Explosive ice multiplication induced by multiplicativenoise fluctuation of mechanical breakup in iceice collisions
(2016) In Journals of the Atmospheric Sciences 73(12). p.46854697 Abstract
The number of ice fragments generated by breakup of large graupel in collisions with small graupel fluctuates randomly owing to fluctuations in relative sizes and densities of colliding graupel particles and the stochastic nature of fracture propagation. This paper investigates the impact of the stochasticity of breakup on ice multiplication. When both the rate of generation of primary ice and the initial number concentration of ice crystals are low, the system most likely loses all the initial ice and graupel owing to a lack of sustaining sources. Even randomness does not change this mean evolution of the system in its phase space. However, a fluctuation of ice breakup number gives a small but finite chance that substantial ice crystal... (More)
The number of ice fragments generated by breakup of large graupel in collisions with small graupel fluctuates randomly owing to fluctuations in relative sizes and densities of colliding graupel particles and the stochastic nature of fracture propagation. This paper investigates the impact of the stochasticity of breakup on ice multiplication. When both the rate of generation of primary ice and the initial number concentration of ice crystals are low, the system most likely loses all the initial ice and graupel owing to a lack of sustaining sources. Even randomness does not change this mean evolution of the system in its phase space. However, a fluctuation of ice breakup number gives a small but finite chance that substantial ice crystal fragments are generated by breakup of large graupel. That, in turn, generates more large graupel. This multiplicative process due to fluctuations potentially leads to a small but finite chance of explosive growth of ice number. A rigorous stochastic analysis demonstrates this point quantitatively. The randomness considered here belongs to a particular category called "multiplicative" noise, because the noise amplitude is proportional to a given physical state. To contrast the multiplicativenoise nature of ice breakup with a standard "additive" noise process, fluctuation of the primary ice generation rate is also considered as an example of the latter. These processes are examined by taking the FokkerPlanck equation that explicitly describes the evolution of the probability distribution with time. As an important conclusion, stability in the phase space of the cloud microphysical system of breakup in iceice collisions is substantially altered by the multiplicative noise.
(Less)
 author
 Yano, JunIchi and Phillips, Vaughan T J ^{LU}
 organization
 publishing date
 2016
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Cloud microphysics
 in
 Journals of the Atmospheric Sciences
 volume
 73
 issue
 12
 pages
 13 pages
 publisher
 Amer Meteorological Soc
 external identifiers

 scopus:85003681002
 wos:000391646500004
 ISSN
 00224928
 DOI
 10.1175/JASD160051.1
 language
 English
 LU publication?
 yes
 id
 f0cbcf51bf274e3e8a4441e76b4949be
 date added to LUP
 20170224 08:10:03
 date last changed
 20170918 11:35:08
@article{f0cbcf51bf274e3e8a4441e76b4949be, abstract = {<p>The number of ice fragments generated by breakup of large graupel in collisions with small graupel fluctuates randomly owing to fluctuations in relative sizes and densities of colliding graupel particles and the stochastic nature of fracture propagation. This paper investigates the impact of the stochasticity of breakup on ice multiplication. When both the rate of generation of primary ice and the initial number concentration of ice crystals are low, the system most likely loses all the initial ice and graupel owing to a lack of sustaining sources. Even randomness does not change this mean evolution of the system in its phase space. However, a fluctuation of ice breakup number gives a small but finite chance that substantial ice crystal fragments are generated by breakup of large graupel. That, in turn, generates more large graupel. This multiplicative process due to fluctuations potentially leads to a small but finite chance of explosive growth of ice number. A rigorous stochastic analysis demonstrates this point quantitatively. The randomness considered here belongs to a particular category called "multiplicative" noise, because the noise amplitude is proportional to a given physical state. To contrast the multiplicativenoise nature of ice breakup with a standard "additive" noise process, fluctuation of the primary ice generation rate is also considered as an example of the latter. These processes are examined by taking the FokkerPlanck equation that explicitly describes the evolution of the probability distribution with time. As an important conclusion, stability in the phase space of the cloud microphysical system of breakup in iceice collisions is substantially altered by the multiplicative noise.</p>}, author = {Yano, JunIchi and Phillips, Vaughan T J}, issn = {00224928}, keyword = {Cloud microphysics}, language = {eng}, number = {12}, pages = {46854697}, publisher = {Amer Meteorological Soc}, series = {Journals of the Atmospheric Sciences}, title = {Explosive ice multiplication induced by multiplicativenoise fluctuation of mechanical breakup in iceice collisions}, url = {http://dx.doi.org/10.1175/JASD160051.1}, volume = {73}, year = {2016}, }