ALBERT

Description: A numerical formulation is provided for secondary ice production during fragmentation of freezing raindrops or drizzle. This is obtained by pooling laboratory observations from published studies and considering the physics of collisions. There are two modes of the scheme: fragmentation during spherical drop freezing (mode 1) and during collisions of supercooled raindrops with more massive ice (mode 2). The empirical scheme is for atmospheric models. Microphysical simulations with a parcel model of fast ascent (8 m s−1) between −10° and −20°C are validated against aircraft observations of tropical maritime deep convection. Ice enhancement by an order of magnitude is predicted from inclusion of raindrop-freezing fragmentation, as observed. The Hallett–Mossop (HM) process was active too. Both secondary ice mechanisms (HM and raindrop freezing) are accelerated by a positive feedback involving collisional raindrop freezing. An energy-based theory is proposed explaining the laboratory observations of mode 1, both of approximate proportionality between drop size and fragment numbers and of their thermal peak. To illustrate the behavior of the scheme in both modes, the glaciation of idealized monodisperse populations of drops is elucidated with an analytical zero-dimensional (0D) theory treating the freezing in drop–ice collisions by a positive feedback of fragmentation. When drops are too few or too small (≪1 mm), especially at temperatures far from −15°C (mode 1), there is little raindrop-freezing fragmentation on realistic time scales of natural clouds, but otherwise, high ice enhancement (IE) ratios of up to 100–1000 are possible. Theoretical formulas for the glaciation time of such drop populations, and their maximum and initial growth rates of IE ratio, are proposed.

Description: A midlatitude hail storm was simulated using a new version of the spectral bin microphysics Hebrew University Cloud Model (HUCM) with a detailed description of time-dependent melting and freezing. In addition to size distributions of drops, plate-, columnar-, and branch-type ice crystals, snow, graupel, and hail, new distributions for freezing drops as well as for liquid water mass within precipitating ice particles were implemented to describe time-dependent freezing and wet growth of hail, graupel, and freezing drops. Simulations carried out using different aerosol loadings show that an increase in aerosol loading leads to a decrease in the total mass of hail but also to a substantial increase in the maximum size of hailstones. Cumulative rain strongly increases with an increase in aerosol concentration from 100 to about 1000 cm−3. At higher cloud condensation nuclei (CCN) concentrations, the sensitivity of hailstones’ size and surface precipitation to aerosols decreases. The physical mechanism of these effects was analyzed. It was shown that the change in aerosol concentration leads to a change in the major mechanisms of hail formation and growth. The main effect of the increase in the aerosol concentration is the increase in the supercooled cloud water content. Accordingly, at high aerosol concentration, the hail grows largely by accretion of cloud droplets in the course of recycling in the cloud updraft zone. The main mechanism of hail formation in the case of low aerosol concentration is freezing of raindrops.

Description: This paper proposes that the maximum entropy principle can be used for determining the drop size distribution of hydrometeors. The maximum entropy principle can be applied to any physical systems with many degrees of freedom in order to determine a distribution of a variable when the following are known: 1) the restriction variable that leads to a homogeneous distribution without constraint and 2) a set of integrals weighted by the distribution, such as mean and variance, that constrain the system. The principle simply seeks a distribution that gives the maximum possible number of partitions among all the possible states. A continuous limit can be taken by assuming a constant bin size for the restriction variable. This paper suggests that the drop mass is the most likely restriction variable, and the laws of conservation of total bulk mass and of total vertical drop mass flux are two of the most likely physical constraints to a hydrometeor drop size distribution. Under this consideration, the distribution is most likely constrained by the total bulk mass when an ensemble of drops under the coalescence–breakup process is confined inside a closed box. Alternatively, for an artificial rain produced from the top of a high ceiling under a constant mass flux of water fall, the total drop mass flux is the most likely constraint to the drop size distribution. Preliminary analysis of already-published data is not inconsistent with the above hypotheses, although the results are rather inconclusive. Data in the large drop size limit are required in order to reach a more definite conclusion.

Description: The number of ice fragments generated by breakup of large graupel in collisions with small graupel fluctuates randomly owing to fluctuations in relative sizes and densities of colliding graupel particles and the stochastic nature of fracture propagation. This paper investigates the impact of the stochasticity of breakup on ice multiplication. When both the rate of generation of primary ice and the initial number concentration of ice crystals are low, the system most likely loses all the initial ice and graupel owing to a lack of sustaining sources. Even randomness does not change this mean evolution of the system in its phase space. However, a fluctuation of ice breakup number gives a small but finite chance that substantial ice crystal fragments are generated by breakup of large graupel. That, in turn, generates more large graupel. This multiplicative process due to fluctuations potentially leads to a small but finite chance of explosive growth of ice number. A rigorous stochastic analysis demonstrates this point quantitatively. The randomness considered here belongs to a particular category called “multiplicative” noise, because the noise amplitude is proportional to a given physical state. To contrast the multiplicative-noise nature of ice breakup with a standard “additive” noise process, fluctuation of the primary ice generation rate is also considered as an example of the latter. These processes are examined by taking the Fokker–Planck equation that explicitly describes the evolution of the probability distribution with time. As an important conclusion, stability in the phase space of the cloud microphysical system of breakup in ice–ice collisions is substantially altered by the multiplicative noise.

Description: After extensive efforts over the course of a decade, convective-scale weather forecasts with horizontal grid spacings of 1–5 km are now operational at national weather services around the world, accompanied by ensemble prediction systems (EPSs). However, though already operational, the capacity of forecasts for this scale is still to be fully exploited by overcoming the fundamental difficulty in prediction: the fully three-dimensional and turbulent nature of the atmosphere. The prediction of this scale is totally different from that of the synoptic scale (103 km), with slowly evolving semigeostrophic dynamics and relatively long predictability on the order of a few days. Even theoretically, very little is understood about the convective scale compared to our extensive knowledge of the synoptic-scale weather regime as a partial differential equation system, as well as in terms of the fluid mechanics, predictability, uncertainties, and stochasticity. Furthermore, there is a requirement for a drastic modification of data assimilation methodologies, physics (e.g., microphysics), and parameterizations, as well as the numerics for use at the convective scale. We need to focus on more fundamental theoretical issues—the Liouville principle and Bayesian probability for probabilistic forecasts—and more fundamental turbulence research to provide robust numerics for the full variety of turbulent flows. The present essay reviews those basic theoretical challenges as comprehensibly as possible. The breadth of the problems that we face is a challenge in itself: an attempt to reduce these into a single critical agenda should be avoided.

Description: In Part I of this two-part paper, a formulation was developed to treat fragmentation in ice–ice collisions. In the present Part II, the formulation is implemented in two microphysically advanced cloud models simulating a convective line observed over the U.S. high plains. One model is 2D with a spectral bin microphysics scheme. The other has a hybrid bin–two-moment bulk microphysics scheme in 3D. The case consists of cumulonimbus cells with cold cloud bases (near 0°C) in a dry troposphere. Only with breakup included in the simulation are aircraft observations of particles with maximum dimensions 〉0.2 mm in the storm adequately predicted by both models. In fact, breakup in ice–ice collisions is by far the most prolific process of ice initiation in the simulated clouds (95%–98% of all nonhomogeneous ice), apart from homogeneous freezing of droplets. Inclusion of breakup in the cloud-resolving model (CRM) simulations increased, by between about one and two orders of magnitude, the average concentration of ice between about 0° and −30°C. Most of the breakup is due to collisions of snow with graupel/hail. It is broadly consistent with the theoretical result in Part I about an explosive tendency for ice multiplication. Breakup in collisions of snow (crystals 〉~1 mm and aggregates) with denser graupel/hail was the main pathway for collisional breakup and initiated about 60%–90% of all ice particles not from homogeneous freezing, in the simulations by both models. Breakup is predicted to reduce accumulated surface precipitation in the simulated storm by about 20%–40%.

Description: For decades, enhancement of ice concentrations above those of active ice nucleus aerosols was observed in deep clouds with tops too warm for homogeneous freezing, indicating fragmentation of ice (multiplication). Several possible mechanisms of fragmentation have been suggested from laboratory studies, and one of these involves fragmentation in ice–ice collisions. In this two-part paper, the role of breakup in ice–ice collisions in a convective storm consisting of many cloud types is assessed with a modeling approach. The colliding ice particles can belong to any microphysical species, such as crystals, snow, graupel, hail, or freezing drops. In the present study (Part I), a full physical formulation of initiation of cloud ice by mechanical breakup in collisions involving snow, graupel, and/or hail is developed based on an energy conservation principle. Theoretically uncertain parameters are estimated by simulating laboratory and field experiments already published in the literature. Here, collision kinetic energy (CKE) is the fundamental governing variable of fragmentation in any collision, because it measures the energy available for breakage by work done to create the new surface of fragments. The developed formulation is general in the sense that it includes all the types of fragmentation observed in previous published studies and encompasses collisions of either snow or crystals with graupel/hail, collisions among only graupel/hail, and collisions among only snow/crystals. It explains the observed dependencies on CKE, size, temperature, and degree of prior riming.

Description: In this two-part paper, influences from environmental factors on lightning in a convective storm are assessed with a model. In Part I, an electrical component is described and applied in the Aerosol-Cloud model (AC). AC treats many types of secondary (e.g. breakup in ice-ice collisions, raindrop-freezing fragmentation, rime-splintering) and primary (heterogeneous, homogeneous freezing) ice initiation. AC represents lightning flashes with a statistical treatment of branching from a fractal law constrained by video imagery. The storm simulated is from the Severe Thunderstorm Electrification and Precipitation Study (STEPS, 19/20 June 2000). The simulation was validated microphysically (e.g., ice/droplet concentrations and mean sizes, liquid water content [LWC], reflectivity, surface precipitation) and dynamically (e.g., ascent) in our 2017 paper. Predicted ice concentrations (~10 L-1) agreed—to within a factor of about two—with aircraft data at flight levels (−10 to −15 °C). Here, electrical statistics of the same simulation are compared with observations. Flash rates (to within a factor of two), triggering altitudes and polarity of flashes, and electric fields, agree with STEPS observations. The ‘normal’ tripole of charge structure observed during an electrical balloon sounding is reproduced by AC. It is related to reversal of polarity of non-inductive charging in ice-ice collisions seen in lab experiments when temperature or LWC are varied. Positively charged graupel and negatively charged snow at most mid-levels, charged away from the fastest updrafts, is predicted to cause the normal tripole. Total charge separated in the simulated storm is dominated by collisions involving secondary ice from fragmentation in graupel-snow collisions.

Description: Cloud simulations and cloud–climate feedbacks in the tropical and subtropical eastern Pacific region in 16 state-of-the-art coupled global climate models (GCMs) and in the International Pacific Research Center (IPRC) Regional Atmospheric Model (iRAM) are examined. The authors find that the simulation of the present-day mean cloud climatology for this region in the GCMs is very poor and that the cloud–climate feedbacks vary widely among the GCMs. By contrast, iRAM simulates mean clouds and interannual cloud variations that are quite similar to those observed in this region. The model also simulates well the observed relationship between lower-tropospheric stability (LTS) and low-level cloud amount. To investigate cloud–climate feedbacks in iRAM, several global warming scenarios were run with boundary conditions appropriate for late twenty-first-century conditions. All the global warming cases simulated with iRAM show a distinct reduction in low-level cloud amount, particularly in the stratocumulus regime, resulting in positive local feedback parameters in these regions in the range of 4–7 W m−2 K−1. Domain-averaged (30°S–30°N, 150°–60°W) feedback parameters from iRAM range between +1.8 and +1.9 W m−2 K−1. At most locations both the LTS and cloud amount are altered in the global warming cases, but the changes in these variables do not follow the empirical relationship found in the present-day experiments. The cloud–climate feedback averaged over the same east Pacific region was also calculated from the Special Report on Emissions Scenarios (SRES) A1B simulations for each of the 16 GCMs with results that varied from −1.0 to +1.3 W m−2 K−1, all less than the values obtained in the comparable iRAM simulations. The iRAM results by themselves cannot be connected definitively to global climate feedbacks; however, among the global GCMs the cloud feedback in the full tropical–subtropical zone is correlated strongly with the east Pacific cloud feedback, and the cloud feedback largely determines the global climate sensitivity. The present iRAM results for cloud feedbacks in the east Pacific provide some support for the high end of current estimates of global climate sensitivity.