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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 [+ or -] 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).sup.1/3][(Re).sup.1/2] = 14.9 [+ or -] 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.

A theoretical framework has been developed describing nonequilibrium formation and maintenance of mixed-phase clouds. The necessary and sufficient conditions required to activate liquid water within a preexisting ice cloud, and thus convert it to mixed phase, are considered for three scenarios: (i) uniform ascent, (ii) harmonic vertical oscillations, and (iii) turbulent fluctuations. The general conditions are the following: 1) First necessary condition: The vertical velocity of an ice cloud parcel must exceed a threshold velocity to activate liquid water. 2) Second necessary condition: The activation of liquid water within an ice cloud parcel, below water saturation, requires a vertical ascent above some threshold altitude to bring the vapor pressure of the parcel to water saturation. Only when the first and second conditions are true do these conditions become sufficient for the activation of liquid water in ice clouds. These required conditions for the generation of mixed-phase cloud are supported by parcel modeling results and analogous conditions for a harmonic oscillation concerning the amplitude and tangential velocity of the parcel motion are proposed. The authors do not assume steadystate conditions, but demonstrate that nonequilibrium evolution of cloud parcels can lead to long-term steady existence of mixed-phase cloud.

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.

Ice particle size distributions (PSDs) can be scaled onto a single exponential distribution for a wide range of observed conditions as demonstrated using data from Atmospheric Research Measurement (ARM) cirrus uncinus, Tropical Rainfall Measurement Mission (TRMM) tropical anvils, and First International Satellite Cloud Climatalogy Project (ISCCP) Regional Experiment (FIRE1) midlatitude cirrus field programs. The successful scaling of the PSDs is the result of the dominance of the aggregation process. The PSD is found to be a function of mean particle size and precipitation rate only. A correlation between precipitation rate and particle mass and fall speed relations is demonstrated and made use of in a semiempirical model of ice cloud that predicts the evolution of PSDs.

This study reports on the evolution of particle size distributions (PSDs) and habits as measured during slow, Lagrangian-type spiral descents through deep subtropical and tropical cloud layers in Florida, Brazil, and Kwajalein, Marshall Islands, most of which were precipitating. The objective of the flight patterns was to learn more about how the PSDs evolved in the vertical and to obtain information of the vertical structure of microphysical properties. New instrumentation yielding better information on the concentrations of particles in the size (D) range between 0.2 and 2 cm, as well as improved particle imagery, produced more comprehensive observations for tropical stratiform precipitation regions and anvils than have been available previously. Collocated radar observations provided additional information on the vertical structure of the cloud layers sampled. Most of the spirals began at cloud top, with temperatures (T) as low as -50[degrees]C, and ended at cloud base or below the melting layer (ML). The PSDs broadened from cloud top toward cloud base, with the largest particles increasing in size from several millimeters at cloud top, to 1 cm or larger toward cloud base. Some continued growth was noted in the upper part of the ML. Concentrations of particles less than 1 mm in size decreased with decreasing height. The result was a consistent change in the PSDs in the vertical. Similarly, systematic changes in the size dependence of the particle cross-sectional area was noted with decreasing height. Aggregation--as ascertained from both the changes in the PSDs and evolution of particle habits as observed in high detail with the cloud particle imager (CPI) probe--was responsible for these trends. The PSDs were generally well-represented by gamma distributions of the form N = [N.sub.0[GAMMA]][D.sup.mu][e.sup.-[lambda][GAMMA]]D that were fitted to the PSDs over 1-km horizontal intervals throughout the spirals. The intercept ([N.sub.0[GAMMA]]), slope ([[lambda].sub.[GAMMA]]), and dispersion ([mu]) values were derived for each PSD. Exponential curves (N = [N.sub.0][e.sup.-[lambda]D]; [mu] = 0) were also fitted to the distributions. The [[lambda].sub.[GAMMA]] values for given spirals varied systematically with temperature as did the values of [lambda] (exponential), and the data generally conformed to values found in previous studies involving exponential fits to size distributions in midlatitude frontal and cirrus layers. Considerable variability often noted in the PSD properties during the loops of individual spirals was manifested primarily in large changes in [N.sub.0[GAMMA]] and [N.sub.0], but [mu], [[lambda].sub.[GAMMA]], and [lambda] remained fairly stable. Temperature is not found to be the sole factor controlling [[lambda].sub.[GAMMA]] or [lambda], but is a primary one. Direct relationships were found between [[lambda].sub.[GAMMA]] and [N.sub.0[GAMMA]], or [[lambda].sub.[GAMMA]] and [mu], for the gamma distributions, and [lambda] and [N.sub.0] for the exponential. The latter relationship was not found as distinctly in earlier studies; observed PSDs in this study had better fidelity with less scatter. The [mu] values changed monotonically with T over the range of temperatures .and were directly related to [N.sub.0[GAMMA]] or [[lambda].sub.[GAMMA]], thereby reducing the number of variables in the PSD functional equation to two. In the upper part of the ML, [N.sub.0], and A continued to decrease, and in the lower part these values began to increase as the largest particles melted. General expressions relating various bulk microphysical, radar, and radiative-transfer-related variables to [N.sub.0[GAMMA]] and [[lambda].sub.[GAMMA]] were developed; they are useful for both tropical and midlatitude clouds. These relationships facilitate the specification of a number of bulk properties in cloud and climate models. The results presented in this paper apply best to temperatures between 0[degrees] and -40[degrees]C, for which the measured radar reflectivities fall in the range of 0 to 25 dB[Z.sub.e].

A key to parameterization of subgrid-scale processes is the probability density function (PDF) of conserved scalars. If the appropriate PDF is known, then grid box average cloud fraction, liquid water content, temperature, and autoconversion can be diagnosed. Despite the fundamental role of PDFs in parameterization, there have been few observational studies of conserved-scalar PDFs in clouds. The present work analyzes PDFs from boundary layers containing stratocumulus, cumulus, and cumulus-rising-into-stratocumulus clouds. Using observational aircraft data, the authors test eight different parameterizations of PDFs, including double delta function, gamma function, Gaussian, and double Gaussian shapes. The Gaussian parameterization, which depends on two parameters, fits most observed PDFs well but fails for large-scale PDFs of cumulus legs. In contrast, three-parameter parameterizations appear to be sufficiently general to model PDFs from a variety of cloudy boundary layers. If a numerical model ignores subgrid variability, the model has biases in diagnoses of grid box average liquid water content, temperature, and Kessler autoconversion, relative to the values it would obtain if subgrid variability were taken into account. The magnitude of such biases is assessed using observational data. The biases can be largely eliminated by three-parameter PDF parameterizations. Prior authors have suggested that boundary layer PDFs from short segments are approximately Gaussian. The present authors find that the hypothesis that PDFs of total specific water content are Gaussian can almost always be rejected for segments as small as 1 km.

A grid box in a numerical model that ignores subgrid variability has biases in certain microphysical and thermodynamic quantities relative to the values that would be obtained if subgrid-scale variability were taken into account. The biases are important because they are systematic and hence have cumulative effects. Several types of biases are discussed in this paper. Namely, numerical models that employ convex autoconversion formulas underpredict (or, more precisely, never overpredict) autoconversion rates, and numerical models that use convex functions to diagnose specific liquid water content and temperature underpredict these latter quantities. One may call these biases the 'grid box average autoconversion bias,' 'grid box average liquid water content bias,' and 'grid box average temperature bias,' respectively, because the biases arise when grid box average values are substituted into formulas valid at a point, not over an extended volume. The existence of these biases can be derived from Jensen's inequality. To assess the magnitude of the biases, the authors analyze observations of boundary layer clouds. Often the biases are small, but the observations demonstrate that the biases can be large in important cases. In addition, the authors prove that the average liquid water content and temperature of an isolated, partly cloudy, constant-pressure volume of air cannot increase, even temporarily. The proof assumes that liquid water content can be written as a convex function of conserved variables with equal diffusivities. The temperature decrease is due to evaporative cooling as cloudy and clear air mix. More generally, the authors prove that if an isolated volume of fluid contains conserved scalars with equal diffusivities, then the average of any convex, twice-differentiable function of the conserved scalars cannot increase.

A physically based method for parameterizing the role of subgrid-scale turbulence in the production and maintenance of supercooled liquid water and mixed-phase clouds is presented. The approach used is to simplify the dynamics of supersaturation fluctuations to a stochastic differential equation that can be solved analytically, giving increments to the prognostic liquid cloud fraction and liquid water content fields in a general circulation model (GCM). Elsewhere, it has been demonstrated that the approach captures the properties of decameter-resolution large-eddy simulations of a turbulent mixed-phase environment. In this paper, it is shown that it can be implemented in a GCM, and the effects that this has on Southern Ocean biases and on Arctic stratus are investigated. [ABSTRACT FROM AUTHOR]

Observations from a Lagrangian spiral descent within altostratus cloud associated with a cold front were used to study the evolution of ice particle spectra by following populations of ice crystals as they fell through the cloud. The flight track was corrected for wind effects and was divided into distinct regions for spatial comparison of ice particle spectra. Analysis of size spectra for particles larger than 800 [[micro]meter] revealed heterogeneity on horizontal scales of 5 km in average particle diameter and concentration. In the temperature range -40 [degrees] to -20 [degrees] C the ice crystal evolution was dominated by diffusional growth, although observations of the evolution of the bimodal size spectra suggested that aggregation was occurring. Between -20 [degrees] and - 10 [degrees] C aggregation dominated evolution.