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Heterogeneous ice nucleation : laboratory freezing results and testing different schemes to describe… Wheeler, Michael James 2015

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HETEROGENEOUS ICE NUCLEATIONLABORATORY FREEZING RESULTS AND TESTING DIFFERENTSCHEMES TO DESCRIBE ICE NUCLEATION IN ATMOSPHERICMODELSbyMICHAEL JAMES WHEELERB. Sc. Honours, Acadia University, 2006A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Chemistry)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2015c©MICHAEL JAMES WHEELER, 2015AbstractIce nucleation occurs throughout the atmosphere. Some atmospheric ice particles are formedthrough nucleation on insoluble atmospheric aerosols known as ice nuclei (IN). The abundanceand chemical composition of these IN affect the properties of clouds and in turn the radiativebalance of the Earth through the indirect effect of IN on climate. The indirect effect of INon climate is one of the least understood topics in climate change. A better understanding ofice nucleation and better capabilities to parameterize ice nucleation are needed to improve thepredictions of the effect of IN on climate.Using a temperature and humidity controlled flow cell coupled to an optical microscope,the ice nucleation properties of three different mineral dust particles are examined in two dif-ferent freezing modes. Results showed that the freezing ability of supermicron dust particlesis lower than that of submicron dust particles of the same type. These freezing results alongwith literature freezing results of nine biological aerosol particles are used to evaluate differentschemes used to parameterize ice nucleation in atmospheric models. These schemes are evalu-ated based on the ability to reproduce the laboratory freezing results. It was found that a singleparameter scheme based on classical nucleation theory was unable to reproduce the freezingresults of all particles studied. However, more complex schemes were able to reproduce thefreezing results.The results in this thesis can be used by atmospheric modellers to improve predictions ofmixed-phase and ice clouds and climate change.iiPrefaceChapters 3 & 4 are co-authored peer-reviewed journal articles and the results from Chapter5 are being prepared for submission to a peer-reviewed journal as a co-authored article. Thedetails of my contribution to each chapter is provided below.Chapter 3 (first author on published journal article): M. J. Wheeler and A. K. Bertram.Deposition nucleation on mineral dust particles: A case against classical nucleation theory withthe assumption of a single contact angle. Atmospheric Chemistry and Physics, 12(2):1189–1201, January 2012. doi: 10.5194/acp-12-1189-2012. URL http://www.atmos-chem-phys.net/12/1189/2012/• Formulated the research question and designed the research project with my supervisor.• Performed all of the ice nucleation experiments.• Performed all of the size measurements of the dust particles.• Performed all of the data analysis.• Developed algorithms to fit experimental data to the four schemes used in the chapter.• Performed the fitting of the experimental data.• Prepared all of the figures for the publication.• Shared writing of the text in the publication with my supervisor.iiiChapter 4 (first author on published journal article): M. J. Wheeler, R. H. Mason, K. Ste-unenberg, M. J. Wagstaff, C. Chou, and A. K. Bertram. Immersion freezing of supermicronmineral dust particles: Freezing results, testing different schemes for describing ice nucleationresults, and ice nucleation active site densities. Journal of Physical Chemistry A, 119(19):4358–4372, 2015b. doi: 10.1021/jp507875q• Formulated the research question and designed the research project with my supervisor.• Performed the ice nucleation experiments with R. H. Mason, K. Steunenberg, and M. J.Wagstaff.• Performed analysis of ice nucleation experiments with R. H. Mason, K. Steunenberg,and M. J. Wagstaff.• Adapted fitting algorithms from Chapter 3 for immersion freezing and performed allfitting of experimental data.• Prepared all the figures for the publication.• Shared the writing of the text in the publication with Dr. C. Chou and my supervisor.• Additional contributions:– D. Horne provided scanning electronc microscopy (SEM) imaging of dust particlesChapter 5 (first author on article under preparation for submission to peer-reviewed jour-nal): M. J. Wheeler, D. I. Haga, R. H. Mason, V. E. Irish, M. J. Wagstaff, R. Iannone, andA. K. Bertram. Testing different schemes for describing immersion freezing of water dropscontaining primary biological aerosol particles. 2015a• Formulated the research question and designed the research project with my supervisor.• Performed fitting analysis of ice nucleation data.• Prepared the figures for the publication.iv• Shared the writing of the text with my supervisor.• Additional contributions from co-authors:– Dr. D. I. Haga, R. H. Mason, M. J. Wagstaff, Dr. R. Iannone and I performed icenucleation experiments on fungal spores and bacteria used in the analysis here.– Dr. D. I. Haga and M. J. Wagstaff performed data analysis of ice nucleation exper-iments from Haga et al. [2013].– Dr. D. I. Haga, M. J. Wagstaff and V. E. Irish performed data analysis of ice nucle-ation experiments from Haga et al. [2015].vTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvList of abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Atmospheric aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Mineral dust aerosols . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1.1 Clay minerals . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Primary biological aerosol particles (PBAPs) . . . . . . . . . . . . . . 31.2 Atmospheric ice nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Deposition nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.2 Immersion freezing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Mineral dust as IN . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7vi1.2.4 PBAPs as IN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 The direct and indirect effect of aerosols on climate . . . . . . . . . . . . . . . 91.3.1 The indirect effect of cloud condensation nucleus (CCN) on climate . . 101.3.2 The indirect effect of IN on climate . . . . . . . . . . . . . . . . . . . 101.3.3 Modelling atmospheric ice nucleation . . . . . . . . . . . . . . . . . . 131.4 Overview of dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Classical nucleation theory (CNT) . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1 Stochastic vs singular nucleation . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Homogeneous nucleation of ice . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Heterogeneous nucleation of ice . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Deposition nucleation of ice . . . . . . . . . . . . . . . . . . . . . . . 192.3.2 Immersion freezing of ice . . . . . . . . . . . . . . . . . . . . . . . . . 203 Deposition nucleation on mineral dust particles: a case against classical nucle-ation theory with the assumption of a single contact angle . . . . . . . . . . . . . 213.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Ice nucleation experiments . . . . . . . . . . . . . . . . . . . . . . . . 243.2.2 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.3 Total surface area, particle size, and particle number . . . . . . . . . . . 273.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Sice,onset as a function of surface area . . . . . . . . . . . . . . . . . . . 293.3.2 Sice, r=0.05 as a function of surface area . . . . . . . . . . . . . . . . . . 323.3.3 Fraction of particles nucleated as a function of Sice, r=0.05 . . . . . . . . 333.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.1 Single-α scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.2 Pdf-α scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38vii3.4.3 Active site scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.4 Deterministic scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4.5 Sensitivity of the results to the assumption of spherical particles . . . . 443.4.6 Comparisons with previous measurements . . . . . . . . . . . . . . . . 453.5 Conclusions and atmospheric implications . . . . . . . . . . . . . . . . . . . . 454 Immersion freezing of supermicron mineral dust particles: freezing results,testing different schemes for describing ice nucleation, and ice nucleation ac-tive site densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.1 Freezing measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 514.2.2 Sample generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.2.3 Surface area per drop . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.4 Size distribution of the mineral dust particles . . . . . . . . . . . . . . 554.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.3.1 Surface area and size distribution of minerals . . . . . . . . . . . . . . 554.3.2 Freezing results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3.3 Testing ice nucleation schemes for use in atmospheric models . . . . . 634.3.3.1 Single-α scheme . . . . . . . . . . . . . . . . . . . . . . . . 634.3.3.2 Pdf-α scheme . . . . . . . . . . . . . . . . . . . . . . . . . 654.3.3.3 Active site scheme . . . . . . . . . . . . . . . . . . . . . . . 664.3.3.4 Deterministic scheme . . . . . . . . . . . . . . . . . . . . . 684.3.3.5 Results from testing different schemes . . . . . . . . . . . . . 694.3.3.6 Comparison of fitting results with other studies . . . . . . . . 744.3.4 Area sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754.3.5 Supermicron ice nucleation active site (INAS) values . . . . . . . . . . 774.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80viii5 Testing different schemes for describing immersion freezing of water drops con-taining primary biological aerosol particles . . . . . . . . . . . . . . . . . . . . . 845.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2.1 Immersion freezing data from Haga et al. [2013] and Haga et al. [2015] 875.3 Fitting schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3.1 Single-α scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3.2 Soccer ball scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3.3 Pdf-α scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.3.4 Deterministic scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1036.1 Ice nucleation properties of mineral dusts . . . . . . . . . . . . . . . . . . . . 1036.1.1 INAS densities of supermicron mineral dust particles . . . . . . . . . . 1046.2 Testing different schemes to describe atmospheric ice nucleation . . . . . . . . 1056.3 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109Appendix A Sensitivity study of the deposition nucleation of kaolinite and illite . . 136Appendix B Fitting PBAP Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143ixList of tablesTable 3.1 Fit parameters obtained for kaolinite. Best fits were obtained by minimizingthe weighted sum of squared residuals (WSSR) between the experimentaldata and the fit function. See text for further discussion on the schemes used. 38Table 3.2 Fit parameters obtained for illite. Best fits were obtained by minimizing theweighted sum of squared residuals (WSSR) between the experimental dataand the fit function. See text for further discussion on the schemes used. . . 38Table 4.1 Results from fitting the Arizona Test Dust (ATD) freezing data to the dif-ferent schemes. Fitting parameters for the best fit are given along with theweighted sum of squared residuals (WSSR) and reduced chi-squared values(χ2red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Table 4.2 Results from fitting the kaolinite freezing data to the different schemes. Fit-ting parameters for the best fit are given along with the weighted sum ofsquared residuals (WSSR) and reduced chi-squared values (χ2red). . . . . . . 72Table 4.3 Variation of median freezing temperature with changing cooling rate forboth ATD and kaolinite. The prediction for each scheme was calculatedby determining the change in median freezing temperature as the coolingrate was changed from 10◦Cmin−1 to 1◦Cmin−1. Variations previouslydetermined in the literature are given for both ATD and kaolinite. . . . . . . 74xTable 4.4 Relative ranking of the ability of different schemes to accurately model het-erogeneous freezing of mineral dust in both the immersion and depositionmode. Schemes are ranked from 1 to 4 where 1 gives the best fit to the dataand 4 the worst. Included are the multi-component stochastic scheme usedby Broadley et al. [2012], which is similar to the pdf-α scheme, and the soc-cer ball scheme of Niedermeier et al. [2011b], which is similar to the activesite scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Table 4.5 Results from fitting the scaled surface area ATD freezing data to the differentschemes. Fits were obtained by scaling the mineral dust surface area by afactor of 50. Fitting parameters for the best fit are given along with theweighted sum of squared residuals (WSSR) and reduced chi-squared values(χ2red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table 4.6 Results from fitting the scaled surface area kaolinite freezing data to thedifferent schemes. Fits were obtained by scaling the mineral dust surfacearea by a factor of 50. Fitting parameters for the best fit are given along withthe weighted sum of squared residuals (WSSR) and reduced chi-squaredvalues (χ2red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Table 5.1 Summary of fungal spores used in the immersion freezing experiments ofHaga et al. [2013]. The freezing data by Haga et al. [2013] is used hereto test different schemes for describing laboratory ice nucleation data. Allspores are assumed to be prolate spheroids based on experimental images.Sizes are given as major axis × minor axis. All dimensions are given in µm. 87xiTable 5.2 Summary of bacteria species used in the immersion freezing experiments byHaga et al. [2015]. The freezing data by Haga et al. [2015] is used here totest different schemes for describing laboratory ice nucleation data. All cellsare assumed to be cylinders with size information based on the literaturevalues of Buchanan and Gibbons [1974]. Sizes are given as major axis ×minor axis. All dimensions are given in µm. . . . . . . . . . . . . . . . . . 88Table 5.3 χ2red values from the fits of all species studied. . . . . . . . . . . . . . . . . 100Table 5.4 Relative rankings of different fitting schemes used for all species studied.Schemes are ranked from 1 to 4 where 1 gives the best fit to the data and 4the worst. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101Table A.1 Fit parameters obtained for kaolinite assuming the surface area equals thegeometric surface area multiplied by 50. Best fits were obtained by mini-mizing the weighted sum of squared residuals (WSSR) between the experi-mental data and the fit function. . . . . . . . . . . . . . . . . . . . . . . . . 137Table A.2 Fit parameters obtained for illite assuming the surface area equals the geo-metric surface area multiplied by 50. Best fits were obtained by minimizingthe weighted sum of squared residuals (WSSR) between the experimentaldata and the fit function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Table B.1 Fitting results for the single-α scheme for all species studied . . . . . . . . . 150Table B.2 Fitting results for the pdf-α scheme for all species studied. . . . . . . . . . . 150Table B.3 Fitting results for the deterministic scheme for all species studied . . . . . . 151Table B.4 Fitting results for the soccer ball scheme for all species studied. . . . . . . . 151xiiList of figuresFigure 1.1 Average composition of mineral dust aerosols by mass determined from15 separate studies. Mineral composition was determined from analysisof collected atmospheric aerosols and bulk analysis of soil samples col-lected from source regions. Samples were obtained from various locationsin North Africa, the Americas, and across the Pacific representing both re-mote and near source regions. (a) shows the overall composition of theaerosol and (b) shows the composition of the clay fraction. Adapted fromMurray et al. [2012]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Figure 1.2 Primary biological aerosol particle (PBAP) composition distribution basedon typical number concentrations determined over vegetated regions. Thevalues next to each PBAP type represent the typical number concentrationper litre of air observed. Adapted from Table 4, Despre´s et al. [2012]. . . . 4Figure 1.3 Schematic of the four different heterogeneous ice nucleation modes as de-scribed by Vali [1985]. IN are shown as brown cubes, liquid water is rep-resented by blue spheres and ice crystals are shown as hexagonal polygons. 6Figure 1.4 Mineral composition of ATD determined by X-ray diffraction. Shown arethe relative amounts of each mineral type contained in a sample of ATD.Adapted from Table 1 from Broadley et al. [2012]. . . . . . . . . . . . . . 8xiiiFigure 1.5 Schematic representation of indirect effects of IN on climate. A compari-son is shown between the solar radiation (blue arrows), terrestrial radiation(red arrows) and precipitation (dashed lines) between clean and pollutedair masses for the indirect effects of IN described in the text. The thicknessof the arrows represents relative intensity of solar or terrestrial radiationand the thickness of the dashed lines represents relative amounts of precip-itation. Cloud drops are shown as blue circles and ice particles are shownas white hexagons. Increases in IN concentration in low altitude cloudsresults in increases in precipitation, shorter lifetimes and decreased over-all cooling. Increases in IN concentration in high altitude clouds results inlarger ice crystals, more extensive clouds, shorter lifetimes and decreasednet warming. Adapted from DeMott et al. [2010]. . . . . . . . . . . . . . . 12Figure 2.1 Classical nucleation theory (CNT) description of the free energy of clus-ter formation as a function of cluster radius. ∆Gcl is calculated accordingto Eq. (2.4) using an ice/vapour interfacial energy of 1.065× 10−5Jcm−2[Pruppacher and Klett, 1997], a molecular volume of ice of 3.2×10−23cm3[Lide, 2001], a temperature of 243 K, a saturation ratio of 1.1 and a contactangle of 80◦. Clusters smaller than r∗cl will favour a reduction in clusterradius while those greater than r∗cl will favour an increase in radius leadingto the growth of a macroscopic ice crystal. The introduction of a hetero-geneous IN reduces the energy barrier to nucleation by a factor, fhet(α),where ∆Gact,1 = fhet(α) ·∆Gact,2, dashed line. This reduction allows fornucleation to occur at warmer temperatures, T , and lower supersaturations,Sice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18xivFigure 3.1 Schematic of the flow cell used for ice nucleation measurements. The flowcell is composed of stainless steel inserted into an aluminium holder. Thebottom of the flow cell is a hydrophobic glass slide and this is separatedfrom the stainless steel through an insulating spacer made of polychlorotri-fluoroethylene (PCTFE) which prevents ice formation on the stainless steelby keeping its temperature slightly above that of the glass slide. Beneaththe flow cell are two additional aluminium blocks, one of which allowscoolant from a temperature controlled chiller to pass through and the othercontains a heater. The combination of the two is used to accurately controlthe temperature of the flow cell which is measured by a platinum resistancetemperature detector (RTD) located beneath the flow cell. A sapphire win-dow in the top of the flow cell enables observation of the particles insidethe flow cell through an optical microscope. Downstream of the flow cellis a frost point hygrometer which allows for accurate measurement of thehumidity supplied to the cell. . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.2 Typical experimental trajectory for the ice nucleation experiments. Exper-iments start below ice saturation and the temperature is decreased until icecrystals are observed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Figure 3.3 Number distributions measured using the optical microscope. N representsthe number of particles and D represents the diameter. The experimentaldata were fit to a log-normal distribution function. Based on fits to the data,the mean geometric diameter (D¯g) and geometric standard deviation (σg)in the experiments were 10.74µm and 0.699 for kaolinite and 7.27µm and0.594 for illite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28xvFigure 3.4 Results for kaolinite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results, and (c) average Sice, r=0.05. The average values arecalculated for four equally sized bins and the horizontal error bars show therange of data points in each bin. The surface area values in (c) representthe average surface area of the points in each bin. Error in Sice,onset is givenas experimental error in measurements of saturation. Error in Sice, r=0.05 isbased on the difference between Sice,onset and Sice,previous as well as the un-certainty in measuring Sice,onset. Error in the average Sice, r=0.05 representsthe 95 % confidence interval. Predictions are shown using the single-αscheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is alsoshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30Figure 3.5 Results for illite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results, and (c) average Sice, r=0.05. The average values arecalculated for four equally sized bins and the horizontal error bars show therange of data points in each bin. The surface area values in (c) representthe average surface area of the points in each bin. Error in Sice,onset is givenas experimental error in measurements of saturation. Error in Sice, r=0.05 isbased on the difference between Sice,onset and Sice,previous as well as the un-certainty in measuring Sice,onset. Error in the average Sice, r=0.05 representsthe 95 % confidence interval. Predictions are shown using the single-αscheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is alsoshown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31xviFigure 3.6 Fraction of particles nucleated as a function of Sice, r=0.05 for kaolinite.Panel (a) shows the nucleated fraction for the individual experimental re-sults. The y-error was calculated from the uncertainty in the value of D¯g.The x-error represents the uncertainty in Sice, r=0.05. Panel (b) shows theaverage nucleated fraction calculated for four size bins. The range of thedata points in each bin is given as the horizontal error and data points rep-resent the average of the Sice, r=0.05 values within each bin. The y-errorbar in panel (b) represents the 95% confidence interval of the average nu-cleated fraction. Fits are shown for the single-α , pdf-α , active site, anddeterministic schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Figure 3.7 Fraction of particles nucleated as a function of Sice, r=0.05 for illite. Panel (a)shows the nucleated fraction for the individual experimental results. They-error was calculated from the uncertainty in the value of D¯g. The x-errorrepresents the uncertainty in Sice, r=0.05. Panel (b) shows the average nucle-ated fraction calculated for four size bins. The range of the data points ineach bin is given as the horizontal error and data points represent the aver-age of the Sice, r=0.05 values within each bin. The y-error bar in panel (b)represents the 95% confidence interval of the average nucleated fraction.Fits are shown for the single-α , pdf-α , active site, and deterministic schemes. 35Figure 3.8 Probability distribution function for the pdf-α scheme and surface densityof active sites, ρ(α), for the active site scheme. Shown are the results forkaolinite particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Figure 3.9 Probability distribution function for the pdf-α scheme and surface densityof active sites, ρ(α), for the active site scheme. Shown are the results forillite particles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41Figure 4.1 Temperature profile used in the freezing experiments. Labels correspondto conditions at which the images in Fig. 4.2 were recorded. . . . . . . . . 53xviiFigure 4.2 Example of optical images collected during a freezing experiment. Pan-els (a) - (d) show images from an ATD experiment while panels (e) - (h)show images from a kaolinite experiment. Rows I-IV correspond to parti-cles before condensing water, particles after condensing water, drops afterfreezing, and inclusions contained in each drop after evaporation, respec-tively. The green traces in row I represent the area included in each dropin row II. See text for further details. Labels I-IV can be used to determinethe temperature and time in the freezing experiment from Fig. 4.1. . . . . . 54Figure 4.3 (a) Size distribution of ATD measured by SEM. Shown are the number,N, distribution (closed circles) and the surface area, S, distribution (closedsquares) functions. (b) - (e) SEM images of individual ATD particles im-pacted on the slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 4.4 (a) Size distribution of kaolinite measured by SEM. Shown are the number,N, distribution (closed circles) and the surface area, S, distribution (closedsquares) functions. (b) - (e) SEM images of individual kaolinite particlesimpacted on the slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 4.5 Distribution of surface area of mineral dust particles per drop for ATDexperiments. The upper abscissa shows the corresponding number of par-ticles contained in each drop based on the average particle size determinedfrom the SEM images (3µm). . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 4.6 Distribution of surface area of mineral dust per drop for kaolinite exper-iments. The upper abscissa shows the corresponding number of particlescontained in each drop based on the average particle size determined fromthe SEM images (2.5µm). . . . . . . . . . . . . . . . . . . . . . . . . . . 60xviiiFigure 4.7 Fraction of drops frozen by homogeneous freezing and immersion freezingof drops containing ATD. Data are shown on both a linear (panel a) and logscale (panel b). Stars represent homogeneous freezing results. The closedcircles represent the median frozen fraction between the upper and lowerlimits as described in the text. The uncertainty in the temperature valuesis ∼ 0.06◦C. The shaded region represents the area where homogeneousfreezing interferes with the heterogeneous freezing results. Heterogeneousdata are only shown at temperatures warmer than this region. . . . . . . . . 61Figure 4.8 Fraction of drops frozen by homogeneous freezing and immersion freez-ing of drops containing kaolinite. Data are shown on both a linear (panela) and log scale (panel b). Stars represent homogeneous freezing results.The closed circles represent the median frozen fraction between the upperand lower limits as described in the text. The uncertainty in the temper-ature values is ∼ 0.06◦C. The shaded region represents the area wherehomogeneous freezing interferes with the heterogeneous freezing results.Heterogeneous data are only shown at temperatures warmer than this region. 62Figure 4.9 Comparison between heterogeneous freezing of drops containing ATD andthe different schemes used to describe heterogeneous ice nucleation. Dataare shown on both a linear (panel a) and a log scale (panel b). The errorin the data points represents the difference between the upper and lowerlimits to the frozen fraction as described in the text. The uncertainty in thetemperature values is ∼ 0.06◦C. The shaded region shows the area wherehomogeneous freezing was observed. . . . . . . . . . . . . . . . . . . . . 70xixFigure 4.10 Comparison between heterogeneous freezing of drops containing kaoliniteand the different schemes used to describe heterogeneous ice nucleation.Data are shown on both a linear (panel a) and a log scale (panel b). Theerror in the data points represents the difference between the upper andlower limits to the frozen fraction as described in the text. The uncertaintyin the temperature values is ∼ 0.06◦C. The shaded region shows the areawhere homogeneous freezing was observed. . . . . . . . . . . . . . . . . . 71Figure 4.11 Ice nucleation active site (INAS) densities as a function of temperaturefor ATD. Results from supermicron particles are in blue while submicrondata are in red. Experiments performed with a mixture of submicron andsupermicron particles are shown in magenta. . . . . . . . . . . . . . . . . . 81Figure 4.12 Ice nucleation active site (INAS) densities as a function of temperature forkaolinite. Results from supermicron particles are in blue while submicrondata are in red. Experiments performed with a mixture of submicron andsupermicron particles are shown in magenta. . . . . . . . . . . . . . . . . . 82Figure 5.1 Fraction of spore containing drops frozen as a function of temperature cal-culated from data presented in Haga et al. [2013]. See text for details. Alsoincluded are results for drops containing no spores taken from Iannone et al.[2011] and referred to as homogeneous freezing here. . . . . . . . . . . . . 90Figure 5.2 Fraction of bacteria containing drops frozen as a function of temperaturecalculated from data presented in Haga et al. [2015]. See text for details.Also included are results for drops containing no bacteria, taken from Ian-none et al. [2011] and referred to as homogeneous freezing here. . . . . . . 91Figure 5.3 Estimation of the relative standard deviation (σrel) of P. allii. A descriptionof the method used to evaluate σrel is given in the text. . . . . . . . . . . . 96xxFigure 5.4 Calculated standard deviations of each dataset as a function of frozen frac-tion. Each data set is shown as a different coloured point. A description ofthe method used to evaluate σ( fd) is given in the text. The best fit to all ofthe datasets is shown as a black line. . . . . . . . . . . . . . . . . . . . . . 97Figure 5.5 Fit results for all fungal spores studied. The shaded region represents theregion where homogeneous freezing was observed and where fits to the ex-perimental data were not considered. Experimental freezing data is shownas filled circles, while best fits are shown as solid lines for each of the fourschemes studied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Figure 5.6 Fit results for all bacteria studied. The shaded region shows the regionwhere homogeneous freezing was observed and where fits to the experi-mental data were not considered. Experimental freezing data is shown asfilled circles, while best fits are shown as solid lines for each of the fourschemes studied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Figure A.1 Results for kaolinite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results and (c) average Sice, r=0.05. The average values arecalculated for four equally sized bins and the horizontal error bars show therange of data points in each bin. The surface area values in (c) representthe average surface area of the points in each bin. Error in Sice,onset is givenas experimental error in measurements of saturation. Error in Sice, r=0.05 isbased on the difference between Sice,onset and Sice,previous as well as the un-certainty in measuring Sice,onset. Error in the average Sice, r=0.05 representsthe 95 % confidence interval. Predictions are shown using the single-αscheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is alsoshown. The surface area was assumed to be the geometric surface areamultiplied by a factor of 50. . . . . . . . . . . . . . . . . . . . . . . . . . 139xxiFigure A.2 Fraction of particles nucleated as a function of Sice, r=0.05 for kaolinite.Panel (a) shows the nucleated fraction for the individual experimental re-sults. The y-error was calculated from the uncertainty in the value of D¯g.The x-error represents the uncertainty in Sice, r=0.05. Panel (b) shows theaverage nucleated fraction calculated for four size bins. The range of thedata points in each bin is given as the horizontal error and data points repre-sent the average of the Sice, r=0.05 values within each bin. The y-error bar inpanel (b) represents the 95% confidence interval of the average nucleatedfraction. Fits are shown for the single-α , pdf-α , active site, and determin-istic schemes. The surface area was assumed to be the geometric surfacearea multiplied by a factor of 50. . . . . . . . . . . . . . . . . . . . . . . . 140Figure A.3 Results for illite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results and (c) average Sice, r=0.05. The average values arecalculated for four equally sized bins and the horizontal error bars show therange of data points in each bin. The surface area values in (c) representthe average surface area of the points in each bin. Error in Sice,onset is givenas experimental error in measurements of saturation. Error in Sice, r=0.05 isbased on the difference between Sice,onset and Sice,previous as well as the un-certainty in measuring Sice,onset. Error in the average Sice, r=0.05 representsthe 95 % confidence interval. Predictions are shown using the single-αscheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is alsoshown. The surface area was assumed to be the geometric surface areamultiplied by a factor of 50. . . . . . . . . . . . . . . . . . . . . . . . . . 141xxiiFigure A.4 Fraction of particles nucleated as a function of Sice, r=0.05 for illite. Panel (a)shows the nucleated fraction for the individual experimental results. They-error was calculated from the uncertainty in the value of D¯g. The x-errorrepresents the uncertainty in Sice, r=0.05. Panel (b) shows the average nu-cleated fraction calculated for four size bins. The range of the data pointsin each bin is given as the horizontal error and data points represent theaverage of the Sice, r=0.05 values within each bin. The y-error bar in panel(b) represents the 95% confidence interval of the average nucleated frac-tion. Fits are shown for the single-α , pdf-α , active site, and deterministicschemes. The surface area was assumed to be the geometric surface areamultiplied by a factor of 50. . . . . . . . . . . . . . . . . . . . . . . . . . 142Figure B.1 Fraction of spore containing drops frozen calculated from immersion freez-ing results for all fungal spores studied plotted on a linear scale. . . . . . . 144Figure B.2 Fraction of bacteria containing drops frozen calculated from immersionfreezing results for all bacteria studied plotted on a linear scale. . . . . . . . 145Figure B.3 Fit results for all fungal spores studied plotted on a linear scale. The shadedregion represents the region where homogeneous freezing was observedand where fits to the experimental data were not considered. Experimentalfreezing data is shown as filled circles, while best fits are shown as solidlines for each of the four schemes studied. . . . . . . . . . . . . . . . . . . 146Figure B.4 Fit results for all bacteria studied plotted on a linear scale. The shadedregion represents the region where homogeneous freezing was observedand where fits to the experimental data were not considered. Experimentalfreezing data is shown as filled circles, while best fits are shown as solidlines for each of the four schemes studied. . . . . . . . . . . . . . . . . . . 147xxiiiFigure B.5 Distribution of spores per drop calculated for each of the fungi studied. Theleft ordinate shows the individual number of drops observed as a functionof the number of spores per drop. The right ordinate shows the fractionof drops containing n spores per drop. This corresponds to P(n) from Eq.(5.1), (5.6) & (5.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Figure B.6 Distribution of bacteria per drop calculated for each of the species stud-ied. The left ordinate shows the individual number of drops observed as afunction of the number of bacteria per drop. The right ordinate shows thefraction of drops containing n bacteria per drop. This corresponds to P(n)from Eq. (5.1), (5.6) & (5.8). . . . . . . . . . . . . . . . . . . . . . . . . . 149xxivList of symbolsA surface area of heterogeneous INA1 fitting parameter for deterministic schemeA2 fitting parameter for deterministic schemeAα area of active site with contact angle αAavg surface area of an average particleAhom homogeneous nucleation pre-exponential factorAp surface area of a particleAsingle area of a single active siteAtotal total surface area available for nucleationα contact angle∆α width of an individual active site binαi contact angle of single active siteb fitting parameter for active site schemeβ1 fitting parameter for active site schemeβ2 fitting parameter for active site schemexxvχ2red reduced chi-squaredD particle diameterD¯g geometric mean diameterfd fraction of drops frozenfhet(α) contact parameter for heterogeneous nucleation/freezing∆Fdiff diffusion free energy∆Gact critical free energy to cluster formation∆Gcl free energy of cluster formation∆Gs free energy of new surface formation∆Gv free energy of bulk water/ice formationh Planck’s constantj0 pre-exponential factor for heterogeneous nucleationjhet heterogeneous nucleation ratejhom homogeneous nucleation rate constantk Boltzmann constantµm micrometerµα mean of normal distribution of contact anglesµi chemical potential of the ice phaseµv chemical potential of the vapour phasexxvin number of particles per dropnice number density of water molecules at the ice-water interfacencl number of molecules in a clusternd number of dropsni number of active sites on a single particlen¯i average number of active sitesnmax maximum number of particles observed per dropns surface density of active sitesnsite number of active sites on a particleNtotal total number of particlesNu number of unfrozen particles/dropsN0 total number of particles/dropsN f number of frozen particles/dropsN fN0fraction of particles/drops nucleatedNi molecular concentration of icenm nanometerνi molecular volume of iceω number of nucleation eventsP(Ai) probability of a drop containing surface area Aixxviip(α) probability density function of normal distributionP¯site(αi) probability that an active site with contact angle αi does not nucleatePfreeze probability of a drop freezingP(n) fraction of drops containing n particlespnum number distribution of particlesPparticle(Sice) probability of a single particle nucleating at SicePsite(α) probability of nucleation of a single active site with contact angle αr rate of nucleationrcl radius of clusterr∗cl ice cluster critical radiusρ(α) surface density of active sitesSice saturation ratio with respect to iceSice,onset onset saturation over iceSice,previous Sice measured immediately before Sice,onsetSice, r=0.05 Sice at which the nucleation rate equals 0.05s−1ssite surface area of an active siteσα standard deviation of normal distribution of contact anglesσg geometric standard deviationσi/v ice-vapour interfacial energyxxviii∆t time step of experimentT temperaturexxixList of abbreviationsATD Arizona Test DustCCN cloud condensation nucleusCMS Clay Minerals SocietyCNT classical nucleation theoryCRM cloud resolving modelGCM general circulation modelIN ice nucleusINAS ice nucleation active sitePBAP primary biological aerosol particlePCTFE polychlorotrifluoroethyleneRTD resistance temperature detectorSEM scanning electronc microscopySOA secondary organic aerosolWSSR weighted sum of squared residualsxxxAcknowledgementsThe completion of a PhD dissertation is an immense undertaking that requires support froma multitude of people. First I would like to thank Dr. J Roscoe for instilling in me a loveof Chemistry and research. To my supervisor, Allan Bertram, thank you for your guidanceand support without which I would not have been able to complete this undertaking. Allan, thementorship and instruction you have provided me throughout my degree have made me into thescientist I am today. Your kindness and understanding have made the process more enjoyableand have created an excellent research environment.Which brings me to the Bertram group. The work presented here would not have beenpossible without the help and support of all of the members of the Bertram group. Whetherproviding help in the lab, answering questions or socializing outside of the lab, you have allcontributed to a fun and constructive working environment. I would like to thank all members,past and present, of the Bertram group: Matt, Mike, Daniel, Pedro, Lori, Simone, Emily, Sarah,Donna, Sebastian, Aidan, Song, Jason, Rich, Ryan, James, Yuan, Lindsay, Matt, Kristina,Amir, Meng, Yuri, Ce´dric, and Vickie. Thank you for all of the support and enjoymentyou’ve provided me. Pedro and Aidan, thank you for all the late night discussions/arguments, Iwouldn’t trade them for anything. A very special thank you to Donna. You’ve been a wonderfulfriend and added enjoyment to long days and late nights waiting for ice to form.I would also like to thank all of the members of the Chemistry department facilities whohelped me throughout my degree. To all members of the Bioservices laboratory, MechanicalEngineering, Electrical Engineering, Glassblowing and IT, your technical support and friend-xxxiship were invaluable to me.To all of my friends and family, I want to thank you for being there for me. I am so fortunateto have each one of you in my life. Finally, I want to thank my parents. Mom and Dad, I wantto thank you for your unconditional love and support. You always made me believe that I couldachieve anything I put my mind to. You have always been there for me and taught me the valueof hard work. I am forever indebted to you for everything you have done for me.xxxiiTo my parents, Jim and Doreen WheelerxxxiiiChapter 1Introduction1.1 Atmospheric aerosolsAn aerosol is a suspension of solid or liquid particles in a gas. Aerosol particles in the atmo-sphere cover a broad range of sizes from several nanometers (nm) to tens of micrometers (µm).The lifetime or residence time of aerosols in the atmosphere can vary significantly dependingon multiple factors such as diameter and removal process. Atmospheric aerosol particles con-tribute to many different processes including the Earth’s radiative balance, precipitation, spreadof pathogens, and human health.Atmospheric aerosols can have both primary and secondary sources. Primary sources referto direct injection of aerosols into the atmosphere. This includes wind-blown dust, volcanicash, sea-spray, and soot from biomass burning. In addition to these primary emissions ofaerosols, some aerosols are produced through secondary processes, which transform atmo-spheric gasses into liquid or solid particles. One common type of aerosol formed throughsecondary processes is secondary organic aerosol (SOA), which is generated by the oxidationof organic precursors [Seinfeld and Pandis, 2006].Atmospheric aerosols can also be divided into natural or anthropogenic sources. Naturallyoccurring aerosols include sea-spray particles, particles from dust storms, fungal spores, andbacteria. Human activity results in the release of aerosol particles through processes such as1fossil fuel combustion and biomass burning. It is often difficult to attribute the source of anaerosol as being from only a natural or an anthropogenic source. Mineral dust particles, forexample, have both a natural and anthropogenic source. Natural activity such as wind actioncauses mineral dust to become suspended. However, human activities like agriculture andchanges in surface water have led to increases in mineral dust aerosol concentrations [Forsteret al., 2007].The focus of this thesis is on two types of primary aerosol, mineral dust and primary bio-logical aerosol particles (PBAPs). A more detailed discussion of the types of aerosol particlesstudied here follows.1.1.1 Mineral dust aerosolsMineral dust make up a significant portion of atmospheric aerosols. Annual estimates of theemission rate of mineral dust particles into the atmosphere range from 1000 – 4000 Tgyr−1[Boucher et al., 2013].Mineral dust particles become suspended primarily through wind action. Mineral dustemissions occur anywhere soil may become eroded by wind action, though arid regions areresponsible for the majority of mineral dust particles emitted into the atmosphere. The vastmajority of mineral dust aerosols originate in the Northern Hemisphere. Emissions from NorthAfrica including the Saharan desert comprise the largest contribution, making up nearly 60%of all mineral dust emitted into the atmosphere [Tanaka and Chiba, 2006]. Regions in Asia,including the Arabian Peninsula and the Gobi desert, also contribute significant quantities ofmineral dust aerosol to the atmosphere [Engelbrecht and Derbyshire, 2010; Tanaka and Chiba,2006].1.1.1.1 Clay mineralsThe mineral dust particles studied in this thesis are classified as clay minerals. This importantclass of aluminosilicate minerals are comprised of alternating layers of alumina (Al2O3) andsilica (SiO2) with other impurities contained in the layers.2Figure 1.1: Average composition of mineral dust aerosols by mass determined from 15separate studies. Mineral composition was determined from analysis of collectedatmospheric aerosols and bulk analysis of soil samples collected from source re-gions. Samples were obtained from various locations in North Africa, the Amer-icas, and across the Pacific representing both remote and near source regions. (a)shows the overall composition of the aerosol and (b) shows the composition of theclay fraction. Adapted from Murray et al. [2012].Figure 1.1 shows the composition of mineral dusts measured from multiple field studies[Murray et al., 2012]. Of the total mineral dust composition, nearly 50% is contained in theclay fraction with the next largest fraction being composed of quartz. The prevalence of clayparticles in the atmosphere is due to the small sizes these minerals typically produce (< 2µm).The small size of clay particles makes them easier to suspend in air and leads to longer atmo-spheric lifetimes than larger particles which settle out after a short time.1.1.2 Primary biological aerosol particles (PBAPs)Another commonly observed class of aerosol particles are primary biological aerosol particles(PBAPs) [Despre´s et al., 2012]. These PBAPs include a large variety of different particle typeswith varying chemical and physical properties. PBAPs can include fungal spores, bacteriacells, pollen, viruses, or any suspended material of biological origin. Estimates of the totalemission rates of PBAPs range from 10–1000 Tgyr−1 [Boucher et al., 2013; Despre´s et al.,2012; Jaenicke, 2005].Work in this thesis examines two sources of PBAPs: bacteria and fungal spores. Figure 1.23Figure 1.2: PBAP composition distribution based on typical number concentrations de-termined over vegetated regions. The values next to each PBAP type representthe typical number concentration per litre of air observed. Adapted from Table 4,Despre´s et al. [2012].shows the relative contribution of different PBAP sources to the total PBAP number concentra-tion determined over vegetated areas [Despre´s et al., 2012]. Typical concentrations are basedon measurements and modelling from multiple sources. Viral particles and bacteria combinedare estimated to make the largest contribution to the total PBAP concentrations. Fungal sporesmake up the majority of the remaining particles with other PBAPs contributing only a smallpercentage to the total concentration.While the measurements above represent ground-level concentrations of PBAPs, the ques-tion remains as to the ability of these particles to reach altitudes in the atmosphere where theycan induce ice nucleation. A recent study by DeLeon-Rodriguez et al. [2013] measured con-centrations of bacteria and fungal spores at altitudes up to 10 km. Results showed that bacteriacells make up on average 20% by number of all aerosol particles 0.25 – 1 µm in diameter withindividual measurements varying between 4 and 95%, indicating a large variability of PBAPconcentrations. Haga et al. [2013] showed through dispersion modelling that between 6 and49% of fungal spores emitted at specific locations in the Northern Hemisphere are able to reachaltitudes high enough to influence ice nucleation. Hoose et al. [2010a] showed using a globalcirculation model that PBAPs exist at altitudes necessary for ice nucleation to occur. Whileresults presented by Hoose et al. [2010a] suggest that PBAPs do not influence atmospheric icenucleation on a global scale, results from other studies suggest that PBAPs may influence icenucleation on a local or regional scale [Costa et al., 2014; Despre´s et al., 2012; Gonc¸alves et al.,2012; Hazra, 2013; Phillips et al., 2008].1.2 Atmospheric ice nucleationThis thesis focuses on the nucleation of ice in the atmosphere. Despite being thermodynam-ically favoured, pure water drops will not freeze near 0◦C. Instead, pure water drops in theatmosphere typically freeze, depending on drop volume, at around −37◦C. This is referred toas the homogeneous freezing temperature of pure water. Colder homogeneous freezing temper-atures occur if the drops contain solutes such as sulphuric acid (H2SO4) or ammonium sulphate((NH4)2SO4), due to the depression of the freezing point by the solutes.The freezing of drops at temperatures above −37◦C are due to the presence of insolubleice nuclei (IN). These IN are responsible for a reduction in the energy barrier to ice nucleationresulting in ice formation at warmer temperatures. The nucleation of ice due to the presence ofinsoluble IN is termed heterogeneous nucleation.Heterogeneous nucleation can occur by four distinct modes [Vali, 1985]: deposition nu-cleation, immersion freezing, contact freezing, and condensation freezing. Figure 1.3 showsa schematic representation of these modes. The first, deposition nucleation, is the only modewhich does not involve the liquid phase. In deposition nucleation, ice forms on IN directlyfrom the vapour phase. Immersion freezing involves the nucleation of ice on IN immersed insupercooled drops. Contact freezing involves the freezing of a supercooled liquid drop uponcoming into contact with an IN. Finally, condensation freezing involves the condensation ofliquid water on IN under supercooled conditions followed immediately by the nucleation of an5ice phase.Deposition NucleationImmersion FreezingContact FreezingCondensation FreezingFigure 1.3: Schematic of the four different heterogeneous ice nucleation modes as de-scribed by Vali [1985]. IN are shown as brown cubes, liquid water is representedby blue spheres and ice crystals are shown as hexagonal polygons.Two of the ice nucleation modes, deposition nucleation and immersion freezing, are exam-ined in this thesis. A more detailed discussion of the two modes follows.1.2.1 Deposition nucleationAs mentioned above, deposition nucleation is unique from the other three modes in that it doesnot involve a liquid phase. Under atmospheric conditions, ice does not form homogeneouslydirectly from water vapour due to the high energy barrier required for homogeneous nucleationfrom the vapour phase [Pruppacher and Klett, 1997]. The addition of an ice nucleus, however,greatly reduces the energy barrier to nucleation and the formation of an ice phase becomes6feasible.1.2.2 Immersion freezingImmersion freezing occurs within supercooled drops. Homogeneous freezing of pure water, asmentioned above, requires temperatures around −37◦C. The introduction of insoluble nucleiinto water drops reduces the energy barrier to nucleation which allows for the formation of iceat temperatures warmer than −37◦C. Similarly, the freezing temperature of solution drops canbe increased due to the presence of IN. Studies have shown the observation of ice particles inmid-level clouds to be preceded by the formation of liquid water [Ansmann et al., 2008, 2009;De Boer et al., 2011; Westbrook and Illingworth, 2011]. This suggests that immersion freezingis an important mode of ice nucleation in the atmosphere. In clouds which contain both liquiddrops and liquid drops with insoluble IN, mixed-phase clouds can form which are a mixture ofboth liquid drops and ice particles.1.2.3 Mineral dust as INMineral dust particles have long been known to be involved in atmospheric ice nucleation.Clay minerals are observed to be more abundant compared to other types of particles at thecentre of snow crystals [Isono, 1955; Kumai, 1961; Kumai and Francis, 1962; Pruppacher andKlett, 1997]. Other field measurements have also shown that mineral dust particles play animportant role in ice nucleation in the atmosphere, primarily in the immersion and depositionmodes [e.g. Ansmann et al., 2008; Cziczo et al., 2004, 2013; DeMott et al., 2003b,a; Ebertet al., 2011; Heintzenberg et al., 1996; Isono et al., 1959; Klein et al., 2010; Kumai, 1961; Liand Min, 2010; Min et al., 2009; Prenni et al., 2009; Pruppacher and Klett, 1997; Richardsonet al., 2007; Sassen, 2002; Sassen et al., 2003; Seifert et al., 2010; Targino et al., 2006; Twohyand Poellot, 2005]. Additionally, a multitude of laboratory studies have shown that mineraldust particles are effective IN in all four modes described above [see Hoose and Mo¨hler, 2012,and references therein].In this thesis the ice nucleation ability of three different mineral types is investigated: kaoli-7Quartz17.1%Feldspar33.2%Carbonate 5.6%Illite7.5%Illite-smectite mixed layer10.2%Other clays24.4%Kaolinite2.0%Figure 1.4: Mineral composition of ATD determined by X-ray diffraction. Shown are therelative amounts of each mineral type contained in a sample of ATD. Adapted fromTable 1 from Broadley et al. [2012].nite, illite, and Arizona Test Dust (ATD). All three of these minerals have been shown to beeffective IN [Hoose and Mo¨hler, 2012; Pruppacher and Klett, 1997, and references therein].Kaolinite and illite are both clay minerals. As shown in Fig. 1.1a, the clay minerals make upthe largest fraction of atmospheric mineral dust particles and kaolinite and illite make up themajority of the clays observed in the atmosphere (Fig. 1.1b). ATD is a commercially avail-able mixture of various minerals including both clays and other mineral types. The chemicalcomposition of ATD is shown in Fig. 1.4. This mixture is commonly used as a surrogate fornatural atmospheric mineral dust and many studies have been conducted on the ice nucleationefficiency of ATD [Hoose and Mo¨hler, 2012; Murray et al., 2012, and references therein].1.2.4 PBAPs as INSome PBAPs have been shown to be effective IN. Many field studies have identified ice nucle-ation active PBAPs [Bowers et al., 2009; Christner et al., 2008a,b; Constantinidou et al., 1990;Garcia et al., 2012; Huffman et al., 2013; Jayaweera and Flanagan, 1982; Lindemann et al.,81982; Maki and Willoughby, 1978; Morris et al., 2008; Pratt et al., 2009; Prenni et al., 2009,2013]. One of the first species identified to have IN activity was the bacteria Pseudomonas sy-ringae [Maki and Galyan, 1974; Vali et al., 1976] which was observed to cause ice nucleationat temperatures as warm as −2◦C. There have been many subsequent laboratory studies whichhave investigated the freezing properties of P. syringae and other IN-active PBAPs, particu-larly bacteria, fungal spores and pollen [Despre´s et al., 2012; Hirano and Upper, 2000; Mo¨hleret al., 2007, and references therein]. The majority of these studies have been conducted in theimmersion freezing mode with fewer studies investigating the deposition nucleation, conden-sation freezing, and contact freezing modes. This thesis focuses on the ice nucleation abilityof multiple species of fungal spores and bacteria cells. As seen in Fig. 1.2 above, both bacteriaand fungal spores make up a significant fraction of the number concentration of PBAPs in theatmosphere.1.3 The direct and indirect effect of aerosols on climateAtmospheric aerosols play an important role in the climate and hydrological cycle of the Earth.Aerosol particles scatter solar radiation which affects both visibility as well as climate. Byreflecting incoming solar radiation, aerosols result in a cooling of the atmosphere [Jacob, 1999].Conversely, certain aerosol particles, such as black carbon, can absorb solar radiation which canoffset the cooling effect of scattering by particles [Seinfeld and Pandis, 2006]. This scatteringand absorption of radiation is termed the aerosol “direct effect” on climate.In contrast to the direct effect, aerosols also influence climate in an indirect way throughthe modification of cloud properties, termed the “indirect effect” on climate. Certain aerosolparticles can act as either cloud condensation nuclei (CCN) or IN. These CCN and IN areresponsible for the nucleation of liquid drops or ice in the atmosphere. Modifications of theconcentration and chemical composition of these CCN or IN can result in various indirect ef-fects on climate. Below, the indirect effect of CCN on climate is first discussed which involvesonly warm clouds. Then, the indirect effect of IN on climate is discussed which involves both9mixed-phase and ice clouds.1.3.1 The indirect effect of CCN on climateThe indirect effect of CCN on climate can occur by two different mechanisms: the cloud albedoeffect and the cloud lifetime effect. As with the direct effect described above, cloud drops alsoscatter incoming solar radiation. If the liquid water content of a cloud is assumed to remainconstant, then increases in CCN concentrations will result in a larger number of smaller clouddrops. This has the effect of increasing the reflectivity of the cloud and is referred to as the“cloud albedo effect” [Twomey, 1974]. The increase in cloud reflectivity (albedo) results ina cooling of the atmosphere since less solar radiation is able to reach the Earth’s surface. Inaddition to the increased albedo of clouds due to the cloud albedo effect, increases in CCNconcentrations may result in increased cloud lifetimes [Albrecht, 1989]. A reduction in pre-cipitation efficiency caused by decreases in droplet size results in longer lived clouds. Theselonger lived clouds result in an overall increase in the fractional cloudiness of the atmospherewhich also increases the overall cloud albedo. This effect, which is estimated to be as signif-icant as the cloud albedo effect [Lohmann and Feichter, 2005], is referred to as the “secondindirect effect” or “cloud lifetime effect”.1.3.2 The indirect effect of IN on climateDepending on environmental conditions, some clouds may be composed entirely of ice par-ticles (ice clouds) or a mixture of liquid drops and ice particles (mixed-phase clouds). Theindirect effect of IN on climate involves both ice clouds and mixed-phase clouds. The indirecteffect of IN on climate is less understood than the indirect effect of CCN on climate [Denmanet al., 2007; Lohmann and Feichter, 2005]. The indirect effect of IN on climate is thought to bedifferent depending on cloud type. Below, the indirect effect of IN on climate is first discussedin the context of mixed-phase clouds and then in the context of ice clouds.Ice particles formed in mixed-phase clouds deplete the liquid water due to the lower vapourpressure of water over ice compared to over liquid water. This process, referred to as the10Wegener-Bergeron-Findeisen process [Pruppacher and Klett, 1997], results in the growth oflarge ice crystals which form precipitation. Increases in the number of IN will result in thedepletion of smaller water drops in favour of the formation of large ice crystals. If the totalamount of water in a cloud remains constant then the surface area available for scattering de-creases. This will result in a decrease of the scattering of radiation from these clouds. Increasesin IN concentrations will also result in an increase in the amount of precipitation from theseclouds. Increased precipitation of clouds will result in shorter lifetimes due to the depletion ofwater. This is referred to as the “glaciation indirect effect” [Lohmann, 2002] and has the effectof offsetting some of the cooling caused by the cloud albedo effect.Unlike mixed-phase clouds which result in a net cooling of the Earth-atmosphere systemby reflecting solar radiation, ice clouds are responsible for a net warming of the atmospheredue the absorption of outgoing terrestrial radiation (the greenhouse effect). All clouds willcontribute with different magnitudes to the cooling of the Earth-atmosphere system throughthe reflection of solar radiation. Similarly, all clouds will, to differing degrees, contribute to thegreenhouse effect by absorbing terrestrial radiation and emitting it back to the Earth’s surface.For clouds closer to the Earth’s surface, such as mixed-phase clouds, the temperature of thecloud is similar to that of the Earth’s surface and there is only a small absorption of terrestrialradiation [Jacob, 1999; Seinfeld and Pandis, 2006]. The result is that the cooling caused bythe indirect effect is more significant than the warming produced by the greenhouse effect.However, for ice clouds which occur at high altitudes, such as cirrus clouds, the temperature ofthe clouds is significantly different than that of the Earth’s surface and the warming caused bythe greenhouse effect is stronger than the cooling produced by the reflection of solar radiation[Jacob, 1999; Seinfeld and Pandis, 2006]. As a result, the overall effect of these ice cloudsis warming of the Earth-atmosphere system. The effect of increasing IN concentrations inice clouds is not well understood. Studies have suggested that increased IN concentrationsmay lead to decreases in the ice crystal concentration of these clouds due to a shift in thefreezing mechanism from homogeneous freezing of supercooled concentrated solution drops11Figure 1.5: Schematic representation of indirect effects of IN on climate. A comparisonis shown between the solar radiation (blue arrows), terrestrial radiation (red arrows)and precipitation (dashed lines) between clean and polluted air masses for the in-direct effects of IN described in the text. The thickness of the arrows representsrelative intensity of solar or terrestrial radiation and the thickness of the dashedlines represents relative amounts of precipitation. Cloud drops are shown as bluecircles and ice particles are shown as white hexagons. Increases in IN concentra-tion in low altitude clouds results in increases in precipitation, shorter lifetimes anddecreased overall cooling. Increases in IN concentration in high altitude clouds re-sults in larger ice crystals, more extensive clouds, shorter lifetimes and decreasednet warming. Adapted from DeMott et al. [2010].to heterogeneous freezing by IN [DeMott et al., 2010; Ka¨rcher and Lohmann, 2003]. Theearlier onset of nucleation by IN will prevent the homogeneous nucleation of liquid drops. Theswitch from homogeneous to heterogeneous nucleation will result in the formation of fewer butlarger ice crystals and will lead to a decrease in the warming caused by these clouds. Shown inFig. 1.5 is a schematic representation of the indirect effect of IN on climate in the context ofboth mixed-phase and ice clouds.121.3.3 Modelling atmospheric ice nucleationIn order to better understand the indirect effect of IN on climate, a better understanding ofice nucleation by atmospheric particles is required. Atmospheric models including large scalegeneral circulation models (GCMs) and smaller scale cloud resolving models (CRMs) are usedto evaluate the indirect effect of IN on climate. However, in order to accurately evaluate theindirect effect of IN on climate, the ice nucleation ability of atmospheric aerosols needs tobe understood and accurately parameterized and incorporated into these models. These pa-rameterizations can be either theoretical or empirical. Empirical parameterizations enable theprediction of ice nucleation based on laboratory [Niemand et al., 2012] and field measurements[DeMott et al., 2010; Phillips et al., 2008, 2009]. For example, DeMott et al. [2010] presents aparameterization based on multiple field studies which relates the number of IN to the concen-tration of aerosol particles with diameters greater than 0.5µm. Phillips et al. [2008] presentsempirical presentations based on different particle types (dust and metallic, inorganic blackcarbon, and insoluble organic aerosols).Theoretical parameterizations are based on some understanding of the nucleation process[Connolly et al., 2009; Fletcher, 1958, 1969; Hartmann et al., 2013; Lu¨o¨nd et al., 2010; Mar-colli et al., 2007; Niedermeier et al., 2011b, 2014] . These parameterizations often rely onclassical nucleation theory (CNT) as a basis for the nucleation process with modifications usedto describe the different nucleation abilities between particles. A more detailed description ofCNT is presented in Chapter 2. Detailed descriptions of the theoretical parameterizations usedin this thesis can be found in Chapters 3, 4, and 5.The goal of this thesis is to improve our understanding of ice nucleation by atmosphericaerosols and to improve the parameterizations or schemes used to describe IN in atmosphericmodels. This research should lead to better predictions of climate change and its ramifications.More specifically, the ice nucleation of different mineral dust types is examined in both the de-position and immersion freezing modes through controlled laboratory studies. Freezing resultsfrom these studies are used to test different schemes commonly used to describe ice nucleation13in atmospheric models. Results from the immersion freezing measurements on mineral dustsare also used to determine ice nucleation active site (INAS) densities, which are often used tocompare the ice nucleation ability of different IN. Experimental results on immersion freezingof different types of PBAPs reported in the literature are also used to test different schemesused to describe ice nucleation in atmospheric models.1.4 Overview of dissertationAs mentioned above, this dissertation focuses on the ice nucleation properties of mineral dustsand PBAPs in the deposition and immersion modes. Chapter 1 (this chapter) gives an intro-duction to aerosols and outlines the importance of ice nucleation on atmospheric particles;Chapter 2 introduces CNT, which is the basis for several of the schemes used in this thesis;Chapters 3–5 are the research chapters; and Chapter 6 presents the conclusions of the researchand suggestions for future work. Chapter 3 examines the surface area dependence of depositionice nucleation on two commonly observed mineral dusts (kaolinite and illite). Experiments areperformed on both minerals to determine the conditions (temperature, T , and saturation ratio,Sice) for ice nucleation as a function of particle surface area. The ice nucleation results are usedto test four different schemes for describing ice nucleation. Chapter 4 describes ice nucleationresults in the immersion mode on two supermicron-sized mineral dust particle types (kaoliniteand ATD). Freezing temperatures of drops with immersed mineral dust particles are measured.The freezing results are used to determine the INAS densities of supermicron dust particles forcomparison with other measurements with the same mineral dusts in the submicron mode. Thefreezing results are also used to test four schemes used to describe ice nucleation. Chapter 5uses freezing data of drops containing fungal spores and bacteria reported in the literature totest different schemes used to describe ice nucleation. This work investigates the best methodfor including PBAP ice nucleation in atmospheric models.14Chapter 2Classical nucleation theory (CNT)2.1 Stochastic vs singular nucleationThe exact nature of the heterogeneous nucleation of ice is not well understood. There exists adebate as to whether heterogeneous nucleation occurs through a stochastic or singular process[Vali, 2014]. “Stochastic” nucleation refers to the formation of ice clusters by random fluctu-ations. This is a time dependent process with nucleation being possible at any temperature aslong as the observation time is long enough. “Singular” nucleation, on the other hand, refers tothe formation of ice on a specific site of an IN at a characteristic temperature and/or saturationratio depending on the type of nucleation. The nucleation of a given site is dependent only onthe characteristic parameters and is independent of the observation time.Evidence for the stochastic nature of nucleation can be derived from the observation ofheterogeneous nucleation in drops held at constant temperature [Murray et al., 2011; Vonnegutand Baldwin, 1984; Welti et al., 2012]. Additionally, the observation of a variable freezing tem-perature with varying cooling rate [Wright et al., 2013], though small, provides further supportfor the stochastic nature of heterogeneous ice nucleation. Conversely, the singular nature ofice nucleation is demonstrated through small variation in the freezing temperature of dropsexposed to repeated freezing and melting cycles [Shaw et al., 2005; Vali, 2008]. Recent workhas suggested that heterogeneous ice nucleation is a combination of stochastic and singular15behaviour [Vali and Stansbury, 1966; Vali, 1994, 2008, 2014].In this thesis laboratory freezing experiments are used to test the ability of a number ofschemes used to describe heterogeneous ice nucleation in atmospheric models. The schemestested include a scheme which is completely stochastic, a scheme which is completely singularas well as several schemes which combine both stochastic and singular nucleation. Several ofthese schemes are based on classical nucleation theory (CNT). As a result, details on CNT aregiven below.CNT was originally developed for the formation of a stable liquid phase from a meta-stablevapour phase [Mullin, 2001]. First the formation of an ice phase from the vapour phase inthe absence of heterogeneous ice nucleus (IN) (i.e. homogeneous nucleation from the vapourphase) will be considered and then expanded for the cases of ice formation in the depositionand immersion modes.2.2 Homogeneous nucleation of iceConsider the formation of an ice cluster from a supersaturated vapour phase. The free energyassociated with the creation of the ice phase, ∆Gcl, is the sum of the free energy contributionsfrom the formation of a new interface, ∆Gs, which is energetically unfavourable (positive ∆Gs),and the free energy contribution associated with the formation of bonds within the volume ofthe ice cluster, ∆Gv, which can be either positive or negative depending on the temperature andamount of water vapour [Murray et al., 2012].∆Gcl = ∆Gs +∆Gv (2.1)∆Gs is governed by the surface tension of the ice phase,σi/v. If the cluster is assumed to bea sphere, then the free energy required to create the new surface is given by∆Gs = 4pir2clσi/v, (2.2)16where rcl is the radius of the cluster.∆Gv can be represented by∆Gv = ncl (µi−µv) =−4pir3cl3νi· kT lnSice, (2.3)where ncl is the number of water molecules in the cluster and µi - µv is the difference inchemical potential between the ice and vapour phases. The number of water molecules can becalculated from the volume of the cluster and the molecular volume of ice, νi. The differencein chemical potential is given by −kT lnSice [Seinfeld and Pandis, 2006] where Sice is theratio of the partial pressure of water vapour to the saturation vapour pressure over ice, k is theBoltzmann constant and T is the temperature of the cluster.Combining Eqs. (2.2) and (2.3) gives∆Gcl =−4pir3cl3νi· kT lnSice +4pir2clσi/v. (2.4)The variation of ∆Gcl with cluster radius is given in Fig. 2.1 (solid line). As can be seen,∆Gcl reaches a maximum at a particular radius, r∗cl. If additional water molecules are added toa cluster with radius r∗cl, then there will be a decrease in the free energy and further additions ofwater molecules becomes energetically favourable. This will lead to the formation of a macro-scopic ice crystal. On the other hand, for clusters which form with radii smaller than r∗cl, theaddition of water molecules is energetically unfavourable and the formation of a macroscopicice crystal is not favoured.The size of the critical radius, r∗cl, can be obtained by calculating the maximum of the freeenergy with respect to the cluster radius (i.e. where d∆Gcldrcl = 0). The size of the critical radiusis given byr∗cl =2σi/vνikT lnSice. (2.5)The height of the energy barrier (activation energy) in Fig. 2.1, ∆Gact, is obtained by170 5 10 15 20 25 30 35rcl (nm)0.00.51.01.52.02.5∆Gcl(J)×10−16r∗cl∆Gact,1∆Gact,2Figure 2.1: Classical nucleation theory (CNT) description of the free energy of clus-ter formation as a function of cluster radius. ∆Gcl is calculated according to Eq.(2.4) using an ice/vapour interfacial energy of 1.065×10−5Jcm−2 [Pruppacher andKlett, 1997], a molecular volume of ice of 3.2×10−23cm3 [Lide, 2001], a temper-ature of 243 K, a saturation ratio of 1.1 and a contact angle of 80◦. Clusters smallerthan r∗cl will favour a reduction in cluster radius while those greater than r∗cl willfavour an increase in radius leading to the growth of a macroscopic ice crystal.The introduction of a heterogeneous IN reduces the energy barrier to nucleation bya factor, fhet(α), where ∆Gact,1 = fhet(α) ·∆Gact,2, dashed line. This reduction al-lows for nucleation to occur at warmer temperatures, T , and lower supersaturations,Sice.18substituting Eq. (2.5) into Eq. (2.4):∆Gact =16piσ3i/vν2i3(kT lnSice)2(2.6)The nucleation rate constant, jhom, takes the form of an Arrhenius equation given byjhom = Ahom exp(−∆GactkT)= Ahom exp(−16piσ3i/vν2i3kT (kT lnSice)2), (2.7)where Ahom is the pre-exponential factor for homogeneous nucleation with units of cm−3s−1.2.3 Heterogeneous nucleation of ice2.3.1 Deposition nucleation of iceIn deposition nucleation, ice forms directly from the vapour phase similar to the process de-scribed above for homogeneous nucleation of water vapour. Unlike the homogeneous casedescribed above, a solid IN is present onto which the ice nucleates. This heterogeneous INreduces the energy barrier to nucleation making nucleation at a given temperature and super-saturation more likely than in the homogeneous case. This is illustrated in Fig. 2.1. The solidline shows the free energy barrier to nucleation in the homogeneous case. The introduction ofa heterogeneous IN reduces the energy barrier as shown by the dashed line. The nucleationprobability is greater for the heterogeneous case due to the decreased energy barrier.The nucleation rate constant for deposition nucleation is given byjhet = j0 exp(−∆Gact fhet(α)kT), (2.8)where ∆Gact is given by Eq. (2.6). The value of ∆Gact is reduced by a factor known as thecontact parameter, fhet(α), with values between 0 and 1. The value of the contact parameterdepends on the IN and is further discussed in Chapters 3 & 4. The pre-exponential factor, j0,19has units of cm−2s−1.2.3.2 Immersion freezing of iceNucleation in the case of immersion freezing is more complicated than for deposition nucle-ation. In the case of immersion freezing, the un-nucleated water molecules exist in the su-percooled liquid phase. In order to form an ice cluster, water molecules must break existinghydrogen bonds in order to associate themselves with the ice cluster. This breaking of bonds re-sults in a second energy barrier to nucleation [Pruppacher and Klett, 1997]. This energy barrieris referred to as the diffusion free energy, ∆Fdiff. The nucleation rate constant for heterogeneousnucleation in the immersion mode is given byjhet = j0 exp(−∆Gact fhet(α)kT− ∆FdiffkT). (2.9)20Chapter 3Deposition nucleation on mineral dustparticles: a case against classicalnucleation theory with the assumption of asingle contact angle3.1 IntroductionAtmospheric aerosol particles can indirectly influence climate by modifying the formation con-ditions and properties of ice and mixed-phase clouds. To better understand this topic, an im-proved understanding of the ice nucleation properties of atmospheric aerosols is required, andthese properties need to be parameterized and incorporated in atmospheric models [Baker andPeter, 2008; Cantrell and Heymsfield, 2005; DeMott, 2002; Hegg and Baker, 2009; Houghtonet al., 2001].Ice nucleation may occur in the atmosphere either homogeneously or heterogeneously. Ho-mogeneous nucleation involves the freezing of liquid droplets. In heterogeneous nucleation,ice forms on insoluble or partially soluble aerosol particles known as ice nuclei (IN). Four dif-21ferent modes of heterogeneous ice nucleation have been identified: immersion, condensation,deposition and contact nucleation. These four modes are discussed in Chapter 1. In the follow-ing we focus on deposition nucleation, which involves the formation of ice on a solid particledirectly from the vapour phase [Pruppacher and Klett, 1997; Vali, 1985].Different schemes have been developed to parameterize heterogeneous nucleation data.One of the simplest is classical nucleation theory (CNT) [Pruppacher and Klett, 1997] com-bined with the assumption of a single contact angle, α . We refer to this as the single-α scheme.This scheme assumes ice nucleation is a stochastic process and can occur at any location onthe surface of a particle with equal probability (i.e. the surface is energetically uniform for icenucleation). Therefore, each particle has the same probability per unit surface area to nucleateice [Pruppacher and Klett, 1997]. Nucleation data is parameterized using a single parameter,the contact angle. Due in part to its simplicity, researchers have used the single-α scheme toparameterize laboratory data for use in atmospheric simulations [e.g. Archuleta et al., 2005;Chen et al., 2008; Chernoff and Bertram, 2010; Eastwood et al., 2008, 2009; Fornea et al.,2009; Hung et al., 2003]. In addition, the single-α scheme has been used to describe hetero-geneous nucleation in atmospheric cloud simulations [e.g. Hoose et al., 2010a,b; Jensen andToon, 1997; Jensen et al., 1998; Ka¨rcher, 1996, 1998; Ka¨rcher et al., 1998; Morrison et al.,2005].A modification of the single-α scheme is the probability distribution function-α scheme(pdf-α scheme) [Lu¨o¨nd et al., 2010; Marcolli et al., 2007]. Similar to the single-α scheme,the pdf-α scheme assumes that ice nucleation is stochastic and can be described by CNT.Nucleation can occur at any location on the surface of a particle with equal probability (i.e. thesurface is energetically uniform for ice nucleation). However, the ice nucleation ability variesfrom particle to particle, which is described by a probability distribution function of contactangles, α . This scheme has recently been used to parameterize laboratory data of Marcolliet al. [2007] and Lu¨o¨nd et al. [2010].Yet another modification to the single-α scheme is the active site scheme [Fletcher, 1969;22Gorbunov and Kakutkina, 1982; Han et al., 2002; Lu¨o¨nd et al., 2010; Marcolli et al., 2007;Martin et al., 2001; Niedermeier et al., 2011b]. In this scheme it is assumed that ice nucleationis a stochastic process and can be described by CNT. However, small areas or sites on a particlemay be more effective at nucleating ice than the remainder of the particle. The distribution andice nucleation properties of these areas, referred to as “active sites,” govern the nucleating abil-ity of a particle. The active site scheme has been used for parameterizing laboratory data andfor describing ice nucleation in atmospheric models [Fletcher, 1969; Gorbunov and Kakutkina,1982; Khvorostyanov and Curry, 2000, 2004, 2005, 2009; Kulkarni and Dobbie, 2010; Lu¨o¨ndet al., 2010; Saunders et al., 2010].The final scheme used here is the deterministic scheme [Connolly et al., 2009; Lu¨o¨nd et al.,2010]. Unlike the other three schemes discussed above, this scheme is not based on classicalnucleation theory. When applied to deposition nucleation, the deterministic scheme assumesparticles have a characteristic number density of surface sites, and ice forms immediately on asurface site upon reaching a definite ice saturation ratio. This scheme has been used recentlyto parameterize immersion nucleation data for mineral dust particles [Connolly et al., 2009;Lu¨o¨nd et al., 2010; Murray et al., 2011; Niedermeier et al., 2010].In the following we investigate deposition nucleation of ice on illite and kaolinite particles,two minerals that are a significant fraction (up to 50 %) of atmospheric mineral dust [Claquinet al., 1999]. Mineral dust particles can play an important role in atmospheric ice formationbased on previous field measurements and modelling studies [e.g. Ansmann et al., 2008; Bara-hona et al., 2010; Cziczo et al., 2004; DeMott et al., 2003a; Heintzenberg et al., 1996; Hooseet al., 2008; Klein et al., 2010; Koehler et al., 2010; Li and Min, 2010; Min et al., 2009; Prenniet al., 2009; Sassen, 2002; Sassen et al., 2003; Seifert et al., 2010; Twohy and Poellot, 2005].We show that the Sice conditions when ice first nucleates on kaolinite and illite particles are astrong function of the surface area available for nucleation. This surface-area dependent datais then used to test the different schemes discussed above. We show that the single-α schemecannot describe the laboratory data, but the pdf-α scheme, the active site scheme and the de-23terministic scheme fit the data within experimental uncertainties. Parameters from the fits tothe data are presented and the atmospheric implications are discussed.3.2 Experimental3.2.1 Ice nucleation experimentsThe apparatus used in these studies has been described in detail previously [Dymarska et al.,2006; Eastwood et al., 2008; Parsons et al., 2004]. Figure 3.1 shows a schematic of the in-strumental setup used. It consists of an optical microscope (Zeiss Axiotech 100 equipped witha 10X objective) coupled to a flow cell in which the saturation ratio and temperature can beaccurately controlled. The saturation ratio, Sice, is defined as the ratio of water vapour partialpressure to the saturation vapour pressure of ice at the same temperature. Mineral dust par-ticles were deposited on the bottom surface of the flow cell; the saturation ratio with respectto ice inside the cell was increased, and the conditions for onset of ice nucleation (when thefirst particle nucleated ice) was determined with a reflected light microscope. We define thisas the onset Sice(Sice,onset). The Sice over the particles was controlled by continuously flowinga mixture of dry and humidified He through the flow cell. The humidity of the gas stream wascontinuously monitored using a frost point hygrometer (General Eastern 1311 DR) which wascalibrated against the ice frost point within the flow cell [Dymarska et al., 2006].The bottom surface of the flow cell, which supported the particles, consisted of a glass coverslide treated with dichlorodimethylsilane to make a hydrophobic surface [Dymarska et al.,2006]. This ensured that ice did not nucleate directly on the surface of the glass slide. TheSice conditions at which all the particles nucleated ice could not be determined since after iceformed on the first particle, the Sice above the other particles was reduced as water vapourcondensed on the first nucleated particle. Each experiment involved determining the Sice,onsetfor an ensemble of particles and this procedure was repeated a number of times with varyingnumbers of particles. Sice,onset was determined for each sample once (i.e. measurements werenot repeated on the same sample).24Figure 3.1: Schematic of the flow cell used for ice nucleation measurements. The flowcell is composed of stainless steel inserted into an aluminium holder. The bottom ofthe flow cell is a hydrophobic glass slide and this is separated from the stainless steelthrough an insulating spacer made of polychlorotrifluoroethylene (PCTFE) whichprevents ice formation on the stainless steel by keeping its temperature slightlyabove that of the glass slide. Beneath the flow cell are two additional aluminiumblocks, one of which allows coolant from a temperature controlled chiller to passthrough and the other contains a heater. The combination of the two is used toaccurately control the temperature of the flow cell which is measured by a platinumresistance temperature detector (RTD) located beneath the flow cell. A sapphirewindow in the top of the flow cell enables observation of the particles inside theflow cell through an optical microscope. Downstream of the flow cell is a frostpoint hygrometer which allows for accurate measurement of the humidity suppliedto the cell.252 3 7 2 3 8 2 3 9 2 4 0 2 4 1 2 4 2 2 4 3 2 4 4 2 4 50 . 60 . 81 . 01 . 21 . 41 . 6  S iceT e m p e r a t u r e  ( K ) E x p e r i m e n t a l  t r a j e c t o r y L i q u i d  w a t e r  s a t u r a t i o n I c e  s a t u r a t i o nFigure 3.2: Typical experimental trajectory for the ice nucleation experiments. Experi-ments start below ice saturation and the temperature is decreased until ice crystalsare observed.Typical experimental Sice trajectories used in these ice nucleation experiments are illus-trated in Fig. 3.2. At the beginning of the experiments, the particles were exposed to a flowof dry He gas at room temperature (Sice < 1%). The temperature of the cell was then rapidlylowered and the Sice was set to approximately 80 %. The nucleation experiments were thenconducted by steadily decreasing the temperature(−0.1Kmin−1)and thus increasing the Siceas shown in Fig. 3.2. The Sice ramp rate was approximately 1%min−1. Optical images wererecorded every 20s, which corresponds to a change of ∼ 0.33%Sice.263.2.2 Sample preparationKaolinite and illite samples were purchased from Fluka (product ID: 03584) and the ClayMinerals Society (product ID: IMt-1), respectively. The mineral samples were deposited onhydrophobic glass slides using the following technique: dry dust particles were placed in aglass vessel immersed in an ultrasonic bath. A flow of ultrahigh-purity N2 was passed throughthe vessel, and vibrations from the ultrasonic bath caused the dust particles to be suspended inthe flow of N2. This flow was directed at the hydrophobic glass slides, and the dust particleswere deposited on the slides by impaction.3.2.3 Total surface area, particle size, and particle numberThe total surface area available for nucleation in each experiment, Atotal, was determined fromthe images recorded with the optical microscope [Chernoff and Bertram, 2010; Dymarska et al.,2006; Eastwood et al., 2008, 2009]. First, the projected (i.e. 2-dimensional) surface area ina given experiment was determined with digital image analysis software (Northern Eclipse).The projected surface area was then multiplied by a factor of 4 to give Atotal. A factor of 4assumes that all particles are spherical, and the surface area available for nucleation can beapproximated by the geometric surface area of the particles. Based on this analysis, the totalsurface area of the mineral dust deposited in any particular experiment ranged from 3.5×10−6to 8×10−3 cm2. Sensitivity to the assumption of spherical particles is explored in Section 3.4.5.The size of the particles in the experiments were also determined with images from theoptical microscope. In total 383 particles were analyzed for kaolinite and 363 particles forillite to extract size information. Shown in Fig. 3.3 are the number distributions of particlesin the kaolinite and illite experiments determined from this analysis. Based on a log-normalfit to the data, the mean geometric diameter (D¯g) and geometric standard deviation (σg) in theexperiments were 10.74µm and 0.669 for kaolinite and 7.27µm and 0.594 for illite. The opti-cal resolution limit of the microscope was approximately 1µm. Scanning electron microscopywas also carried out on some slides to ensure that the number of particles less than 1µm on the270 . 1 1 1 0 1 0 001 0 02 0 03 0 04 0 05 0 06 0 001 0 02 0 03 0 04 0 05 0 06 0 07 0 0   I l l i t e  e x p e r i m e n t a l  d a t a F i t  t o  e x p e r i m e n t a l  d a t adN/dlog 10D D  ( µm )   K a o l i n i t e  e x p e r i m e n t a l  d a t a F i t  t o  e x p e r i m e n t a l  d a t adN/dlog 10DFigure 3.3: Number distributions measured using the optical microscope. N representsthe number of particles and D represents the diameter. The experimental data werefit to a log-normal distribution function. Based on fits to the data, the mean geomet-ric diameter (D¯g) and geometric standard deviation (σg) in the experiments were10.74µm and 0.699 for kaolinite and 7.27µm and 0.594 for illite.slides was small. From the electron microscope images we concluded that < 0.5% of the totalsurface area lies in the sub-micrometer range. Also note that from the images recorded dur-ing the freezing experiments we can conclude that ice nucleation always occurred on particles> 1µm in diameter, further confirming that particles with diameters < 1µm are not importantin our experiment. The size distribution presented in Fig. 3.3 is different from the size distri-bution reported by Welti et al. [2009] for kaolinite samples also purchased from Fluka sinceour method of depositing particles on slides favours particles with diameters > 1µm.28The number of particles in each experiment was calculated by the following equation:Ntotal =AtotalAavg, (3.1)where Ntotal is the number of particles, Atotal is the total surface area of particles calculated asdescribed above, and Aavg is the average surface area of the particles. The value of Aavg wascalculated using the following equation [Reist, 1992]:Aavg = piD¯g2 exp(2σ2g), (3.2)where D¯g and σg are the geometric mean diameter and geometric standard deviation of thenumber distributions discussed above and calculated form the data shown in Fig. 3.3. In eachexperiment the number of particles on a slide ranged from 1 to ∼ 1000.3.3 Results3.3.1 Sice,onset as a function of surface areaThe individual onset results obtained for kaolinite and illite particles are shown in Figs. 3.4aand 3.5a respectively. Each data point represents the onset conditions observed for a singlesample of dust particles, and the error bars are based on the manufacturer’s stated uncertaintiesfor the frost point hygrometer, RTD, and temperature readout. A few of the results for kaoliniteparticles are at Sice,onset values < 1 including error bars. This suggests that the uncertainties inSice,onset are slightly larger than reported. There should not be an offset in our measurementssince the relative humidity was calibrated with the ice frost point within the cell as mentionedabove.A total of 84 and 52 individual nucleation experiments were performed for kaolinite andillite, respectively. Measurements made with surface areas greater than ∼ 10−4 cm2 show bothkaolinite and illite to be very good ice nuclei; nucleation occurred at supersaturations of less291 0 - 5 1 0 - 4 1 0 - 3 1 0 - 20 . 9 00 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 5 1 1 0 1 0 0 1 0 0 01 0 - 5 1 0 - 4 1 0 - 3 1 0 - 20 . 9 00 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 01 1 0 1 0 0 1 0 0 01 0 - 5 1 0 - 4 1 0 - 3 1 0 - 20 . 9 81 . 0 01 . 0 21 . 0 41 . 0 61 . 0 81 . 1 01 . 1 21 . 1 4 1 1 0 1 0 0 1 0 0 0S ice, onset S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e s( b )( a )S ice, r=0.05 S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e sa  =  3 oa  =  7 o a  =  1 4 oS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 )( c ) N u m b e r  o f  p a r t i c l e sFigure 3.4: Results for kaolinite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results, and (c) average Sice, r=0.05. The average values are calcu-lated for four equally sized bins and the horizontal error bars show the range ofdata points in each bin. The surface area values in (c) represent the average surfacearea of the points in each bin. Error in Sice,onset is given as experimental error inmeasurements of saturation. Error in Sice, r=0.05 is based on the difference betweenSice,onset and Sice,previous as well as the uncertainty in measuring Sice,onset. Errorin the average Sice, r=0.05 represents the 95 % confidence interval. Predictions areshown using the single-α scheme (orange lines) calculated using Eq. (3.7). In ad-dition to surface area, the corresponding number of particles calculated from Aavgis also shown.301 0 - 5 1 0 - 4 1 0 - 30 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 1 0 1 0 01 0 - 5 1 0 - 4 1 0 - 30 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 1 0 1 0 01 0 - 5 1 0 - 4 1 0 - 31 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 01 1 0 1 0 0S ice, onset S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e sS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e sa  =  3 oa  =  7 oa  =  1 4 oa  =  2 0 oS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 )( b )( a )( c )N u m b e r  o f  p a r t i c l e s  Figure 3.5: Results for illite particles: (a) individual onset measurements, (b) individualSice, r=0.05 results, and (c) average Sice, r=0.05. The average values are calculated forfour equally sized bins and the horizontal error bars show the range of data pointsin each bin. The surface area values in (c) represent the average surface area of thepoints in each bin. Error in Sice,onset is given as experimental error in measurementsof saturation. Error in Sice, r=0.05 is based on the difference between Sice,onset andSice,previous as well as the uncertainty in measuring Sice,onset. Error in the averageSice, r=0.05 represents the 95 % confidence interval. Predictions are shown using thesingle-α scheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is also shown.31than 5 %. These results are consistent with previous measurements for both kaolinite and illiteparticles [Bailey and Hallett, 2002; Chernoff and Bertram, 2010; Eastwood et al., 2008; Kanjiet al., 2008; Mo¨hler et al., 2008a,c; Salam et al., 2006; Welti et al., 2009; Zimmermann et al.,2007, 2008]. The measurements made at low surface coverages(< 10−4 cm2), however, showa different trend than was observed for high surface coverages. Onset values were observedover a broad range of saturation ratios (100 % to 125 %). The spread in onset values betweendifferent experiments is greater than the uncertainty in the measurements of Sice.3.3.2 Sice, r=0.05 as a function of surface areaSice,onset values reported in Figs. 3.4a and 3.5a correspond to the conditions when the number ofnucleation events is greater than or equal to 1. Since the time between images is 20s, at Sice,onsetthe rate of nucleation, r, is ≥ 0.05s−1. In the previous image (collected before Sice,onset, whichwe define as Sice,previous) there was no nucleation, i.e. r = 0s−1. As a result, r = 0.05s−1somewhere within the range Sice,onset to Sice,previous. For the calculations that follow, we definea new variable, the ice saturation ratio at which the nucleation rate equals 0.05s−1 (Sice, r=0.05).Sice, r=0.05 can be calculated with the following equation:Sice, r=0.05 =(Sice,previous +Sice,onset)2. (3.3)Figures 3.4b and 3.5b show individual Sice, r=0.05 values as a function of surface area. Theuncertainty in Sice, r=0.05 includes the difference between Sice,onset and Sice,previous as well as theuncertainty in measuring Sice,onset. Sice,onset and Sice, r=0.05 are very similar, but Sice, r=0.05 ismore useful when discussing nucleation rates.Figures 3.4c and 3.5c show average Sice, r=0.05 values calculated from the data presented inFigs. 3.4b and 3.5b. To determine averages, the data were binned as a function of surface areainto equally spaced bins on a logarithmic scale. The uncertainty in the average Sice, r=0.05 valuesreported in Figs. 3.4c and 3.5c correspond to the 95 % confidence interval for the averages. Ascan be seen from the figures, the average Sice, r=0.05 values clearly increase with decreasing32surface area. Kanji and Abbatt [2010] observed a similar trend for deposition nucleation.3.3.3 Fraction of particles nucleated as a function of Sice, r=0.05A convenient way of displaying the data involves calculating the fraction of particles nucleatedin an experiment as a function of Sice. Presenting the data in this manner allows for a directcomparison with the pdf-α scheme, the active site scheme, and the deterministic scheme (seebelow). Since the number of particles nucleated at Sice, r=0.05 equals 1, the fraction nucleated iscalculated by dividing 1 by the total number of particles available to nucleate ice (Ntotal).In Figs. 3.6a and 3.7a we show the fraction of particles nucleated as a function of Sice, r=0.05for each of the individual experimental results. Shown in Figs. 3.6b and 3.7b are averagefraction nucleated values calculated from the data shown in Figs. 3.6a and 3.7a. To deter-mine averages, the data was binned as a function of Sice, r=0.05 into four equally spaced bins.Figures 3.6b and 3.7b show an increase in fraction nucleated with increasing Sice, r=0.05 as ex-pected.3.4 Discussion3.4.1 Single-α schemeAs discussed in Chapter 2, CNT [Pruppacher and Klett, 1997] relates the rate of heterogeneousice nucleation ( jhet, in units of cm−2 s−1) to the energy barrier for ice cluster formation on thesubstrate surface:jhet = j0 exp(−∆Gact f (α)kT)= j0 exp{−16piσ3i/v3kT [kT Ni lnSice]2fhet(α)}, (3.4)where ∆Gact is the activation barrier to ice nucleation, fhet(α) is the contact parameter ofthe cluster on the surface, j0 is the pre-exponential factor in cm−2 s−1, k is the Boltzmannconstant, and T is the temperature in degrees Kelvin. σi/v is the ice-vapour interfacial energyin Jcm−2, Ni is the molecular concentration of ice in cm−3, and Sice is the saturation ratio over330 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 51 0 - 11 0 0 0 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 50 . 0 10 . 11   E x p e r i m e n t a l  d a t a S i n g l e - α m o d e l P D F - α m o d e l A c t i v e  s i t e  m o d e l D e t e r m i n i s t i c  m o d e lFraction nucleatedS i c e ,  r = 0 . 0 5( a )( b )  Fraction nucleatedS i c e ,  r = 0 . 0 5Figure 3.6: Fraction of particles nucleated as a function of Sice, r=0.05 for kaolinite. Panel(a) shows the nucleated fraction for the individual experimental results. The y-errorwas calculated from the uncertainty in the value of D¯g. The x-error represents theuncertainty in Sice, r=0.05. Panel (b) shows the average nucleated fraction calculatedfor four size bins. The range of the data points in each bin is given as the horizontalerror and data points represent the average of the Sice, r=0.05 values within eachbin. The y-error bar in panel (b) represents the 95% confidence interval of theaverage nucleated fraction. Fits are shown for the single-α , pdf-α , active site, anddeterministic schemes.340 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 5 1 . 3 01 0 - 31 0 - 21 0 - 11 0 0 0 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 5 1 . 3 01 0- 31 0 - 21 0 - 11 0 0   E x p e r i m e n t a l  d a t a S i n g l e - α m o d e l P D F - α m o d e l A c t i v e  s i t e  m o d e l D e t e r m i n i s t i c  m o d e lFraction nucleatedS i c e ,  r = 0 . 0 5 ( b )( a )  Fraction nucleatedS i c e ,  r = 0 . 0 5Figure 3.7: Fraction of particles nucleated as a function of Sice, r=0.05 for illite. Panel (a)shows the nucleated fraction for the individual experimental results. The y-errorwas calculated from the uncertainty in the value of D¯g. The x-error represents theuncertainty in Sice, r=0.05. Panel (b) shows the average nucleated fraction calculatedfor four size bins. The range of the data points in each bin is given as the horizontalerror and data points represent the average of the Sice, r=0.05 values within eachbin. The y-error bar in panel (b) represents the 95% confidence interval of theaverage nucleated fraction. Fits are shown for the single-α , pdf-α , active site, anddeterministic schemes.35the particles.For particle radii significantly larger than the radius of an ice cluster (a good approximationunder our conditions), fhet(α) can be described by the following equation:fhet(α) =(2+ cosα)(1− cosα)24, (3.5)where α is the contact angle of the ice cluster on the particle surface. The physical meaningof the contact angle is not well understood and it is often used as a means of parameterizinglaboratory data.The heterogeneous nucleation rate can be expressed as a function of area, time and numberof nucleation events using the following equation:jhet =ωAtotal∆t, (3.6)where ω is the number of nucleation events, Atotal is the total surface area of particles in cm2and ∆t is the time scale of the measurements. Equations (3.4) and (3.6) can be combined togive the following relationship between Sice, area, time and the number of nucleation events:lnSice =√√√√√16piσ3i/v fhet(α)3kT ln(Atotal j0∆tω)1NikT. (3.7)Equation (3.7) can be used to predict the relationship between Sice, r=0.05 and surface area.At Sice, r=0.05 the number of nucleation events, ω , is, by definition, 1, and the time for nucleationis 20 s.In Figs. 3.4c and 3.5c (solid lines) we have calculated Sice, r=0.05 as a function of Atotal usingEq. (3.7), ω = 1, ∆t = 20s and different contact angles. We also used an interfacial energy of1.065× 10−5 Jcm−2 [Pruppacher and Klett, 1997], a pre-exponential factor of 1025 cm−2 s−1[Fletcher, 1958, 1959; Pruppacher and Klett, 1997] and a molecular concentration of ice of363.1× 1022 cm−3 (calculated from the molecular mass and density of ice [Lide, 2001]). Boththe values of σi/v and Ni are calculated for hexagonal ice. Recent findings have shown thatcubic ice is formed preferentially for homogeneous nucleation [Murray and Bertram, 2006;Murray et al., 2005] but more information is needed to determine the polymorph of ice that isformed by heterogeneous nucleation.It can be seen in Figs. 3.4c and 3.5c that there is no single contact angle capable of accu-rately describing the data. Measurements made at high surface areas are described by a lowvalue of the contact angle (α ≈ 3◦ for kaolinite and α ≈ 7◦ for illite). Comparatively, themeasurements made at the lowest surface areas are described by a much larger contact angle(α ≈ 14◦ for kaolinite and α ≈ 20◦ for illite).The single-α scheme can also be used to predict the fraction of particles nucleated as afunction of Sice, r=0.05 as in Figs. 3.6b and 3.7b. Equation (3.8) shows the relationship betweenthe fraction of particles nucleated and the heterogeneous nucleation rate [Pruppacher and Klett,1997]:N fN0= 1−∫ ∞0exp[−piD2 jhet (α,T,Sice)∆t]pnum (D)dD, (3.8)whereN fN0is the fraction of particles nucleated, jhet is the heterogeneous nucleation rate whichcan be calculated from Eq. (3.4), D is the diameter of a single kaolinite or illite particle, andpnum(D) is the number distribution calculated from data presented in Fig. 3.3. The valuepnum (D)dD represents the fraction of particles having a diameter between D and D+dD.Shown in Figs. 3.6b and 3.7b (orange lines) are fits to the fraction nucleated as a functionof Sice, r=0.05 obtained by numerical rectangular integration of Eq. (3.8) and assuming a singlecontact angle. In these calculations 20 s was used for the time scale of the experiment as doneabove. It can be seen from Figs. 3.6b and 3.7b that the single-α scheme cannot describe ourexperimental data. The parameters from the fitting procedure are listed in Tables 3.1 and 3.2.37Table 3.1: Fit parameters obtained for kaolinite. Best fits were obtained by minimizingthe weighted sum of squared residuals (WSSR) between the experimental data andthe fit function. See text for further discussion on the schemes used.Scheme Parameter Value WSSRasingle-α α 12.53◦ 9.443pdf-α µα 0◦3.888σα 26.08◦active siteb 6.19×109m−25.081β1 0.01β2 0.001deterministic A1 2.31×106cm−2 0.718A2 −0.8845a Weighted sum of squared residualsTable 3.2: Fit parameters obtained for illite. Best fits were obtained by minimizing theweighted sum of squared residuals (WSSR) between the experimental data and thefit function. See text for further discussion on the schemes used.Scheme Parameter Value WSSRasingle-α α 21.75◦ 9.778pdf-α µα 28.94◦0.0468σα 12.75◦active siteb 8.70×109m−20.490β1 0.1351β2 1.0×10−4deterministic A1 1.78×106cm−2 0.0190A2 −0.9481a Weighted sum of squared residuals3.4.2 Pdf-α schemeAs mentioned above, the pdf-α scheme is a modification of the single-α scheme [Lu¨o¨nd et al.,2010; Marcolli et al., 2007]. This scheme assumes that a single contact angle can describeice nucleation on an individual particle, but that a distribution of contact angles exists foran ensemble of particles. Assuming a normal distribution of contact angles, the fraction ofnucleated particles is given byN fN0= 1−∫ ∞0∫ pi0exp[−piD2 jhet (α,T,Sice)∆t]p(α)pnum (D)dα dD, (3.9)38where p(α) is the normal probability distribution at a particular value of α . The value p(α)dαis the fraction of particles having a contact angle between α and α + dα . The normal proba-bility distribution is described by the following equation:p(α) = 1σα√2piexp[−(α−µα)22σ2α], (3.10)where µα and σα are the mean and standard deviation of the distribution, respectively. Thevalue of µα is constrained such that µα ≥ 0 and p(α) is normalized such that∫ pi0 p(α)dα = 1.The blue lines in Figs. 3.6b and 3.7b show calculations of the fraction nucleated as a func-tion of Sice, r=0.05 using Eq. (3.9). Similar to the previous calculations, an experimental timeof 20s was used. The data was fit by numerical rectangular integration of Eq. (3.9) and byvarying the parameters µα and σα .The best fit to the kaolinite data (blue line in Fig. 3.6b) gave a mean contact angle (µα )of 0◦ and a width (σα ) of 26.1◦. The best fit to the illite data (blue line in Fig. 3.7b) gavea mean contact angle of 28.9◦ and a standard deviation of 12.8◦. The distribution of contactangles are shown (black lines) in Fig. 3.8 for kaolinite and Fig. 3.9 for illite. Figures 3.6b and3.7b show that the pdf-α scheme agrees with the experimental data within the uncertainty ofthe measurements.3.4.3 Active site schemeThe third method used to fit the experimental data was the active site scheme, which is amodification of the single-α scheme that includes the existence of active sites [Fletcher, 1969;Gorbunov and Kakutkina, 1982; Han et al., 2002; Lu¨o¨nd et al., 2010; Marcolli et al., 2007;Niedermeier et al., 2011b]. The equations presented here are the same as those presented byLu¨o¨nd et al. [2010].In contrast to the previous schemes, the active site scheme assumes ice nucleation occursmore readily on small sites on the particle surface as opposed being equally probable anywhereon the particle surface. For consistency, we assume that the size of an active site is constant390 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 00 . 0 0 00 . 0 0 50 . 0 1 00 . 0 1 50 . 0 2 00 . 0 2 50 . 0 3 001 x 1 0 92 x 1 0 93 x 1 0 94 x 1 0 95 x 1 0 96 x 1 0 9f α(α)α ( d e g r e e s )  Surface density of active sites (m-2 )Figure 3.8: Probability distribution function for the pdf-α scheme and surface density ofactive sites, ρ(α), for the active site scheme. Shown are the results for kaoliniteparticles.and equal to 6 nm2 as done by Lu¨o¨nd et al. [2010]. This is calculated from the critical icecluster size determined for homogeneous nucleation of liquid water at 239 K using classicalnucleation theory. The active site scheme assumes that the probability of ice nucleation on anactive site is defined by a contact angle, αi, and this contact angle can vary from site to site.Similar to Eq. (3.8) presented above, the probability of nucleation on a single active sitewith contact angle, α , isPsite(α) = 1− exp [−AαJhet (α,T,Sice)∆t] , (3.11)where Psite(α) is the probability of nucleation, jhet (α,T,Sice) is the temperature, saturation and400 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 00 . 0 0 00 . 0 0 50 . 0 1 00 . 0 1 50 . 0 2 00 . 0 2 50 . 0 3 00 . 0 3 50 . 02 . 0 x 1 094 . 0 x 1 0 96 . 0 x 1 098 . 0 x 1 0 9f α(α)α ( d e g r e e s )  Surface density of active sites (m-2 )Figure 3.9: Probability distribution function for the pdf-α scheme and surface densityof active sites, ρ(α), for the active site scheme. Shown are the results for illiteparticles.contact angle dependent heterogeneous nucleation rate given by Eq. (3.4), Aα is the area of theactive site (6 nm2), and ∆t is the time of observation. Similarly, the probability that nucleationdoes not occur on a single active site with contact angle α isP¯site(α) = exp [−AαJhet (α,T,Sice)∆t] . (3.12)The probability of nucleation of a single particle is described by the following equation, whichtakes into account the assumptions that a single particle can have multiple active sites and41active sites can have a range of contact angles:Pparticle (Sice) = 1−m∏i=1P¯site (αi) = 1−m∏i=1exp [−AαiJhet (αi,T,Sice)∆t] , (3.13)where Pparticle(Sice) is the probability of nucleation of a single particle and P¯site(αi) is the prob-ability that an active site with a contact angle of αi does not nucleate ice. Aαi is the total surfacearea of active sites with a contact angle in the range (αi, αi +∆α) where ∆α is the width of theindividual bin such that the total number of bins is equal to m. Aαi represents the summationof all active sites within the specified range, each with an area of 6 nm2. Therefore, Aαi is aninteger multiple of the single active site area(Aαi = ni(6nm2)).The average number of active sites on a single particle in the range (αi,αi +∆α), n¯i, isgiven byn¯i = pi D2ρ (αi)∆α, (3.14)where D is the diameter of the particle and ρ(α) is the contact angle dependent surface densityof active sites (i.e. number of active sites per unit surface area per unit contact angle interval).The number of active sites on a single particle, ni, in the range (αi,αi +∆α), was assignedusing Poisson distributed random variables with the expectation value given by Eq. (3.14).The ni values determined from Poisson statistics were then used in Eq. (3.13) to determinethe nucleation probabilities, Pparticle(Sice), of a single particle. This whole process was thenrepeated 1000 times to determine nucleation probabilities of an ensemble of 1000 particles.The diameter of each particle was assigned using uniform random numbers in the range [0,1]and the cumulative distribution functions calculated from the data presented in Fig. 3.3. Thenucleated fraction was then determined using the following equation:N fN0= 11000j=1000∑j=1Pparticle, j (Sice) . (3.15)As was done by Marcolli et al. [2007] and Lu¨o¨nd et al. [2010], the surface density of active42sites was described using a three parameter exponential function of the following form:ρ(α) = bexp( −β1α−β2). (3.16)The experimentally determined nucleated fractions were fit to the active site scheme byvarying the parameters, b, β1, and β2. Results are shown (green lines) in Figs. 3.6b and 3.7bfor kaolinite and illite, respectively. As can be seen in the figures, the active site scheme fits thedata within the experimental error. Fit parameters are reported in Table 3.1 and 3.2 for kaoliniteand illite, respectively. Other combinations of two of the fitting parameters, β1 and β2, werefound which provided equivalent fits to the ones presented (i.e. no single set of parameters bestdescribed the data). This was attributed to the low number of data points upon which the fitsare based.The fact that the experimental data is in agreement with the active site scheme is consistentwith recent computer simulations of ice nucleation at the molecular level. These simulationsshow that the good ice nucleation characteristics of mineral dust is not likely due to the crystal-lographic match between the mineral surface and hexagonal ice, but rather may be due to icenucleation on defects such as trenches [Croteau et al., 2008, 2010; Hu and Michaelides, 2007].3.4.4 Deterministic schemeA final scheme used here is the deterministic scheme [Connolly et al., 2009; Lu¨o¨nd et al., 2010].For deposition nucleation, we assume that the particles have a surface density of active sites,ns, that is a function of Sice, r=0.05, but independent of temperature over the narrow range oftemperatures investigated (239−242K). The assumption of temperature independence for nsshould be reasonable based on previous measurements of Sice,onset as a function of temperaturefor kaolinite particles [Eastwood et al., 2008], which show that Sice,onset is relatively insensitiveto temperature over the range of 236− 246K. It is also assumed that the fraction of particlesnucleated at a given Sice is independent of time but related to ns (Sice) through the following43equation:N fN0= 1−∫ ∞0exp[−piD2 ns (Sice)]pnum (D)dD. (3.17)The surface density of active sites, ns (Sice), was described by [Connolly et al., 2009; Lu¨o¨ndet al., 2010],ns (Sice) =0, Sice ≤−A2 or Sice ≤ 1A1 (Sice +A2)2 , otherwise.(3.18)Using Eqs. (3.17) and (3.18), the experimentally determined nucleated fractions were fitusing the parameters A1 and A2. Good agreement was found between the experimental dataand the deterministic scheme (red lines in Figs. 3.6b and 3.7b). Fit parameters can be found inTables 3.1 and 3.2 for kaolinite and illite, respectively.3.4.5 Sensitivity of the results to the assumption of spherical particlesThe calculations above were carried out with the assumption that the surface area of a particleequals the geometric surface area (i.e. the particles are spherical). We assume this is a lowerlimit to the total surface area available for nucleation. Based on scanning electron microscopemeasurements of a limited number of mineral particles, we estimate that an upper limit to thesurface area of the particles equals the geometric surface area multiplied by a factor of 50[Eastwood et al., 2008]. We have reanalyzed the experimental data and redone the calculationswith the assumption that the surface area of the particles equals the geometric surface areamultiplied by 50. The results from this analysis and calculations are shown in Appendix A(Tables A.1 and A.2 and Figs. A.1 - A.4).In short, when using a geometric surface area multiplied by 50, the single-α scheme doesnot describe the data but the pdf-α scheme, active site scheme, and deterministic scheme all fitthe data within the experimental error. The fit parameters for the single-α and pdf-α schemesvary by less than 3 % compared with the parameters presented in Tables 3.1 and 3.2. For thedeterministic scheme, the parameter A2 is the same as presented in Tables 3.1 and 3.2 and theparameter A1 is reduced by a factor of 50.443.4.6 Comparisons with previous measurementsPrevious studies have also used various nucleation data to test whether or not the single-αscheme can be used to accurately describe heterogeneous ice nucleation data for mineral dustparticles. Several studies have shown that modifications to the single-α scheme are requiredfor accurate predictions of heterogeneous nucleation data [Archuleta et al., 2005; Hung et al.,2003; Lu¨o¨nd et al., 2010; Marcolli et al., 2007; Welti et al., 2009]. Most similar to our studies,Welti et al. [2009] studied ice nucleation on mineral dust particles, including illite and kaolinite,in the deposition mode. Relative humidities with respect to ice required to activate 1% of thedust particles as ice nuclei (IN) were reported as a function of temperature. An explicit sizedependence of the ice formation efficiency was observed for all dust types. Particles 800nmin diameter required the lowest Sice to activate. Similar to the main conclusions in our study,these authors found that a single contact angle could not describe freezing results for differentparticle diameters of a single mineral.Murray et al. [2011] investigated immersion freezing by kaolinite particles as a function ofdust concentration and cooling rate. In contrast with the references mentioned above, the datafrom this study were consistent with classical nucleation theory and the assumption of a singlecontact angle (the single-α scheme). The source of the kaolinite material used by Murray et al.was the Clay Minerals Society, which is a different source compared to our experiments. Inaddition, the work of Murray et al. investigated immersion freezing while our work examineddeposition nucleation. Future studies investigating the ice nucleation properties of differentmineral sources may provide some insight into the apparent discrepancies.3.5 Conclusions and atmospheric implicationsDeposition nucleation of ice on kaolinite and illite particles, two abundant minerals in the at-mosphere, was investigated. The onset Sice conditions for ice nucleation were a strong functionof the surface area available for ice nucleation. For example, in the kaolinite experiments onsetSice values ranged from 100 % to 125 % depending on the surface area used in the experiments.45The surface area dependent results were used to test the applicability of classical nucleationtheory with a single contact angle as a method to parameterize heterogeneous ice nucleationdata. The surface area dependent data could not be described accurately using this scheme.These results add to the growing body of evidence that suggests that, in many cases, the single-α scheme is not appropriate for predictions of heterogeneous nucleation. The results alsosuggest that caution should be applied when using contact angles determined from the single-α scheme and onset data. This is because different contact angles can be derived from onsetSice data and the single-α scheme depending on the surface area used in the experiments. As anexample, the contact angle consistent with our kaolinite data varied from 3◦ to 14◦ dependingon the surface area. Fits were also performed using the pdf-α scheme, the active site scheme,and the deterministic scheme. In contrast to the single-α scheme, the other schemes used all fitthe data within experimental uncertainties. Parameters from the fits to the data were presented.These parameters are applicable to the temperature range studied (239 - 242 K). Further studiesare needed to determine if the parameters apply to temperatures outside this range.46Chapter 4Immersion freezing of supermicronmineral dust particles: freezing results,testing different schemes for describing icenucleation, and ice nucleation active sitedensities4.1 IntroductionIce nucleation in the atmosphere can influence precipitation and the properties of clouds, whichcan in turn influence the radiative properties of the Earth-atmosphere system [DeMott et al.,2010; Denman et al., 2007; Lohmann and Feichter, 2005]. A better understanding of the con-ditions necessary for ice nucleation may enable more accurate modelling of clouds and precip-itation and may reduce uncertainties in climate models. Ice nucleation in the atmosphere canoccur through two mechanisms: homogeneous or heterogeneous ice nucleation. Homogeneousice nucleation occurs within a supercooled solution drop in the absence of insoluble ice nuclei47(IN) and is limited to temperatures < -37 ◦C, whereas heterogeneous ice nucleation requiresthe presence of an IN and can occur at warmer temperatures. Heterogeneous ice nucleation canoccur through several different modes: deposition, immersion, condensation and contact nucle-ation [Vali, 1985]. A detailed description of these different modes can be found in Chapter 1.Here we focus on immersion freezing of pure water drops with mineral dust inclusions.Based on field, laboratory, and modelling studies, mineral dust is known to be an importantheterogeneous ice nuclei in the atmosphere. For example, previous field studies have observedthat mineral dust particles are an important component of the atmospheric IN population [Cz-iczo et al., 2004, 2013; DeMott et al., 2003b,a; Ebert et al., 2011; Isono et al., 1959; Kumai,1961; Prenni et al., 2009; Pruppacher and Klett, 1997; Richardson et al., 2007; Sassen et al.,2003; Seifert et al., 2010; Targino et al., 2006]. Many laboratory studies have also found thatmineral dust particles are efficient IN [Atkinson et al., 2013; Connolly et al., 2009; Eastwoodet al., 2008; Hoose and Mo¨hler, 2012; Knopf and Koop, 2006; Lu¨o¨nd et al., 2010; Marcolliet al., 2007; Murray et al., 2011; Niedermeier et al., 2010; Pinti et al., 2012; Roberts andHallett, 1968; Welti et al., 2012; Wheeler and Bertram, 2012; Yakobi-Hancock et al., 2013;Zimmermann et al., 2008]. In addition, modelling studies have shown that mineral dust par-ticles can cause ice to form in clouds at warmer temperatures than required for homogeneousfreezing [Diehl and Wurzler, 2010; Hoose et al., 2008, 2010a,b; Lohmann and Diehl, 2006].To accurately implement ice nucleation in atmospheric models, a suitable theory or schemeis desired to represent freezing data in atmospheric models. Recent work has illustrated thatthe cloud properties predicted with atmospheric models are sensitive to the scheme used todescribe ice nucleation in the models [Eidhammer et al., 2009; Ervens and Feingold, 2012;Kulkarni et al., 2012; Wang and Liu, 2014; Wang et al., 2014]. For example, Ervens andFeingold [2012] implemented five different schemes for ice nucleation into an adiabatic parcelmodel and found that for polydisperse IN, differences of up to an order of magnitude are seen inthe ice number concentration and ice water content of a cloud depending on the scheme used.Since atmospheric modelling shows that predictions are sensitive to schemes for describing48ice nucleation, information on which scheme is best able to reproduce freezing data would beuseful. Relative rankings of the different schemes in terms of ability to reproduce freezing datamay be useful when deciding which schemes are to be used in modelling studies and whenconsidering trade-offs between accuracy and computational efficiency.Listed below are four different schemes that have been used in the past to represent labora-tory data in atmospheric models. These schemes have been discussed in Chapter 3 and are onlybriefly discussed here. The first scheme, the single-α scheme [Fletcher, 1958; Pruppacher andKlett, 1997], contains one parameter and is based on classical nucleation theory. Nucleation isassumed to be a stochastic process and can occur with equal probability anywhere on a particlesurface. The nucleation ability of a particle is described with a single parameter, the contactangle (α). The second scheme, the pdf-α scheme [Lu¨o¨nd et al., 2010; Marcolli et al., 2007], isa modification of the single-α scheme allowing for a distribution of contact angles among anensemble of particles. The third scheme, the active site scheme [Fletcher, 1969; Lu¨o¨nd et al.,2010; Niedermeier et al., 2011b], further extends the single-α scheme by allowing nucleationto occur only on small sites on the particle surface, termed “active sites”. A distribution ofthese active sites among the particles is assumed to be responsible for the freezing behaviour.The final scheme used here is the deterministic scheme [Connolly et al., 2009] which, unlikethe previous schemes, is not derived from classical nucleation theory. Instead, nucleation isassumed to occur instantaneously on a particle upon reaching a characteristic freezing temper-ature.There have been several previous studies that have compared laboratory results of mineraldust freezing properties with different schemes for describing ice nucleation [Broadley et al.,2012; Lu¨o¨nd et al., 2010; Marcolli et al., 2007; Murray et al., 2011; Niedermeier et al., 2010;Welti et al., 2012; Wheeler and Bertram, 2012]. However, there is still no consensus in termsof which scheme is best able to reproduce laboratory freezing data. Here we investigate theimmersion freezing of size-selected Arizona Test Dust (ATD) and kaolinite particles with amajority of diameters in the supermicron mode. The new size-selected freezing data is used49to test the four different schemes discussed above (single-α scheme, pdf-α scheme, active sitescheme, and deterministic scheme).In addition to testing different schemes for describing ice nucleation, we also determinedfrom our immersion freezing data the ice nucleation active site (INAS) density of the size-selected supermicron mineral dust particles studied. This is the first study to determine INASdensities of size-selected supermicron dust particles. This information is compared to INASdensities previously determined in the literature. INAS densities can be used to summarizethe freezing properties of particles, to determine the relative importance of different types ofatmospheric particles, and to make atmospheric predictions. As pointed out by Hoose andMo¨hler [2012], the size dependence of INAS densities has not been studied carefully in thepast. If there is a difference between INAS densities for submicron and supermicron particles,then this needs to be considered when using INAS values for atmospheric predictions and forcomparing different types of IN.Kaolinite was chosen for these studies because it makes up a significant portion of atmo-spheric mineral dust (up to 60 %) [Claquin et al., 1999; Glaccum and Prospero, 1980]. Inaddition, the freezing properties of kaolinite particles has been studied extensively as an icenucleus in the laboratory [Friedman et al., 2011; Hoffer, 1961; Lu¨o¨nd et al., 2010; Murrayet al., 2011; Pinti et al., 2012; Pitter and Pruppacher, 1973; Roberts and Hallett, 1968; Weltiet al., 2009; Zimmermann et al., 2008]. Since the kaolinite used here (Clay Minerals Soci-ety (CMS) KGa-1b) contains very little contamination by other mineral types (96 % kaolinite[Chipera and Bish, 2001]), this mineral is suited to test the single component stochastic scheme(single-α) discussed above. ATD was chosen for these studies because it is a multi-componentdust [Broadley et al., 2012] (like natural atmospheric dust) and because it contains mineralsthat have been observed in natural mineral dust [Broadley et al., 2012; Claquin et al., 1999;Glaccum and Prospero, 1980] (see Fig. 1.4 in Chapter 1 for the mineral composition of ATD).In addition, many investigations of immersion freezing have used ATD, which provides a largedataset for comparison purposes [Connolly et al., 2009; Cziczo et al., 2009; Hoyle et al., 2011;50Kanji and Abbatt, 2010; Knopf and Koop, 2006; Koehler et al., 2010; Koop and Zobrist, 2009;Marcolli et al., 2007; Niedermeier et al., 2010, 2011a; Niemand et al., 2012; Reitz et al., 2011;Welti et al., 2009].4.2 Experimental4.2.1 Freezing measurementsThe immersion freezing of dust particles was measured using an optical microscope coupledto a flow cell. Figure 3.1 shows a schematic of the instrumental setup. The flow cell used herehas both temperature and humidity control and has been used previously to measure ice nu-cleation in both the immersion and deposition modes [Chernoff and Bertram, 2010; Dymarskaet al., 2006; Eastwood et al., 2008, 2009; Haga et al., 2013; Iannone et al., 2011; Wheeler andBertram, 2012]. The apparatus is based in part on an earlier design that used an optical mi-croscope coupled to a freezing cell to investigate homogeneous freezing [Koop et al., 2000].Below is a brief description of the apparatus used here and the experimental protocol.Particles of interest were deposited on a hydrophobic glass slide (Hampton Research). Theglass slide containing the dust particles was then placed at the bottom of the flow cell. The latterwas contained in an aluminum block which allowed for accurate control of the temperature. Agas stream was passed over the particles to control the humidity to which the particles wereexposed. The flow cell used in the present study was modified from that shown in Fig. 3.1by placing a gold coated silicon wafer between the Al block and the glass slide containingthe sample to provide better contrast in the optical images. The addition of the silicon waferdid not produce a difference in freezing temperature which was confirmed by measuring thehomogeneous freezing of pure water drops (∼ 100µm diameter) both with and without thesilicon wafer. The median homogeneous freezing temperatures were not statistically differentwith and without the silicon wafer. The particles inside the flow cell were observed using anoptical microscope (Zeiss Axiolab 50X magnification).The experimental procedure began by increasing the humidity to above water saturation51in order to condense water on the particles held at a constant temperature of 0 ◦C. After thedrops were grown, the relative humidity was decreased in order to slightly evaporate the dropsallowing more space between each drop. After partial evaporation, the size of the drops rangedfrom 10µm and 70µm. The temperature of the cell was then lowered at a constant rate of10◦Cmin−1 until all the drops froze. A cooling rate of 10◦Cmin−1 was chosen in order toreduce the amount of vapour transfer between frozen and unfrozen drops during the courseof a single experiment. Video of the drops was recorded throughout the entire experiment.Video recorded during water condensation was used to determine the surface area of mineraldust particles within each drop while video taken during freezing was used to determine thefreezing temperature of each drop.Figure 4.1 shows the temperature profile used for these measurements. Figure 4.2 showsthe particles at different steps of the experiment with the Roman numerals indicating the corre-sponding time and temperature in Fig. 4.1. From top to bottom, the images correspond to thedrops at the beginning of an experiment, the drops after water condensation and evaporation,the ice crystals after freezing of all the drops, and the remaining particles after melting of theice crystals and evaporation of the drops.4.2.2 Sample generationATD (Ultrafine A1) was acquired from Powder Technologies Inc. and kaolinite (KGa-1b) wasacquired from the Clay Minerals Society (CMS). We employed a dry generation method herein order to more accurately represent freshly emitted mineral dust. Studies have shown thatthe method of sample generation (wet versus dry generation) can affect both the CCN and INactivity of mineral dust particles [Herich et al., 2009; Koehler et al., 2010], most likely dueto the dissolution of soluble material on the particle surface during wet generation methods.The dust samples were aerosolized using a fluidized bed (TSI model 3400A) with the cycloneattachment removed. The aerosolized sample was then passed through a six-stage Andersencascade impactor with a hydrophobic glass slide placed on the fourth stage of the impactor.52Figure 4.1: Temperature profile used in the freezing experiments. Labels correspond toconditions at which the images in Fig. 4.2 were recorded.The fourth stage of the impactor has a nominal aerodynamic size cut of 2.0− 3.5µm whenoperated at 28 lpm [Andersen, 1958]. This corresponds to a geometric diameter size cut of1.3−2.2µm for mineral dust, assuming an average density of 2.5gcm−3.4.2.3 Surface area per dropSurface areas of solid particles contained in each drop were determined from images recordedduring the freezing experiments before and after condensing water. First, the individual dropswere identified from images recorded after condensing water (see row II from Fig. 4.2). Eachdrop was then traced backwards in time to when no water was condensed on the slide (rowI from Fig. 4.2) to determine which dust particles were contained within each drop. This isillustrated in Fig. 4.2, row I, where the green traces outline the dust particles contained in each53ATD KaoliniteI T = 0◦CII T = 0◦CIII T = -40◦CIV T = 12◦CFigure 4.2: Example of optical images collected during a freezing experiment. Panels(a) - (d) show images from an ATD experiment while panels (e) - (h) show imagesfrom a kaolinite experiment. Rows I-IV correspond to particles before condensingwater, particles after condensing water, drops after freezing, and inclusions con-tained in each drop after evaporation, respectively. The green traces in row I rep-resent the area included in each drop in row II. See text for further details. LabelsI-IV can be used to determine the temperature and time in the freezing experimentfrom Fig. 4.1.54drop. Only those drops where all of the particles were contained within the original field ofview were included in the analysis. The surface area of dust contained within each drop wasmeasured using image processing software (ImageJ [Rasband, 1997-2014]), resulting in theprojected 2-dimensional geometric area of dust contained in each drop. In order to relate theprojected 2-dimensional area to a 3-dimensional geometric surface area, the area measured wasscaled by a factor of 4 (which assumes spherical particles).4.2.4 Size distribution of the mineral dust particlesIn experiments separate from the freezing experiments discussed above, size distributions ofthe mineral dust particles were determined using scanning electron microscopy (SEM; HitachiS-2600N). Hydrophobic glass slides containing the mineral dust particles were prepared usingthe same procedure outlined above for the freezing experiments. A total of 81 separate slideswere analyzed, and the projected 2-dimensional area of 5243 individual particles deposited onthe glass slides was determined from the SEM images. The corresponding data were used toobtain the number and surface area distribution of the particles for both mineral dusts. Highresolution SEM images (Hitachi S-4700) of the individual dust particles were also obtained toexamine the morphology of the dust particles.4.3 Results and discussion4.3.1 Surface area and size distribution of mineralsThe size distributions measured by SEM are shown in Figs. 4.3a and 4.4a for ATD and kaoli-nite, respectively. Based on these distributions, 15% of the ATD particles and 33% of thekaolinite particles have a diameter below 1µm. This represents less than 0.5% and 2% of thetotal measured surface areas for ATD and kaolinite respectively, indicating that a large fractionof the surface area of the particles studied lies in the supermicron range. The particle sizes ob-tained for kaolinite and ATD are slightly larger than was predicted by the specifications of theAndersen impactor (1.3−2.2µm), likely due to the non-spherical nature of the dust particles55(see SEM images of individual particles in Figs. 4.3b and 4.4b) or charging of the mineral dustparticles during the aerosolization process with the fluidized bed. High resolution SEM imagesof ATD and kaolinite particles are shown in Figs. 4.3b and 4.4b.Shown in Figs. 4.5 and 4.6 are the distribution of surface areas per drop in the freezingexperiments. Also shown is the number of particles per drop calculated using the mean particlediameter obtained from SEM images (mean diameter 3.0 and 2.5µm for ATD and kaoliniteparticles, respectively). Based on Figs. 4.5 and 4.6, the number of particles per drop in thefreezing experiments ranged from approximately 1-100.4.3.2 Freezing resultsPrior to studying the freezing of drops with ATD or kaolinite inclusions, we first measuredfreezing of drops (average size of 30µm) without inclusions (stars in Figs. 4.7 and 4.8). Mea-surements of the melting point of pure ice were used to correct the temperature of all freezingmeasurements. Repeated melting point measurements gave a standard deviation of 0.06◦C.This indicates the uncertainty in the temperature measurements obtained with this apparatus.The corrected median freezing temperature of the drops without inclusions was−37.7±0.2◦C.This temperature is within 0.1◦C of the median freezing temperature of 30µm pure water dropscalculated using Eq. 7-51 from Pruppacher and Klett [1997] and parameterizations for ice andwater properties from Pruppacher and Klett [1997] and Zobrist et al. [2007]. The agreementbetween our results and the calculated values indicates the hydrophobic surface does not causesignificant heterogeneous freezing and the results for drops without inclusions correspond tohomogeneous freezing. The median homogeneous freezing temperature reported here is colderthan previously reported using the same apparatus [Iannone et al., 2011]. This difference is dueto the smaller drops used here compared to those used by Iannone et al. [2011].In the heterogeneous freezing experiments, freezing occurred by both immersion freezingand contact freezing. Here immersion freezing refers to freezing of drops by IN immersed inthe liquid drops, and contact freezing refers to freezing of liquid drops by contact with neigh-5610−1 100 101Diameter (µm)010002000300040005000dN/dlogD(a)dN/dlogDdS/dlogD020000400006000080000100000120000140000160000180000dS/dlogD(b) (c)(d) (e)Figure 4.3: (a) Size distribution of ATD measured by SEM. Shown are the number, N,distribution (closed circles) and the surface area, S, distribution (closed squares)functions. (b) - (e) SEM images of individual ATD particles impacted on the slides.5710−1 100 101 102Diameter (µm)050010001500200025003000350040004500dN/dlogD(a)dN/dlogDdS/dlogD050000100000150000200000250000300000dS/dlogD(b) (c)(d) (e)Figure 4.4: (a) Size distribution of kaolinite measured by SEM. Shown are the number,N, distribution (closed circles) and the surface area, S, distribution (closed squares)functions. (b) - (e) SEM images of individual kaolinite particles impacted on theslides.5810−7 10−6 10−5 10−4Surface area/drop (cm2)01020304050Numberofdrops100 101 102Number of particles/dropFigure 4.5: Distribution of surface area of mineral dust particles per drop for ATD exper-iments. The upper abscissa shows the corresponding number of particles containedin each drop based on the average particle size determined from the SEM images(3µm).bouring frozen drops. Frozen drops can grow by vapour transfer and eventually can come incontact with their neighbouring liquid drops. Alternatively, frozen drops can cause their liquidneighbours to evaporate completely by vapour transfer from liquid drops to frozen drops dueto the lower saturation vapour pressure over ice compared with that over supercooled water.In Figs. 4.7 and 4.8 (closed circles), the fraction of drops which froze by immersion freezingare reported. When calculating the fraction frozen, the contact freezing and complete evapo-ration of supercooled drops was dealt with in two ways. In the first case we assumed that thedrops removed by contact freezing and evaporation froze by immersion freezing. This providesan upper limit to the fraction frozen by immersion freezing. In the second case we assumedthat the drops which were removed by contact freezing and evaporation remain liquid untilthe homogeneous freezing temperatures were reached. Since these drops contained mineraldust inclusions and could have frozen at temperatures warmer than homogeneous freezing, thisgives a lower limit to the fraction of drops frozen by immersion freezing. Calculations of the5910−8 10−7 10−6 10−5 10−4Surface area/drop (cm2)01020304050607080Numberofdrops10−1 100 101 102Number of particles/dropFigure 4.6: Distribution of surface area of mineral dust per drop for kaolinite experi-ments. The upper abscissa shows the corresponding number of particles containedin each drop based on the average particle size determined from the SEM images(2.5µm).fraction frozen were done at 0.5◦C intervals down to the onset of homogeneous freezing. Theclosed circles represent the median between the upper and lower limits at each temperature.As can be seen from Figs. 4.7 and 4.8, ATD in our experiments induces immersion freezingat warmer temperatures than kaolinite. The median freezing temperature of drops containingATD was measured to be approximately −30◦C compared with approximately −36◦C forkaolinite. The ATD containing drops were all observed to be frozen at temperatures warmerthan homogeneous freezing. Kaolinite containing drops on the other hand were not all frozenupon reaching temperatures where homogeneous freezing occurred.The results presented here are the first size-selected freezing studies to focus on supermi-cron dust particles. The median freezing temperatures for the supermicron dust fall within therange of median freezing temperatures measured previously for submicron dust particles of thesame composition [Hoffer, 1961; Hoyle et al., 2011; Lu¨o¨nd et al., 2010; Murray et al., 2011;Niedermeier et al., 2010, 2011a; Pitter and Pruppacher, 1973; Welti et al., 2012]. However,60−40 −35 −30 −25 −20 −15 −10 −5 0Temperature (◦C)0.00.20.40.60.81.0Fractionofdropsfrozen(a)ATD HeterogeneousHomogeneous−40 −35 −30 −25 −20 −15 −10 −5 0Temperature (◦C)10−310−210−1100Fractionofdropsfrozen(b)ATD HeterogeneousHomogeneousFigure 4.7: Fraction of drops frozen by homogeneous freezing and immersion freezingof drops containing ATD. Data are shown on both a linear (panel a) and log scale(panel b). Stars represent homogeneous freezing results. The closed circles repre-sent the median frozen fraction between the upper and lower limits as described inthe text. The uncertainty in the temperature values is ∼ 0.06◦C. The shaded regionrepresents the area where homogeneous freezing interferes with the heterogeneousfreezing results. Heterogeneous data are only shown at temperatures warmer thanthis region.61−40 −35 −30 −25 −20 −15 −10 −5 0Temperature (◦C)0.00.20.40.60.81.0Fractionofdropsfrozen(a)Kaolinite HeterogeneousHomogeneous−40 −35 −30 −25 −20 −15 −10 −5 0Temperature (◦C)10−310−210−1100Fractionofdropsfrozen(b)Kaolinite HeterogeneousHomogeneousFigure 4.8: Fraction of drops frozen by homogeneous freezing and immersion freezing ofdrops containing kaolinite. Data are shown on both a linear (panel a) and log scale(panel b). Stars represent homogeneous freezing results. The closed circles repre-sent the median frozen fraction between the upper and lower limits as described inthe text. The uncertainty in the temperature values is ∼ 0.06◦C. The shaded regionrepresents the area where homogeneous freezing interferes with the heterogeneousfreezing results. Heterogeneous data are only shown at temperatures warmer thanthis region.62the median freezing temperature is not the best method for inter-comparison of heterogeneousfreezing results since median freezing temperature can depend on the amount of mineral dustin each drop. A more useful metric for inter-comparison of the freezing studies is the icenucleation active site (INAS) density, which takes into account the surface area of solid ma-terial in each drop. A detailed examination of the INAS densities and comparison with othermeasurements is presented below.4.3.3 Testing ice nucleation schemes for use in atmospheric modelsThe new freezing results presented above were used to test four different schemes previouslyused to describe ice nucleation in atmospheric models. These schemes are referred to as thesingle-α , pdf-α , active site, and deterministic schemes. These schemes were described inChapter 3 for deposition nucleation. Below these four schemes are described for immersionfreezing.4.3.3.1 Single-α schemeThe single-α scheme [Fletcher, 1958; Pruppacher and Klett, 1997] is the simplest of the fourschemes used here. This scheme is based on classical nucleation theory. Nucleation is assumedto be a stochastic process and can occur with equal probability anywhere on a particle surface.All particles have equal probability per unit surface area to nucleate ice. A single parameter,the contact angle (α), is used to parameterize the data. This scheme has been used in manyatmospheric modelling studies [Eidhammer et al., 2009; Ervens and Feingold, 2012; Hooseet al., 2010a,b; Jensen et al., 1994; Jensen and Toon, 1997; Jensen et al., 1998; Ka¨rcher, 1996,1998; Ka¨rcher et al., 1998; Khvorostyanov and Curry, 2000, 2004, 2005, 2009; Kulkarni et al.,2012; Liu et al., 2007; Morrison et al., 2005].As shown in Chapter 2, classical nucleation theory can relate the heterogeneous nucleationrate constant for immersion freezing to the energy barrier for embryo formation on a solid63surface [Pruppacher and Klett, 1997; Zobrist et al., 2007]:jhet(T,α) =kT nicehexp(−∆Fdiff(T )kT)exp(−∆Gact(T ) fhet(α)kT)(4.1)where k is the Boltzmann constant, nice is the number density of water molecules at the icenucleus-water interface, h is Planck’s constant, ∆Fdiff(T ) is the diffusion activation energy fortransfer of water molecules across the ice nucleus-water interface, ∆Gact(T ) is the activationenergy for critical embryo formation and fhet(α) is the contact parameter (given by Eq. (4.2))which describes the reduction in the Gibbs free energy barrier due to the presence of a hetero-geneous nucleus. Parameterizations for nice, ∆Gact(T ), and ∆Fdiff(T ) are given by Zobrist et al.[2007].As was done in Chapter 3 for deposition nucleation, the contact parameter for a givencontact angle, α , is given byfhet(α) =(2+ cosα)(1− cosα)24. (4.2)This equation assumes that the radius of curvature of the particle is significantly larger than theradius of the critical embryo, a valid assumption for our measurements.The single-α scheme assumes that classical nucleation theory can describe the nucleationrate of ice embryos on the surface of particles and that every particle has the same contactangle. For an ensemble of drops each containing the same surface area of solid inclusions, thefraction of drops frozen at a temperature T can be related to the heterogeneous nucleation rateconstant predicted with the single-α scheme byfd(T ) = 1− exp(−A jhet(T,α)∆t) , (4.3)where fd is the fraction of drops frozen at some temperature T , A is the surface area availableto nucleate in each drop, jhet is the heterogeneous nucleation rate constant in (cm−2 s−1) at64temperature T , and ∆t is the time step.Since the experiments presented here do not involve equal surface areas in each drop (seeFigs. 4.5 and 4.6), Eq. (4.3) needs to be modified to take the difference in surface area perdrop into account. Equation (4.4) shows the fraction of drops frozen according to the single-αscheme when each drop does not contain the same surface area of solid inclusions.fd(T ) = 1−nd∑i=1exp [−Ai jhet(T,α)∆t]P(Ai) (4.4)where nd is the number of drops with unique surface areas observed in the experiments, Ai isthe surface area (in cm2) contained in drop i, jhet(T,α) is the heterogeneous nucleation rateconstant (in cm−2 s−1) at temperature T , ∆t is the time step, and P(Ai) is the probability ofa drop containing surface area Ai. For all calculations, the time step ∆t is taken as 3s. Thisrepresents the time between successive 0.5◦C intervals when using a cooling rate of -10◦C/min.4.3.3.2 Pdf-α schemeThe pdf-α scheme [Lu¨o¨nd et al., 2010; Marcolli et al., 2007] is a modification of the single-αscheme presented above allowing for a distribution of freezing probabilities among the indi-vidual dust particles. In this scheme, each particle nucleates stochastically as in the single-αscheme according to classical nucleation theory with a nucleation rate constant given by Eq.(4.1). The nucleation probability per unit surface area differs, however, from particle to par-ticle. This scheme has been used previously to describe freezing data [Lu¨o¨nd et al., 2010;Marcolli et al., 2007; Welti et al., 2012; Wheeler and Bertram, 2012] and in model comparisonstudies [Ervens and Feingold, 2012; Kulkarni et al., 2012].To describe the nucleation probability of all particles, a distribution of contact angles isassumed for an ensemble of particles. Here, we test a normal distribution of contact anglesdescribed byp(α) = 1σα√2piexp[−(α−µα)22σ2α], (4.5)where µα and σ2α describe the mean and variance of the normal distribution, respectively. This65gives two parameters to describe the nucleation ability of both the ATD and kaolinite particles.For an ensemble of drops each containing a single solid inclusion of the same size, thefraction of drops frozen at temperature T described by the pdf-α scheme is given byfd(T ) = 1−∫ pi0exp [−A jhet(T,α)∆t] p(α)dα, (4.6)where fd is the fraction of drops frozen at temperature T , p(α)dα is the probability of havinga contact angle in the range [α,α +dα], A is the surface area of the immersed particle, jhet isthe heterogeneous nucleation rate constant given by Eq. (4.1), and ∆t is the time step.Since the experiments presented here do not involve only a single solid particle per drop(see Figs. 4.5 and 4.6), Eq. (4.6) above needs to be modified to take into account the possibilityof more than one solid inclusion per drop. The fraction of drops frozen according to the pdf-αscheme when each drop does not contain the same number of solid inclusions is given byfd(T ) = 1−nmax∑n=1{∫ pi0exp[−Aavg jhet(T,α)∆t]p(α)dα}nP(n), (4.7)where Aavg is the surface area of an average particle immersed in the drop, n is the numberof particles per drop, P(n) is the probability of having n particles per drop, and nmax is themaximum number of particles per drop observed in the experiment. The exponent in Eq.(4.7) is included since the probability of a drop containing n solid inclusions of area Aavgremaining liquid at temperature T will be the product of the probability of each individualparticle not nucleating at temperature T . Numerical integration of Eq. (4.7) was performedusing rectangular integration.4.3.3.3 Active site schemeAs a further extension of the single-α scheme, the active site scheme [Fletcher, 1969; Lu¨o¨ndet al., 2010; Niedermeier et al., 2011b], assumes that there are certain regions (i.e. activesites) of the particle surface that have a greater probability to nucleate ice. Each active site66nucleates stochastically according to classical nucleation theory as in the single-α and pdf-αschemes, but nucleation is assumed to occur only on these small active sites. Each particle hasa particular distribution of active sites determined by the density of active sites (ρ(α)). Thescheme used here is the same as described by Lu¨o¨nd et al. [2010] and Welti et al. [2012].According to the active site scheme, the probability that a single drop containing a singlesolid inclusion will freeze is given by the following equation, which takes into account that asolid particle can have multiple active sites and that the contact angle can vary from site to site:Pfreeze(T ) = 1−m∏i=1exp [− jhet(T,αi)Aαi∆t] (4.8)where Aαi is the total area of active sites with contact angle in the range of αi to αi +∆α , ∆αis the width of an individual bin such that the total number of bins is equal to m. The area of asingle active site is fixed at 6 nm2 [Lu¨o¨nd et al., 2010] and Aαi represents an integer multipleof the area of a single site (Aαi = niAsingle where Asingle = 6nm2).The average number of active sites contained in a drop in each contact angle interval(αi,αi +∆α) is given byn¯i = Aρ(αi)∆α, (4.9)where A is the surface area of the solid inclusion immersed in the drop, ρ(αi) is the density ofactive sites in the interval (αi,αi +∆α) given by Eq. (4.10).ρ(α) = bexp( −β1α−β2)(4.10)The number of active sites with contact angles in range (αi,αi+∆α) can be assigned usingPoisson distributed random variables with the expectation value given by Eq. (4.9). To accountfor multiple particles per drop, the total surface area immersed in the drop was used in place ofthe surface area of the individual particle in Eq. (4.9).The freezing probabilities, Pfreeze(T ), of 1000 drops were calculated using Eq. (4.8). Sincethere is a distribution of surface areas per drop (see Figs. 4.5 and 4.6), surface areas were67randomly assigned to each drop based on the surface area distributions shown in Figs. 4.5 and4.6. The fraction of drops frozen was then calculated as:fd(T ) =N f (T )N0= 1− Nu(T )N0= 1N 0N0∑k=1Pfreeze,k(T ), (4.11)where Nu and N f are the number of unfrozen and frozen drops, respectively, N0 is the totalnumber of drops (i.e. 1000), and Pfreeze,k is the probability that drop k will freeze.To account for the statistical variability associated with using a limited number of randomlyassigned contact angles and areas, averages of 10 individual runs of 1000 drops were used.4.3.3.4 Deterministic schemeUnlike the single-α , pdf-α and active site schemes presented above, the deterministic scheme[Connolly et al., 2009] is not derived from classical nucleation theory. Nucleation in the im-mersion mode according to the deterministic scheme is assumed to be independent of timeand depends only on the temperature. This scheme has been used previously to parameterizeimmersion freezing data [Connolly et al., 2009; Lu¨o¨nd et al., 2010; Murray et al., 2011; Nie-dermeier et al., 2010; Welti et al., 2012] and in model comparison studies [Eidhammer et al.,2009; Ervens and Feingold, 2012; Kulkarni et al., 2012].The fraction of frozen drops for the deterministic scheme is given byfd(T ) = 1−nd∑i=1exp [−Ains(T )]P(Ai), (4.12)where nd is the number of drops with unique surface areas observed in the experiments, ns(T )is the surface density of active sites at a temperature T given by Eq. (4.13) [Connolly et al.,2009; Lu¨o¨nd et al., 2010; Welti et al., 2012], and P(Ai) is the probability of a drop containingsurface area Ai. The density of active sites, ns(T ), is described using two parameters, A1 andA2, which are used to fit the experimental data.68ns(T ) =A1(T +A2)2, T <−A20, T ≥−A2(4.13)4.3.3.5 Results from testing different schemesThe experimental freezing data for ATD and kaolinite were fit to the schemes presented aboveby reducing the weighted sum of squared residuals (WSSR) between the median frozen frac-tions (as shown in Figs. 4.7 and 4.8) and the predictions. Owing to the greater uncertainty inthe frozen fraction at colder temperatures, a weighting function was used to fit the data. Theweighting function used is given by [Wolberg, 2006]Wi =1σ2i, (4.14)where σi is half the distance between the upper and lower limits of the frozen fraction presentedin Figs. 4.7 and 4.8. To avoid interferences with homogeneous freezing, only those freezingevents which occurred at temperatures warmer than homogeneous freezing were used to fit eachscheme. This cut-off temperature was taken as the warmest observed freezing temperature forthe homogeneous data shown in Figs. 4.7 and 4.8 (i.e. T = -36.9◦C).The results from fitting the freezing data to the different schemes are shown in Figs. 4.9 and4.10 for ATD and kaolinite respectively. Tables 4.1 and 4.2 show the best fit parameters, theWSSR and reduced chi-squared values (χ2red). The value of χ2red gives a means of comparingthe goodness of fit of different schemes with different numbers of fitting parameters. A valueclose to unity indicates a good fit to the data.As can be seen in Figs. 4.9 and 4.10 and Tables 4.1 and 4.2, the single-α scheme is unableto represent the freezing of either ATD or kaolinite particles. The scheme prediction is toosteep to represent the experimental data, and the χ2red values are much greater than unity. Giventhat kaolinite is a single-component mineral, the single-α scheme assumes that the nucleation69−40 −35 −30 −25 −20 −15Temperature (◦C)0.20.40.60.81.0Fractionofdropsfrozen(a)single-αpdf-αdeterministicactiveATD freezing−40 −35 −30 −25 −20 −15Temperature (◦C)10−310−210−1100Fractionofdropsfrozen(b)single-αpdf-αdeterministicactiveATD freezingFigure 4.9: Comparison between heterogeneous freezing of drops containing ATD andthe different schemes used to describe heterogeneous ice nucleation. Data areshown on both a linear (panel a) and a log scale (panel b). The error in the datapoints represents the difference between the upper and lower limits to the frozenfraction as described in the text. The uncertainty in the temperature values is∼ 0.06◦C. The shaded region shows the area where homogeneous freezing wasobserved.70−40 −35 −30 −25 −20 −15Temperature (◦C)0.20.40.60.81.0Fractionofdropsfrozen(a)single-αpdf-αdeterministicactiveKaolinite freezing−40 −35 −30 −25 −20 −15Temperature (◦C)10−310−210−1100Fractionofdropsfrozen(b)single-αpdf-αdeterministicactiveKaolinite freezingFigure 4.10: Comparison between heterogeneous freezing of drops containing kaoliniteand the different schemes used to describe heterogeneous ice nucleation. Dataare shown on both a linear (panel a) and a log scale (panel b). The error in thedata points represents the difference between the upper and lower limits to thefrozen fraction as described in the text. The uncertainty in the temperature valuesis ∼ 0.06◦C. The shaded region shows the area where homogeneous freezing wasobserved.71Table 4.1: Results from fitting the ATD freezing data to the different schemes. Fittingparameters for the best fit are given along with the weighted sum of squared residuals(WSSR) and reduced chi-squared values (χ2red).Scheme Parameters WSSR χ2redsingle-α α = 79.5◦ 810.5 26.14pdf-α µα = 101.9◦119.9 3.998σα = 10.5◦deterministicA1 = 1117.7cm−2 131.6 4.385A2 = 21.04◦Cactive siteb = 6×108 cm−220.7 0.646β1 = 3.14β2 = 0.613Table 4.2: Results from fitting the kaolinite freezing data to the different schemes. Fittingparameters for the best fit are given along with the weighted sum of squared residuals(WSSR) and reduced chi-squared values (χ2red).Scheme Parameters WSSR χ2redsingle-α α = 108.3◦ 775.3 33.71pdf-α µα = 130.2◦465.4 21.15σα = 13.7◦deterministicA1 = 177.9cm−2 148.0 6.729A2 = 23.98◦Cactive siteb = 2×1011 cm−25.8 0.243β1 = 16.52β2 = 0.055probability per unit area is equal for all particles. The results presented here suggest that theassumption of equal nucleation probability is incorrect. The large χ2red gives further supportthat a simple stochastic approach is not sufficient to describe ice nucleation on most mineraldusts, consistent with recent conclusions in the literature [Broadley et al., 2012; Lu¨o¨nd et al.,2010; Marcolli et al., 2007; Vali, 2008, 2014; Welti et al., 2012; Wheeler and Bertram, 2012].The pdf-α and deterministic schemes are better at describing the freezing data than thesingle-α scheme but both the pdf-α and deterministic schemes give χ2red values significantlyabove 1 for both minerals, suggesting they do not give optimal fits; the deviation between the72fits and the experiments is greater than the uncertainty in the measurements. In contrast, theactive site model is able to describe well the freezing of ATD and kaolinite particles as shownwith χ2red values close to one. χ2red values less than one indicate an overestimation of the errorused in the weighting function (Eq. (4.14)).In terms of ability to fit the ATD data (quantified with χ2red values), the following trend isobserved (from best to worst): active site, pdf-α , deterministic, single-α . For kaolinite, thefollowing trend is observed (from best to worst): active site, deterministic, pdf-α , single-α .Our data suggests that the active site scheme is the most accurate for describing the freezing ofthe ATD and kaolinite particles tested here. If this scheme cannot be used due to computationalexpense, then the pdf-α or deterministic scheme should be used, not the single-α scheme.The changes in median freezing temperatures predicted by each of the stochastic schemesper decade change in the cooling rate is presented in Table 4.3. This was determined by cal-culating the difference in the median freezing temperature predicted by the different schemeswhen using the fit parameters to the experimental data (Tables 4.1 and 4.2) and a cooling rateof 10◦Cmin−1 and 1◦Cmin−1. Table 4.3 shows that the active site scheme gave the largestchange in median freezing temperature with a decade change in cooling rate. The determin-istic scheme (by definition) does not depend on the cooling rate and so no change in medianfreezing temperature is expected from this scheme.Also shown in Table 4.3 are changes in the median freezing temperatures with a decadechange in cooling rate based on experimental results presented in the literature. The valuesof Wright et al. [2013] are based on a logarithmic fit to the median freezing temperaturesmeasured at multiple cooling rates. Samples used by Wright et al. [2013] contained a mixtureof submicron and supermicron particles, and the kaolinite sample used by Wright et al. [2013]was from a different source than the kaolinite used in this study. A combination of experimentalresults and fitting to the experimental data by Murray et al. [2011] suggests a variation in themedian freezing temperature of approximately −2◦C per decade change in cooling rate forkaolinite particles. Samples used by Murray et al. [2011] contained a mixture of submicron73Table 4.3: Variation of median freezing temperature with changing cooling rate for bothATD and kaolinite. The prediction for each scheme was calculated by determiningthe change in median freezing temperature as the cooling rate was changed from10◦Cmin−1 to 1◦Cmin−1. Variations previously determined in the literature aregiven for both ATD and kaolinite.Scheme or StudyPredicted/measuredchange in medianfreezing per decadechange in cooling ratefor ATD (◦C)Predicted/measuredchange in medianfreezing per decadechange in cooling ratefor kaolinite (◦C)single-α -0.57 -0.58pdf-α -0.60 -0.62deterministic 0 0active site -1.0 -1.1Wright et al. [2013] -0.5 -1.3Murray et al. [2011] not measured -2and supermicron particles and the kaolinite sample used by Murray et al. [2011] was from thesame source as that used here.A few conclusions can be made from Table 4.3. First, the experimental studies suggest thatthe median freezing temperature depends on cooling rate, although the dependence is weak.This is in contrast to the deterministic model, which predicts the median freezing temperatureis independent of cooling rate. Second, the single-α , pdf-α , and active site schemes all agreewith the experimental results within roughly a factor of two. To further differentiate betweenthe different schemes using the experimental results shown in Table 4.3, an uncertainty analysisof the experimental and modelling results is required.4.3.3.6 Comparison of fitting results with other studiesThe trend from best to worst for ATD and kaolinite in terms of ability to fit the data in ourstudies (quantified with χ2red values) is summarized in Table 4.4. For comparison, we have alsosummarized results from other studies that have compared different schemes, again rankingthe schemes from best to worst in terms of their ability to fit experimental data. The activesite scheme ranked first or tied for first in five out of the six studies where it was implemented.The pdf-α model ranked first or tied for first in four out of the seven studies where it was74implemented while the deterministic model ranked first or tied for first in three out of the eightstudies where it was implemented. The single-α scheme ranked first or tied for first in only twoout of the nine studies where it was tested. Studies by Murray et al. [2011] and Niedermeieret al. [2010] both indicate that the single-α scheme provides the best fit to the data or is tiedfor best fit, however these studies did not test the pdf-α or active site schemes. In addition,the single-α model was ranked last in seven out of the nine studies where it was implemented.The summary in Table 4.4 suggests that the active site scheme is often the most accurate atdescribing experimental freezing data for mineral dust.4.3.4 Area sensitivityAs described above, the area determined in these experiments represents the geometric areaof the individual particles. SEM images of both kaolinite and ATD (Figs. 4.5b and 4.6b)show that these particles contain additional structure not captured in the area measurements.For this reason, the areas presented in this study represent lower limits to the actual surfacearea present in each drop. To examine the sensitivity of the fit parameters to the surface areaand to determine if the relative rankings of the different schemes was sensitive to the surfacearea, we performed a sensitivity study by scaling the total surface area in each drop by afactor of 50 [Eastwood et al., 2008; Wheeler and Bertram, 2012]. The resulting fit parameters,WSSR values, and reduced chi-squared values are given in Tables 4.5 and 4.6 for both ATDand kaolinite. Results from the scaled fitting shows that the χ2red values for each of the fourschemes do not vary drastically when the area is scaled by a factor of 50. More important, therelative rankings of the different schemes when the area was scaled by a factor of 50 remainthe same. In terms of the parameters from the fits, the parameters derived for the single-α andpdf-α schemes vary by less than 40% when the area was scaled by a factor of 50. On the otherhand, the parameters derived for the deterministic scheme and the active site scheme vary byup to a factor of 300 when the area was scaled by a factor of 50.75Table 4.4: Relative ranking of the ability of different schemes to accurately model het-erogeneous freezing of mineral dust in both the immersion and deposition mode.Schemes are ranked from 1 to 4 where 1 gives the best fit to the data and 4 the worst.Included are the multi-component stochastic scheme used by Broadley et al. [2012],which is similar to the pdf-α scheme, and the soccer ball scheme of Niedermeieret al. [2011b], which is similar to the active site scheme.Mineral,mode, sizeStudySchemesingle-α pdf-α deterministic active sitekaolinite,deposition,supermicronWheeler andBertram [2012]4 1 1 1kaolinite,immersion,supermicronthis study 4 3 2 1kaolinite,immersion,mixed1Murray et al.[2011]1 NT2 2 NTkaolinite,immersion,submicronLu¨o¨nd et al.[2010]4 1 1 1kaolinite,immersion,submicronWelti et al. [2012] 4 1 3 2ATD,immersion,supermicronthis study 4 2 3 1ATD,immersion,mixedMarcolli et al.[2007]4 2 NT 1ATD,immersion,submicronNiedermeier et al.[2010]1 NT 1 NTillite,immersion,mixedBroadley et al.[2012]4 1 2 NT1 mixed here refers to a mixture of submicron and supermicron particles used.2 NT indicates that this scheme was not tested.76Table 4.5: Results from fitting the scaled surface area ATD freezing data to the differentschemes. Fits were obtained by scaling the mineral dust surface area by a factorof 50. Fitting parameters for the best fit are given along with the weighted sum ofsquared residuals (WSSR) and reduced chi-squared values (χ2red).Scheme Parameters WSSR χ2redsingle-α α = 82.5◦ 819.7 26.44pdf-α µα = 124.3◦123.9 4.131σα = 13.6◦deterministicA1 = 22.38cm−2 131.6 4.385A2 = 21.04◦Cactive siteb = 2×106 cm−217.0 0.533β1 = 2.11β2 = 0.650Table 4.6: Results from fitting the scaled surface area kaolinite freezing data to the differ-ent schemes. Fits were obtained by scaling the mineral dust surface area by a factorof 50. Fitting parameters for the best fit are given along with the weighted sum ofsquared residuals (WSSR) and reduced chi-squared values (χ2red).Scheme Parameters WSSR χ2redsingle-α α = 116.0◦ 782.1 34.01pdf-α µα = 134.0◦741.8 33.72σα = 8.7◦deterministicA1 = 3.557cm−2 148.0 6.729A2 = 23.98◦Cactive siteb = 1×1010 cm−26.8 0.284β1 = 18.52β2 = 0.0064.3.5 Supermicron INAS valuesThe density of ice nucleation active surface sites has been used previously as a means of nor-malizing data to surface area [DeMott, 1995; Connolly et al., 2009; Hoose and Mo¨hler, 2012;Murray et al., 2012; Niemand et al., 2012]. INAS densities represent the number of ice nu-cleation sites per unit area (cm−2) of solid inclusion. These values have been used to makeconclusions on the importance of different ice nuclei in the atmosphere and to compare resultsfrom different laboratories [Hoose and Mo¨hler, 2012; Murray et al., 2012].We use the method described by Vali [1971] to calculate the value of ns by first binning77the data according to the surface areas shown in Figs. 4.5 and 4.6. The value of ns at eachtemperature is then calculated according to the following formula:ns(T ) =m∑i=1− ln(Nu,i(T )N0,i)·N0,im∑i=1N0,i ·Ai(4.15)where the data are divided into m bins, Ai is the surface area per drop contained in bin i,Nu,i(T ) is the number of unfrozen drops at temperature T in bin i, and N0,i is the total numberof drops in bin i. This method has recently been used to determine the INAS densities of otherimmersion freezing data using the same apparatus [Haga et al., 2013].Using this method, the INAS densities for ATD and kaolinite were calculated using theupper and lower limits for Nu(T ) described above. This provided upper and lower limits forthe INAS values. In addition, only bins containing at least 5 data points were included in orderto ensure reasonable statistics in each bin.In Figs. 4.11 and 4.12, the blue shaded areas show the INAS density for ATD and kaolinitebased on the measurements presented here. These INAS values do not span the entire rangeof temperatures shown in Figs. 4.7 and 4.8 due to the binning of the data in Eq. (4.15). Sincethe numerator in Eq. (4.15) is infinite for values of Nu,i = 0, values of ns only exist wherevalues in all bins are not infinite. Also included in Figs. 4.11 and 4.12 for comparison areother experimental data presented in Hoose and Mo¨hler [2012] along with data from Haderet al. [2014]. The data from the literature presented in Figs. 4.11 and 4.12 include measure-ments of immersion freezing as well as condensation freezing. The data shown in Figs. 4.11and 4.12 have been grouped based on the size range of particles used in the studies, with redsymbols representing studies that used submicron particles, blue symbols representing studiesthat used supermicron particles, and magenta symbols representing studies that used a mixtureof submicron and supermicron particles.Although there is substantial scatter in each group, Figs. 4.11 and 4.12 suggest that overthe range of -26 to −20◦C for ATD and -35 and −25◦C for kaolinite, the INAS density of78supermicron particles studied here is lower than that of submicron particles shown in Figs.4.11 and 4.12 (cf. red points in Figs. 4.11 and 4.12 with experimental results shown as blueregions). One possible explanation for the difference in INAS densities between submicronand supermicron particles is that the mechanical action of breaking up a mineral into smallersizes results in the formation of more ice nucleation sites per unit surface area. This finding isconsistent with recent experiments by Hiranuma et al. [2014]. These authors showed that thecreation of surface irregularities by milling cubic hematite particles can result in an increase inthe INAS density of an order of magnitude.Another possible explanation for the difference in INAS densities between submicron andsupermicron ATD particles is that the particle composition depends on particle size. It is con-ceivable that in the case of a multi-component mineral such as ATD, size selecting particlesmay result in preferential selection of a particular mineral from the mixture. This may beresponsible, at least partially, for the size dependent freezing results shown in Fig. 4.11.Some of the differences between the supermicron results and the submicron results shownin Figs. 4.11 and 4.12 may also be related to the instrumentation used to determine INAS den-sities. The majority of the submicron studies were carried out using a continuous flow diffu-sion chamber, which employed a different method of determining surface area, and a differentmethod of detecting ice nucleation than that employed in the present study. Additionally, dif-ferent mineral sources may be partially responsible for the differences seen in Figs. 4.11 and4.12. In the case of kaolinite, Murray et al. [2011] and Zimmermann et al. [2008] used thesame source of kaolinite as in our experiments (i.e. CMS KGa-1b); Lu¨o¨nd et al. [2010] andWelti et al. [2009] used kaolinite obtained from Fluka; Friedman et al. [2011] and Roberts andHallett [1968] did not indicate the source of the kaolinite used in their study; and Pinti et al.[2012] used multiple sources of kaolinite including the KGa-1b used in this study. In the caseof ATD, Niedermeier et al. [2010] and Sullivan et al. [2010] both used the same type of ATDas used in this study (i.e. ATD Ultrafine A1). Knopf and Koop [2006], Marcolli et al. [2007]and Niemand et al. [2012] use other ultrafine samples of ATD. The source of ATD used in the79other studies was not indicated.Figs. 4.11 and 4.12 also show that the INAS results from the supermicron studies (bluesymbols) roughly fall within the range of INAS results determined with a mixture of submi-cron and supermicron particles (magenta symbols). The reasonable agreement between thesupermicron and mixed particle results could in part be due to the fact that many of the mixedparticle results were carried out with a drop freezing technique similar to the technique em-ployed here.Some of the mixed particle data (i.e. experiments with submicron and supermicron parti-cles) presented in Figs. 4.11 and 4.12 use gas-adsorption derived surface areas in the determi-nation of INAS densities (Hader et al. [2014]; Marcolli et al. [2007]; Murray et al. [2011]; Pintiet al. [2012]). As pointed out by Hoose and Mo¨hler [2012], the use of gas-adsorption derivedsurface areas is likely to result in lower INAS values determined compared with the use ofgeometric surface areas as was done in the present study. Hiranuma et al. [2014] examinedthe difference in calculating the INAS densities of cubic and milled hematite particles. Theirresults showed that for cubic and milled hematite particles, the difference in INAS densities de-termined using gas-adsorption surface areas compared with those determined using geometricsurface areas were less than one order of magnitude.4.4 ConclusionsThe ice nucleation ability of supermicron particles of two mineral species, kaolinite and Ari-zona Test Dust (ATD), was investigated in the immersion freezing mode. Results showed thatsupermicron ATD nucleates at warmer temperatures than supermicron kaolinite particles in theimmersion mode. Kaolinite had a median freezing temperature of −36◦C while ATD had amedian freezing temperature of −30◦C. Both minerals show median nucleation temperatureswhich are warmer than homogeneous freezing.The experimental data were fit to four different freezing schemes: the single-α , pdf-α , ac-tive site, and deterministic schemes. The one-parameter classical nucleation single-α scheme80−50 −40 −30 −20 −10 0Temperature (◦C)1021031041051061071081091010101110121013INASdensity(m−2 )MixedSubmicronSupermicronConnolly et al. (2009)Hader et al. (2014)Kanji et al. (2011)Knopf & Koop (2006)Marcolli et al. (2007)/Pinti et al. (2012)Niemand et al. (2012)Hoyle et al. (2011)Kanji & Abbatt (2010)Koehler et al. (2010)Niedermeier et al. (2010)Sullivan et al. (2010)Welti et al. (2009)This studyFigure 4.11: Ice nucleation active site (INAS) densities as a function of temperature forATD. Results from supermicron particles are in blue while submicron data arein red. Experiments performed with a mixture of submicron and supermicronparticles are shown in magenta.is incapable of describing the nucleation of supermicron ATD or kaolinite particles. The ac-tive site scheme is the most accurate at reproducing the freezing results of ATD and kaoliniteparticles and the pdf-α and deterministic schemes fall between the active site scheme and thesingle-α scheme in terms of ability to fit the freezing results (quantified using the χ2red values).The variation in the predicted median freezing temperature per decade change in the coolingrate for each of the schemes was also compared with experimental results from other studies.The deterministic scheme predicts the median freezing temperature to be independent of cool-ing rate, while the experimental results show a weak dependence on cooling rate. The single-α ,pdf-α , and active site schemes all agree with the experimental results within roughly a factorof two.Based on our results and previous results where different schemes were tested, the activesite scheme is recommended for describing the freezing of ATD and kaolinite particles. Thecurrent study was carried out using a single cooling rate (10◦Cmin−1) and over a relatively81−50 −40 −30 −20 −10 0Temperature (◦C)10210310410510610710810910101011101210131014INASdensity(m−2 )MixedSubmicronSupermicronMurray et al. (2011)Pinti et al. (2012)Roberts & Hallett (1968)Friedman et al. (2011)Lüönd et al. (2010)Welti et al. (2009)Zimmermann et al. (2008)This studyFigure 4.12: Ice nucleation active site (INAS) densities as a function of temperature forkaolinite. Results from supermicron particles are in blue while submicron dataare in red. Experiments performed with a mixture of submicron and supermicronparticles are shown in magenta.limited range of temperatures. Additional studies with different cooling rates and differentnumbers of particles per drop (which would extend the temperature range studied) would beuseful to further test the schemes.INAS densities were calculated from the experimental data and compared with other resultspresented in Hoose and Mo¨hler [2012] and Hader et al. [2014]. The supermicron particlesstudied here were observed to have a lower INAS density than submicron particles for bothATD and kaolinite reported in the literature. For kaolinite, the differences may be related tothe different sources of kaolinite used in the studies. In the case of ATD, the differences maybe due to the mechanical processing of the particles to produce smaller sized particles whichmay lead to greater surface imperfections in submicron particles compared with supermicronparticles. Recent studies with hematite particles are consistent with this finding [Hiranumaet al., 2014].Maring et al. [2003] has shown that there is a significant fraction of mineral dust parti-82cles that lie in the supermicron range even after transport. This combined with the differencebetween the freezing abilities of supermicron and submicron particles indicates the need forfurther study into freezing on supermicron dust particles.83Chapter 5Testing different schemes for describingimmersion freezing of water dropscontaining primary biological aerosolparticles5.1 IntroductionIce nucleation in the atmosphere can occur through two distinct processes: homogeneous nu-cleation and heterogeneous nucleation. Heterogeneous nucleation refers to the formation ofthe ice phase due to the presence of an insoluble (or partially insoluble) particle referred to asan ice nucleus (IN).Heterogeneous ice nucleation can influence the extent and lifetime of both ice and mixed-phase clouds [Boucher et al., 2013; DeMott et al., 2010; Lohmann and Feichter, 2005; Lohmannand Diehl, 2006] which in turn can lead to changes in radiative forcing and precipitation. Therestill remains a large uncertainty in our understanding of the nature of heterogeneous ice nucle-ation in the atmosphere [Boucher et al., 2013; Murray et al., 2012] and by consequence in the84ability to accurately predict heterogeneous ice nucleation in atmospheric models.There is now strong evidence that mineral dust particles are an important atmospheric IN.Evidence in favour of this has been presented in laboratory, field and modelling studies [Hooseand Mo¨hler, 2012; Murray et al., 2012]. Another potentially important atmospheric IN is pri-mary biological aerosol particles (PBAPs). PBAPs include fungi, bacteria, pollen, and virusesas well as fragment or excretions from biological organisms [Despre´s et al., 2012]. Althoughrecent atmospheric simulations have shown that PBAPs may not be important on a global an-nual scale [Burrows et al., 2013; Hoose et al., 2010a,b; Sesartic et al., 2012, 2013] they maystill be important both regionally and seasonally. For example, numerous field studies haveidentified ice nucleation active PBAPs [Bowers et al., 2009; Christner et al., 2008a,b; Con-stantinidou et al., 1990; Garcia et al., 2012; Huffman et al., 2013; Jayaweera and Flanagan,1982; Lindemann et al., 1982; Maki and Willoughby, 1978; Morris et al., 2008; Pratt et al.,2009; Prenni et al., 2009, 2013]. In addition, modelling studies suggest that ice nucleation ofPBAPs may be important when concentrations of other important IN are low or concentrationsof PBAPs are high [Phillips et al., 2008; Hazra, 2013; Gonc¸alves et al., 2012; Costa et al., 2014;Despre´s et al., 2012]In order to implement ice nucleation into atmospheric models, an appropriate scheme isnecessary in order to accurately describe the freezing behaviour of the IN particles in ques-tion. Modelling studies have shown that varying the scheme used to represent ice nucleationin the model can produce significant variation in the predicted cloud properties [Eidhammeret al., 2009; Ervens and Feingold, 2012; Kulkarni et al., 2012; Wang and Liu, 2014; Wanget al., 2014]. For example, Ervens and Feingold [2012] compared five different schemes fordescribing ice nucleation on kaolinite particles in an adiabatic parcel model. Results showedsignificant differences in the number of IN predicted depending on the scheme used to describeice nucleation. These differences were greatest for simulations which employed polydisperseIN compared with monodispersed particles.Recently, several studies have focused on testing difference schemes for describing labora-85tory freezing of mineral dusts [Broadley et al., 2012; Lu¨o¨nd et al., 2010; Marcolli et al., 2007;Murray et al., 2011; Niedermeier et al., 2010; Welti et al., 2012; Wheeler and Bertram, 2012;Wheeler et al., 2015b]. Some of the results from this work is summarized in Chapter 4, Section4.3.3.6. Four schemes were mainly tested: the single-α , pdf-α , active site and deterministicschemes. Three of these schemes are stochastic schemes (single-α , pdf-α , active site) basedon CNT. The results of these tests suggest that the active site scheme is most capable of de-scribing ice nucleation on mineral dust particles with the pdf-α scheme performing almost aswell followed by the deterministic scheme. In the majority of studies, the single-α schemewas the worst at predicting the ice nucleation behaviour of mineral dust particles. The studieswhich suggest that the single-α scheme most accurately describes the freezing behaviour didnot examine the pdf-α or active site schemes.There have also been a few studies that have tested different schemes for describing labora-tory freezing studies of PBAPs, although the number of these studies is fewer than for mineraldusts. Hartmann et al. [2013] tested the CHESS (stoCHastic modEl of similar and poiSSondistributed ice nuclei) scheme for representing the ice nucleation of Pseudomonas syringaeand SnowmaxTM (an industrial formulation containing non-viable P. syringae cells). Augustinet al. [2013] tested the CHESS scheme, single-α scheme and an active site scheme (soccerball, described below) using the immersion freezing of ice nucleating macromolecules fromtwo samples of Birch pollen. Empirical parameterizations have also been proposed for PBAPs[Tobo et al., 2013; Diehl and Wurzler, 2004; Diehl et al., 2006; Phillips et al., 2008], althoughthese have not been compared with the other schemes described above.In the following we test four different schemes using the freezing data of bacteria andfungal spores measured by Haga et al. [2013] and Haga et al. [2015]. The schemes tested werethe single-α scheme, the pdf-α scheme, the soccer ball scheme and the deterministic scheme.The single-α , pdf-α and deterministic schemes are the same as presented in Chapter 4. Thesoccer ball scheme is similar to the active site scheme presented in Chapters 3 and 4. Resultsfrom the test were used to rank the different schemes in terms of their ability to describe the86freezing data. These relative rankings of the different schemes may be useful when decidingwhich schemes to use in modelling studies and when considering trade-offs between accuracyand computational efficiency.5.2 Methods5.2.1 Immersion freezing data from Haga et al. [2013] and Haga et al.[2015]The immersion freezing temperatures of six species of fungal spore as well as eight species ofbacteria cells were previously examined using a temperature and humidity controlled flow cell[Haga et al., 2013, 2015]. A full description of the experimental technique can be found in theprevious references.The list of fungal spores studied can be found in Table 5.1. They comprise two differ-ent classes of fungi. Four rust species were examined: Puccinia graminis, Puccinia triticina,Puccinia allii and Endocronartium harknessii. Two species of bunt fungi were also exam-ined: Tilletia laevis and Tilletia tritici. Both of these classes of fungi represent common plantpathogens.Table 5.1: Summary of fungal spores used in the immersion freezing experiments of Hagaet al. [2013]. The freezing data by Haga et al. [2013] is used here to test differentschemes for describing laboratory ice nucleation data. All spores are assumed to beprolate spheroids based on experimental images. Sizes are given as major axis ×minor axis. All dimensions are given in µm.Type Species Spore Size1Rust fungiPuccinia graminis f. sp. tritici 20.8×12.5Puccinia triticina 21.6×18.0Puccinia allii 23.0×17.6Endocronartium harknessii 23.8×17.0Bunt fungiTilletia laevis 18.2×14.8Tilletia tritici 17.9×15.91Spore size determined from optical images of individualspores.87P. graminis and P. triticina spores were obtained from the Cereal Research Centre, Agricul-ture and Agri-Food Canada, Winnipeg, Manitoba. P. allii (sample held at the UBC Herbariumunder label AKB 4) was harvested from leek plants in Vancouver, British Columbia, Canada.E. harknessii (UBC Herbarium, AKB 5) was obtained from a pine tree in Terrace, BritishColumbia, Canada. T. laevis and T. tritici spores were obtained from infected wheat heads ac-quired from the Lethbridge Research Centre, Agriculture and Agri-Food Canada, Lethbridge,Alberta.The list of the bacteria species studied are shown in Table 5.2 along with the size of theindividual cells. A total of eight species were examined by Haga et al. [2015], however wehave limited the analysis here to three species since these were the only species which showedany significant amount of IN activity warmer than homogeneous freezing (cf. homogeneousfreezing with samples B. subtillis, C. testosteroni, M. luteus, P. putida, and S. albidoflavus fromHaga et al. [2015]).Table 5.2: Summary of bacteria species used in the immersion freezing experiments byHaga et al. [2015]. The freezing data by Haga et al. [2015] is used here to testdifferent schemes for describing laboratory ice nucleation data. All cells are assumedto be cylinders with size information based on the literature values of Buchanan andGibbons [1974]. Sizes are given as major axis × minor axis. All dimensions aregiven in µm.Species Cell SizeBacillus cereus 4×1.1Pseudomonas graminis (strain 13b-3) 4.25×0.75Pseudomonas syringae (strain 31R1) 2.25×0.95Bacillus cereus was obtained from the Bioservices Laboratory bacterial collection (De-partment of Chemistry, University of British Columbia, Vancouver, Canada), collection num-ber 1062. Pseudomonas graminis (strain 13b-3) was provided by P. Amato (Laboratoire deSynthe`se et E´tude de Syste`mes a` Inte´reˆt Biologique, CNRS-Universite´ Blaise Pascal, Aubie`re,France). Pseudomonas syringae (strain 31R1) was provided by S. Lindow (Department ofPlant and Microbial Biology, University of California, Berkley, U.S.A.).88All bacteria species were cultured according to the method outline by Mo¨hler et al. [2008b].Bacteria were deposited on the glass slides by nebulizing a suspension of the cells after cultur-ing. Further details on the sample preparation method can be found in Haga et al. [2015].Shown in Figs. 5.1 and 5.2 are the freezing data from Haga et al. [2013] and Haga et al.[2015]. Plotted are the fraction of drops frozen as a function of temperature. In these exper-iments, drops contained one or more fungal spore or bacteria cell inclusion. The distributionof fungal spores or bacteria cells per drop can be found in Figs. B.5 and B.6. Details on howthese values were determined can be found in Haga et al. [2013] and Haga et al. [2015]. Alsoincluded for comparison purposes in Figs. 5.1 and 5.2 are the homogeneous freezing resultsfrom Iannone et al. [2011].The data shown in Figs. 5.1 and 5.2 have been replotted from what was plotted in Hagaet al. [2013] and Haga et al. [2015]. In the original publications, the frozen fraction of dropswas presented as a function of temperature with each plotted point representing an individualfreezing event. In order to more easily fit the ice nucleation schemes to the experimental data,the fraction frozen presented here has been calculated at 0.5◦C intervals from 0◦C to −40◦C.For measurements taken at a constant cooling rate (as is the case in these studies) this ensures aconstant time between subsequent frozen fraction values when fitting the data to the stochastictime dependent schemes.5.3 Fitting schemesThe single-α scheme, the pdf-α scheme, and the deterministic scheme are the same as pre-sented in Chapter 4. Only the details specific to the implementation to the data described hereare discussed along with a more detailed description of the soccer ball scheme.5.3.1 Single-α schemeThe single-α scheme is described in Chapter 4. As was the case for the data presented inChapter 4, each drop contains multiple particles. For the experiments performed here, however,8945 40 35 30 25 20 15Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. graminisP. triticinaP. alliiE. harknessiiT. laevisT. triticiHomogeneousFigure 5.1: Fraction of spore containing drops frozen as a function of temperature calcu-lated from data presented in Haga et al. [2013]. See text for details. Also includedare results for drops containing no spores taken from Iannone et al. [2011] andreferred to as homogeneous freezing here.there is only a small variation in size among the particles. Due to this, we assume that each ofthe particles contained in a drop are all of equal size as shown in Tables 5.1 and 5.2. With thisassumption, the resulting fraction of drops frozen as a function of temperature is given by,fd(T ) = 1−nmax∑n=0exp [−nAp jhet(T,α)∆t]P(n), (5.1)where n is the number of particles contained in a drop, Ap is the surface area of a single particle,P(n) is the fraction of drops containing n particles, and jhet is the temperature and contactangle dependent heterogeneous nucleation rate constant given by Eq. (4.1). A time step of 6s(the time between successive 0.5◦C intervals at a ramp rate of −5◦Cmin−1) was used for all9045 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of cells frozenB. cereusP. graminisP. syringaeHomogeneousFigure 5.2: Fraction of bacteria containing drops frozen as a function of temperature cal-culated from data presented in Haga et al. [2015]. See text for details. Also includedare results for drops containing no bacteria, taken from Iannone et al. [2011] andreferred to as homogeneous freezing here.samples studied except for the P. syringae samples where a ramp rate of −10◦Cmin−1 led to atime step of 3s.5.3.2 Soccer ball schemeFletcher [1969] was the first to propose a theoretical model to describe the existence of pref-erential nucleation sites on a particle surface, termed “active sites”. These active sites wereassumed to be physical deformities on the particle surface having a contact angle of zero. En-sembles of particles could be modelled assuming a size dependent density of active site on theparticle surface. This form of the active site model is similar to that used by Lu¨o¨nd et al. [2010]and Welti et al. [2012].91Niedermeier et al. [2011b] proposed a variation to the active site model described abovecalled the “soccer ball” model. In this model the particle is divided up into a number of equallysized sites and the contact angle is allowed to vary from site to site. Using a Monte Carlosimulation, ensembles of particles were modelled and the freezing probability of the ensemblewas determined. More recently, Niedermeier et al. [2014] proposed a modified version ofthe soccer ball model. This model is less computationally expensive and has been shown toproduce the same results as the previous Monte Carlo simulation.The soccer ball scheme starts by dividing each particle up into a number (nsite) of equallysized nucleation sites. The contact angle of each site is assumed to follow a normal distributionwith a mean (µα ) and a standard deviation (σα ). Each site nucleates according to the single-αscheme described above.If we consider a situation where each drop contains only a single particle and each particleis composed of a single site (nsite = 1), then each particle can be described by a single contactangle and the distribution of these contact angles is given by the normal distribution. Thesurface area of each site (ssite) is equal to the surface area of the particle (Ap). The probabilityof a single drop being unfrozen at temperature T is given by,Phetunfr(T,µα ,σα , t) =∫ pi0p(α)exp(− jhet(T,α)ssitet)dα+∫ 0−∞p(α)exp(− jhet(T,α = 0)ssitet)dα+∫ ∞pip(α)exp(− jhet(T,α = pi)ssitet)dα (5.2)where p(α) is the probability density function of the normal distribution given by Eq. (5.3)and ssite is the area of the active site. The three terms in Eq. (5.2) account for the fact that thenormal distribution of contact angles (Eq. (5.3)) is a continuous function outside of the intervalof contact angles we define (0,pi). The contact angle is set to 0 for values of the distributionwith α < 0 while the contact angle is set to pi for values of the distribution with α > pi . Thisensures that the freezing probability covers the interval [0,1].92p(α) = 1√2piσexp[−(α−µ)22σ2](5.3)The frozen fraction of drops is given as the probability that a single drop will freeze het-erogeneously. This is given by:fice(T,µα ,σα , t) = 1−Phetunfr(T,µα ,σα , t). (5.4)If we now consider a situation where there are multiple sites on each particle (nsite > 1),the area of a single site is ssite = Ap/nsite where Ap is the surface area of a single particle. Theprobability of a single site remaining unfrozen at temperature T is given by Eq. (5.2). Sincethe freezing of each site is independent of the other, the probability of all sites on a particleremaining liquid at temperature T is given by:Pall sitesunfrozen(T,µα ,σα , t) = [Phetunfr(T,µα ,σα , t)]nsite . (5.5)Since the measurements presented here do not contain a single particle in each drop, wemust consider the probability of each of these individual particles freezing. Similar to theintroduction of multiple sites on a single particle above, the introduction of multiple particlesper drop results in a product of the freezing probabilities of the individual particles resultingin:Pallparticlesunfr =nmax∑n=1{[Phetunfr(T,µα ,σα , t)]nsite}n P(n), (5.6)where P(n) is the probability of having n particles per drop.The fraction of drops frozen is given byfd(T ) = 1−Pallparticlesunfr. (5.7)Due to the necessity of performing a numerical integration of Eq. (5.2), the probability93Phetunfr will not equal exactly one even at temperatures close to 0◦C. This will lead to a non zerofraction frozen calculated at 0◦C. For a value of nsite = 1 this error remains quite low (∼ 10−15),but for higher values of nsite in Eq. (5.6), the error is compounded by the power of nsite. Thus,for high values of nsite the error in frozen fraction calculated with the soccer ball scheme iscomparable to the experimental frozen fraction values. For this reason, we have limited themaximum value of nsite in these calculations to be 108 such that the error in calculated frozenfraction will remain several orders of magnitude below the lowest experimental frozen fraction.Numerical integration was performed using trapezoidal integration.5.3.3 Pdf-α schemeThis model is the same as the soccer-ball model shown in Eq. (5.7) where the number of sitesis set to unity (nsite = 1). Here we use the soccer ball scheme in the special case where nsite = 1to evaluate the pdf-α scheme and compare these results with the three parameter soccer ballscheme. This is equivalent to the pdf-α scheme presented in Chapter 4.5.3.4 Deterministic schemeThe deterministic scheme is the same as was presented in Chapter 4. As described for thesingle-α scheme, we assume that the size of all particles of a given type is the same for thesemeasurements (i.e. the particles are monodisperse). Based on this assumption, the fraction ofdrops frozen at temperature T considering a distribution of particles per drop is given by,fd(T ) = 1−nmax∑n=0exp [−nApns(T )] ·P(n) (5.8)where n is the number of particles contained in each drop, P(n) is the probability of having nparticles per drop, and Ap is the surface area of a single particle. The density of sites active ata temperature T , ns(T ), is given by Eq. (4.13).945.4 Results and discussionThe experimental freezing data (Figs. 5.1 and 5.2) were fit to the different schemes describedabove by minimizing the weighted sum of squared residuals (WSSR) between the schemeoutput and the experimental results. WSSR was calculate asWSSR =n∑i=1wi (yi− fd(Ti,γ1, ...,γm))2 , (5.9)where wi is the weighting function employed, yi is the individual fraction frozen at temperatureTi, and γ1, ...,γm represents the variable number of fitting parameters (1 for the single-α scheme,2 for the pdf-α and deterministic schemes, and 3 for the soccer ball scheme). Input to thedifferent schemes included the size of the individual fungal spores or bacteria cells (Tables 5.1and 5.2) and the number of spores or bacteria cells per drop (Figs. B.5 and B.6).In order to avoid influence from homogeneous freezing, heterogeneous freezing data attemperatures ≤−36◦C was not included in the fitting of the four schemes based on the homo-geneous freezing data of Iannone et al. [2011]. Iannone et al. [2011] measured homogeneousfreezing with the same apparatus used by Haga et al. [2013] and Haga et al. [2015].Due to the variation in uncertainty as a function of frozen fraction, a weighting functionwas used in fitting the experimental data. The inverse of the variance at each point was chosenas a weighting function [Wolberg, 2006] which applied greater weighting to points which hada lower level of uncertainty. The weighting function employed is given aswi =1σ2 ( fd)(5.10)where σ2 ( fd) represents the variance as a function of frozen fraction. In order to estimatethe variance of the measurements, the original freezing data for each species were randomlydivided into two equally sized groups. The frozen fraction was calculated independently forthe two groups and the difference between the values of the two groups was calculated at each95temperature. An example of this is shown in Fig. 5.3 for the P. allii dataset. The blue andgreen traces show the frozen fractions each calculated from half of the complete dataset. Thered trace represents the midpoint between the green and blue traces. The standard deviation ateach temperature was calculated as half the difference between the blue and the green traces.An average standard deviation at each temperature was obtained by repeating the above process100 times for each species. This process was repeated for each of the nine species and theresulting average standard deviations as a function of frozen fraction is shown in Fig. 5.4. Abest fit to the data presented in Fig. 5.4 was used to calculate the variance in Eq. (5.9).34 32 30 28 26 24 22Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of drops frozenP. allii dataset 1P. allii dataset 2MidpointFigure 5.3: Estimation of the relative standard deviation (σrel) of P. allii. A descriptionof the method used to evaluate σrel is given in the text.The standard deviations determined using the method described above should be consideredconservative estimates of the actual standard deviation since they were determined by splittingeach of the datasets in half. Since the freezing data used in the measurements analyzed here960.050.040.030.020.01σ (f d)1.00.80.60.40.20.0Frozen fractionBest fit: σ = 0.01018 + 0.1198fd- 0.1198fd2Figure 5.4: Calculated standard deviations of each dataset as a function of frozen fraction.Each data set is shown as a different coloured point. A description of the methodused to evaluate σ( fd) is given in the text. The best fit to all of the datasets is shownas a black line.are based on twice the number of freezing events, the standard deviation determined here isexpected to be an upper limit to the relative standard deviation of the measurements.In order to evaluate the different schemes in terms of their ability to represent the experi-mental data, the reduced chi-squared (χ2red) was employed as a means of normalizing the WSSRto the number of measurements as well as the different models. A value of χ2red > 1 indicatesthat the model is not completely representing the data. A value of χ2red < 1 indicates that themeasurement variance used is too high.The fraction of drops frozen by fungal spores shown in Fig. 5.1 and bacteria shown in Fig.5.2 were fit using the schemes described above. Figures 5.5 and 5.6 show the fitting results forthe fungal spore and bacteria species studied, respectively. The resulting fit parameters are also97tabulated in Appendix B in Tables B.1, B.2, B.3, and B.4 for the single-α , pdf-α , deterministicand soccer ball schemes, respectively. For the soccer ball scheme (Table B.4), the best fitshave nsite = 1 for four of the spore types studied (P. graminis, P. triticina, P. allii, and T. tritici)indicating that the results from the soccer ball scheme are equivalent to the pdf-α scheme. Itshould be noted that in the cases where the soccer ball scheme was the same as the pdf-αscheme, the values of χ2red are larger for the soccer ball scheme than for the pdf-α scheme dueto the greater number of fitting parameters for the soccer ball scheme compared with the pdf-αscheme.Table 5.3 summarizes the χ2red values for each of the schemes and each of the spore typesand bacteria studied. As mentioned above, a χ2red value close to unity indicates a good fit to thedata. In all cases, the single-α model gave χ2red values above unity indicating a misfit betweenthe experimental data and the nucleation scheme. The deterministic scheme also produces fitswith χ2red > 1 in seven of the nine species studied. The χ2red values were, however, significantlysmaller than with the single-α scheme in all cases. On the other hand, the soccer ball andpdf-α schemes produced values close to or less than one in the majority of cases, indicatingthat these schemes were able to reproduce the experimental freezing results. For many of thespecies studied, only a small difference was observed between the best fit of the pdf-α schemeand the soccer ball scheme. Only E. harknessii shows a substantial difference in the resultingχ2red value for the pdf-α scheme compared with the soccer ball scheme. Some of the results inTable 5.3 for the pdf-α , deterministic, and soccer ball schemes are less than one indicating anoverestimation of the variance used to calculate χ2red.Table 5.4 shows relative ranking of each of the four schemes investigated based on the χ2redvalues from Table 5.3. In cases where the soccer ball scheme gave a best fit with nsite = 1,the soccer ball scheme was ranked the same as the pdf-α scheme despite the difference in χ2redvalues as described above. As can be seen from the data, in all cases the single-α model isthe worst at fitting the heterogeneous freezing results of the fungal spores and bacteria studied.This finding is consistent with previous studies of mineral dust particles [Broadley et al., 2012;9845 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. graminissingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. triticinasingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. alliisingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenE. harknessiisingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenT. laevissingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenT. triticisingle-αdeterministicpdf-α/soccer ballFigure 5.5: Fit results for all fungal spores studied. The shaded region represents the re-gion where homogeneous freezing was observed and where fits to the experimentaldata were not considered. Experimental freezing data is shown as filled circles,while best fits are shown as solid lines for each of the four schemes studied.9945 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenB. cereussingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. graminissingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)10-310-210-1100Fraction of spores frozenP. syringaesingle-αdeterministicpdf-αsoccer ballFigure 5.6: Fit results for all bacteria studied. The shaded region shows the region wherehomogeneous freezing was observed and where fits to the experimental data werenot considered. Experimental freezing data is shown as filled circles, while best fitsare shown as solid lines for each of the four schemes studied.Table 5.3: χ2red values from the fits of all species studied.Particle Type Species single-α pdf-α deterministic soccer ballFungiP. graminis 25.248 6.900 0.862 7.176P. triticina 32.152 1.079 3.552 1.135P. allii 38.160 5.075 1.282 5.286E. harknessii 7.739 1.587 3.203 0.921T. laevis 31.145 0.853 6.618 0.891T. tritici 28.353 0.293 5.319 0.309BacteriaB. cereus 8.083 0.953 2.531 0.916P. graminis 6.256 0.186 0.478 0.194P. syringae 6.914 2.836 3.209 2.838100Table 5.4: Relative rankings of different fitting schemes used for all species studied.Schemes are ranked from 1 to 4 where 1 gives the best fit to the data and 4 theworst.Particle Type Species single-α pdf-α deterministic soccer ballFungiP. graminis 4 2 1 2P. triticina 4 1 3 1P. allii 4 2 1 2E. harknessii 4 2 3 1T. laevis 4 1 3 2T. tritici 4 1 3 1BacteriaB. cereus 4 2 3 1P. graminis 4 1 3 2P. syringae 4 1 3 2Lu¨o¨nd et al., 2010; Marcolli et al., 2007; Vali, 2008, 2014; Welti et al., 2012; Wheeler andBertram, 2012; Wheeler et al., 2015b]. In seven out of the nine species of fungal spores orbacteria studied, the deterministic scheme ranks third. Only for P. graminis and P. allii doesthe deterministic scheme perform better than the stochastic, pdf-α , or soccer ball schemes.In five of the nine species of fungal spores or bacteria studied the pdf-α scheme ranks first,and in all other cases it ranks second. The soccer ball scheme ranks first in four of the ninespecies studied and ranks second in all other cases. Despite producing equivalent or lowerWSSR values than the pdf-α scheme in all cases (c.f. WSSR values from Tables B.2 and B.4),the soccer ball scheme only results in smaller χ2red values in two of the species studied. Thereduction in WSSR of the soccer ball scheme is insufficient to overcome the decrease in thedegrees of freedom from the soccer ball scheme. These results suggest that the pdf-α schemegives the highest accuracy when fitting laboratory freezing data of PBAPs.Two other studies have examined the ability of different nucleation schemes to representlaboratory freezing data of PBAPs. Hartmann et al. [2013] tested the recently developedCHESS (stoCHastic modEl of similar and poiSSon distributed ice nuclei) scheme (not testedin this study) and the single-α scheme on the freezing results of Pseudomonas syringae andSnowmaxTM (an industrial formulation containing non-viable P. syringae cells) from multiple101studies and showed better agreement between scheme and experimental results for the CHESSscheme than the single-α scheme. Augustin et al. [2013] tested the CHESS scheme, single-αscheme, and the soccer ball scheme against the immersion freezing of ice nucleating macro-molecules from two samples of Birch pollen. Results showed that the CHESS and soccer ballschemes were both able to reproduce the experimentally determined nucleation rates but thatthe single-α scheme was not. These results are consistent with the findings of the current studyshowing that the single-α scheme is least effective at representing heterogeneous freezing dataof PBAPs.5.5 ConclusionsThe ability of four different nucleation schemes to represent freezing results from six speciesof fungal spores and three species of bacteria cells was investigated. Fitting was limited foreach scheme to temperatures above−36◦C to avoid interferences with homogeneous freezing.Results show that the single-α scheme was unable to represent the freezing behaviour of allof the samples studied. In five of the nine species studied, the pdf-α scheme provided the bestfit to the experimental data. The soccer ball scheme produced fits which were equivalent to thepdf-α scheme in four out of nine species while resulting in fits which were better than the pdf-αscheme in two of the species studied. The pdf-α scheme resulted in fits which were better thanthe soccer ball scheme in three of the species studied. Only in two cases did the deterministicscheme provide better results than either the pdf-α or soccer ball scheme. The fitting resultssuggest that the pdf-α scheme can more accurately represent the laboratory freezing data ofPBAPs.102Chapter 6Conclusions and future work6.1 Ice nucleation properties of mineral dustsThe heterogeneous ice nucleation properties of three different mineral dust species were ex-amined using an optical microscope coupled to a humidity and temperature controlled flowcell.In Chapter 3, the nucleation conditions of two minerals, kaolinite and illite, in the deposi-tion mode were examined. The onset conditions were determined as a function of total surfacearea available for nucleation. Results showed that both kaolinite and illite were efficient icenuclei (IN), being able to nucleate ice at supersaturations of less than 5% over the temper-ature range of 239–242 K. This is consistent with previous measurements of deposition icenucleation on both kaolinite and illite [Bailey and Hallett, 2002; Chernoff and Bertram, 2010;Eastwood et al., 2008; Kanji et al., 2008; Mo¨hler et al., 2008a,c; Salam et al., 2006; Welti et al.,2009; Zimmermann et al., 2007, 2008]. The variation in the onset conditions as a function ofavailable surface area for nucleation showed that when only a small number of particles areavailable for nucleation, the onset saturation for nucleation varies between 100 and 125%.In Chapter 4, the immersion freezing properties of two mineral dust species, kaolinite andArizona Test Dust (ATD), were studied. Examination of these species was limited to supermi-cron sized particles. The results presented are the first size-selected freezing studies to focus on103supermicron dust particles. The freezing temperatures of pure water drops with differing num-bers of supermicron mineral dust particles were measured using the same flow cell apparatusas for the deposition measurements in Chapter 3. Results from the freezing showed that bothkaolinite and ATD induced nucleation at temperatures warmer than the homogeneous freezingtemperature of pure water. ATD was shown to be a more efficient IN than kaolinite with amedian freezing temperature of −30◦C compared with −36◦C for kaolinite.6.1.1 INAS densities of supermicron mineral dust particlesAlso in Chapter 4, the ice nucleation active site (INAS) densities of the supermicron dust par-ticles were calculated and compared with other observations in the literature. INAS densitiesare useful for comparison of the freezing results of different particle types [Hoose and Mo¨hler,2012]. The INAS densities of supermicron kaolinite and ATD were shown to be lower thanthose of submicron particles. Overlap was observed between the results presented here andthose experiments where mixtures of supermicron and submicron particles were used. Differ-ences between the INAS densities of kaolinite in the supermicron and submicron mode maybe, in part, due to the difference in source of the mineral dust particles studied. For ATD, thedifference between supermicron and submicron results may be due to the processing of mineraldust particles, wherein the production of smaller sized particles may lead to greater surface im-perfections in these particles. Recent work by Hiranuma et al. [2014] suggests that processingof mineral particles to smaller sizes can increase the INAS densities of these particles. This issignificant since a substantial fraction of supermicron mineral dust particles have been shownto exist in the atmosphere [Maring et al., 2003]. Differences in the freezing properties of super-micron and submicron particles should be taken into account when predicting heterogeneousice nucleation in the atmosphere.1046.2 Testing different schemes to describe atmospheric icenucleationIn Chapter 3, the deposition freezing results on kaolinite and illite particles was used to testschemes used to describe ice nucleation in atmospheric models. Results showed that the oneparameter single-α scheme was unable to describe the results of either the kaolinite or illitedata. This is consistent with work by Welti et al. [2009] who showed that a single contact anglewas not able to describe deposition ice nucleation on illite or kaolinite. The other schemes,pdf-α , active site, and deterministic, were all able to describe the data within experimentaluncertainty. This is consistent with measurements which show that modifications to the single-α scheme are required to accurately predict heterogeneous nucleation data [Archuleta et al.,2005; Hung et al., 2003; Lu¨o¨nd et al., 2010; Marcolli et al., 2007; Welti et al., 2009].In Chapter 4 the immersion freezing results of supermicron kaolinite and ATD particleswere used to test the same four schemes as in Chapter 3. The schemes were modified to takeinto account the variability in the number of particles contained in each drop. Results againshowed that the single-α scheme was unable to reproduce freezing results from either kaoliniteor ATD particles. The active site scheme was shown to be most effective at describing theexperimental data with the deterministic and pdf-α schemes falling in between the single-αand active site schemes in terms of their ability to represent the data. In addition, the variationin median freezing temperature with changes in the cooling rate predicted by each scheme wascompared with experimental values determined in the literature for both kaolinite and ATD.Results showed that the three stochastic schemes are consistent with the experimental resultswithin a factor of two while the deterministic scheme is inconsistent with experimental datasince no change in freezing temperature is expected for the deterministic scheme with variationin the cooling rate.In Chapter 5, freezing results for nine different types of primary biological aerosol parti-cles (PBAPs) taken from Haga et al. [2013, 2015] were used to test schemes similar to thosedescribed above. Immersion freezing data from six different species of fungal spore and three105species of bacteria were used. The single-α and deterministic schemes from Chapters 3 & 4were used along with a new formulation of the “soccer ball model” [Niedermeier et al., 2014]which was used to evaluate the pdf-α and active site schemes. Results showed that the single-αscheme is unable to represent the freezing of PBAPs while the pdf-α scheme was found to bethe best at representing the freezing data.Overall, deposition and immersion freezing data for mineral dust particles and immersionfreezing data for PBAPs were used to test four schemes: the single-α scheme, the pdf-αscheme, the deterministic scheme, and the active site scheme. The tests showed that the single-α scheme is unable to represent deposition nucleation on mineral dust particles or immersionfreezing on either mineral dust or PBAP particles. It remains unclear which of the remainingschemes is best at describing deposition nucleation on mineral dust particles. In the case of im-mersion freezing, the active site scheme was most capable of describing the freezing of mineraldust particles while the pdf-α scheme was best at describing the freezing of PBAPs. The bestfit of the immersion freezing of mineral dust particles was described using a three parameterscheme while the immersion freezing of PBAPs was best described using the two parameterpdf-α scheme. A possible explanation for this difference is due to the greater variability insurface properties between the mineral dust and the PBAPs. In the case of mineral dust parti-cles, there is a great amount of irregularity in the surface structure from particle to particle. ForPBAPs, each of the particles of the same species has much less surface variability since theyare all created through the same biological process.Recent work has shown that the predictions of classical nucleation theory (CNT) can varyby as many as 25 orders of magnitude depending on the values of the free parameters used[Ickes et al., 2015], most notably the interfacial energy and the energy of self-diffusion. Whilethe values of the fits performed here will vary depending on the values of the input parametersused, the conclusions presented here are not expected to change. The fits presented here can beused to predict the freezing results in climate simulations as long as the same input parametersare used as those used here. Additionally, the relative ability of the different schemes to fit the106experimental data is not expected to depend on the parameters used in the fitting.The single-α scheme has been used extensively to represent heterogeneous ice nucleationin atmospheric models [e.g. Hoose et al., 2010a,b; Jensen and Toon, 1997; Jensen et al., 1998;Ka¨rcher, 1996, 1998; Ka¨rcher et al., 1998; Khvorostyanov and Curry, 2000, 2004, 2005, 2009;Kulkarni et al., 2012; Liu et al., 2007; Morrison et al., 2005]. The results presented here alongwith recent modelling studies which show the cloud properties determined from atmosphericmodels to be dependent on the nucleation scheme used [Eidhammer et al., 2009; Ervens andFeingold, 2012; Kulkarni et al., 2012; Wang and Liu, 2014; Wang et al., 2014] suggest thatthe predictions of the indirect effect of IN on climate may actually be different than whathas been predicted by previous modelling studies which utilize the single-α scheme. Resultsfrom testing the different schemes presented here should allow modellers to better select howheterogeneous ice nucleation is incorporated into atmospheric models. Additionally, the fittingparameters from the studies presented here may be used to describe heterogeneous freezing bycertain particle types in cloud or climate models.6.3 Future researchOur understanding of the fundamental processes involved in heterogeneous ice nucleation isstill lacking and many research questions remain about ice nucleation. For example, Marcolli[2014] recently suggested that deposition nucleation may not represent a unique mode of icenucleation but rather is homogeneous or heterogeneous immersion freezing of supercooledwater condensed in pores on the particle surface. This would represent a fundamental changein our understanding of the nucleation process. A more detailed examination involving icenucleation experiments on pore-free surfaces such as freshly cleaved mica surfaces may helpdetermine the conditions for deposition nucleation. Additionally, molecular simulations build-ing on the work of Croteau et al. [2010] examining the formation of ice in pores comparedwith flat surfaces may provide insight into deposition nucleation. In Chapter 4 the nucleatingefficiency of supermicron dust particles was shown to be different than that of submicron dust107particles. Further laboratory studies examining both submicron and supermicron dust particlesprepared in the same manner and measuring the freezing temperature using the same appara-tus would help answer the question of size dependence on ice nucleation. As mineral dust isthought to be one of the main IN in the atmosphere [Hoose et al., 2008], it would be interest-ing to incorporate the results obtained from the fitting of supermicron dust particles alongsidesubmicron dust particles. Finally, data on parameterizing PBAPs for incorporation into atmo-spheric models is limited. Work by Hoose et al. [2010a] suggests that PBAPs do not contributesignificantly to the total atmospheric ice nucleation rate. However, recent studies have sug-gested that PBAPs may influence cloud properties on regional or local scales [Hazra, 2013;Gonc¸alves et al., 2012; Costa et al., 2014]. This may indicate a need for more informationregarding the types of PBAPs responsible for ice nucleation in regional air masses and mea-surements of the ice nucleating ability of these particles. Field studies examining the PBAPsfound in and out of clouds would allow for better determination of the specific species whichmay be responsible for ice formation. The freezing ability of these particles must be carefullymeasured and parameterized in order to be included in any modelling of regional climate andweather.108BibliographyB. A. Albrecht. Aerosols, cloud microphysics, and fractional cloudiness. 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URLhttp://adsabs.harvard.edu/abs/1994JAtS...51.1843Vhttp://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281994%29051%3C1843%3AFRDTHN%3E2.0.CO%3B2. → pages 16G. Vali. Repeatability and randomness in heterogeneous freezing nucleation. AtmosphericChemistry and Physics, 8(16):5017–5031, August 2008. doi: 10.5194/acp-8-5017-2008.URL http://www.atmos-chem-phys.net/8/5017/2008/. → pages 15, 16, 72, 101132G. Vali. Interpretation of freezing nucleation experiments: Singular and stochastic; sites andsurfaces. Atmospheric Chemistry and Physics, 14(11):5271–5294, June 2014. doi:10.5194/acp-14-5271-2014. URL http://www.atmos-chem-phys.net/14/5271/2014/. →pages 15, 16, 72, 101G. Vali and E. J. Stansbury. Time-dependent characteristics of the heterogeneous nucleationof ice. Canadian Journal of Physics, 44(3):477–502, March 1966. doi: 10.1139/p66-044.URL http://www.nrcresearchpress.com/doi/abs/10.1139/p66-044. → pages 16G. Vali, M. Christensen, R. W. Fresh, E. L. Galyan, L. R. Maki, and R. C. Schnell. Biogenicice nuclei. Part II: Bacterial Sources. Journal of the Atmospheric Sciences, 33(8):1565–1570, August 1976. doi: 10.1175/1520-0469(1976)033〈1565:BINPIB〉2.0.CO;2.URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281976%29033%3C1565%3ABINPIB%3E2.0.CO%3B2. → pages 9B. Vonnegut and M. Baldwin. Repeated nucleation of a supercooled water sample thatcontains silver iodide particles. Journal of Climate and Applied Meteorology, 23(3):486–490, March 1984. doi: 10.1175/1520-0450(1984)023〈0486:RNOASW〉2.0.CO;2.URL http://journals.ametsoc.org/doi/abs/10.1175/1520-0450(1984)023〈0486:RNOASW〉2.0.CO;2. → pages 15Y. Wang and X. Liu. Immersion freezing by natural dust based on a soccer ball model withthe Community Atmospheric Model version 5: climate effects. Environmental ResearchLetters, 9(12):124020, 2014. ISSN 1748-9326. doi: 10.1088/1748-9326/9/12/124020.URL http://stacks.iop.org/1748-9326/9/i=12/a=124020?key=crossref.62715e4343d591224296a3de99f05d15. → pages 48, 85, 107Y. 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URL http://www.atmos-chem-phys.net/12/9893/2012/. →pages 15, 48, 49, 60, 65, 67, 68, 72, 76, 86, 91, 101C. D. Westbrook and A. J. Illingworth. Evidence that ice forms primarily in supercooledliquid clouds at temperatures ¿-27C. Geophysical Research Letters, 38(May):1–4, 2011.doi: 10.1029/2011GL048021. → pages 7M. J. Wheeler and A. K. Bertram. Deposition nucleation on mineral dust particles: A caseagainst classical nucleation theory with the assumption of a single contact angle.Atmospheric Chemistry and Physics, 12(2):1189–1201, January 2012. doi:10.5194/acp-12-1189-2012. URL http://www.atmos-chem-phys.net/12/1189/2012/. →pages 48, 49, 51, 65, 72, 75, 76, 86, 101M. J. Wheeler, D. I. Haga, R. H. Mason, V. E. Irish, M. J. Wagstaff, R. Iannone, and A. K.Bertram. Testing different schemes for describing immersion freezing of water dropscontaining primary biological aerosol particles. 2015a. → pagesM. J. Wheeler, R. H. Mason, K. Steunenberg, M. J. Wagstaff, C. Chou, and A. K. Bertram.Immersion freezing of supermicron mineral dust particles: Freezing results, testingdifferent schemes for describing ice nucleation results, and ice nucleation active sitedensities. Journal of Physical Chemistry A, 119(19):4358–4372, 2015b. doi:10.1021/jp507875q. → pages 86, 101J. Wolberg. Data analysis using the method of least squares. Springer-Verlag, Heidelberg,2006. ISBN 3-540-25674-1. → pages 69, 95T. P. Wright, M. D. Petters, J. D. Hader, T. Morton, and A. L. Holder. Minimal cooling ratedependence of ice nuclei activity in the immersion mode. Journal of GeophysicalResearch: Atmospheres, 118(18):10,535–10,543, September 2013. doi:10.1002/jgrd.50810. URL http://doi.wiley.com/10.1002/jgrd.50810. → pages 15, 73, 74J. D. Yakobi-Hancock, L. A. Ladino, and J. P. D. Abbatt. Feldspar minerals as efficientdeposition ice nuclei. Atmospheric Chemistry and Physics, 13(22):11175–11185,November 2013. doi: 10.5194/acp-13-11175-2013. URLhttp://www.atmos-chem-phys.net/13/11175/2013/. → pages 48134F. Zimmermann, M. Ebert, A. Worringen, L. Schu¨tz, and S. Weinbruch. Environmentalscanning electron microscopy (ESEM) as a new technique to determine the ice nucleationcapability of individual atmospheric aerosol particles. Atmospheric Environment, 41(37):8219–8227, December 2007. doi: 10.1016/j.atmosenv.2007.06.023. URLhttp://linkinghub.elsevier.com/retrieve/pii/S1352231007005882. → pages 32, 103F. Zimmermann, S. Weinbruch, L. Schu¨tz, H. Hofmann, M. Ebert, K. Kandler, andA. Worringen. Ice nucleation properties of the most abundant mineral dust phases. Journalof Geophysical Research, 113(D23):D23204, December 2008. doi:10.1029/2008JD010655. URLhttp://www.agu.org/pubs/crossref/2008/2008JD010655.shtml. → pages 32, 48, 50, 79, 103B. Zobrist, T. Koop, B. P. Luo, C. Marcolli, and T. Peter. Heterogeneous ice nucleation ratecoefficient of water droplets coated by a nonadecanol monolayer. Journal of PhysicalChemistry C, 111(5):2149–2155, February 2007. doi: 10.1021/jp066080w. URLhttp://pubs.acs.org/cgi-bin/doilookup/?10.1021/jp066080w. → pages 56, 64135Appendix ASensitivity study of the depositionnucleation of kaolinite and illiteWe have performed an additional series of calculations to assess the sensitivity of the resultsin Chapter 3 to the assumption of spherical particles. In Chapter 3 we assumed the surfacearea of a particle was equal to the geometric surface area (i.e. the particles are spherical). Herewe reanalyze the results with the assumption that the surface area equals the geometric surfacearea multiplied by 50 [Eastwood et al., 2008], as an upper limit to the surface area.136Table A.1: Fit parameters obtained for kaolinite assuming the surface area equals the ge-ometric surface area multiplied by 50. Best fits were obtained by minimizing theweighted sum of squared residuals (WSSR) between the experimental data and thefit function.Scheme Parameter Value WSSRasingle-α α 12.77◦ 9.444pdf-αµα 0◦3.934σα 26.66◦active siteb 1.24×108m−25.091β1 0.01β2 0.001deterministicA1 4.63×104cm−20.718A2 −0.8845a Weighted sum of squared residuals137Table A.2: Fit parameters obtained for illite assuming the surface area equals the geo-metric surface area multiplied by 50. Best fits were obtained by minimizing theweighted sum of squared residuals (WSSR) between the experimental data and thefit function.Scheme Parameter Value WSSRasingle-α α 22.19◦ 9.778pdf-αµα 29.52◦0.0464σα 13.0◦active siteb 1.44×108m−20.538β1 0.1305β2 1.0×10−4deterministicA1 3.55×104cm−20.0190A2 −0.9480a Weighted sum of squared residuals1381 0 - 3 1 0 - 2 1 0 - 10 . 9 00 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 5 1 0 0 1 0 0 0 1 0 0 0 01 0 - 3 1 0 - 2 1 0 - 10 . 9 00 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 0 0 1 0 0 0 1 0 0 0 01 0 - 3 1 0 - 2 1 0 - 10 . 9 81 . 0 01 . 0 21 . 0 41 . 0 61 . 0 81 . 1 01 . 1 21 . 1 4 1 0 0 1 0 0 0 1 0 0 0 0S ice, onset S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e s( b )( a )S ice, r=0.05 S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e sa  =  3 oa  =  7 o a  =  1 4 oS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 )( c ) N u m b e r  o f  p a r t i c l e sFigure A.1: Results for kaolinite particles: (a) individual onset measurements, (b) indi-vidual Sice, r=0.05 results and (c) average Sice, r=0.05. The average values are cal-culated for four equally sized bins and the horizontal error bars show the rangeof data points in each bin. The surface area values in (c) represent the averagesurface area of the points in each bin. Error in Sice,onset is given as experimentalerror in measurements of saturation. Error in Sice, r=0.05 is based on the differencebetween Sice,onset and Sice,previous as well as the uncertainty in measuring Sice,onset.Error in the average Sice, r=0.05 represents the 95 % confidence interval. Predictionsare shown using the single-α scheme (orange lines) calculated using Eq. (3.7).In addition to surface area, the corresponding number of particles calculated fromAavg is also shown. The surface area was assumed to be the geometric surface areamultiplied by a factor of 50.1390 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 51 0 - 21 0 - 11 0 00 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 51 0 - 11 0 0( b )  Fraction nucleated S i c e ,  r = 0 . 0 5 ( a )   E x p e r i m e n t a l  d a t a S i n g l e - α m o d e l P D F - α m o d e l A c t i v e  s i t e  m o d e l D e t e r m i n i s t i c  m o d e lFraction nucleated S i c e ,  r = 0 . 0 5Figure A.2: Fraction of particles nucleated as a function of Sice, r=0.05 for kaolinite. Panel(a) shows the nucleated fraction for the individual experimental results. The y-errorwas calculated from the uncertainty in the value of D¯g. The x-error represents theuncertainty in Sice, r=0.05. Panel (b) shows the average nucleated fraction calculatedfor four size bins. The range of the data points in each bin is given as the horizontalerror and data points represent the average of the Sice, r=0.05 values within eachbin. The y-error bar in panel (b) represents the 95% confidence interval of theaverage nucleated fraction. Fits are shown for the single-α , pdf-α , active site, anddeterministic schemes. The surface area was assumed to be the geometric surfacearea multiplied by a factor of 50.1401 0 - 4 1 0 - 3 1 0 - 2 1 0 - 10 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 0 0 1 0 0 0 1 0 0 0 01 0 - 4 1 0 - 3 1 0 - 2 1 0 - 11 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 0 0 1 0 0 0 1 0 0 0 01 0 - 4 1 0 - 3 1 0 - 2 1 0 - 10 . 9 51 . 0 01 . 0 51 . 1 01 . 1 51 . 2 01 . 2 51 . 3 0 1 0 0 1 0 0 0 1 0 0 0 0S ice, onset S u r f a c e  a r e a  ( c m 2 ) N u m b e r  o f  p a r t i c l e sa  =  2 0 oa  =  3 oa  =  7 oa  =  1 4 oS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 )( c ) N u m b e r  o f  p a r t i c l e sS ice, r=0.05 S u r f a c e  a r e a  ( c m 2 )( b )( a ) N u m b e r  o f  p a r t i c l e sFigure A.3: Results for illite particles: (a) individual onset measurements, (b) individualSice, r=0.05 results and (c) average Sice, r=0.05. The average values are calculated forfour equally sized bins and the horizontal error bars show the range of data pointsin each bin. The surface area values in (c) represent the average surface area of thepoints in each bin. Error in Sice,onset is given as experimental error in measurementsof saturation. Error in Sice, r=0.05 is based on the difference between Sice,onset andSice,previous as well as the uncertainty in measuring Sice,onset. Error in the averageSice, r=0.05 represents the 95 % confidence interval. Predictions are shown using thesingle-α scheme (orange lines) calculated using Eq. (3.7). In addition to surfacearea, the corresponding number of particles calculated from Aavg is also shown.The surface area was assumed to be the geometric surface area multiplied by afactor of 50.1410 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 5 1 . 3 01 0 - 31 0 - 21 0 - 11 0 00 . 9 5 1 . 0 0 1 . 0 5 1 . 1 0 1 . 1 5 1 . 2 0 1 . 2 5 1 . 3 01 0 - 31 0 - 21 0 - 11 0 0( b )Fraction nucleated S i c e ,  r = 0 . 0 5 ( a )   E x p e r i m e n t a l  d a t a S i n g l e - α m o d e l P D F - α m o d e l A c t i v e  s i t e  m o d e l D e t e r m i n i s t i c  m o d e lFraction nucleated S i c e ,  r = 0 . 0 5Figure A.4: Fraction of particles nucleated as a function of Sice, r=0.05 for illite. Panel (a)shows the nucleated fraction for the individual experimental results. The y-errorwas calculated from the uncertainty in the value of D¯g. The x-error represents theuncertainty in Sice, r=0.05. Panel (b) shows the average nucleated fraction calculatedfor four size bins. The range of the data points in each bin is given as the horizontalerror and data points represent the average of the Sice, r=0.05 values within eachbin. The y-error bar in panel (b) represents the 95% confidence interval of theaverage nucleated fraction. Fits are shown for the single-α , pdf-α , active site, anddeterministic schemes. The surface area was assumed to be the geometric surfacearea multiplied by a factor of 50.142Appendix BFitting PBAP DataFraction frozen plots from Section 5.4 above are replotted here using a linearly scaled ordinateaxis. Also shown are the fitting results from each of the schemes investigated along with thefitting results plotted on a linearly scaled ordinate axis. Finally, the distributions of particlesper drop measured in the freezing experiments is plotted for each of the species studied.14345 40 35 30 25 20 15Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. graminisP. triticinaP. alliiE. harknessiiT. laevisT. triticiHomogeneousFigure B.1: Fraction of spore containing drops frozen calculated from immersion freez-ing results for all fungal spores studied plotted on a linear scale.14445 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of cells frozenB. cereusP. graminisP. syringaeHomogeneousFigure B.2: Fraction of bacteria containing drops frozen calculated from immersionfreezing results for all bacteria studied plotted on a linear scale.14545 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. graminissingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. triticinasingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. alliisingle-αdeterministicpdf-α/soccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenE. harknessiisingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenT. laevissingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenT. triticisingle-αdeterministicpdf-α/soccer ballFigure B.3: Fit results for all fungal spores studied plotted on a linear scale. The shadedregion represents the region where homogeneous freezing was observed and wherefits to the experimental data were not considered. Experimental freezing data isshown as filled circles, while best fits are shown as solid lines for each of the fourschemes studied.14645 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenB. cereussingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. graminissingle-αdeterministicpdf-αsoccer ball45 40 35 30 25 20 15 10 5 0Temperature ( ◦ C)0.00.20.40.60.81.0Fraction of spores frozenP. syringaesingle-αdeterministicpdf-αsoccer ballFigure B.4: Fit results for all bacteria studied plotted on a linear scale. The shaded regionrepresents the region where homogeneous freezing was observed and where fits tothe experimental data were not considered. Experimental freezing data is shown asfilled circles, while best fits are shown as solid lines for each of the four schemesstudied.1470 20 40 60 80 100 120Number of spores per drop01020304050Number of drops0.00.10.20.30.4Probability of n spores per dropP. graminis0 10 20 30 40 50 60 70 80 90Number of spores per drop0102030405060Number of drops0.00.10.20.30.40.50.60.7Probability of n spores per dropP. triticina0 2 4 6 8 10Number of spores per drop051015202530Number of drops0.00.51.01.52.02.53.0Probability of n spores per dropP. allii0 5 10 15 20 25 30 35 40Number of spores per drop051015202530Number of drops0.00.10.20.30.40.50.60.70.8Probability of n spores per dropE. harknessii0 20 40 60 80 100 120Number of spores per drop0510152025Number of drops0.000.050.100.150.20Probability of n spores per dropT. laevis0 20 40 60 80 100 120Number of spores per drop0246810121416Number of drops0.000.020.040.060.080.100.120.14Probability of n spores per dropT triticiFigure B.5: Distribution of spores per drop calculated for each of the fungi studied. Theleft ordinate shows the individual number of drops observed as a function of thenumber of spores per drop. The right ordinate shows the fraction of drops contain-ing n spores per drop. This corresponds to P(n) from Eq. (5.1), (5.6) & (5.8).1480 5 10 15 20 25 30 35 40Number of cells per drop0510152025Number of drops0.00.10.20.30.40.50.6Probability of n cells per dropB. cereus0 5 10 15 20 25 30Number of cells per drop024681012Number of drops0.000.050.100.150.200.250.300.350.40Probability of n cells per dropP. graminis0 5 10 15 20 25 30 35 40Number of cells per drop024681012Number of drops0.000.050.100.150.200.250.30Probability of n cells per dropP. syringaeFigure B.6: Distribution of bacteria per drop calculated for each of the species studied.The left ordinate shows the individual number of drops observed as a function ofthe number of bacteria per drop. The right ordinate shows the fraction of dropscontaining n bacteria per drop. This corresponds to P(n) from Eq. (5.1), (5.6) &(5.8).149Table B.1: Fitting results for the single-α scheme for all species studiedParticle Type Species α WSSR χ2redFungiP. graminis 75.7◦ 681.70 25.248P. triticina 83.9◦ 675.19 32.152P. allii 73.9◦ 992.15 38.160E. harknessii 71.3◦ 263.13 7.739T. laevis 92.8◦ 560.61 31.145T. tritici 92.6◦ 567.06 28.353BacteriaB. cereus 105.2◦ 105.07 8.083P. graminis 106.7◦ 137.63 6.256P. syringae 35.0◦ 435.58 6.914Table B.2: Fitting results for the pdf-α scheme for all species studied.Particle Type Species µα σα WSSR χ2redFungiP. graminis 85.3◦ 6.4◦ 179.40 6.900P. triticina 87.8◦ 6.5◦ 21.57 1.079P. allii 79.7◦ 7.9◦ 126.86 5.075E. harknessii 73.1◦ 2.7◦ 52.38 1.587T. laevis 104.5◦ 10.0◦ 14.51 0.853T. tritici 104.1◦ 9.7◦ 5.56 0.293BacteriaB. cereus 127.1◦ 14.2◦ 11.43 0.953P. graminis 199.7◦ 44.0◦ 3.90 0.186P. syringae 41.2◦ 3.9◦ 175.81 2.836150Table B.3: Fitting results for the deterministic scheme for all species studiedParticle Type Species A1 (cm−2) A2 (◦C) WSSR χ2redFungiP. graminis 1506.95 24.07 22.41 0.862P. triticina 3416.80 26.45 71.04 3.552P. allii 1504.41 21.93 32.04 1.282E. harknessii 11450.8 23.68 105.69 3.203T. laevis 1916.86 29.08 112.51 6.618T. tritici 1789.52 29.05 101.07 5.319BacteriaB. cereus 15971 31.70 30.37 2.531P. graminis 420.14 20.71 10.05 0.478P. syringae 263390 7.06 198.93 3.209Table B.4: Fitting results for the soccer ball scheme for all species studied.Particle Type Species nsite µα σα WSSR χ2redFungiP. graminis 1 85.3◦ 6.4◦ 179.40 7.176P. triticina 1 87.8◦ 6.5◦ 21.57 1.135P. allii 1 79.7◦ 7.9◦ 126.86 5.286E. harknessii 100000000 108.3◦ 8.3◦ 29.46 0.921T. laevis 2 109.3◦ 11.2◦ 14.26 0.891T. tritici 1 104.1◦ 9.7◦ 5.56 0.309BacteriaB. cereus 1298 168.7◦ 19.2◦ 10.08 0.916P. graminis 5 236.0◦ 49.0◦ 3.88 0.194P. syringae 98779108 87.4◦ 9.5◦ 173.12 2.838151

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