Editing Log-normal distribution (section)

=== Physical sciences ===

*In [[hydrology]], the log-normal distribution is used to analyze extreme values of such variables as monthly and annual maximum values of daily rainfall and river discharge volumes.<ref>{{cite book | last = Oosterbaan | first = R.J. | editor-last = Ritzema | editor-first = H.P. | chapter = 6: Frequency and Regression Analysis | year = 1994 | title = Drainage Principles and Applications, Publication 16 | publisher = International Institute for Land Reclamation and Improvement (ILRI) | location = Wageningen, The Netherlands | pages = [https://archive.org/details/drainageprincipl0000unse/page/175 175–224] | chapter-url = http://www.waterlog.info/pdf/freqtxt.pdf | isbn = 978-90-70754-33-4 | url = https://archive.org/details/drainageprincipl0000unse/page/175 }}</ref>
**The image on the right illustrates an example of fitting the log-normal distribution to ranked annually maximum one-day rainfalls showing also the 90% [[confidence belt]] based on the [[binomial distribution]].<ref>[https://www.waterlog.info/cumfreq.htm CumFreq, free software for distribution fitting]</ref>
**The rainfall data are represented by [[plotting position]]s as part of a [[cumulative frequency analysis]].
*In [[physical oceanography]], the sizes of icebergs in the midwinter Southern Atlantic Ocean were found to follow a log-normal size distribution. The iceberg sizes, measured visually and by radar from the F.S. ''Polarstern'' in 1986, were thought to be controlled by wave action in heavy seas causing them to flex and break.<ref>{{cite journal | last1 = Wadhams | first1 = Peter | date = 1988 | title = Winter observations of iceberg frequencies and sizes in the South Atlantic Ocean | journal = Journal of Geophysical Research: Oceans | volume = 93 | issue = C4 | pages = 3583–3590 | doi = 10.1029/JC093iC04p03583 }}</ref>
*In [[atmospheric science]], log-normal distributions (or distributions made by combining multiple log-normal functions) have been used to characterize both measurements and models of the sizes and concentrations of many different types of particles, from volcanic ash, to clouds and rain, to airborne microbes.<ref>{{cite journal | last1 = Heintzenberg | first1 = Jost | date =1994 | title = Properties of the Log-Normal Particle Size Distribution | journal = Aerosol Science and Technology | volume = 21 | issue = 1 | pages = 46–48 | doi = 10.1080/02786829408959695 | doi-access= free }}</ref><ref>{{cite journal | last1 = Limpert | first1 = Eckhard | last2 = Stahel | first2 =Werner A. | last3 = Abbt | first3 = Markus | date =2001 | title = Log-normal Distributions across the Sciences: Keys and Clues | journal = BioScience | volume = 51 | issue = 5 | pages = 341–352 | doi = 10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2 }}</ref><ref>{{cite journal | last1 = Di Giorgio | first1 = C | last2 =Krempff | first2 =A | last3 =Guiraud | first3 =H | last4 =Binder | first4 =P | last5 =Tiret | first5 = C | last6 =Dumenil | first6 = G | date =1996 | title = Atmospheric pollution by airborne microorganisms in the city of Marseilles | journal = Atmospheric Environment | volume = 30 | pages = 155–160 | doi = 10.1016/1352-2310(95)00143-M }}</ref><ref>{{cite journal | last1 =Sheridan | first1 =M.F. | last2 =Wohletz | first2 =K.H. | last3 =Dehn | first3 =J. | date =1987 | title = Discrimination of grain-size subpopulations in pyroclastic deposits | journal = Geology | volume = 15 | issue =4 | pages = 367–370 | doi = 10.1130/0091-7613(1987)15<367:DOGSIP>2.0.CO;2 }}</ref> The log-normal distribution is strictly empirical, so more physically-based distributions have been adopted to better understand processes controlling size distributions of particles such as volcanic ash.<ref>{{cite journal | last1 = Wohletz | first1 = K.H. | last2 = Sheridan | first2 = M.F. | last3 = Brown | first3 = W.K. | date = 1989 | title = Particle size distributions and the sequential fragmentation/transport theory applied to volcanic ash | journal = Journal of Geophysical Research: Solid Earth | volume = 94 | issue = B11 | pages = 15703–15721 | doi = 10.1029/JB094iB11p15703 }}</ref>