet spectra turned out to be common phenomena in stratiform clouds, and on average, they occupy about 14% of cloud space. Their occurrence practically does not depend on droplet concentration, cloud temperature, height or presence of ice crystals. Classifications of bimodal spectra shapes and their spatial evolution are suggested. Statistical distributions of difference of modal diameters, mode ratio and lengths of cloud volumes with bimodal spectra are presented. The obtained experimental results made it possible to formulate some hypotheses of mechanisms of bimodal spectra formation. The first mechanism is mixing of unimodal spectra with different modal diameters. The formation of droplet spectra with different modal diameters at the same cloud level may be caused by vertical (upward or downward) motions of individual volumes within non-adiabatic cloud layer. Another mechanism is induced by activation of the interstitial condensation nuclei. Analytical numerical modelling of droplet spectra evolution confirm the suggested assumptions. The formation of bimodal droplet spectra in stratiform clouds is closely connected with turbulence.

A droplet generator was used to calibrate and study some features of the forward-scattering spectrometer probe (FSSP). The generator produces a stable jet of monodisperse droplets with the rate of 50–500 droplets per second and a velocity between 0.4 and 1.3 m s−1. The estimated standard deviation of the diameter of the droplets is not larger than 1%. Because of the low rate of generated droplets, there were no coincidence problems during the measurements, that is, no multiple droplets in the laser beam. The results of FSSP calibration in its operating ranges 0 and 1 are presented in this paper. The experiments revealed minor differences (