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The growth of ice crystals at the expense of water droplets, the Wegener–Bergeron–Findeisen (WBF) process, is of major importance for the production of precipitation in mixed-phase clouds. The effects of entrainment and mixing on WBF, however, are not well understood, and small-scale inhomogeneities in the thermodynamic and hydrometeor fields are typically neglected in current models. By applying the linear eddy model, a millimeter-resolution representation of turbulent deformation and molecular diffusion, we investigate these small-scale effects on WBF. While we show that entrainment is accelerating WBF by contributing to the evaporation of liquid droplets, entrainment may also cause aforementioned inhomogeneities, particularly regions filled with exclusively ice or liquid hydrometeors, which tend to decelerate WBF if the ice crystal concentration exceeds 100 L−1. At lower ice crystal concentrations, even weak turbulence can homogenize hydrometeor and thermodynamic fields sufficiently fast so as to not affect WBF. Independent of the ice crystal concentration, it is shown that a fully resolved entrainment and mixing process may delay the nucleation of entrained aerosols to ice crystals, thereby delaying the uptake of water vapor by the ice phase, further slowing down WBF. All in all, this study indicates that, under specific conditions, small-scale inhomogeneities associated with entrainment and mixing counteract the accelerated WBF in entraining clouds. However, further research is required to assess the importance of the newly discovered processes more broadly in fully coupled, evolving mixed-phase cloud systems.

We systematically investigate the effects of Wegener–Bergeron–Findeisen process (hereafter WBF) on black carbon (BC) scavenging efficiency, surface BCair, deposition flux, concentration in snow (BCsnow, ng g−1), and washout ratio using a global 3-D chemical transport model (GEOS-Chem). We differentiate riming- versus WBF-dominated in-cloud scavenging based on liquid water content (LWC) and temperature. Specifically, we implement an implied WBF parameterization using either temperature or ice mass fraction (IMF) in mixed-phase clouds based on field measurements. We find that at Jungfraujoch, Switzerland, and Abisko, Sweden, where WBF dominates in-cloud scavenging, including the WBF effect strongly reduces the discrepancies of simulated BC scavenging efficiency and washout ratio against observations (from a factor of 3 to 10 % and from a factor of 4–5 to a factor of 2). However, at Zeppelin, Norway, where riming dominates, simulation of BC scavenging efficiency, BCair, and washout ratio become worse (relative to observations) when WBF is included. There is thus an urgent need for extensive observations to distinguish and characterize riming- versus WBF-dominated aerosol scavenging in mixed-phase clouds and the associated BC scavenging efficiency. Our model results show that including the WBF effect lowers global BC scavenging efficiency, with a higher reduction at higher latitudes (8 % in the tropics and up to 76 % in the Arctic). The resulting annual mean BCair increases by up to 156 % at high altitudes and at northern high latitudes because of lower temperature and higher IMF. Overall, WBF halves the model–observation discrepancy (from −65 to −30 %) of BCair across North America, Europe, China and the Arctic. Globally WBF increases BC burden from 0.22 to 0.29–0.35 mg m−2 yr−1, which partially explains the gap between observed and previous model-simulated BC burdens over land. In addition, WBF significantly increases BC lifetime from 5.7 to ∼ 8 days. Additionally, WBF results in a significant redistribution of BC deposition in source and remote regions. Specifically, it lowers BC wet deposition (by 37–63 % at northern mid-latitudes and by 21–29 % in the Arctic), while it increases dry deposition (by 3–16 % at mid-latitudes and by 81–159 % in the Arctic). The resulting total BC deposition is lower at mid-latitudes (by 12–34 %) but higher in the Arctic (by 2–29 %). We find that WBF decreases BCsnow at mid-latitudes (by ∼ 15 %) but increases it in the Arctic (by 26 %) while improving model comparisons with observations. In addition, WBF dramatically reduces the model–observation discrepancy of washout ratios in winter (from a factor of 16 to 4). The remaining discrepancies in BCair, BCsnow and BC washout ratios suggest that in-cloud removal in mixed-phased clouds is likely still excessive over land.

The Wegener-Bergeron-Findeisen process refers to the rapid growth of ice crystals at the expense of surrounding cloud droplets, which frequently occurs in atmospheric mixed-phase clouds. The process is a result of the difference in saturation vapor pressures with respect to liquid and ice, and may in some circumstances lead to abrupt and complete cloud glaciation at temperatures between −40 °C and 0 °C in the Earth's atmosphere. The process is named after three eminent scientists who were active in the first half of the 20th century, among them being German meteorologist Walter Findeisen (1909–1945). In his classical paper published in 1938, Findeisen described the contemporary understanding of the Wegener-Bergeron-Findeisen process and other key cloud microphysical processes. Here, we compare the understanding of the aforementioned processes at the time with that of the present, and find that they are remarkably similar. We also discuss how the Wegener-Bergeron-Findeisen process is implemented in state-of-the-art numerical models of the atmosphere, and highlight its importance for both weather and climate.

Diffusion ofwater vapor is the dominant growth mechanism for smallwater droplets and ice crystals in clouds. In current cloud models, Maxwell’s theory is used for describing growth of cloud particles. In this approach the local interaction between particles is neglected; the particles can only grow due to changes in environmental conditions, which are assumed as boundary conditions at infinity. This assumption is meaningful if the particles are well separated and far away from each other. However, turbulent motions might change the distances between cloud particles and thus these particles are no longer well separated leading to direct local interactions. In this study we develop a reference model for investigating the direct interaction of cloud particles in mixed-phase clouds as driven by diffusion processes. The model is numerically integrated using finite elements. Additionally, we develop a numerical method based on generalized finite elements for including moving particles and their direct interactions with respect to diffusional growth and evaporation. Several idealized simulations are carried out for investigating direct interactions of liquid droplets and ice particles in a mixed-phase cloud. The results show that local interaction between cloud particles might enhance life times of droplets and ice particles and thus lead to changes in mixed-phase cloud life time and properties.

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

[1] Two types of Arctic mixed‐phase clouds observed during the ISDAC and M‐PACE field campaigns are simulated using a 3‐dimensional cloud‐resolving model (CRM) with size‐resolved cloud microphysics. The modeled cloud properties agree reasonably well with aircraft measurements and surface‐based retrievals. Cloud properties such as the probability density function (PDF) of vertical velocity (w), cloud liquid and ice, regimes of cloud particle growth, including the Wegener–Bergeron–Findeisen (WBF) process, and the relationships among properties/processes in mixed‐phase clouds are examined to gain insights for improving their representation in General Circulation Models (GCMs). The PDF of the simulated w is well represented by a Gaussian function, validating, at least for arctic clouds, the subgrid treatment used in GCMs. The PDFs of liquid and ice water contents can be approximated by Gamma functions, and a Gaussian function can describe the total water distribution, but a fixed variance assumption should be avoided in both cases. The CRM results support the assumption frequently used in GCMs that mixed phase clouds maintain water vapor near liquid saturation. Thus, ice continues to grow throughout the stratiform cloud but the WBF process occurs in about 50% of cloud volume where liquid and ice co‐exist, predominantly in downdrafts. In updrafts, liquid and ice particles grow simultaneously. The relationship between the ice depositional growth rate and cloud ice strongly depends on the capacitance of ice particles. The simplified size‐independent capacitance of ice particles used in GCMs could lead to large deviations in ice depositional growth.

Overview At this point in our step-by-step study of cloud formation, we assume that a set of cloud particles exists via aerosol activation or nucleation. Liquid cloud droplets likely formed by condensation of water vapor onto cloud condensation nuclei, and ice crystals may be present if the temperature were sufficiently low and ice nuclei were active. We ask next how rapidly and by what mechanism the particles grow under any given set of conditions (i.e., temperature, pressure, supersaturation). In the most general sense, growth takes place in one of two ways: a particle may grow from the vapor phase, meaning that it increases in size molecule by molecule; or, a particle may grow by collecting other particles, in which case the particle grows in size particle by particle. Both categories of growth may operate simultaneously, but we treat them separately to facilitate presentation of the underlying physics. Growth by collection is discussed in the next chapter. A net amount of water vapor deposits onto a surface whenever the partial pressure of vapor ( e ) exceeds the equilibrium value ( e eq ) of the surface. How rapidly the vapor deposits depends on the partial pressure excess ( e - e eq ), the temperature and nature of the surface, and the total air pressure. If the surface is liquid, the equilibrium vapor pressure is that of a solution droplet having the given temperature, solute concentration, and size.

A new parameterization of the Wegener–Bergeron–Findeisen (WBF) process has been developed, and implemented in the general circulation model CAM-Oslo. The new parameterization scheme has important implications for the process of phase transition in mixed-phase clouds. The new treatment of the WBF process replaces a previous formulation, in which the onset of the WBF effect depended on a threshold value of the mixing ratio of cloud ice. As no observational guidance for such a threshold value exists, the previous treatment added uncertainty to estimates of aerosol effects on mixed-phase clouds. The new scheme takes subgrid variability into account when simulating the WBF process, allowing for smoother phase transitions in mixed-phase clouds compared to the previous approach. The new parameterization yields a model state which gives reasonable agreement with observed quantities, allowing for calculations of aerosol effects on mixed-phase clouds involving a reduced number of tunable parameters. Furthermore, we find a significant sensitivity to perturbations in ice nuclei concentrations with the new parameterization, which leads to a reversal of the traditional cloud lifetime effect.