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  1. The time-dependent freezing rate (TDFR) model here described represents the formation of ice particles by immersion freezing within an air parcel. The air parcel trajectory follows an adiabatic ascent and includes a period in time when the parcel remains stationary at the top of its ascent. The description of the ice nucleating particles (INPs) in the air parcel is taken from laboratory experiments with cloud and precipitation samples and is assumed to represent the INP content of the cloud droplets in the parcel. Time dependence is included to account for variations in updraft velocity and for the continued formation of ice particles under isothermal conditions. The magnitudes of these factors are assessed on the basis of laboratory measurements. Results show that both factors give rise to three-fold variations in ice concentration for a realistic range of the input parameters. Refinements of the parameters specifying time dependence and INP concentrations are needed to make the results more specific to different atmospheric aerosol types. The simple model framework described in this paper can be adapted to more elaborate cloud models. The results here presented can help guide decisions on whether to include a time-dependent ice nucleation scheme or a simpler singular description in models. 
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  2. Model equations used to either diagnose or prognose the concentration of heterogeneously nucleated ice crystals depend on combinations of cloud temperature, aerosol properties, and elapsed time of supersaturated-vapor or supercooled-liquid conditions. The validity of these equations has been questioned. Among many uncertain factors there is a concern that practical limitations on aerosol particle time of exposure to supercooled-liquid conditions, within ice nucleus counters, has biased the predictions of a diagnostic model equation. In response to this concern, this work analyzes airborne measurements of crystals made within the downwind glaciated portions of wave clouds. A streamline model is used to connect a measurement of aerosol concentration, made upwind of a cloud, to a downwind ice crystal (IC) concentration. Four parameters are derived for 80 streamlines: (1) minimum cloud temperature along the streamline, (2) aerosol particle concentration (diameter, D > 0.5 μm) measured within ascending air upwind of the cloud, (3) IC concentration measured in descending air downwind, and (4) the duration of water-saturated conditions along the streamline. The latter are between 38 and 507 s and the minimum temperatures are between −34 and −14 °C. Values of minimum temperature, D > 0.5 μm aerosol concentration, and IC concentration are fitted using the equation developed for ice nucleating particles (INPs) by by DeMott et al. (2010; D10). Overall, there is reasonable agreement among measured IC concentrations, INP concentrations derived using D10's fit equation, and IC concentrations derived by fitting the airborne measurements with the equation developed by D10. 
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  3. Data from both laboratory studies and atmospheric measurements are used to develop an empirical parameterization for the immersion freezing activity of natural mineral dust particles. Measurements made with the Colorado State University (CSU) continuous flow diffusion chamber (CFDC) when processing mineral dust aerosols at a nominal 105% relative humidity with respect to water (RHw) are taken as a measure of the immersion freezing nucleation activity of particles. Ice active frozen fractions vs. temperature for dusts representative of Saharan and Asian desert sources were consistent with similar measurements in atmospheric dust plumes for a limited set of comparisons available. The parameterization developed follows the form of one suggested previously for atmospheric particles of non-specific composition in quantifying ice nucleating particle concentrations as functions of temperature and the total number concentration of particles larger than 0.5 μm diameter. Such an approach does not explicitly account for surface area and time dependencies for ice nucleation, but sufficiently encapsulates the activation properties for potential use in regional and global modeling simulations, and possible application in developing remote sensing retrievals for ice nucleating particles. A calibration factor is introduced to account for the apparent underestimate (by approximately 3, on average) of the immersion freezing fraction of mineral dust particles for CSU CFDC data processed at an RHw of 105% vs. maximum fractions active at higher RHw. Instrumental factors that affect activation behavior vs. RHw in CFDC instruments remain to be fully explored in future studies. Nevertheless, the use of this calibration factor is supported by comparison to ice activation data obtained for the same aerosols from Aerosol Interactions and Dynamics of the Atmosphere (AIDA) expansion chamber cloud parcel experiments. Further comparison of the new parameterization, including calibration correction, to predictions of the immersion freezing surface active site density parameterization for mineral dust particles, developed separately from AIDA experimental data alone, shows excellent agreement for data collected in a descent through a Saharan aerosol layer. These studies support the utility of laboratory measurements to obtain atmospherically relevant data on the ice nucleation properties of dust and other particle types, and suggest the suitability of considering all mineral dust as a single type of ice nucleating particle as a useful first-order approximation in numerical modeling investigations. 
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