Advanced

Explosive ice multiplication induced by multiplicative-noise fluctuation of mechanical breakup in ice-ice collisions

Yano, Jun-Ichi and Phillips, Vaughan T J LU (2016) In Journals of the Atmospheric Sciences 73(12). p.4685-4697
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 multiplicative-noise 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 Fokker-Planck 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 ice-ice collisions is substantially altered by the multiplicative noise.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
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
0022-4928
DOI
10.1175/JAS-D-16-0051.1
language
English
LU publication?
yes
id
f0cbcf51-bf27-4e3e-8a44-41e76b4949be
date added to LUP
2017-02-24 08:10:03
date last changed
2017-09-18 11:35:08
@article{f0cbcf51-bf27-4e3e-8a44-41e76b4949be,
  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 multiplicative-noise 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 Fokker-Planck 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 ice-ice collisions is substantially altered by the multiplicative noise.</p>},
  author       = {Yano, Jun-Ichi and Phillips, Vaughan T J},
  issn         = {0022-4928},
  keyword      = {Cloud microphysics},
  language     = {eng},
  number       = {12},
  pages        = {4685--4697},
  publisher    = {Amer Meteorological Soc},
  series       = {Journals of the Atmospheric Sciences},
  title        = {Explosive ice multiplication induced by multiplicative-noise fluctuation of mechanical breakup in ice-ice collisions},
  url          = {http://dx.doi.org/10.1175/JAS-D-16-0051.1},
  volume       = {73},
  year         = {2016},
}