A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments
<p>A suite of generally applicable statistical methods based on empirical bootstrapping is presented for calculating uncertainty and testing the significance of quantitative differences in temperature and/or ice active site densities between ice nucleation temperature spectra derived from drop...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2022-11-01
|
| Series: | Atmospheric Measurement Techniques |
| Online Access: | https://amt.copernicus.org/articles/15/6819/2022/amt-15-6819-2022.pdf |
| _version_ | 1798015720413462528 |
|---|---|
| author | W. D. Fahy W. D. Fahy C. R. Shalizi C. R. Shalizi R. C. Sullivan |
| author_facet | W. D. Fahy W. D. Fahy C. R. Shalizi C. R. Shalizi R. C. Sullivan |
| author_sort | W. D. Fahy |
| collection | DOAJ |
| description | <p>A suite of generally applicable statistical methods based
on empirical bootstrapping is presented for calculating uncertainty and
testing the significance of quantitative differences in temperature and/or
ice active site densities between ice nucleation temperature spectra derived
from droplet freezing experiments. Such experiments are widely used to
determine the heterogeneous ice nucleation properties and ice nucleation
particle concentration spectra of different particle samples, as well as in
studies of homogeneous freezing. Our methods avoid most of the assumptions
and approximations inherent to existing approaches, and when sufficiently
large sample sizes are used (approximately <span class="inline-formula">>150</span> droplets and
<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>></mo><mo>=</mo><mn mathvariant="normal">1000</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="31e7f63df9caf37e2f2e0b96a1eef36d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-15-6819-2022-ie00001.svg" width="44pt" height="10pt" src="amt-15-6819-2022-ie00001.png"/></svg:svg></span></span> bootstrap samples in our system), can capture the full
range of random variability and error in ice nucleation spectra.
Applications include calculation of accurate confidence intervals and
confidence bands, quantitative statistical testing of differences between
observed freezing spectra, accurate subtraction of the background filtered
water freezing signal, and calculation of a range of statistical parameters
using data from a single droplet array freezing experiment if necessary. By
providing additional statistical tools to the community, this work will
improve the quality and accuracy of statistical tests and representations of
uncertainty in future ice nucleation research, and will allow quantitative
comparisons of the ice nucleation ability of different particles and
surfaces.</p> |
| first_indexed | 2024-04-11T15:39:24Z |
| format | Article |
| id | doaj.art-910ec23b4f8c4892a1003f6c840ae4b9 |
| institution | Directory Open Access Journal |
| issn | 1867-1381 1867-8548 |
| language | English |
| last_indexed | 2024-04-11T15:39:24Z |
| publishDate | 2022-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Atmospheric Measurement Techniques |
| spelling | doaj.art-910ec23b4f8c4892a1003f6c840ae4b92022-12-22T04:15:53ZengCopernicus PublicationsAtmospheric Measurement Techniques1867-13811867-85482022-11-01156819683610.5194/amt-15-6819-2022A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experimentsW. D. Fahy0W. D. Fahy1C. R. Shalizi2C. R. Shalizi3R. C. Sullivan4Department of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USAnow at: Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, CanadaDepartment of Statistics and Data Science, Carnegie Mellon University, Pittsburgh, PA 15213, USASanta Fe Institute, Santa Fe, NM 87501, USADepartment of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA<p>A suite of generally applicable statistical methods based on empirical bootstrapping is presented for calculating uncertainty and testing the significance of quantitative differences in temperature and/or ice active site densities between ice nucleation temperature spectra derived from droplet freezing experiments. Such experiments are widely used to determine the heterogeneous ice nucleation properties and ice nucleation particle concentration spectra of different particle samples, as well as in studies of homogeneous freezing. Our methods avoid most of the assumptions and approximations inherent to existing approaches, and when sufficiently large sample sizes are used (approximately <span class="inline-formula">>150</span> droplets and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M2" display="inline" overflow="scroll" dspmath="mathml"><mrow><mo>></mo><mo>=</mo><mn mathvariant="normal">1000</mn></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="44pt" height="10pt" class="svg-formula" dspmath="mathimg" md5hash="31e7f63df9caf37e2f2e0b96a1eef36d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="amt-15-6819-2022-ie00001.svg" width="44pt" height="10pt" src="amt-15-6819-2022-ie00001.png"/></svg:svg></span></span> bootstrap samples in our system), can capture the full range of random variability and error in ice nucleation spectra. Applications include calculation of accurate confidence intervals and confidence bands, quantitative statistical testing of differences between observed freezing spectra, accurate subtraction of the background filtered water freezing signal, and calculation of a range of statistical parameters using data from a single droplet array freezing experiment if necessary. By providing additional statistical tools to the community, this work will improve the quality and accuracy of statistical tests and representations of uncertainty in future ice nucleation research, and will allow quantitative comparisons of the ice nucleation ability of different particles and surfaces.</p>https://amt.copernicus.org/articles/15/6819/2022/amt-15-6819-2022.pdf |
| spellingShingle | W. D. Fahy W. D. Fahy C. R. Shalizi C. R. Shalizi R. C. Sullivan A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments Atmospheric Measurement Techniques |
| title | A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| title_full | A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| title_fullStr | A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| title_full_unstemmed | A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| title_short | A universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| title_sort | universally applicable method of calculating confidence bands for ice nucleation spectra derived from droplet freezing experiments |
| url | https://amt.copernicus.org/articles/15/6819/2022/amt-15-6819-2022.pdf |
| work_keys_str_mv | AT wdfahy auniversallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT wdfahy auniversallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT crshalizi auniversallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT crshalizi auniversallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT rcsullivan auniversallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT wdfahy universallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT wdfahy universallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT crshalizi universallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT crshalizi universallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments AT rcsullivan universallyapplicablemethodofcalculatingconfidencebandsforicenucleationspectraderivedfromdropletfreezingexperiments |