Articles | Volume 15, issue 22
https://doi.org/10.5194/amt-15-6819-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-15-6819-2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
24 Nov 2022
Research article |
| 24 Nov 2022
| 24 Nov 2022
A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments
Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA
now at: Department of Chemistry, University of Toronto, Toronto,
ON M5S 3H6, Canada
Cosma Rohilla Shalizi
Department of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Santa Fe Institute, Santa Fe, NM 87501, USA
Ryan Christopher Sullivan
Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Cited articles
Agresti, A. and Coull, B. A.: Approximate is better than “Exact” for
interval estimation of binomial proportions, Am. Stat., 52, 119–126,
https://doi.org/10.1080/00031305.1998.10480550, 1998.
Alpert, P. A. and Knopf, D. A.: Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model, Atmos. Chem. Phys., 16, 2083–2107, https://doi.org/10.5194/acp-16-2083-2016, 2016.
Altman, D. G. and Royston, P.: The cost of dichotomising continuous
variables, Br. Med. J., 332, 1080,
https://doi.org/10.1136/bmj.332.7549.1080, 2006.
Atkinson, J. D., Murray, B. J., Woodhouse, M. T., Whale, T. F., Baustian, K.
J., Carslaw, K. S., Dobbie, S., O'Sullivan, D., and Malkin, T. L.: The
importance of feldspar for ice nucleation by mineral dust in mixed-phase
clouds, Nature, 498, 355–358, https://doi.org/10.1038/nature12278, 2013.
Barahona, D.: On the ice nucleation spectrum, Atmos. Chem. Phys., 12, 3733–3752, https://doi.org/10.5194/acp-12-3733-2012, 2012.
Barde, P. J. and Barde, M. P.: What to use to express the variability of
data: Standard deviation or standard error of mean?, Perspect. Clin. Res.,
3, 113–116, https://doi.org/10.4103/2229-3485.100662, 2012.
Belia, S., Fidler, F., Williams, J., and Cumming, G.: Researchers
misunderstand confidence intervals and standard error bars, Psychol.
Methods, 10, 389–396, https://doi.org/10.1037/1082-989X.10.4.389, 2005.
Beydoun, H., Polen, M., and Sullivan, R. C.: Effect of particle surface area on ice active site densities retrieved from droplet freezing spectra, Atmos. Chem. Phys., 16, 13359–13378, https://doi.org/10.5194/acp-16-13359-2016, 2016.
Beydoun, H., Polen, M., and Sullivan, R. C.: A new multicomponent heterogeneous ice nucleation model and its application to Snomax bacterial particles and a Snomax–illite mineral particle mixture, Atmos. Chem. Phys., 17, 13545–13557, https://doi.org/10.5194/acp-17-13545-2017, 2017.
Brubaker, T., Polen, M., Cheng, P., Ekambaram, V., Somers, J., Anna, S. L.,
and Sullivan, R. C.: Development and characterization of a “store and
create” microfluidic device to determine the heterogeneous freezing
properties of ice nucleating particles, Aerosol Sci. Technol., 54, 79–93,
https://doi.org/10.1080/02786826.2019.1679349, 2020.
Budke, C. and Koop, T.: BINARY: an optical freezing array for assessing temperature and time dependence of heterogeneous ice nucleation, Atmos. Meas. Tech., 8, 689–703, https://doi.org/10.5194/amt-8-689-2015, 2015.
Canty, A. J., Davison, A. C., Hinkley, D. v., and Ventura, V.: Bootstrap
diagnostics and remedies, Can, J. Stat., 34, 5–27,
https://doi.org/10.1002/cjs.5550340103, 2006.
Chen, J., Pei, X., Wang, H., Chen, J., Zhu, Y., Tang, M., and Wu, Z.:
Development, characterization, and validation of a cold stage-based ice
nucleation array (PKU-INA), Atmosphere, 9, 357,
https://doi.org/10.3390/atmos9090357, 2018.
Chen, J.-P., Hazra, A., and Levin, Z.: Parameterizing ice nucleation rates using contact angle and activation energy derived from laboratory data, Atmos. Chem. Phys., 8, 7431–7449, https://doi.org/10.5194/acp-8-7431-2008, 2008.
Chong, E., Marak, K. E., Li, Y., and Freedman, M. A.: Ice nucleation
activity of iron oxides via immersion freezing and an examination of the
high ice nucleation activity of FeO, Phys. Chem. Chem. Phys., 23,
3565–3573, https://doi.org/10.1039/d0cp04220j, 2021.
Davison, A. C. and Hinkley, D. V.: Bootstrap Methods and Their Application,
Cambridge University Press, Cambridge,
https://doi.org/10.1017/CBO9780511802843, 1997.
Diciccio, T. J. and Efron, B.: Bootstrap Confidence Intervals, Stat. Sci.,
11, 189–228, 1996.
Efron, B.: Bootstrap Methods: Another Look at the Jackknife, Ann. Stat., 7,
1–26, https://doi.org/10.1214/aos/1176344552, 1979.
Efron, B.: Better bootstrap confidence intervals, J. Am. Stat. Assoc., 82,
171–185, https://doi.org/10.1080/01621459.1987.10478410, 1987.
Efron, B. and Tibshirani, R. J.: An Introduction to the Bootstrap, edited
by: Cox, D. R., Hinkley, D. V., Reid, N., Rubin, D. B., and Silverman, B.
W., Chapman & Hall, Inc., https://doi.org/10.1201/9780429246593, 1994.
Fahy, W. D., Shalizi, C. R., and Sullivan, R. C.: Code and data accompanying
“A universally applicable method of calculating confidence bands for ice
nucleation spectra derived from droplet freezing experiments”, KiltHub [data set, code],
https://doi.org/10.1184/R1/19494188, 2022a.
Fahy, W. D., Maters, E. C., Giese Miranda, R., Adams, M. P., Jahn, L. G.,
Sullivan, R. C., and Murray, B. J.: Volcanic ash ice nucleation activity is
variably reduced by aging in water and sulfuric acid: the effects of
leaching, dissolution, and precipitation, Environ. Sci. Atmos., 2, 85–99,
https://doi.org/10.1039/d1ea00071c, 2022b.
Fletcher, N. H.: Active Sites and Ice Crystal Nucleation, J. Atmos. Sci.,
26, 1266–1271, https://doi.org/10.1175/1520-0469(1969)026<1266:asaicn>2.0.co;2, 1969.
Friddle, R. W. and Thürmer, K.: Mapping ice formation to mineral-surface topography using a micro mixing chamber with video and atomic-force microscopy, Atmos. Meas. Tech., 13, 2209–2218, https://doi.org/10.5194/amt-13-2209-2020, 2020.
Froyd, K. D., Yu, P., Schill, G. P., Brock, C. A., Kupc, A., Williamson, C.
J., Jensen, E. J., Ray, E., Rosenlof, K. H., Bian, H., Darmenov, A. S.,
Colarco, P. R., Diskin, G. S., Bui, T., and Murphy, D. M.: Dominant role of
mineral dust in cirrus cloud formation revealed by global-scale
measurements, Nat. Geosci., 15, 177–183,
https://doi.org/10.1038/s41561-022-00901-w, 2022.
Gehlke, C. E. and Biehl, K.: Certain Effects of Grouping upon the Size of
the Correlation Coefficient in Census Tract Material, J. Am. Stat. Assoc.,
29, 169–170, https://doi.org/10.1080/01621459.1934.10506247, 1934.
Gettelman, A., Liu, X., Barahona, D., Lohmann, U., and Chen, C.: Climate
impacts of ice nucleation, J. Geophys. Res.-Atmos., 117, 1–14,
https://doi.org/10.1029/2012JD017950, 2012.
Gong, X., Wex, H., Müller, T., Wiedensohler, A., Höhler, K., Kandler, K., Ma, N., Dietel, B., Schiebel, T., Möhler, O., and Stratmann, F.: Characterization of aerosol properties at Cyprus, focusing on cloud condensation nuclei and ice-nucleating particles, Atmos. Chem. Phys., 19, 10883–10900, https://doi.org/10.5194/acp-19-10883-2019, 2019.
Gong, X., Wex, H., van Pinxteren, M., Triesch, N., Fomba, K. W., Lubitz, J., Stolle, C., Robinson, T.-B., Müller, T., Herrmann, H., and Stratmann, F.: Characterization of aerosol particles at Cabo Verde close to sea level and at the cloud level – Part 2: Ice-nucleating particles in air, cloud and seawater, Atmos. Chem. Phys., 20, 1451–1468, https://doi.org/10.5194/acp-20-1451-2020, 2020.
Grubbs, F. E.: American Society for Quality Procedures for Detecting
Outlying Observations in Samples, 1–21 pp., 1969.
Gute, E. and Abbatt, J. P. D.: Ice nucleating behavior of different tree
pollen in the immersion mode, Atmos. Environ., 231, 117488,
https://doi.org/10.1016/j.atmosenv.2020.117488, 2020.
Harrison, A. D., Whale, T. F., Carpenter, M. A., Holden, M. A., Neve, L., O'Sullivan, D., Vergara Temprado, J., and Murray, B. J.: Not all feldspars are equal: a survey of ice nucleating properties across the feldspar group of minerals, Atmos. Chem. Phys., 16, 10927–10940, https://doi.org/10.5194/acp-16-10927-2016, 2016.
Harrison, A. D., Lever, K., Sanchez-Marroquin, A., Holden, M. A., Whale, T. F., Tarn, M. D., McQuaid, J. B., and Murray, B. J.: The ice-nucleating ability of quartz immersed in water and its atmospheric importance compared to K-feldspar, Atmos. Chem. Phys., 19, 11343–11361, https://doi.org/10.5194/acp-19-11343-2019, 2019.
Herbert, R. J., Murray, B. J., Whale, T. F., Dobbie, S. J., and Atkinson, J. D.: Representing time-dependent freezing behaviour in immersion mode ice nucleation, Atmos. Chem. Phys., 14, 8501–8520, https://doi.org/10.5194/acp-14-8501-2014, 2014.
Hesterberg, T. C.: What Teachers Should Know About the Bootstrap: Resampling
in the Undergraduate Statistics Curriculum, Am. Stat., 69, 371–386,
https://doi.org/10.1080/00031305.2015.1089789, 2015.
Holden, M. A., Whale, T. F., Tarn, M. D., O'Sullivan, D., Walshaw, R. D.,
Murray, B. J., Meldrum, F. C., and Christenson, H. K.: High-speed imaging of
ice nucleation in water proves the existence of active sites, Sci. Adv., 5,
eaav4316, https://doi.org/10.1126/sciadv.aav4316, 2019.
Ickes, L., Welti, A., and Lohmann, U.: Classical nucleation theory of immersion freezing: sensitivity of contact angle schemes to thermodynamic and kinetic parameters, Atmos. Chem. Phys., 17, 1713–1739, https://doi.org/10.5194/acp-17-1713-2017, 2017.
Jahl, L. G., Brubaker, T. A., Polen, M. J., Jahn, L. G., Cain, K. P.,
Bowers, B. B., Fahy, W. D., Graves, S., and Sullivan, R. C.: Atmospheric
aging enhances the ice nucleation ability of biomass-burning aerosol, Sci.
Adv., 7, eabd3440, https://doi.org/10.1126/sciadv.abd3440, 2021.
Jahn, L. G., Fahy, W. D., Williams, D. B., and Sullivan, R. C.: Role of
Feldspar and Pyroxene Minerals in the Ice Nucleating Ability of Three
Volcanic Ashes, ACS Earth Space Chem., 3, 626–636,
https://doi.org/10.1021/acsearthspacechem.9b00004, 2019.
Johnson, N. J.: Modified t tests and confidence intervals for asymmetrical
populations, J. Am. Stat. Assoc., 73, 536–544,
https://doi.org/10.1080/01621459.1978.10480051, 1978.
Kanji, Z. A., Welti, A., Chou, C., Stetzer, O., and Lohmann, U.: Laboratory studies of immersion and deposition mode ice nucleation of ozone aged mineral dust particles, Atmos. Chem. Phys., 13, 9097–9118, https://doi.org/10.5194/acp-13-9097-2013, 2013.
Kaufmann, L., Marcolli, C., Luo, B., and Peter, T.: Refreeze experiments with water droplets containing different types of ice nuclei interpreted by classical nucleation theory, Atmos. Chem. Phys., 17, 3525–3552, https://doi.org/10.5194/acp-17-3525-2017, 2017.
Kiselev, A., Bachmann, F., Pedevilla, P., Cox, S. J., Michaelides, A.,
Gerthsen, D., and Leisner, T.: Active sites in heterogeneous ice
nucleation-the example of K-rich feldspars, Science, 355, 367–371,
https://doi.org/10.1126/science.aai8034, 2017.
Knopf, D. A., Alpert, P. A., Zipori, A., Reicher, N., and Rudich, Y.:
Stochastic nucleation processes and substrate abundance explain
time-dependent freezing in supercooled droplets, NPJ Clim. Atmos. Sci., 3,
2, https://doi.org/10.1038/s41612-020-0106-4, 2020.
Koop, T., Luo, B., Biermann, U. M., Crutzen, P. J., and Peter, T.: Freezing
of HNO3/H2SO4/H2O solutions at stratospheric temperatures: Nucleation
statistics and experiments, J. Phys. Chem. A, 101, 1117–1133,
https://doi.org/10.1021/jp9626531, 1997.
Kumar, A., Marcolli, C., and Peter, T.: Ice nucleation activity of silicates and aluminosilicates in pure water and aqueous solutions – Part 3: Aluminosilicates, Atmos. Chem. Phys., 19, 6059–6084, https://doi.org/10.5194/acp-19-6059-2019, 2019.
Losey, D. J., Sihvonen, S. K., Veghte, D. P., Chong, E., and Freedman, M.
A.: Acidic processing of fly ash: chemical characterization, morphology, and
immersion freezing, Environ. Sci. Process. Impacts, 20, 1581–1592,
https://doi.org/10.1039/c8em00319j, 2018.
MacCallum, R. C., Zhang, S., Preacher, K. J., and Rucker, D. D.: On the
practice of dichotomization of quantitative variables, Psychol. Methods, 7,
19–40, https://doi.org/10.1037/1082-989X.7.1.19, 2002.
Manley, D.: Scale, aggregation, and the modifiable areal unit problem, in:
Handbook of Regional Science, edited by: Fischer, M. M. and Nijkamp, P.,
Springer Berlin Heidelberg, 1157–1171,
https://doi.org/10.1007/978-3-642-23430-9_69, 2014.
Maters, E. C., Cimarelli, C., Casas, A. S., Dingwell, D. B., and Murray, B.
J.: Volcanic ash ice-nucleating activity can be enhanced or depressed by
ash-gas interaction in the eruption plume, Earth Planet. Sci. Lett., 551,
116587, https://doi.org/10.1016/j.epsl.2020.116587, 2020.
McCluskey, C. S., Hill, T. C. J., Humphries, R. S., Rauker, A. M., Moreau,
S., Strutton, P. G., Chambers, S. D., Williams, A. G., McRobert, I., Ward,
J., Keywood, M. D., Harnwell, J., Ponsonby, W., Loh, Z. M., Krummel, P. B.,
Protat, A., Kreidenweis, S. M., and DeMott, P. J.: Observations of Ice
Nucleating Particles Over Southern Ocean Waters, Geophys. Res. Lett., 45,
11989–11997, https://doi.org/10.1029/2018GL079981, 2018.
Mülmenstädt, J., Sourdeval, O., Delanoë, J., and Quaas, J.:
Frequency of occurrence of rain from liquid-, mixed-, and ice-phase clouds
derived from A-Train satellite retrievals, Geophys. Res. Lett., 42,
6502–6509, https://doi.org/10.1002/2015GL064604, 2015.
Niedermeier, D., Shaw, R. A., Hartmann, S., Wex, H., Clauss, T., Voigtländer, J., and Stratmann, F.: Heterogeneous ice nucleation: exploring the transition from stochastic to singular freezing behavior, Atmos. Chem. Phys., 11, 8767–8775, https://doi.org/10.5194/acp-11-8767-2011, 2011.
Niedermeier, D., Augustin-Bauditz, S., Hartmann, S., Wex, H., Ignatius, K.,
and Stratmann, F.: Can we define an asymptotic value for the ice active
surface site density for heterogeneous ice nucleation?, J. Geophys. Res.,
120, 5036–5046, https://doi.org/10.1002/2014JD022814, 2015.
Peckhaus, A., Kiselev, A., Hiron, T., Ebert, M., and Leisner, T.: A comparative study of K-rich and Na/Ca-rich feldspar ice-nucleating particles in a nanoliter droplet freezing assay, Atmos. Chem. Phys., 16, 11477–11496, https://doi.org/10.5194/acp-16-11477-2016, 2016.
Perkins, R. J., Gillette, S. M., Hill, T. C. J., and DeMott, P. J.: The
Labile Nature of Ice Nucleation by Arizona Test Dust, ACS Earth Space Chem.,
4, 133–141, https://doi.org/10.1021/acsearthspacechem.9b00304, 2020.
Polen, M., Brubaker, T., Somers, J., and Sullivan, R. C.: Cleaning up our water: reducing interferences from nonhomogeneous freezing of “pure” water in droplet freezing assays of ice-nucleating particles, Atmos. Meas. Tech., 11, 5315–5334, https://doi.org/10.5194/amt-11-5315-2018, 2018.
Price, H. C., Baustian, K. J., McQuaid, J. B., Blyth, A., Bower, K. N.,
Choularton, T., Cotton, R. J., Cui, Z., Field, P. R., Gallagher, M., Hawker,
R., Merrington, A., Miltenberger, A., Neely, R. R., Parker, S. T.,
Rosenberg, P. D., Taylor, J. W., Trembath, J., Vergara-Temprado, J., Whale,
T. F., Wilson, T. W., Young, G., and Murray, B. J.: Atmospheric
Ice-Nucleating Particles in the Dusty Tropical Atlantic, J. Geophys. Res.-Atmos., 123, 2175–2193, https://doi.org/10.1002/2017JD027560, 2018.
Reicher, N., Segev, L., and Rudich, Y.: The WeIzmann Supercooled Droplets Observation on a Microarray (WISDOM) and application for ambient dust, Atmos. Meas. Tech., 11, 233–248, https://doi.org/10.5194/amt-11-233-2018, 2018.
Roy, P., House, M. L., and Dutcher, C. S.: A microfluidic device for
automated high throughput detection of ice nucleation of
snomax®, Micromachines, 12, 1–18,
https://doi.org/10.3390/mi12030296, 2021.
Selvin, S.: Two issues concerning the analysis of grouped data, Eur. J.
Epidemiol., 3, 284–287, https://doi.org/10.1007/BF00149737, 1987.
Shalizi, C. R.: The Bootstrap, in: Advanced data analysis from an elementary
point of view, 126–150, Cambridge University Press, in press, 2022.
Stan, C. A., Schneider, G. F., Shevkoplyas, S. S., Hashimoto, M., Ibanescu,
M., Wiley, B. J., and Whitesides, G. M.: A microfluidic apparatus for the
study of ice nucleation in supercooled water drops, Lab. Chip, 9,
2293–2305, https://doi.org/10.1039/b906198c, 2009.
Suski, K. J., Hill, T. C. J., Levin, E. J. T., Miller, A., DeMott, P. J., and Kreidenweis, S. M.: Agricultural harvesting emissions of ice-nucleating particles, Atmos. Chem. Phys., 18, 13755–13771, https://doi.org/10.5194/acp-18-13755-2018, 2018.
Tarn, M. D., Sikora, S. N. F., Porter, G. C. E., O'Sullivan, D., Adams, M.,
Whale, T. F., Harrison, A. D., Vergara-Temprado, J., Wilson, T. W., Shim, J.
uk, and Murray, B. J.: The study of atmospheric ice-nucleating particles via
microfluidically generated droplets, Microfluid. Nanofluidics, 22, 52,
https://doi.org/10.1007/s10404-018-2069-x, 2018.
Thompson, R.: A Note on Restricted Maximum Likelihood Estimation with an
Alternative Outlier Model, J. Roy. Stat. Soc. B, 47, 53–55,
https://doi.org/10.1111/j.2517-6161.1985.tb01329.x, 1985.
Tukey, J. W.: Exploratory data analysis, Addison-Wesley Pub. Co., Reading,
Mass., 1977.
Vali, G.: Quantitative Evaluation of Experimental Results an the
Heterogeneous Freezing Nucleation of Supercooled Liquids, J. Atmos. Sci.,
28, 402–409, https://doi.org/10.1175/1520-0469(1971)028<0402:qeoera>2.0.co;2, 1971.
Vali, G.: Interpretation of freezing nucleation experiments: singular and stochastic; sites and surfaces, Atmos. Chem. Phys., 14, 5271–5294, https://doi.org/10.5194/acp-14-5271-2014, 2014.
Vali, G.: Revisiting the differential freezing nucleus spectra derived from drop-freezing experiments: methods of calculation, applications, and confidence limits, Atmos. Meas. Tech., 12, 1219–1231, https://doi.org/10.5194/amt-12-1219-2019, 2019.
Vali, G., DeMott, P. J., Möhler, O., and Whale, T. F.: Technical Note: A proposal for ice nucleation terminology, Atmos. Chem. Phys., 15, 10263–10270, https://doi.org/10.5194/acp-15-10263-2015, 2015.
van Leeuwen, J., Smeets, J. B. J., and Belopolsky, A. v.: Forget binning and
get SMART: Getting more out of the time-course of response data, Atten.
Percept. Psychophys., 81, 2956–2967,
https://doi.org/10.3758/s13414-019-01788-3, 2019.
Vergara-Temprado, J., Murray, B. J., Wilson, T. W., O'Sullivan, D., Browse, J., Pringle, K. J., Ardon-Dryer, K., Bertram, A. K., Burrows, S. M., Ceburnis, D., DeMott, P. J., Mason, R. H., O'Dowd, C. D., Rinaldi, M., and Carslaw, K. S.: Contribution of feldspar and marine organic aerosols to global ice nucleating particle concentrations, Atmos. Chem. Phys., 17, 3637–3658, https://doi.org/10.5194/acp-17-3637-2017, 2017.
Virkar, Y. and Clauset, A.: Power-law distributions in binned empirical
data, Ann. Appl. Stat., 8, 89–119, https://doi.org/10.1214/13-AOAS710,
2014.
Wang, B., Knopf, D. A., China, S., Arey, B. W., Harder, T. H., Gilles, M.
K., and Laskin, A.: Direct observation of ice nucleation events on
individual atmospheric particles, Phys. Chem. Chem. Phys., 18, 29721–29731,
https://doi.org/10.1039/c6cp05253c, 2016.
Weng, L., Tessier, S. N., Smith, K., Edd, J. F., Stott, S. L., and Toner,
M.: Bacterial Ice Nucleation in Monodisperse D2O and H2O-in-Oil Emulsions,
Langmuir, 32, 9229–9236, https://doi.org/10.1021/acs.langmuir.6b02212,
2016.
Wex, H., Huang, L., Zhang, W., Hung, H., Traversi, R., Becagli, S., Sheesley, R. J., Moffett, C. E., Barrett, T. E., Bossi, R., Skov, H., Hünerbein, A., Lubitz, J., Löffler, M., Linke, O., Hartmann, M., Herenz, P., and Stratmann, F.: Annual variability of ice-nucleating particle concentrations at different Arctic locations, Atmos. Chem. Phys., 19, 5293–5311, https://doi.org/10.5194/acp-19-5293-2019, 2019.
Whale, T. F., Murray, B. J., O'Sullivan, D., Wilson, T. W., Umo, N. S., Baustian, K. J., Atkinson, J. D., Workneh, D. A., and Morris, G. J.: A technique for quantifying heterogeneous ice nucleation in microlitre supercooled water droplets, Atmos. Meas. Tech., 8, 2437–2447, https://doi.org/10.5194/amt-8-2437-2015, 2015.
Whale, T. F., Holden, M. A., Kulak, A. N., Kim, Y.-Y., Meldrum, F. C.,
Christenson, H. K., and Murray, B. J.: The role of phase separation and
related topography in the exceptional ice-nucleating ability of alkali
feldspars, Phys. Chem. Chem. Phys., 19, 31186–31193,
https://doi.org/10.1039/C7CP04898J, 2017.
Worthy, S. E., Kumar, A., Xi, Y., Yun, J., Chen, J., Xu, C., Irish, V. E., Amato, P., and Bertram, A. K.: The effect of (NH4)2SO4 on the freezing properties of non-mineral dust ice-nucleating substances of atmospheric relevance, Atmos. Chem. Phys., 21, 14631–14648, https://doi.org/10.5194/acp-21-14631-2021, 2021.
Wright, T. P. and Petters, M. D.: The role of time in heterogeneous freezing
nucleation, J. Geophys. Res.-Atmos., 118, 3731–3743,
https://doi.org/10.1002/jgrd.50365, 2013.
Yun, J., Kumar, A., Removski, N., Shchukarev, A., Link, N., Boily, J. F.,
and Bertram, A. K.: Effects of Inorganic Acids and Organic Solutes on the
Ice Nucleating Ability and Surface Properties of Potassium-Rich Feldspar,
ACS Earth Space Chem., 5, 1212–1222,
https://doi.org/10.1021/acsearthspacechem.1c00034, 2021.
Short summary
Heterogeneous ice nucleation (IN) alters cloud microphysics and climate, and droplet freezing assays are widely used to determine a material's IN ability. Existing statistical procedures require restrictive assumptions that may bias reported results, and there is no rigorous way to compare IN spectra. To improve the accuracy of reported IN data, we present a method for calculating statistics and confidence bands and testing statistical differences between IN activities in different materials.
Heterogeneous ice nucleation (IN) alters cloud microphysics and climate, and droplet freezing...
