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Ice particles play an important role in precipitation formation and radiation balance. Therefore, an accurate description of ice initiation in the atmosphere is of great importance for weather prediction models and climate simulations. Despite the abundance of ice crystals in the atmosphere, the mechanisms for their formation remain not well understood. There are two major sets of mechanisms of ice initiation in the atmosphere: primary nucleation and secondary ice production. Secondary ice production occurs in the presence of preexisting ice, which results in an enhancement of the concentration of ice particles. Until recently, secondary ice production was mainly attributed to the rime-splintering mechanism, known as the Hallett–Mossop process, which is active in a relatively narrow temperature range from −3 to −8 ∘C. The existence of the Hallett–Mossop process was well supported by in situ observations. The present study provides an explicit in situ observation of secondary ice production at temperatures as low as −27 ∘C, which is well outside the range of the Hallett–Mossop process. This observation expands our knowledge of the temperature range of initiation of secondary ice in clouds. The obtained results are intended to stimulate laboratory and theoretical studies to develop physically based parameterizations for weather prediction and climate models.

Aircraft flying through areas of high ice water content (HIWC) can experience engine damage and/or failure. HIWC is typically associated with convection and the microphysical properties of tropical oceanic and coastal convection are well documented as a result of several field campaigns in the past decade. HIWC appears to be less common in extratropical convection, but instances of HIWC-related aircraft issues have been recorded in extratropical weather, even during winter. The present study documents the microphysical properties of HIWC between −25° and 0°C and the meteorological and thermodynamic conditions around that HIWC from five flights from the In-Cloud Icing and Large-Drop Experiment (ICICLE) in the midwestern United States in February 2019. All five cases contained elevated convection above a strong low-level temperature inversion. Values for top-of-inversion mixing ratios and total column precipitable water were about 5 g kg−1 and 20 mm, respectively, according to soundings near each case. A maximum ice water content of 2.1 g m−3 was observed over a length scale of about 500 m, and ice particle size distributions had mean volume equivalent diameters around 1000 μm. Supercooled drizzle droplets were also observed in the vicinity of the HIWC, raising questions about the possible role of secondary ice production via the freezing and shattering of supercooled large droplets in HIWC formation. The generalizability of these results is limited by the small number of cases, but they provide some of the first in situ observations of extratropical winter HIWC and highlight the need for continued research on these conditions. Significance Statement High ice water content (HIWC) conditions can cause engine damage, stall, and failure in aircraft and can cause air data probes to report erroneous values. Most research on HIWC has focused on tropical convection. This paper serves to draw more attention to the aviation hazard posed by extratropical winter HIWC and the need for additional research into these environments. The cases examined also contained supercooled precipitation-sized liquid droplets. Combined with other recent research, these observations may help to motivate laboratory experiments investigating the role of secondary ice production via droplet freezing and shattering in the formation of HIWC.

High ice water content (HIWC) regions with small ice crystals, where ice water contents (IWCs) are greater than 1.5 g m-3 and median mass diameters (MMDs) less than about 300 micrometers, occur above tropical mesoscale convective systems (MCSs) and can have detrimental impacts on aircraft engines. Data collected by the French Falcon aircraft and the National Research Council of Canada Convair-580 during the 2014 and 2015 High Altitude Ice Crystals and High Ice Water Content (HAIC/HIWC) projects are revisited here along with coordinated modeling studies to investigate processes that can produce such HIWCs. In particular, data collected from 2014 in the vicinity of Darwin Australia and from 2015 in the vicinity of Cayenne French Guyana are used to determine how bulk microphysical properties (e.g., number concentration, IWC, median volume diameter) and characteristics of ice crystal size distributions (i.e., multimodal nature, parameters fit to gamma distributions for each mode) vary with environmental conditions such as temperature, vertical velocity, MCS age, distance from MCS core, and surface characteristics. It is determined that temperature and vertical velocity are the biggest controls of small ice crystals, but younger cells, stronger convective strengths and closer proximity to convective cores also increase the relative importance of small crystals.Numerical simulations conducted using the Weather Research and Forecasting model with four different bulk microphysics schemes generally reproduce the observed temperature, dew-point, and wind structure. However, comparison of regime-specific observations against properties simulated over Cayenne using a variety of existing parameterization schemes show that although the coverage and evolution of convection is well predicted, simulations overestimate the intensity and spatial extent of observed airborne X-band radar reflectivity and do not well depict the peak of observed size distributions with maximum dimensions between 0.1 and 1 mm. To explore formation mechanisms for large numbers of small ice crystals, a series of simulations varying the representation of secondary ice production (SIP) processes were conducted. Simulations including one of three SIP mechanisms separately (i.e., the Hallett–Mossop mechanism, fragmentation during ice–ice collisions, and shattering of freezing droplets) did not replicate the observed ratio of number concentration divided by IWC. However, the simulation including all three SIP processes produced HIWC regions consistent with observations in terms of number concentration and radar reflectivity, which was not replicated using the original P3 two-ice category configuration that only included the Hallett-Mossop mechanism. In summary, observations and simulations show primary ice production plays a key role in generating HIWC regions at temperatures < -40 Celsius, shattering of freezing droplets dominates ice particle production in HIWC regions between -15 and 0 Celsius during the early stage of convection, and fragmentation during ice–ice collisions dominates between -15 and 0 Celsius during the later stage of convection and between -40 and -20 Celsius over the whole convection period. This study thus shows the dominant role of SIP processes in the formation of numerous small crystals in HIWC regions. Implications for future measurement and modeling needs are discussed.

The prediction of supercooled large drops (SLD) from the Thompson-Eidhammer (TE) microphysics scheme—run as part of the High-Resolution Rapid Refresh (HRRR) model— is evaluated with observations from the In-Cloud Icing and Large drop Experiment (ICICLE) field campaign. These observations are also used to train a random forest machine-learning (ML) model, which is then used to predict SLD from several variables derived fromHRRRmodel output. Results provide insight on the limitations and benefits of each model. Generally, the ML model results in an increase in the probability of detection (POD) and false alarm rate (FAR) of SLD compared to prediction from TE microphysics. Additionally, the POD of SLD increases with increasing forecast lead time for both models, likely since clouds and precipitation have more time to develop as forecast length increases. Since SLD take time to develop in TE microphysics and may be poorly represented in short-term (< 3 h) forecasts, the ML model can provide improved short-term guidance on supercooled large-drop icing conditions. Results also show that TE microphysics predicts a frequency of SLD in cold (< −10°C) or high ice water content (IWC) environments that is too low compared to observations, whereas the ML model better captures the relative frequency of SLD in these environments.

The process of glaciation in mixed-phase stratiform clouds was investigated by a novel Lagrangian–Eulerian model (LEM) in which thousands of adjoining Lagrangian parcels moved within a turbulent-like velocity field with statistical parameters typical of the Arctic boundary layer. We used detailed bin microphysics to describe the condensation/evaporation processes in each parcel, in which droplets, aerosols, and ice particles were described using size distributions of 500 mass bins. The model also calculated aerosol mass inside droplets and ice particles. Gravitational sedimentation of droplets and ice particles was also accounted for. Assuming that droplet freezing is the primary source of ice particles, the Arctic clouds observed in Indirect and Semi-Direct Aerosol Campaign (ISDAC) were successfully simulated. The model showed that at a low ice particle concentration typical of ISDAC, large vortices (eddies) led to a quasi-stationary regime, in which mixed-phase St existed for a long time. The large eddies controlled the water partitioning in the mixed-phase clouds. Droplets formed and grew in updrafts, typically reaching the cloud top, and evaporated in downdrafts. Ice particles grew in updrafts and downdrafts. The Wegener–Bergeron–Findeisen (WBF) mechanism was efficient in downdrafts and some parts of updrafts, depending on ice concentration and vertical velocity. At low ice concentrations, the effect of ice on the phase partitioning was negligible. In this regime, liquid droplets were found near the cloud top, whereas ice particles precipitated through the cloud base. When ice concentration exceeded about 10 L−1, the WBF mechanism led to glaciation of almost the entire cloud, with the exception of narrow cloud regions associated with strong updrafts. At ice particle concentrations of a few tens per liter, the oscillatory regime took place due to the ice–liquid interaction. The microphysical structure of mixed-phase St forms as a combined effect of cloud dynamics (large eddies) and the WBF mechanism.

Dual-wavelength (3.2 and 0.32 cm, i.e., X- and W-radar bands) radar ratio (DWR) measurements in ice clouds and precipitation using Canada's National Research Council Institute for Aerospace Research airborne radar are compared to closely collocated particle microphysical in situ sampling data in order to develop relations between DWR and characteristic hydrometeor size. This study uses the radar and in situ data sets collected during the In-Cloud ICing and Large-drop Experiment (ICICLE) campaign in midlatitude frontal clouds. Since atmospheric particle scattering at X band is predominantly in the Rayleigh regime and the W-band frequency is the highest frequency usually used for hydrometeor remote sensing, the X–W-band combination provides a relatively strong dual-wavelength reflectivity difference. This study considers radar and in situ measurements conducted in relatively homogeneous cloud and precipitation conditions. Measurements show that under these conditions, the difference between the X-band radar reflectivities observed with vertical and horizontal pointing of the radar beam are generally small and often negligible. However, W-band reflectivities at vertical beam pointing are, on average, larger than those for horizontal beam pointing by about 4 dB, which is a non-Rayleigh scattering effect from preferentially oriented non-spherical particles. A horizontal radar beam DWR–mean volume particle size relation, Dv, provides robust estimates of this characteristic size for populations of particles with different habits. Uncertainties of Dv retrievals using DWR are around 0.6 mm when Dv is greater than approximately 1 mm. Size estimates using vertical radar beam DWRs have larger uncertainties due to smaller dual-wavelength signals and stronger influences of hydrometeor habits and orientations at this geometry of beam pointing. Mean relations among different characteristic sizes, which describe the entire particle size distribution (PSD), such as Dv, and other sizes used in various applications (e.g., the mean, effective, and median sizes) are derived, so the results of this study can be used for estimating different PSD characteristic sizes.

The article analyzes short circuit current reduction due to three main factors: electrical arc, cable heating and contact and coil resistance in auxiliary network of traction substations. The research was made using ETAP software module Unbalance Short Circuit, where mathematical model of dynamic arc, as it is described by Russian and abroad scientists, iterative cable heating as it is described in Russian and European standards and contact resistance were implemented. Mathematical model includes power grid, auxiliary transformer, circuit breakers, current transformer, and cable. Cable size varies to show influence of each above-mentioned factors. Calculations were made using phase domain method and all the parts of auxiliary network were considered. The results show up to 60 percent decrease in three-phase short circuit current considering three factors together. It influences the ability to trip short circuit current by backup protections, fault-clearing time, cable sizing and the power supply quality. Neglect of one or more factors may, in some cases, mean insensitivity of the protection and the inability to trip the short circuit current in time.

Secondary ice production (SIP) plays a key role in the formation of ice particles in tropospheric clouds. Future improvement of the accuracy of weather prediction and climate models relies on a proper description of SIP in numerical simulations. For now, laboratory studies remain a primary tool for developing physically based parameterizations for cloud modeling. Over the past 7 decades, six different SIP-identifying mechanisms have emerged: (1) shattering during droplet freezing, (2) the rime-splintering (Hallett–Mossop) process, (3) fragmentation due to ice–ice collision, (4) ice particle fragmentation due to thermal shock, (5) fragmentation of sublimating ice, and (6) activation of ice-nucleating particles in transient supersaturation around freezing drops. This work presents a critical review of the laboratory studies related to secondary ice production. While some of the six mechanisms have received little research attention, for others contradictory results have been obtained by different research groups. Unfortunately, despite vast investigative efforts, the lack of consistency and the gaps in the accumulated knowledge hinder the development of quantitative descriptions of any of the six SIP mechanisms. The present work aims to identify gaps in our knowledge of SIP as well as to stimulate further laboratory studies focused on obtaining a quantitative description of efficiencies for each SIP mechanism.

Secondary ice production (SIP) is an important physical phenomenon that results in an increase in the ice particle concentration and can therefore have a significant impact on the evolution of clouds. In this study, idealized simulations of a mesoscale convective system (MCS) were conducted using a high-resolution (250 m horizontal grid spacing) mesoscale model and a detailed bulk microphysics scheme in order to examine the impacts of SIP on the microphysics and dynamics of a simulated tropical MCS. The simulations were compared to airborne in situ and remote sensing observations collected during the “High Altitude Ice Crystals – High Ice Water Content” (HAIC-HIWC) field campaign in 2015. It was found that the observed high ice number concentration can only be simulated by models that include SIP processes. The inclusion of SIP processes in the microphysics scheme is crucial for the production and maintenance of the high ice water content observed in tropical convection. It was shown that SIP can enhance the strength of the existing convective updrafts and result in the initiation of new updrafts above the melting layer. Agreement between the simulations and observations highlights the impacts of SIP on the maintenance of tropical MCSs in nature and the importance of including SIP parameterizations in models.

High ice water content (HIWC) regions in tropical deep convective clouds, composed of high concentrations of small ice crystals, were not reproduced by Weather Research and Forecasting (WRF) model simulations at 1 km horizontal grid spacing using four different bulk microphysics schemes (i.e., the WRF single‐moment 6‐class microphysics scheme (WSM6), the Morrison scheme and the Predicted Particle Properties (P3) scheme with one- and two-ice options) for conditions encountered during the High Altitude Ice Crystals (HAIC) and HIWC experiment. Instead, overestimates of radar reflectivity and underestimates of ice number concentrations were realized. To explore formation mechanisms for large numbers of small ice crystals in tropical convection, a series of quasi-idealized WRF simulations varying the model resolution, aerosol profile, and representation of secondary ice production (SIP) processes are conducted based on an observed radiosonde released at Cayenne during the HAIC-HIWC field campaign. The P3 two-ice category configuration, which has two “free” ice categories to represent all ice-phase hydrometeors, is used. Regardless of the horizontal grid spacing or aerosol profile used, without including SIP processes the model produces total ice number concentrations about 2 orders of magnitude less than observed at −10 ∘C and about an order of magnitude less than observed at −30 ∘C but slightly overestimates the total ice number concentrations at −45 ∘C. Three simulations including one of three SIP mechanisms separately (i.e., the Hallett–Mossop mechanism, fragmentation during ice–ice collisions, and shattering of freezing droplets) also do not replicate observed HIWCs, with the results of the simulation including shattering of freezing droplets most closely resembling the observations. The simulation including all three SIP processes produces HIWC regions at all temperature levels, remarkably consistent with the observations in terms of ice number concentrations and radar reflectivity, which is not replicated using the original P3 two-ice category configuration. This simulation shows that primary ice production plays a key role in generating HIWC regions at temperatures <-40 ∘C, shattering of freezing droplets dominates ice particle production in HIWC regions at temperatures between −15 and 0 ∘C during the early stage of convection, and fragmentation during ice–ice collisions dominates at temperatures between −15 and 0 ∘C during the later stage of convection and at temperatures between −40 and −20 ∘C over the whole convection period. This study confirms the dominant role of SIP processes in the formation of numerous small crystals in HIWC regions.

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.

We consider difference and differential Stackelberg game theoretic models with several followers of opinion control in marketing networks. It is assumed that in the stage of analysis of the network its opinion leaders have already been found and are the only objects of control. The leading player determines the marketing budgets of the followers by resource allocation. In the basic version of the models both the leader and the followers maximize the summary opinions of the network agents. In the second version the leader has a target value of the summary opinion. In all four models we have found the Stackelberg equilibrium and the respective payoffs of the players analytically. It is shown that the hierarchical control system is ideally compatible in all cases.

The simulation of clouds containing Supercooled Large Droplets has received increasing attention due to the introduction of Appendix O and future associated requirements for means of compliance. Supercooled Large Droplet conditions can cover four orders of magnitude in drop sizes, imposing a larger instrument measurement challenge than for Appendix C conditions. Wind tunnel facilities have adopted different instrumentation for liquid water content measurement, with fundamentally different principles of operation. In order to explore the comparability of the different instruments used for Appendix C and SLD measurement, and its impact on confidence in measurements used for means of compliance, a project was established to conduct a series of dedicated tests at three wind tunnel facilities. To date, liquid water content measurements have been completed using a Multi-Element sensor as the common instrument at two of the facilities. The data have provided preliminary information suggesting that substantial inter-facility differences likely exist in liquid water content estimates in Supercooled Large Droplet conditions that appear to be largely attributable to the choice of calibration instruments. These results are dependent on the assumption that the Multi-Element probe would produce equivalent measurements at the two facilities if the liquid water content were the same, regardless of other environmental differences that may exist between the two facilities. Planned further testing with other liquid water content measurement techniques may provide further information to confirm or refute the results of this study., AIAA Aviation 2021 Forum, August 2-6, 2021, Virtual Event

A collaborative effort to better understand cloud characterization probes in Supercooled Large Drop (SLD) conditions, as well the ability to simulate these conditions in several icing wind tunnels, was undertaken by NASA, NRCC, CIRA, ECCC, FAA and Met Analytics, Inc. Both drop sizing and liquid water content, LWC, were measured with various probes using current to emerging technologies. To ensure the best possible data quality from the newest probes, the probe manufacturers, SEA, Inc. and Artium, Inc. were invited to support testing and data analysis efforts. A common set of probes was identified to test in each of the three participating facilities: NRCC’s Altitude Icing Wind Tunnel, NASA’s Icing Research Tunnel and CIRA’s Icing Wind Tunnel. From the common set of probes, a subset were identified to use for comparison across the three facilities. These were the CDP-2 and 2D-S for drop sizing, and the Multi-wire for LWC. The LWC value was also checked by measuring the ice accretion thickness under hard rime conditions on a NACA-0012 airfoil. A common test matrix with sweeps in both LWC and median volume diameter, MVD, was developed. Each facility achieved these conditions as determined by their own calibration. The MVD ranged from 20 to at least 200 um, and LWC ranged from 0.5 to 3 g/m3. The comparison probes tested at common conditions in each facility were intended to allow for a direct comparison, and check of potential facility bias.

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.

Mixed-phase clouds are globally omnipresent and play a major role in the Earth's radiation budget and precipitation formation. The existence of liquid droplets in presence of ice particles is microphysically unstable and depends on a delicate balance of several competing processes. Understanding mechanisms that govern ice initiation and moisture supply are important to understand the life-cycle of such clouds. This study presents observations that reveal the onset of drizzle inside a ∼600 m deep mixed-phase layer embedded in a stratiform precipitation system. Using Doppler spectra analysis, we show how large supercooled liquid droplets are generated in Kelvin-Helmholtz (K-H) instability despite ice particles falling from upper cloud layers. The spectral width of supercooled liquid water mode in radar Doppler spectrum is used to identify a region of increased turbulence. The observations show that large liquid droplets, characterized by reflectivity values larger than −20 dBZ, are generated in this region. In addition to cloud droplets, Doppler spectral analysis reveals the production of the columnar ice crystals in the K-H billows. The modelling study estimates that the concentration of these ice crystals is 3 ∼ 8 L−1, which is at least one order of magnitude higher than that of primary ice nucleating particles. Given the detail of the observations, we show that multiple populations of secondary ice particles are generated in regions where larger cloud droplets are produced and not at some constant level within the cloud. It is therefore hypothesized that K-H instability provides conditions favorable for enhanced droplet growth and formation of secondary ice particles.

In situ cloud data from three international flight campaigns are compared to the Federal Aviation Administration (FAA) Title 14 Code of Federal Regulations Part 33 Appendix D mixed-phase/glaciated environmental envelope and the corresponding identical European Union Aviation Safety Agency (EASA) CS-25 Appendix P envelope. The appendices consist of a temperature-altitude envelope, a 99th percentile total water content (TWC) envelope at the 17.4 Nm distance scale, a distance factor for estimation at other distance scales, ice crystal median mass diameter (MMD), and recommended liquid water content (LWC) levels in mixed-phase icing conditions. The data were collected during 54 flights out of one subtropical and two tropical locations, with 472 runs from about 17,000 ft to 39,000 ft in approximately 115 clouds. The campaigns provide about 29,600 Nm of in situ data in deep convection over four targeted temperature intervals: −10°C, −30°C, −40°C, and −50°C, all ±5°C. The dataset is a modern and unique documentation of the deep convective cloud ice crystal icing (ICI) environment, and the results described in this article will contribute to regulatory and industry assessment of Appendices D and P.

Supercooled large drop (SLD) icing poses a unique hazard for aircraft and has resulted in new regulations regarding aircraft certification to fly in regions of known or forecast SLD icing conditions. The new regulations define two SLD icing categories based upon the maximum supercooled liquid water drop diameter (Dmax): freezing drizzle (100–500 μm) and freezing rain (> 500 μm). Recent upgrades to U.S. operational numerical weather prediction models lay a foundation to provide more relevant aircraft icing guidance including the potential to predict explicit drop size. The primary focus of this paper is to evaluate a proposed method for estimating the maximum drop size from model forecast data to differentiate freezing drizzle from freezing rain conditions. Using in-situ cloud microphysical measurements collected in icing conditions during two field campaigns between January and March 2017, this study shows that the High-Resolution Rapid Refresh model is capable of distinguishing SLD icing categories of freezing drizzle and freezing rain using a Dmax extracted from the rain category of the microphysics output. It is shown that the extracted Dmax from the model correctly predicted the observed SLD icing category as much as 99% of the time when the HRRR accurately forecast SLD conditions; however, performance varied by the method to define Dmax and by the field campaign dataset used for verification.

The National Science Foundation (NSF) provided the funding support for this workshop through grant number AGS-1945681. We are grateful to the following: Susannah Burrows (Pacific Northwest National Laboratory), Hermann Gerber (Gerber Scientific), and Fan Yang (Brookhaven National Laboratory) for looking over the meeting summary for accuracy; Jessica Brassard of Michigan Technological University for invaluable support and advising on the strategy, organization, and logistics of the workshop, as well as for the artistic musings shown in Figure 1; Peter Sullivan and Wojciech Grabowski for facilitating the coordination and co-sponsorship by the Geophysical Turbulence Program; Kris Marwitz of NCAR for administrative and logistical support; And to the more than 60 attendees who actively engaged in brainstorms and discussions, without whom this meeting summary would not have been possible Clouds and aerosols, ubiquitously embedded in turbulent flows, are central to the prediction of weather and climate. The purpose of the workshop described here was to explore scientific questions and set priorities for a large-scale aerosol-cloud-turbulence laboratory facility. (Here, “facility” denotes one or more aerosol/cloud chambers and the associated instrumentation and technical/scientific staff.) Specifically, at the workshop we attempted to gauge community interest and to obtain a sense of priorities for the scientific challenges likely to be amenable to laboratory investigation.

Secondary ice production (SIP) plays a key role in the formation of ice particles in tropospheric clouds. Future improvement of the accuracy of the weather predictions and climate models relies on a proper description of SIP in numerical simulations. For now, laboratory studies remain a primary tool for developing physically based parameterizations for cloud modeling. Over the past seven decades, six different SIP-identifying mechanisms have emerged: (1) shattering during droplet freezing; (2) the rime splintering (Hallett-Mossop) process; (3) fragmentation due to ice-ice collision; (4) ice particle fragmentation due to thermal shock; (5) fragmentation of sublimating ice; (6) activation of ice nucleating particles in transient supersaturation around freezing drops. This work presents a critical review of the laboratory studies related to secondary ice production. While some of the six mechanisms have received little research attention, others consist of contradictory results obtained by different research groups. Unfortunately, despite past investigative efforts, the lack of consistency and the gaps in the accumulated knowledge hinder the development of quantitative descriptions of any of the six SIP mechanisms. The present work is aimed at identifying gaps in our knowledge on SIP and on stimulating further laboratory studies in obtaining a quantitative description of efficiencies for each of SIP mechanism.

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.

In this paper we introduce stochastic parameters into the network game model with production and knowledge externalities. This model was proposed by V. Matveenko and A. Korolev as a generalization of the two-period Romer model. Agents differ in their productivities which have deterministic and stochastic (Wiener) components. We study the dynamics of a single agent and the dynamics of a dyad where two agents are aggregated. We derive explicit expressions for the dynamics of a single agent and dyad dynamics in the form of Brownian random processes, and qualitatively analyze the solutions of stochastic equations and systems of stochastic equations.

This paper presents a methodology for ice water content (IWC) retrieval from a dual-polarization side-looking X-band airborne radar. Measured IWC from aircraft in situ probes is weighted by a function of the radar differential reflectivity (Zdr) to reduce the effects of ice crystal shape and orientation on the variation in IWC – specific differential phase (Kdp) joint distribution. A theoretical study indicates that the proposed method, which does not require a knowledge of the particle size distribution (PSD) and number density of ice crystals, is suitable for high-ice-water-content (HIWC) regions in tropical convective clouds. Using datasets collected during the High Altitude Ice Crystals – High Ice Water Content (HAIC-HIWC) international field campaign in Cayenne, French Guiana (2015), it is shown that the proposed method improves the estimation bias by 35 % and increases the correlation by 4 % on average, compared to the method using specific differential phase (Kdp) alone.

Over the decades, the cloud physics community has debated the nature and role of aerosol particles in ice initiation. The present study shows that the measured concentration of ice crystals in tropical mesoscale convective systems exceeds the concentration of ice nucleating particles (INPs) by several orders of magnitude. The concentration of INPs was assessed from the measured aerosol particle concentration in the size range of 0.5 to 1 μm. The observations from this study suggest that primary ice crystals formed on INPs make only a minor contribution to the total concentration of ice crystals in tropical mesoscale convective systems. This is found by comparing the predicted INP number concentrations with in situ ice particle number concentrations. The obtained measurements suggest that ice multiplication is the likely explanation for the observed high concentrations of ice crystals in this type of convective system.

The present study considers final stages of in-cloud mixing in the framework of classical concept of homogeneous and extreme inhomogeneous mixing. Simple analytical relationships between basic microphysical parameters were obtained for homogeneous and extreme inhomogeneous mixing based on the adiabatic consideration. It was demonstrated that during homogeneous mixing the functional relationships between the moments of the droplets size distribution hold only during the primary stage of mixing. Subsequent random mixing between already mixed parcels and undiluted cloud parcels breaks these relationships. However, during extreme inhomogeneous mixing the functional relationships between the microphysical parameters hold both for primary and subsequent mixing. The obtained relationships can be used to identify the type of mixing from in situ observations. The effectiveness of the developed method was demonstrated using in situ data collected in convective clouds. It was found that for the specific set of in situ measurements the interaction between cloudy and entrained environments was dominated by extreme inhomogeneous mixing.

An idealized model of time-dependent mixing between cloud and non-cloud volumes is analyzed. Initial droplet size distribution (DSD) in cloud volume is assumed to be monodisperse. Both analytical investigation and parcel model investigation are used to study mixing processes and solve diffusion-evaporation equations. It is shown that the evolution of microphysical variables and the final equilibrium stage are unambiguously determined by two non-dimensional parameters. The first parameter, R, which is proportional to the ratio of the saturation deficit to the liquid water content in a cloud volume, determines whether the equilibrium stage is reached at 100 % relative humidity, or, rather, leads to a full evaporation of cloud droplets. The second parameter, Da, is the Damkölher number, which is equal to the ratio of the characteristic mixing time and phase relaxation time. This parameter (together with parameter R) determines whether mixing takes place according to a homogeneous or an inhomogeneous scenario. An analysis of the results obtained within a wide range of parameters R and Da is presented. It is shown that there is no pure homogeneous mixing, since the first stage of mixing is always inhomogeneous. Turbulent mixing between different volumes always starts as inhomogeneous and the mixing type can change during the mixing process. At any values of governing parameters, mixing leads to the formation of a tail of small droplets in the DSD and therefore to DSD broadening. The broadening depends onDa and the final DSD dispersion can be as large as 0.2 at large Da. The total duration of the mixing process varies from several to one hundred phase relaxation times, depending on R and Da. Delimitation between the types of mixing on the Da–R plane is carried out. The definitions of homogeneous and inhomogeneous mixings are reconsidered and clarified. The paper also compares the results of the current study with those obtained with classical mixing concepts.

The Convective Precipitation Experiment (COPE) was a joint U.K.–U.S. field campaign held during the summer of 2013 in the southwest peninsula of England, designed to study convective clouds that produce heavy rain leading to flash floods. The clouds form along convergence lines that develop regularly as a result of the topography. Major flash floods have occurred in the past, most famously at Boscastle in 2004. It has been suggested that much of the rain was produced by warm rain processes, similar to some flash floods that have occurred in the United States. The overarching goal of COPE is to improve quantitative convective precipitation forecasting by understanding the interactions of the cloud microphysics and dynamics and thereby to improve numerical weather prediction (NWP) model skill for forecasts of flash floods. Two research aircraft, the University of Wyoming King Air and the U.K. BAe 146, obtained detailed in situ and remote sensing measurements in, around, and below storms on several days. A new fast-scanning X-band dual-polarization Doppler radar made 360° volume scans over 10 elevation angles approximately every 5 min and was augmented by two Met Office C-band radars and the Chilbolton S-band radar. Detailed aerosol measurements were made on the aircraft and on the ground. This paper i) provides an overview of the COPE field campaign and the resulting dataset, ii) presents examples of heavy convective rainfall in clouds containing ice and also in relatively shallow clouds through the warm rain process alone, and iii) explains how COPE data will be used to improve high-resolution NWP models for operational use.

Results from twenty‐two airborne field campaigns, including more than ten million high‐resolution particle images collected in cirrus formed in situ and in convective anvils, are interpreted in terms of particle shapes and their potential impact on radiative transfer. Emphasis is placed on characterizing ice particle shapes in Tropical Maritime and Mid‐Latitude Continental anvil cirrus, as well as in cirrus formed in situ in the upper troposphere, and subvisible cirrus in the upper tropical troposphere layer. There is a distinctive difference in cirrus ice particle shapes formed in situ compared to those in anvils that are generated in close proximity to convection. More than half the mass in cirrus formed in situ are rosette‐shapes (polycrystals and bullet rosettes). Cirrus formed from fresh convective anvils is mostly devoid of rosette‐shaped particles. However, small frozen drops may experience regrowth downwind of an aged anvil in a regime with RHice > ~ 120%, and then grow into rosette shapes. Identifiable particle shapes in Tropical Maritime anvils that have not been impacted by continental influences typically contain mostly single plate‐like and columnar crystals and aggregates. Mid‐Latitude Continental anvils contain single rimed particles, more and larger aggregates with riming, and chains of small ice particles when in a highly electrified environment. The particles in subvisible cirrus are < ~ 100 μm and quasi‐spherical with some plates and rare trigonal shapes. Percentages of particle shapes and power laws relating mean particle area and mass to dimension are provided to improve parameterization of remote retrievals and numerical simulations.