Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”
- Cooperative Institute for Mesoscale Meteorological Studies, University of Oklahoma, Norman, Oklahoma
- Cooperative Institute for Mesoscale Meteorological Studies, and School of Meteorology, University of Oklahoma, Norman, Oklahoma
We welcome the opportunity to correct the misunderstandings and misinterpretations contained in Yano’s comment that led him to incorrectly state that Wu and McFarquhar misunderstood the maximum entropy (MaxEnt) principle. As correctly stated by Yano, the principle itself does not suffer from the problem of a lack of invariance. But, as restated in this reply and in Wu and McFarquhar, the commonly used Shannon–Gibbs entropy does suffer from a lack of invariance for coordinate transform when applied in continuous cases, and this problem is resolved by the use of the relative entropy. Further, it is restated that the Wu and McFarquhar derivation of the PSD form using MaxEnt is more general than the formulation by Yano and allows more constraints with any functional relations to be applied. The derivation of Yano is nothing new but the representation of PSDs in other variables.
- Research Organization:
- Univ. of Oklahoma, Norman, OK (United States); University Corporation for Atmospheric Research, Boulder, CO (United States)
- Sponsoring Organization:
- National Science Foundation (NSF); USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
- Grant/Contract Number:
- SC0014065; SC0016476
- OSTI ID:
- 1576870
- Alternate ID(s):
- OSTI ID: 1593780
- Journal Information:
- Journal of the Atmospheric Sciences, Journal Name: Journal of the Atmospheric Sciences Journal Issue: 12 Vol. 76; ISSN 0022-4928
- Publisher:
- American Meteorological SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English