Abstract
Abstract. Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets, droplets in a continuous-flow diffusion chamber (CFDC), the Leipzig aerosol cloud interaction simulator (LACIS), and the aerosol interaction and dynamics in the atmosphere (AIDA) cloud chamber. Observed time-dependent isothermal frozen fractions exhibiting non-exponential behavior can be readily explained by this model considering varying ISA. An apparent cooling-rate dependence of Jhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling-rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. The model simulations allow for a quantitative experimental uncertainty analysis for parameters Ntot, T, RH, and the ISA variability. The implications of our results for experimental analysis and interpretation of the immersion freezing process are discussed.
Highlights
Ice crystals in tropospheric clouds form at altitudes where temperatures fall below the ice melting point, known as supercooled temperatures, and for conditions in which water partial pressure exceeds the saturation vapor pressure with respect to ice (Pruppacher and Klett, 1997; Hegg and Baker, 2009)
A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable INP surface area (ISA) per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T )
This implies that a laboratory experiment using a small Ntot, is statistically less significant compared to an experiment with greater Ntot
Summary
Ice crystals in tropospheric clouds form at altitudes where temperatures fall below the ice melting point, known as supercooled temperatures, and for conditions in which water partial pressure exceeds the saturation vapor pressure with respect to ice (Pruppacher and Klett, 1997; Hegg and Baker, 2009). The ABIMF is a holistic and computationally efficient description of the immersion freezing process for prediction of ice nucleation for atmospherically relevant conditions and applicable for a variety of experimental methods, including the droplet-on-substrate approach (Zobrist et al, 2007; Knopf and Forrester, 2011; Alpert et al, 2011a, b; Iannone et al, 2011; Murray et al, 2011; Broadley et al, 2012; Rigg et al, 2013), oil-encased droplets (Murray et al, 2011; Broadley et al, 2012; Wright and Petters, 2013), differential scanning calorimetry (Marcolli et al, 2007; Pinti et al, 2012), and continuous-flow diffusion (Rogers et al, 2001; Archuleta et al, 2005; Hartmann et al, 2011; Kulkarni et al, 2012; Wex et al, 2014) These previous studies represent a subset of a much broader selection of experimental methods and designs. A rigorous uncertainty analysis of the ice nucleation kinetics for typical ranges in experimental conditions is presented and discussed for laboratory application
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