We present new measurements of the time dependence of the ice-nucleating ability of a wide range of materials including the minerals montmorillonite and kaolinite, the biological proxy ice nuclei Icemax, and flame soot generated from the incomplete combustion of ethylene gas. We also present time dependence for ambient ice nuclei collected from rainwater samples. Our data show that the time dependence for all materials studied here is weak, suggesting that the modified singular approximation is valid over the range of times and temperatures encountered for mixed phase clouds.
 Immersion mode ice nuclei (IN) are particles that catalyze ice formation in supercooled cloud droplets at temperatures warmer than the homogeneous freezing temperature. In the atmosphere the ice phase plays an important role in tropical rain formation [Lau and Wu, 2003] and changes in ice nuclei concentrations are suspected to indirectly perturb the radiative budget at the top of the atmosphere [Lohmann and Feichter, 2005]. For example, global model simulations suggest that an order of magnitude increase in IN concentrations may lead to a net cloud radiative forcing increase of 1 W m−2 [DeMott et al., 2010]. This sensitivity is comparable in magnitude to the current Intergovernmental Panel on Climate Change estimate of the cloud albedo effect [Intergovernmental Panel on Climate Change, 2007]. Accurate quantification of the various indirect effects of ice nuclei on clouds and climate require a better understanding of the sources, evolution, and sinks of atmospheric ice nuclei, as well as an improved understanding of ice nuclei mechanisms at the process level.
 Atmospheric IN concentrations are typically measured using continuous flow cloud chambers. These chambers expose aerosol to a specified temperature and ice supersaturation and count the number of particles that form ice [e.g., Stetzer et al., 2008; Kanji and Abbatt, 2009; Petters et al., 2009; Friedman et al., 2011; Hartmann et al., 2011]. Continuous flow cloud chambers have a long history and are frequently deployed in ground-based [e.g., Prenni et al., 2009; Chou et al., 2011] and aircraft-based [e.g., Rogers et al., 2001; Avramov et al., 2011] field campaigns. These instruments utilize a short residence time for the aerosols prior to ice detection (a few seconds) relative to residence times in clouds (minutes to hours). Short residence times are potentially problematic because classical nucleation theory holds that heterogeneous freezing nucleation is described by a nucleation rate. From a process perspective this implies that measured ice nucleation concentrations are tied to the applied residence time. If nucleation is time-dependent and not all available IN nucleated within the time scale of the experiment, longer residence times would result in larger measured IN concentrations. Instruments with short residence times may then lead to an underestimate of the available ambient IN population. Whether or not such an underestimate is important for the development of parameterizations that are suitable for atmospheric modeling [e.g., DeMott et al., 2010; Phillips et al., 2013] will depend on the relative sensitivities of the nucleation rate to time and supercooling temperature.
 The relative sensitivities of time versus temperature in heterogonous freezing nucleation have been debated since the beginning of systematic studies on ice nucleation. The two main competing descriptions are classical nucleation theory, which holds that ice formation is described via a nucleation rate on an otherwise homogeneous surface, and singular models, which hold that ice nucleation proceeds independently of time on active sites at a given deterministic supercooling temperature. Several recent studies have reanalyzed these models to better understand these seemingly contradictory descriptions [Niedermeier et al., 2011; Broadley et al., 2012; Murray et al., 2012; Wright and Petters, 2013; Sear, 2013; Ervens and Feingold, 2012]. While these studies differ widely in approach and methodology, there appears to be consensus that (1) the cooling rate dependence or time dependence of the freezing process is weak relative to the temperature dependence, (2) the slope of nucleation rate versus temperature will govern the time dependence of the process, and (3) the heterogeneity of particle surfaces modulates the apparent cooling rate trends in experimental studies.
 To date, relatively few studies have systematically investigated the role of time for ice nucleation via laboratory experiments [Welti et al., 2012; Broadley et al., 2012; Murray et al., 2012, and references therein; Hoose and Möhler, 2012, and references therein; Wright and Petters, 2013]. To the best of our knowledge the previous studies have focused on proxy aerosol types such as soil samples, various test dusts, black carbon, or silver iodide [Hoose and Möhler, 2012; Murray et al., 2012; Phillips et al., 2013]. In previous work, we introduced a cold stage droplet freezing assay setup that can perform steady cooling of bulk samples at rates as slow as 0.01 K min−1 [Wright and Petters, 2013]. In that study we demonstrate that for Arizona Test Dust (ATD) aerosol, the dependence of the average number of freeze events on the cooling rate is weak. Further, we show through model simulations that the random variability of the observed freezing temperature is tied directly to the slope of the nucleation rate with temperature. Droplet freezing assays provide two types of experiments to characterize the time dependence of ice nucleation: repeated freezing and thawing and tracking the freezing temperature of individual droplets at the same cooling rate and repeated freezing and thawing of a bulk sample and tracking the temperature where a fixed fraction of the droplet dispersion has induced freezing. In this study we apply this methodology to different classes of IN to test whether the conclusions about the time dependence reached for ATD apply for atmospheric IN. The additional substances tested are the minerals kaolinite and montmorillonite, the proteinaceous IN contained in Icemax, black carbon sampled from a diffusion burner, and multiple rainwater samples containing an unknown mix of ambient IN.
 To motivate our selection of materials and the specific objective for this study we briefly summarize the main theoretical arguments outlined in detail in Wright and Petters . Guided by classical nucleation theory, the temperature dependence of the nucleation rate J [#/s] for a single active site can be parameterized as
where Tc is the characteristic temperature of the active site, T is the temperature, and u is a measure of the slope of the temperature dependence. For large values of u, J (T) approaches a step function and a droplet with an ice nucleus inclusion will appear to freeze deterministically at temperature Tc. Values of u can be inferred for individual samples via experiment using cold stage assays. From a theoretical perspective, u depends on properties of the fluid (e.g., latent heat, surface tension, or activation energy for self-diffusion) and the substrate that catalyzes ice formation (e.g., the compatibility parameter of the active site, adsorbed water in equilibrium with the germ, or size of the active site). A priori, it is unclear whether u is determined mostly by fluid properties or substrate properties. Furthermore, u might depend on characteristic temperature of the active site.
 The main motivation for this study is to determine to what extent u, and in turn the time dependence of the freezing process, is dependent on the properties of a particular active site. Therefore, the materials discussed in this study include a broad selection of possible types of active sites that also span a range of characteristic temperatures between –5°C and –35°C. For example, biological particles within the commercially available product Icemax originate from freeze-dried, irradiated, non-plant pathogenic strains of the bacterium Pseudomonas syringae [manufacturer specifications]. The molecular mechanism leading to ice nucleation of these particles is not yet fully understood, but it requires a protein conformation that leads to hydrogen bonds with the ice and that ice nucleation activity is aided by the cell membrane [Lagriffoul et al., 2010]. A different mechanism is expected for graphitic soot particles, where ice nucleation is thought to proceed on sites with enhanced surface concentration of chemical groups [Gorbunov et al., 2001] or inside micropores or mesopores of the graphitic structure [Persiantseva et al., 2004]. A similar yet distinct mechanism is at play for mineral dust particles, where crystal defects in substrate [Vonnegut, 1947] or pores, cracks, or ledges etched on the surface [Knight, 1979; Sear, 2011] are thought to serve as sites for ice nucleation. Finally, another mechanism for nucleation is the self-arrangement of liquid alcohol (e.g., nonadecanol) monolayers on water droplets such that the organic functional group associated with the carbon chain mimics the crystalline structure of ice upon which the nucleus forms [Gavish et al., 1990; Zobrist et al., 2007]. The compounds for which experimental data will be presented include samples from each of these four classes (minerals/ash: montmorillonite, kaolinite, ATD, soil, and volcanic ash; biological particles: Icemax; graphitic particles: flame soot and carbon black; and alcohol monolayers: nonadecanol).
 In addition to the proxy materials, ice nuclei contained in rainwater samples are analyzed to obtain a survey of different types of active sites for ambient IN. The atmospheric water cycle is used as a cloud system scale particle into liquid sampling system where ambient ice nuclei are incorporated into the precipitation via nucleation scavenging and/or washout processes. Here the purpose of using rainwater samples is to collect particles that may serve as potential ice nuclei in the atmosphere. Whether or not these nuclei participated in actual cold cloud processes that lead to the formation of the particular rain event studied is not considered here. The rainwater samples contained a mixture of dissolved (water soluble) aerosol components, presumably a mixture of sulfates, nitrates, and organic compounds as well as undissolved aerosol components that may or may not serve as IN (e.g., dust, black carbon, or pollen). The concentration of dissolved solutes in rainwater is similar to that of cloud water since rain arises via collision/coalescence process [Köhler, 1936; Bormann et al., 1989]. However, aqueous phase production of sulfates and organics as well as material added by scavenging may produce rainwater that contains more solutes relative to cloud water samples. Nevertheless, the aqueous medium is not expected to be too dissimilar to that of cloud and drizzle droplets. Thus, the immersion mechanisms of ice nucleation on active sites for these particles should approximate conditions in clouds, although some changes in characteristic temperature due to homogenization of the cloud/rainwater matrix during collection may have occurred. These changes arise from the sometimes detrimental and sometimes absent effect of solute coatings on IN activity [Chernoff and Bertram, 2010; Sullivan et al., 2010a, 2010b; Niedermeier et al., 2011]. Rainwater samples were collected during the spring/summer season in the South Eastern U.S. and may not have contained all types of active sites, but the data provide an initial survey over the range that might be expected for ambient IN. Filtered rainwater followed by resuspension of particles collected on the filter is used to increase the likelihood to sample active sites that only require minimal amounts of supercooling to induce freezing.
 Because the main objective of this study is to sample a diversity of active sites, fully quantitative relationships between the number/surface area/volume/mass concentration of IN active material and ice nucleation spectra are not investigated. For carefully characterized dust samples, these can be inferred from auxiliary data [Wright and Petters, 2013]. For black carbon and rainwater samples, the number of residues in the bulk is unknown. Therefore, the data here are not suitable for interpretations of active site density per unit surface area.
3.1 Chemicals Used
 Squalene (≥99% purity; Acros Organics); sulfuric acid analytical grade (Fischer Scientific); isopropyl alcohol (laboratory grade; Fisher Chemical); AquaSil Siliconizing Fluid (TS-42799; Thermo-Scientific); Arizona Test Dust (Powder Technology, Inc. ISO 12103-1, A4 Coarse); kaolinite (Clay Mineral Society, Kaolin KGa-2); montmorollonite (Clay Mineral Society, Na-Montmorillonite (Wyoming) SWy-2); Icemax (Johnson Controls); ultrapure water (in-house generated, 18.2 MΩ resistivity, < 5 ppm of organic content); and ethylene gas (CP grade; Air Gas). Detailed information on the chemical composition of the minerals provided by the manufacturer is summarized in the supplement. All purchased chemicals were used without further purification. Black carbon (flame soot) was generated by incomplete combustion of ethylene gas using a Santoro-type diffusion burner [Santoro et al., 1983] that is similar in design to that of Khalizov et al. . The burner was operated with 22 L min−1 filtered air flow and 0.4 L min−1 ethylene fuel flow. A Swagelok-Tee fitting was placed approximately 50 cm above the flame to sample the soot-rich air flow onto Nucleopore track-etched membrane filters (200 nm pore size) at a flow rate of 5 L min−1 for a period of 4 h, which yielded ~4 mg of black carbon. The filter was placed in a vial along with 3 ml of ultrapure water and sonicated, resulting in a thick suspension of black carbon and water. Before further processing, the suspension was shaken to minimize adherence to the walls.
3.2 Sample Collection and Preparation
 All glassware was cleaned using an acid bath (concentrated H2SO4) followed by a rinse with ultrapure water and drying at ~100°C. Nonrainwater aqueous suspensions ranging from 0.1 to 1% w/w were prepared from the bulk chemicals. For flame soot the weight fraction of soot in the droplets may have differed slightly from the bulk due to difficulty keeping the suspension well mixed due to the hydrophobic character of the sample.
 Rainwater samples were collected during the spring/summer season by placing glass dishes on the roof of Jordan Hall, a five story building located in an urban setting in Raleigh, North Carolina. Approximately 10 ml of the rainwater was set aside to be analyzed in unfiltered measurements. The remaining rainwater (~200 ml) was filtered through a 200 nm pore size Nucleopore filter. Residues with diameters > ~200 nm are expected to be captured on the filter surface. The filter was then placed in a clean vial where 2 or 3 ml of ultraclean water was added and the vial was sonicated for 3 min. The rainwater extracts thus contain a mix of larger particles that are preconcentrated at ~1:10 to 1:100 level, depending on the total amount filtered. Atmospheric IN concentrations are correlated with particles with diameters greater than 500 nm [DeMott et al., 2010]. Therefore, the preconcentrated filter extracts are expected to contain a selection of IN representative of those present in the atmosphere. The resulting sample extract was used in filtered rainwater measurements.
3.3 Ice Nuclei Measurement
 Ice nuclei spectra were measured on a cold stage freezing assay described in detail in Wright and Petters . Briefly, an aliquot of ~15 µl of the aqueous water suspension (see sample preparation) is transferred into a clean vial and covered with 2 ml of squalene. The squalene/water mixture is either shaken by hand or with the help of a vortex mixer to create an oil/water suspension with droplet diameters ranging between 50 and 300 µm in diameter. Particles contained in each droplet are considered to be immersed, although migration of inclusions to the droplet/oil interface is possible, especially for hydrophobic black carbon particles. The oil/water suspension is poured into an aluminum dish with a silanized glass cover slip placed on the bottom. Water droplets are allowed to settle to the glass surface. The squalene oil matrix surrounding the droplets isolates individual droplets from the gas phase and prevents the freezing of one droplet, inducing further freezing on other droplets. Subsequent to the settling, the dish is cooled at a preset linear rate starting at −5°C for all experiments except those samples containing Icemax which were started at +2°C. During cooling, the droplets are frequently imaged using a stereomicroscope outfitted with a high-resolution digital camera. The temperature on the surface of the slide is calibrated against the temperature of the aluminum block and is recorded via a LabView data acquisition system. Freeze events are detected by a change in the grey-scale image of the droplet and are extracted with the help of user-guided data-processing software.
 Cleanliness of the experimental procedures was ensured by periodically testing the system with ultrapure water [Wright and Petters, 2013] and inspection of the freezing spectra against expected values for homogeneous freezing [Langham and Mason, 1958]. For refreeze experiments the temperature of the dish was cooled to a preset temperature (e.g., −5°C) at the fastest possible rate and held steady for 90 sec. Then the dish was cooled at a rate of 1 K min−1. After all the droplets were frozen, the dish was warmed to 3°C until the drops were thawed. This freeze/thaw cycle was repeated 40 times. The freezing temperatures of individual drops were tracked across all 40 cycles. The standard deviation of the freezing temperature σrefreeze for individual droplets is directly proportional to the slope parameter of the nucleation rate with temperature defined in equation ((1)) (u) and the cooling rate dependence of the population median freezing temperature [c.f. Wright and Petters, 2013]. In the limit of a time-independent model, σrefreeze = 0, i.e., deterministic freezing where the drop always freezes at its characteristic temperature Tc.
3.4 Statistical Analysis
 Freezing temperatures of individual drops can change due to random and nonrandom variability. Systematic changes can occur if the nucleus migrates to or away from the droplet interface or [Shaw et al., 2005; Durant and Shaw, 2005; Fornea et al., 2009] if the surface changes after a freeze event [Vali, 2008; Sear, 2011; Wang et al., 2012]. We used the autocorrelation test described in Wright and Petters  to identify droplets that exhibit nonrandom variability. Briefly, the test computes the Pearson correlation coefficient R for k lags and determines the probability that the thus found set of R(k) could be generated from a completely random data set. For a set comprising 40 freeze/thaw cycles, this autocorrelation test successfully identifies samples that exhibit systematic changes, e.g., have a single step change in the freezing temperature [cf. Durant and Shaw, 2005, Figure 1; Wright and Petters, 2013, Figure 3].
3.5 Experimental Uncertainties
 Temperature uncertainties arise due to the experimental setup. During standard operation, a thermistor measures the temperature of the aluminum dish and not the temperature of the glass slide and the overlying squalene/water suspension. Calibration measurements were taken by submersing a second thermistor into the squalene and measuring the temperature difference between the aluminum and the squalene during a typical cooling cycle. A cooling rate dependent empirical correction is applied to the thermistor temperature to yield the temperatures reported within this paper. Reproducibility of homogeneous freezing suggests a remaining temperature uncertainty of ~1°C. Because the drops are resting on a solid surface and because the interface is oil/water instead of air/water, it is possible that the substrate could be the source of ice nucleation rather than particles contained within the sample water. This, however, is unlikely as homogeneous freezing can be routinely observed with pure water samples. Some ice nuclei have different nucleation rates depending on whether they are in the immersion or contact mode [Fornea et al., 2009]. The experimental setup presented here is unable to determine whether the sample particles are fully immersed in the water droplets or whether they exist at the oil/water interface and switching between the modes may have enhanced the variability in freezing temperatures between cycles. If this was the case, our data would overestimate the cooling rate/time dependence of the process, i.e., the actual cooling rate dependence would be less than what we report in this work. In previous studies, some materials exhibit cooling rate dependence only at high particle concentrations [Broadley et al., 2012]. This may be due to inclusion of multiple IN/active sites competing for nucleation inside a single droplet. This effect may have resulted in a bias of the filtered rainwater and black carbon experiments, since these samples relied on high loadings to sample active sites that induce freezing at temperatures > −25°C. Again, if true, the overall impact is that the actual cooling rate dependence is weaker than suggested by the data presented in this study.
 Results for the proxy IN substances and rainwater samples are summarized in Figures 1 and 2. Figures 1a–1d and 2a–2d show the freezing temperature of select individual droplets for each of the forty cooling cycles. For each substance two example drops that show random variability (Figures 1a–1b and 2a–2b) and two example drops that exhibit systematic changes (Figures 1c–1d and 2c–2d) were selected. Drops in rows a, b and rows c, d pass and fail the autocorrelation test, respectively. Failing the autocorrelation test may be due to a marked step change in the freezing temperature (e.g., Figures 1c,1; 1d,2; or 2c,3 drops), due to systematic gradual changes occurring during successive cooling cycles (e.g., Figures 1c,5 or 1d,5 drops) or due to a combination of both (e.g., Figures 1c,2; 1c,4; or 2d,3 drops). For each sample, a set of ~100–500 drops with cooling cycle data were analyzed. The behavior of each droplet is described by three statistical parameters, the individual drop average freezing temperature, the standard deviation of the individual drop average freezing temperature, and a flag that indicates whether the drop passes or fails the autocorrelation test. These data are summarized in Figures 1e and 2e. Gray shaded droplets failed the autocorrelation test. The data show that (1) drops with average freezing temperatures ranging between −4°C and −33°C were sampled; (2) drops that pass the autocorrelation test have slightly lower standard deviation in the freezing temperature is compared to the overall population; (3) some compounds are dominated by droplets that do not pass the autocorrelation test (e.g., Icemax and flame soot), while other samples have larger proportions of droplets with random freezing behavior; and (4) with the exception of montmorillonite, a large majority of drops that did pass the autocorrelation test have standard deviations of the freezing temperature that do not exceed 1°C.
 Figures 1f and 2f summarize results showing the variation of the population median freezing temperature with the cooling rate of the sample. For these experiments a fresh suspension of droplets was prepared, i.e., they present a different population of drops compared to Figures 1a–1e and 2a–2e. Differences in the droplet size distribution and random placement of IN within the droplets explains why the population median freezing temperature at the cooling rate of 1 K min−1 may slightly differ from the population median implied in Figures 1e and 2e. However, the population of drops is identical for each of the cooling rates graphed for an individual sample. This gives a total run time for the combined cooling rate experiment of up to 4 days. A cooling rate of 0.01 K min−1 corresponds to 50 h for 30 K of cooling and thus brackets the expected upper end residence times for IN within clouds. The number of cooling rates and span of the experiments varied between samples due to time constraints. The data show that for Icemax the population median freezing temperature only weakly increases with decreasing cooling rate/increasing residence time. The strongest cooling rate dependence is seen for kaolinite, montmorillonite, and flame soot and the change in the median freezing temperature for these samples approaches 3 K when extending the experiment from 30 min (~1 K min−1) to 50 h (~ 0.01 K min−1). The rainwater sample from 4 July 2012 showed the strongest cooling rate dependence for ambient IN, and medium freezing temperatures did not change more than1 K over this range.
 Figure 3 summarizes the population average of the standard deviation (σrefreeze) values (Figures 1e and 2e) for the various ice nucleation samples. Only drops that passed the autocorrelation test were included in the analysis. The various ice nuclei samples are sorted along the abscissa by the population average freezing temperature to give an indication of the typical characteristic temperatures of the active sites sampled. Additional data for filtered and unfiltered rain samples not shown in Figure 2 are also included on the graph. For the filtered rain, the mean refreeze temperature for each rain event fell within 5° of each other with a spread in the standard deviation of 0.46°C. The unfiltered rain samples had a mean freezing temperature within 6.5°C of each other and a standard deviation of 0.43°C. Across all experiments performed, the average freezing temperatures of the drops varied from about −5°C for Icemax to −30°C for 6 August unfiltered rain and the average of the standard deviation of the freezing temperatures (σrefreeze) ranged from about 0.4 to 1.3°C. For individual drops, the observed σrefreeze values across all materials in the study ranged from 0.1°C for Icemax to as high as 2.9°C for ATD and are within the range of values of other materials reported in previous studies. Specifically, soil was characterized to have an average ~1°C [Vali, 2008]. The standard deviation in freezing temperature for volcanic ash changed depending on the nucleation mode and ranged from 1°C (for contact mode) to 2°C (for immersion mode) [Fornea et al., 2009]. Finally, long chain alcohol molecules, such as nonadecanol, appear to have an exceptionally low variability in the freezing temperature of ~0.2°C [Zobrist et al., 2007]. We point out that most of the samples from previous studies are based on very few drops. For example, the Fornea et al. results represent averages of 5–6 drops per compound. The largest difference in Figure 3 is between the carbon lampblack [Fornea et al., 2009] and flame soot from this study. These are derived from incomplete combustion of different fuel sources and thus may have different chemical composition. Although direct comparisons between these soot samples are unavailable, ratios in hydrophobic (C–H) and hydrophilic groups (C═O) depend on combustion conditions [Han et al., 2012], and thus may also leading to different IN properties. However, the observed differences may also be due to statistical chance, as our flame soot sample also produced a significant number of droplets that had variability that is similar to the observations of Fornea et al. .
5 Discussion and Conclusions
 The average temperature at which water droplets freeze heterogeneously is a function of the number concentration/surface area/mass of the ice-nucleating material that is present within the droplets. Both ATD [Wright and Petters, 2013] and NX-illite powder [Broadley et al., 2012, data not shown here] demonstrated an increase in the median freezing temperature as the mass concentration of dust immersed in the water increased. It is therefore important to note that the measured average freezing temperature is dependent on both the material and the number concentration/surface area/mass concentration of substance dissolved in the droplet. The unfiltered rain data show that no freeze events occurred at T > −20°C, suggesting that IN concentrations are low. The filtered samples amplify the signal by concentrating the rainwater droplets by approximately 100:1. This allows for the detection of rarer IN that are active at temperatures between −20 and −11°C. Figure 4 shows the combined set of rainwater data, also including events not shown in Figure 3. As expected, the mean freezing temperature depends on the concentration of aerosol in the drop, with warmer IN being sampled in more concentrated drops. The standard deviation of the freezing temperature seems not to depend on the average freezing temperature, although visually there appears to be a slight trend toward reduced standard deviation at warmer temperatures.
 Discrete event simulations using a version of the multiple-component stochastic model of heterogeneous freezing nucleation [cf. Wright and Petters, 2013] suggest that the standard deviation of the freezing temperature of individual drops (Figures 1e and 2e) is a measure of the slope of the nucleation rate with temperature and thus a predictor of the cooling rate dependence of the population median freezing temperature (Figures 1f and 2f). Although the dynamic range is relatively small, this seems to be confirmed by the results. The three samples with the highest standard deviation (kaolinite, montmorillonite, and flame soot) are also the samples that have the strongest cooling rate dependence.
 Although only weakly, the mineral type does influence the observed time/cooling rate dependence. Montmorillonite and kaolinite both exhibit similar cooling rate dependence with each other and have values approaching that of NX-illite powder. For drops containing high concentrations of NX-illite the cooling rate dependence approached 1.5 to 2 K per decade change in cooling rate [Broadley et al., 2012]. In contrast, ATD has markedly lower cooling rate dependence. The difference in cooling rate dependence between ATD and the other minerals could be from manufacturing processes as ATD is milled during production [Murray et al., 2012]. Another difference is the mineral composition of the materials. ATD is comprised mostly of quartz and feldspar [Broadley et al., 2012] which are primary minerals that have remained unchanged since their igneous formation. However, montmorillonite, kaolinite, and illite are clay minerals which are produced naturally through the chemical aging of other minerals (e.g., feldspar) [Deer et al., 1992]. Furthermore, the presence of different mineral components in a single particle influences the active site densities of the dust [Atkinson et al., 2013]. We hypothesize that these mineral differences may contribute to the observed surface area dependence on the cooling rate of NX-illite that was observed by Broadley et al. . The authors attributed the change in cooling rate dependence to the surface area of NX-illite present in each of the drops suggesting that even amongst the same material, different active sites can be present with different surface area concentrations. This is in contrast to ATD where the variability in the refreeze temperature is independent of the surface area within the droplets [Wright and Petters, 2013, Figure 4] suggesting that ATD has a more uniform mechanism for ice nucleation. These observations suggest that different mineral types provide different possible mechanisms for ice nucleation, and these differences may provide a starting point for more fundamental studies into the molecular description of the nucleation process.
 It is interesting to observe that the proteinaceous IN (Icemax) and graphitic IN (flame soot) are most prone to active site modification (or nonrandom freezing behavior). This might be expected based on the different molecular mechanisms discussed earlier (section 2). For example, soot-water interaction can lead to irreversible restructuring of micropores [Popovicheva et al., 2008], thereby altering or destroying the active site similar to the mechanism described by Wang et al. . Similarly, the freezing of water on the protein/cell membrane complex may change or destroy the configuration of the protein and thus alter the active site and its average nucleation temperature. Conversely, the crystalline structure of mineral dust can be expected to be more robust against strain induced by volume expansion upon freezing, making active site modification less likely. Our observations shown in Figure 1 seem to support this view, where flame soot and Icemax show strong nonrandomness in the refreeze results, while the mineral dust samples do not.
 Several recent reviews summarize the results of previous experiments that investigate time dependence of heterogeneous nucleation [Hoose and Möhler, 2012; Murray et al., 2012, and citations therein]. Specific results from these studies that are pertinent to this work are included here. Kaolinite results from this study have the same trends as those found by Murray et al.  and Welti et al. , namely that the freezing temperature of a drop containing kaolinite decreased with decreasing cooling rate. Soot measurements by DeMott  found no significant change in freezing temperature when the cooling rate was changed from 1 K min−1 to 2 K min−1. This is not in conflict with our result since the change in cooling rate by 1 K min−1 is small relative the two order magnitude change (0.01 K min−1 versus 1 K min−1) investigated here. Furthermore, differences in fuel types and soot generation methods may result in different cooling rate dependence.
 The main result from this study is that the different types of active sites and nucleation mechanisms all have similar and weak cooling rate or time dependence. At most, the median freezing temperature of a population of particles shifts by 3° if the exposure time increases from 30 min to 50 h. None of the proxies for the different ice nucleation mechanisms exhibit strong time dependence. Further, weak time dependence was also observed in the ambient rain samples. None of the freeze/thaw cycle experiments presented here and elsewhere show large variability in the freezing temperature of individual droplets. Due to this weak time dependence, instruments with short residence times, such as the continuous flow diffusion chamber, will exhibit minimal error. Combined, these observations support the use of quasideterministic freezing behavior in most models, suggesting that cloud glaciation via primary ice formation is governed by the available ice nuclei population (particle concentration, chemical composition, and size) and cloud temperature. Ice crystal concentrations will only minimally depend on the cooling rate of the parcel and can be computed via a suitable time-dependent freezing rate parameterization [e.g., Vali, 1994, equation (12)].
 This research was funded by the National Science Foundation (NSF) award NSF-AGS 1010851. We thank the three anonymous reviewers for providing constructive critique during the review process.