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,

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

Ice crystals in tropospheric clouds form at altitudes where
temperatures fall below the ice melting point, also known as
supercooled temperatures, and for conditions in which water partial
pressure exceeds the saturation vapor pressure with respect to ice

Laboratory studies are necessary to investigate at which thermodynamic
conditions, i.e., temperature,

Classical nucleation theory (CNT) is currently the only available
physical theory to describe ice nucleation. Simply stated, CNT
quantifies a maximum Gibbs free energy barrier corresponding to the
minimum number of water molecules in a cluster that has to be overcome
to initiate ice nucleation

Immersion freezing can be described by CNT by reducing the free energy
barrier due to the presence of a solid surface. Ice nucleation remains
a stochastic process, but is dependent on the available ice nucleating
surface area,

Different parameterizations of

The major difficulty with a variety of experimental techniques is how
accuracy and uncertainty of

The immersed ISA per droplet is important for experimental derivation
of

We introduce a newly developed model simulation in which ice
nucleation is treated explicitly as a stochastic process applicable
for isothermal and cooling-rate experiments. Previous experimental
results using different experimental methods are simulated and
compared for a wide range of atmospherically relevant
conditions. However, this analysis is applied to laboratory-generated particles only and may not
be applicable to field or natural samples because of the difficulty to separate INPs from others.
Sensitivity studies on frozen fraction data and
experimentally derived

Stochastic immersion freezing simulations (IFSs) are performed to
evaluate the effect of variable ISA on droplet immersion freezing
experiments conducted in the laboratory. As discussed above, different
droplets in a laboratory experiment will possess different ISA. To account for this fact, ISA in
each simulated droplet is sampled from a distribution to mimic this variability. Surface area can be
any real positive value and can change by orders of magnitude. For this reason, a lognormal
distribution can be assumed with the most probable ISA being

The ISA in a single droplet is a measurable quantity with a corresponding
measurement uncertainty. It is unlikely that every droplet prepared in an
immersion freezing experiment has identical ISA. For the same particle type,
there will exist a systematic ISA uncertainty with respect to a particular
droplet preparation technique. This systematic uncertainty is

A record of

An ensemble of IFSs, referred to as a model simulation, requires the
selection of parameters, e.g.,

When a cooling rate is applied in model simulations, droplet freezing
is simulated in discrete temperature intervals and therefore

Resulting calculations from Eqs. (

Cooling-rate-dependent IFSs are performed to evaluate the effect of
stochastic freezing and variable ISA in laboratory immersion freezing
experiments. Again, the ISA for a single droplet is sampled; however, Eqs. (

It is important to note that application of

Summary of parameters used in isothermal model simulations.

Figure

Sensitivity calculations of the unfrozen droplet
fraction,

Model simulations Iso3 and Iso4 are shown in Fig.

In some previous experimental isothermal immersion freezing studies,
the number of liquid droplets and an estimate of the average ISA per
droplet are provided or can be derived. However, the validity of the
assumption that all droplets possess the same ISA is rarely
investigated or quantified. Similarly,

Experimental data by

To further evaluate the validity of the simulations, the parameters
used are compared with experimental conditions given in

The new model simulation presented here based entirely on CNT can
describe freezing experiments by

Simulated and experimentally

Figure

The selection of parameters and ISA distribution used in IsoBR are discussed.

In the model simulation IsoHE1, parameters

Immersion freezing data of

Model simulations IsoDI1-3 of isothermal immersion freezing
experiments by

Simulated and experimentally

Depending on ISA variability, trajectories of model derived

Cooling-rate IFSs were performed to investigate the effects of
variable ISA and

The simulated freezing record is treated as a freezing data set from
which the assumption of identical ISA can be tested. This is
accomplished by re-calculating

Poisson statistics are used to derive upper and lower fiducial limits
of

Figure

Sensitivity calculations of heterogeneous ice
nucleation rate coefficients,

Summary of parameters used in cooling-rate model simulations.

According to CNT, two immersion freezing cooling-rate experiments
conducted at different

Towards warmer

Previous immersion freezing experiments by

Figure

Frozen droplet fractions,

Figure

The differences between

Model simulations CrDI1 and CrDI2 of immersion freezing experiments by

Frozen droplet fractions,

Figure

A major inconsistency between experiment and simulation is shown in Fig.

Model simulations IsoCFDC and IsoLACIS (see Table

Frozen droplet fractions,

Figure

Calculations of

Frozen droplet fractions,

IFSs are used to describe AIDA chamber immersion freezing experiments
applying natural dust by

Figure

Notice that in Fig.

Uncertainty analysis derived from immersion freezing
model simulations. The relative error in the experimentally derived
heterogeneous ice nucleation rate coefficient,

Our results strongly suggest that laboratory immersion freezing
studies should provide accurate estimates of ISA variability in
droplets. We find that simplified assumptions about ISA can result in
misinterpretation and miscalculation of

The model simulation and laboratory data sets investigated here were
performed for INPs immersed in pure water droplets. However, aqueous
solution droplets having

Uncertainty analysis is crucial for the interpretation of laboratory
immersion freezing results. Here we present a quantitative uncertainty
analysis of

The uncertainty due to stochastic freezing is derived by running

Figure

We test our analysis to reproduce experimentally derived
uncertainty. In

Model simulations reproduced observations of immersion freezing due to
illite by

Experimental

Immersion freezing simulations based on a droplet resolved stochastic
ice nucleation process applicable for various types of INPs and
experiments are presented here for both isothermal conditions and
applying a cooling rate,

The sensitivity of

Cooling-rate model simulations were used to test the validity of
assuming uniform ISA. This was accomplished by recalculating

Model simulations in which variable ISA was considered reproduced
laboratory experiments using Arizona test dust (ATD)

A quantitative uncertainty analysis of

Applying too few

For different INP types, the slope of

The greatest source of error stems from RH, or

Droplets in laboratory immersion freezing experiments will not
have identical ISA, but will vary from droplet to droplet (

Surface area and nucleation timescales clearly affect immersion freezing data. Common assumptions of ISA and neglecting the impact of variable experimental timescales will lead to an incomplete experimental accuracy and uncertainty. Consideration of these effects is recommended to narrow the uncertainty in predicting ice crystal formation.

Considering that INPs have variable ISA may impact
atmospheric ice crystal numbers. For a broad surface area distribution of
INPs, ice nucleation should occur over a broader range of time and
temperature, when compared with a narrow INP surface area distribution. This
results in greater ice particle production at warmer temperatures, important
for mixed phase cloud formation and their evolution. We suggest that field
measurements determine and consider the entire aerosol size distribution as
a source of INPs for implementation of a stochastic, time-dependent ice
nucleation process characterized by

Our findings concerning laboratory immersion freezing experiments emphasize
the importance of setting constraints on the minimum number of droplets and
experimental trials that need to be employed for improved characterization of
ISA per droplet. The results presented here resolves commonly used
assumptions that contribute to additional uncertainty in predicting immersion
freezing data for model implementation. The simulations use ABIFM, shown to
be valid for various INP types. We demonstrate that the ABIFM can reproduce
immersion freezing by mineral dust for many vastly different experimental
designs and measurement methods. Laboratory derived

This research was supported by the US Department of Energy, Office of Science (BER), under award number DE-SC0008613. Edited by: H. Grothe