Abstract

The primary goal of this study is to derive ice particle terminal velocities from micron to centimeter sizes and for atmospheric pressures covering the range 200–1000 hPa from data spanning a wide range of locations, temperatures, and altitudes and to parameterize the results for use in cloud through cloud models. The study uses data from 10 field programs spanning the temperature range −86° to 0°C and encompassing a total of about 800 000 km of cloud horizontal pathlengths and includes measurements of ice particle size distributions (PSDs) and direct measurements of the ice water content (IWC). The necessary ice particle variables are derived using variables that are interconnected rather than varying independently from observations reported in the literature. A secondary goal of the study is to quantify the properties of ice cloud particle ensembles over a wide range of temperatures to further the understanding of how ice particle ensembles and ice clouds develop.

Functional forms for the PSDs and mass– and area–dimensional relationships are developed from the observations and summarized in a table. The PSDs are found to be nearly exponential at temperatures from about −40° to −10°C although deviations from exponentiality are noted outside of this range. It is demonstrated that previous pressure-dependent corrections to ice fall speeds lead to overestimated terminal velocities for particles smaller than 1 mm, particularly so for sizes below 100 μm, with consequent effects on modeled lifetimes of cold ice clouds.

Abstract

Using airborne data from several recent field projects, the authors have taken another look at the properties of exponential ice particle size distributions (PSDs) when the PSDs are broad. Two primary questions are addressed: for what ranges of ice water content (IWC) and equivalent radar reflectivity (Z_e ) do exponentials produce accurate estimates of these higher moments of the PSD, and why is there a lower limit to the value to the slope of exponential fits to PSD, λ, as has been found from airborne measurements?

Earlier studies at temperatures primarily above −10°C have found that λ measured in snow during spiral descents through deep ice cloud layers decreases to about 9 cm⁻¹ and then remains there. Several physical processes have been advanced to explain these observations. If reliable, the data could be used to improve retrieval of ice cloud properties through remote sensing and for cloud model representations of ice cloud microphysical properties.

For data acquired from 2D probes, recent evidence indicates shattering of large ice particles ahead of, but attributable to, the probe’s sensing area, generating small crystals that the probe then senses. Shattered artifacts have been objectively removed from the data. Comparisons of size distributions before and after removal of suspected shattered particles suggest that the reported minimum may have been due to shattering and/or other instrument errors.

The revised PSDs indicate that for λ < 40 cm ^{− 1}, 0.1 g m⁻¹ < IWC, and 5 dB < Z_e , moments two (IWC) through four (Z_e ) of the PSD are dominated by particles larger than a few hundred microns. Analytical representations with more variables than exponentials (e.g., gamma PSD) are not required to accurately derive these moments from the PSD. In these situations, the intercept parameter of the exponential PSD, N ₀ ≈ 1 cm⁻⁴, is 5 to 30 times larger than assumed earlier.

Abstract

The detailed microphysical processes and properties within the melting layer (ML)—the continued growth of the aggregates by the collection of the small particles, the breakup of these aggregates, the effects of relative humidity on particle melting—are largely unresolved. This study focuses on addressing these questions for in-cloud heights from just above to just below the ML. Observations from four field programs employing in situ measurements from above to below the ML are used to characterize the microphysics through this region. With increasing temperatures from about −4° to +1°C, and for saturated conditions, slope and intercept parameters of exponential fits to the particle size distributions (PSD) fitted to the data continue to decrease downward, the maximum particle size (largest particle sampled for each 5-s PSD) increases, and melting proceeds from the smallest to the largest particles. With increasing temperature from about −4° to +2°C for highly subsaturated conditions, the PSD slope and intercept continue to decrease downward, the maximum particle size increases, and there is relatively little melting, but all particles experience sublimation.

Abstract

Many microphysical process rates involving snow are proportional to moments of the snow particle size distribution (PSD), and in this study a moment estimation parameterization applicable to both midlatitude and tropical ice clouds is proposed. To this end aircraft snow PSD data were analyzed from tropical anvils [Tropical Rainfall Measuring Mission/Kwajelein Experiment (TRMM/KWAJEX), Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE)] and midlatitude stratiform cloud [First International Satellite Cloud Climatology Project Research Experiment (FIRE), Atmospheric Radiation Measurement Program (ARM)]. For half of the dataset, moments of the PSDs are computed and a parameterization is generated for estimating other PSD moments when the second moment (proportional to the ice water content when particle mass is proportional to size squared) and temperature are known. Subsequently the parameterization was tested with the other half of the dataset to facilitate an independent comparison. The parameterization for estimating moments can be applied to midlatitude or tropical clouds without requiring prior knowledge of the regime of interest. Rescaling of the tropical and midlatitude size distributions is presented along with fits to allow the user to recreate realistic PSDs given estimates of ice water content and temperature. The effects of using different time averaging were investigated and were found not to be adverse. Finally, the merits of a single-moment snow microphysics versus multimoment representations are discussed, and speculation on the physical differences between the rescaled size distributions from the Tropics and midlatitudes is presented.

Abstract

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.

Abstract

This two-part study attempts to find appropriate mass dimension and terminal velocity relationships that, when considered together with particle size distributions (PSD), agree with coincident measurements of ice water content (IWC), and with variables related to higher moments such as the mean mass-weighted fall speed. Reliable relationships are required for improving microphysical parameterizations for weather forecast models and developing methods for evaluating them, subjects addressed in detail in Part II of this study.

Here, a range of values from 1.5 to 2.3 is assumed for the exponent b in the mass dimension relationship, m = aD^b , where D is the maximum particle dimension, to bound its likely value for sizes above about 100 μm. Measured IWC and size spectra are used to find appropriate values for the coefficient a. It is demonstrated that all values of the exponent b, with appropriate a coefficients, can fit the IWC measurements. Coincident information on particle cross-sectional areas with the m(D) relationships is used to develop general fall velocity relationships of the form V_t = AD^B . These assessments use five midlatitude, synoptically generated ice layers, and 10 low-latitude, convectively generated ice cloud layers, spanning the temperature range from −60° to 0°C.

The coefficients a and A and exponent B are represented in terms of the exponent b and are shown to be temperature-dependent for the synoptic clouds and relatively independent of it in the convective clouds, a result of particle mixing through the cloud column. Consistency is found with earlier results and with analytic considerations. It is found that the fall velocity is inversely proportional to the air density to approximately the exponent 0.54, close to values assumed in earlier studies.

Abstract

Anvils produced by vigorous tropical convection contribute significantly to the earth’s radiation balance, and their radiative properties depend largely on the concentrations and sizes of the ice particles that form them. These microphysical properties are determined to an important extent by the fate of supercooled droplets, with diameters from 3 to about 20 microns, lofted in the updrafts. The present study addresses the question of whether most or all of these droplets are captured by ice particles or if they remain uncollected until arriving at the −38°C level where they freeze by homogeneous nucleation, producing high concentrations of very small ice particles that can persist and dominate the albedo.

Aircraft data of ice particle and water droplet size distributions from seven field campaigns at latitudes from 25°N to 11°S are combined with a numerical model in order to examine the conditions under which significant numbers of supercooled water droplets can be lofted to the homogeneous nucleation level. Microphysical data were collected in pristine to heavily dust-laden maritime environments, isolated convective updrafts, and tropical cyclone updrafts with peak velocities reaching 25 m s⁻¹. The cumulative horizontal distance of in-cloud sampling at temperatures of −20°C and below exceeds 50 000 km. Analysis reveals that most of the condensate in these convective updrafts is removed before reaching the −20°C level, and the total condensate continues to diminish linearly upward. The amount of condensate in small (<50 μm in diameter) droplets and ice particles, however, increases upward, suggesting new droplet activation with an appreciable radiative impact. Conditions promoting the generation of large numbers of small ice particles through homogeneous ice nucleation include high concentrations of cloud condensation nuclei (sometimes from dust), removal of most of the water substance between cloud base and the −38°C levels, and acceleration of the updrafts at mid- and upper levels such that velocities exceed 5–7 m s⁻¹.

Abstract

The mass–dimensional relationship put forth by Brown and Francis has been widely used for developing parameterizations for representing ice cloud microphysical properties. This relationship forms the cornerstone for past and forthcoming retrievals of ice cloud properties from ground-based and spaceborne active and passive sensors but has yet to be rigorously evaluated. This study uses data from six field campaigns to evaluate this mass–dimensional relationship in a variety of ice cloud types and temperatures and to account for the deviations observed with temperature and size, based on properties of the ice particle ensembles. Although the Brown and Francis relationship provides a good match to the observations in a mean sense, it fails to capture dependences on temperature and particle size that are a result of the complex microphysical processes operative within most ice cloud layers. Mass–dimensional relationships that provide a better fit to the observations are developed.

Abstract

The ventilation factor and capacitance used in numerical models to represent ice crystal aggregates directly affects the growth rate of the ice crystal aggregates, and consequently the sink of atmospheric water vapor. Currently, numerical models that prognose ice water content (IWC) and water vapor mixing ratio represent the capacitance and ventilation factor of precipitation-sized particles with simplified geometries, such as hexagonal plates. The geometries of actual precipitation-sized particles are often more complex, and a test of the values being employed is needed. Aircraft observations obtained during a Lagrangian spiral descent through the sublimation zone of a tropical anvil cloud have been used to determine an estimate of combined dimensionless capacitance and ventilation factor for the nonpristine geometries exhibited by ice crystal aggregates. By combining measurements of bulk ice water content, the particle size distribution, and environmental subsaturation, the change in ice water content was modeled throughout the spiral descent and compared with observations of the change in ice water content. Uncertainties resulting from potential systematic biases in the measurements and parameterizations used in the analysis were investigated with sensitivity tests. Most of the uncertainty was related to an assumed maximum potential bias in the measurement of IWC of ±45%. The resulting combined ventilation factor and dimensionless capacitance value was 1.3 (with a range of 0.6–1.9, defined by 68% of sensitivity test trials) for a particle size–weighted mean value of (Sc)^1/3(Re)^1/2 = 14.9 ± 1.7, where Sc is the Schmidt number and Re is the Reynolds number. Results from commonly adopted combinations of ventilation factor relations and capacitances are compared with the observations presented here, and, finally, surrogate dimensionless capacitances are suggested that when combined with commonly used ventilation factor relations are consistent with the results presented herein.

Abstract

The possibility is suggested of estimating particle size distributions (PSD) solely based on the bulk quantities of the hydrometeors. The method, inspired by the maximum entropy principle, can be applied to any predefined general PSD form as long as the number of the free parameters is equal to or less than that of the bulk quantities available. As long as an adopted distribution is “physically based,” these bulk characterizations can recover a fairly accurate PSD estimate.

This method is tested for ice particle measurements from the Tropical Composition, Cloud and Climate Coupling Experiment (TC4). The total particle number, total mass, and mean size are taken as bulk quantities. The gamma distribution and two distributions obtained under the maximum entropy principle by taking the size and the particle mass, respectively, as a restriction variable are adopted for fit. The fitting error for the two maximum entropy–based distributions is comparable to that of a standard direct fitting method with the gamma distribution. The same procedure works almost equally well when the mean size is removed from the constraint, especially for an exponential distribution.

The results suggest that the total particle number and the total mass of the hydrometeors are sufficient for determining the PSD to a reasonable accuracy when a “physically based” distribution is assumed. In addition to the in situ cloud measurements, remote sensing measurements such as those from radar as well as satellite can be adopted as physical constraints. Possibilities of exploiting different types of measurements should be further pursued.