Norihiko Fukuta

The Growth of Atmospheric Ice Crystals: A Summary of Findings in Vertical Supercooled Cloud Tunnel Studies

Measurements of ice crystal growth under free fall in a generation of vertical supercooled cloud tunnels and some static cloud chambers as well as the related theoretical works are summarized. Growth parameters, that is, mass (m), dimensions, apparent density, and fall velocity ( w), show extrema at about 258, 2108, and 2158C where crystals are predominantly column-needle, isometric, and plate-stellardendrite, respectively. Crystal shape enhances with time (t) at about 258 and 2158C, whereas at 2108C the effect is minimal and crystals show strongest tendency to grow into graupel due to the fall velocity maximum discovered early in the series of present studies. At this temperature, switch-over of growth mode toward graupel occurs more quickly as liquid water content (WL) increases. Under a fixed cloud condition, the shape-enhanced crystals hardly grow into graupel and vice versa. The diffusional growth theory, with Maxwellian surface condition and without ventilation, describes well the behaviors of intermediate size crystals for which m } t 3/2 } (2w) 3/2 } (2z) 3/4; z, being the fall distance, is identified. Small crystals grow more slowly due to accommodation coefficient effects and larger ones grow faster due to enhanced ventilation and riming. To include these effects, a generalized growth theory is formulated. A simple theory is developed for graupel/hail growth where m } (WLt) 6 } w6 } (2z) 3, ra being the air density. 23 ra Based on these relationships, the dominance of diffusional growth mechanism for precipitation development in shallow, convectively weak, winter clouds and that of graupel/hail-type riming growth in deep, convectively strong, summer clouds is explained.

Water supersaturation in convective clouds

Abstract The microphysics-dynamics interaction of clouds was theoretically studied in the zone after maximum supersaturation (S−1)mc where the droplet number concentration remains nearly constant. The analytic solution obtained, employing the Maxwellian droplet growth theory, describes (S−1) mc =Iw u 3 4 n − 1 2 , where I is the proportionality constant, wu the updraft velocity and n the number concentration of the droplets. This solution agrees well with previous studies. Factor I increases with altitude in the adiabatic atmosphere, decreases with temperature under constant pressure and increases with pressure under constant temperature. For the zone sufficiently after (S−1)mc, an approximate relationship (S−1) ∝r −1 ∝t − 1 3 is shown to hold, where (S−1) is the supersaturation, f the average droplet radius and t the time. Using the diffusion-kinetic theory of droplet growth, which includes the effects of thermal accomodation and condensation coefficients, numerically soluble relationships are derived for (S−1), r and t. Application of this theory is shown to increase (S−1)mc considerably. The Maxwellian analytic solution that is obtained, the variation of Factor I under different atmospheric conditions and the effect of condensation and thermal accomoddation coefficients through the use of the diffusion-kinetic droplet growth theory suggest that maximum supersaturation may reach as high as 10% and beyond in convective clouds.

Large, unique radar echoes in a new, self-enhancing cloud seeding

1999 . The total number of ice crystals with the nucleant remains essentially constant after the moment of the nucleation. The horizontally laid ice crystal thermal in the cloud, like cumulus convection, rolls up in the form of twin cylinders and turbulently spreads with the help of the buoyant motion caused by the heat of ice crystal growth or phase . change Fukuta, 1973 . The supercooled cloud volume, slowly and continually taken into the ice thermal during the ascent, sustains the condition and time for crystal growth, the heat generation, and the buoyancy to a maximum extent in feedback. When the enlarging thermal reaches the temperature inversion, which often exists at the cloud top, the thermal spreads horizontally in an anvil shape, but the crystals there have already acquired sufficient size to fall through the supercooled cloud volume below, grow, and generate heat. The heating induces lifting of the underlying cloudy, as well as moist air,

The effect of diffusion kinetics on the supersaturation in clouds

Abstract To describe the nucleation–growth interaction at and above the cloud base, a cloud model has been formulated including the haze process below the cloud base and before nucleation of cloud droplets, and a proper diffusion-kinetic droplet growth equation. Analytical equations for the maximum supersaturation by Twomey [Twomey, S., 1959. The nuclei of natural cloud formation: Part II. The supersaturation in natural clouds and the variation of cloud droplet concentration. Geofis. Pura Appl. 43, 243–249; Twomey, S., 1977. Atmospheric Aerosols. Elsevier, Amsterdam, 302 pp.] and by Fukuta and Xu [Fukuta, N., Xu, N., 1996. Nucleation–droplet growth interactions and microphysical property development in convective clouds. Atmos. Res. 41, 1–22], both employing the Maxwellian growth theory, are compared with the model outputs, and the model outputs are found to be the smallest. To preserve the clarity and usefulness of the analytical equations, a correction factor to the latter is obtained in comparison with the model results for different condensation coefficient ( β ) and cloud condensation nucleus activity spectra of typical continental and maritime air masses. Effect of β is found to be larger for small β and in continental clouds.

Empirical equations of ice crystal growth microphysics for modeling and analysis. I: Mass and dimensions

Abstract Experimental data that simulated the free-falling natural ice crystal growth for time periods up to 30 min were analyzed. First, some specific features of ice crystal growth theories were tested with the data. Second, time-dependent equations of mass, dimensions and fall velocity applicable to different regimes of growth were developed by considering both the data and the functional styles of theories and not by merely obtaining a set of best-fitting polynomials. Third, an empirical equation was derived by similar means to express the aerodynamic behavior of the falling ice crystal with the relationship among the hydrodynamical nondimensional numbers and the axial ratio. Finally, a set of simplified parameterized equations was obtained that is experimentally consistent and suitable for cloud modeling and analysis. This paper reports the portion related to the mass and the dimensions of growing crystals.

Surface microphysical mechanism for ice crystal growth habit development

Abstract The basic mechanism that controls the shape of ice crystal grown under different temperature and supersaturation, or the so-called “ice crystal growth habit,” has been investigated. The habit change is characterized by the existence of a maximum and a minimum in growth rates of prism and basal planes as a function of temperature. Under equilibrium condition, a liquid-like layer exists on the ice surface. During ice crystal growth in air due to vapor condensation, another transitional adsorption layer appears on the the crystal surface. This layer is shown to play a key role in the formation of habit change by making two-dimensional nucleation-controlled crystal plane growth possible. The crystal plane growth rate is maintained under steady-state by the balance of the sequential processes, the vapor condensation at the liquid-vapor interface and the freezing growth at the liquid-solid interface. When the temperature is sufficiently low, the slower of the two, or the condensational growth, dominates. With the temperature increase, however, the freezing process eventually slows down due to weakening in two-dimensional nucleation mechanism and becomes rate determining, resulting in formation of the plane growth rate maximum. As the temperature increases further towards the melting point, the plane growth rate is reported to increase again. If it does, the expected surface roughening may be responsible for the increase, reversing the slowing down tendency of the plane growth rate with temperature and resulting in the formation of the minimum.

Simultaneous Measurement of Condensation and Thermal Accommodation Coefficients for Cloud Droplet Growth in Due Consideration of a New Moving Surface-Boundary Effect

Abstract A droplet growth theory that describes a new effect of vapor and temperature field shift due to the growth-based movement of droplet surface boundary (moving boundary effect) was derived and found to enhance the growth rate as a function of supersaturation (S − 1) and droplet radius (a) in second order. The theory plays the role of a missing link and resolves the gap that exists among the measured data; the high (S − 1) used was found to overestimate thermal accommodation and condensation coefficients, α and β. The theory provided the basis for bettering the measurement and correction for data analyzed without the moving boundary effect, and suggested the broadening effect in the droplet size spectrum by accelerating the growth on the larger end together with the growth slowdown effect of α, β on the smaller. Measurements employing a horizontal-flow thermal diffusion chamber and the Mie scattering method using a He–Ne laser for droplet size estimation at temperature T = 277 K, (S − 1) = 0.32%, a ...

Nucleation-droplet growth interactions and microphysical property development in convective clouds

In the microphysics-dynamics interaction above the convective cloud base, the analytic solutions with the Maxwellian droplet growth system obtained by Squires (1958) and Fukuta (1993), without including the relationship of the cloud condensation nucleus (CCN) activity spectrum, are shown to be partial or diagnostic solutions and that of Twomey (1959) as a complete or prognostic solution within its approximation. The diagnostic solutions of the diffusion-kinetic (DK) droplet growth system are numerically evaluated, and significant effects of accommodation coefficients to raise the supersaturation and droplet number concentration maxima are found. The relationship among the diagnostic solution, the prognostic solution, and the CCN activity spectrum is graphically explained, and a graphical method to obtain the DK prognostic solution is described. The prognostic solution with the Maxwellian system has been derived in a back-tracking manner and the solution is found to agree with that of Twomey in the functional relationship. The effect of parameters in the CCN activity spectrum on the maximum droplet number concentration has been assessed for the Maxwellian system. The prognostic solution of the DK system graphically obtained shows the droplet concentration increase from that of the Maxwellian typically by a factor between 1.5 and 2 with condensation coefficient of 0.03 and thermal accommodation coefficient of 1.0.

Empirical equations of ice crystal growth microphysics for modeling and analysis. II. Fall velocity

Abstract The aerodynamic behavior of ice crystals growing under cloud conditions was theoretically analyzed, and on the basis of this analysis, a time-dependent expression that reasonably fit several experimental data of crystal fall velocity was obtained. To make the expression applicable to outside of the original ranges of the experimental data, further empirical relationships between the Reynolds number and the Best number as well as the correction factor for shape variation were developed.

The maximum rate of homogeneous ice nucleation in air by cooling

Extensive ice nucleation occurs in moist a i r without the help of foreign particles i f cooled strongly. Experimental [1] as well as theoretical [2] evidences indicate that the mechanism is homogeneous condensation of water vapor followed by homogeneous freezing of the formed droplets due to the rate of homogeneous condensation nucleation being faster than that of homogeneous deposition nucleation. Dry ice generates ice crystals by this mechanism [3, 4]. The homogeneous ice nucleation begins when the air temperature lowers to approximately -40°C and the nucleation rate increases as the lowering continues. Experimental evidences, however, suggest that the rate increase rapidly slows down and becomes negligible as the temperature goes below about -60°C [5]. This effect is of interest not only from the viewpoint of ice nucleation kinetics but also for homogeneous ice nucleation technology in weather modification. In this paper, we shall theoretical ly investigate processes that are responsible for occurrence of the virtual nucleation rate plateau as the temperature of coolant lowers.