## This content will become publicly available on December 3, 2020

# Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”

## Abstract

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. We state the derivation of Yano is nothing new but the representation of PSDs in other variables.

- Authors:

- Univ. of Oklahoma, Norman, OK (United States)

- Publication Date:

- Research Org.:
- Univ. of Oklahoma, Norman, OK (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23); National Science Foundation (NSF)

- OSTI Identifier:
- 1593780

- Alternate Identifier(s):
- OSTI ID: 1576870

- Grant/Contract Number:
- SC0016476; SC0014065; AGS-1213311; AGS-1762096

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of the Atmospheric Sciences

- Additional Journal Information:
- Journal Volume: 76; Journal Issue: 12; Journal ID: ISSN 0022-4928

- Publisher:
- American Meteorological Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; Cloud microphysics; Clouds; Drop size distribution; Statistical techniques; Spectral analysis/models/distribution

### Citation Formats

```
Wu, Wei, and McFarquhar, Greg M. Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”. United States: N. p., 2019.
Web. doi:10.1175/JAS-D-18-0374.1.
```

```
Wu, Wei, & McFarquhar, Greg M. Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”. United States. doi:10.1175/JAS-D-18-0374.1.
```

```
Wu, Wei, and McFarquhar, Greg M. Tue .
"Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”". United States. doi:10.1175/JAS-D-18-0374.1.
```

```
@article{osti_1593780,
```

title = {Reply to “What Is the Maximum Entropy Principle? Comments on ‘Statistical Theory on the Functional Form of Cloud Particle Size Distributions’”},

author = {Wu, Wei and McFarquhar, Greg M.},

abstractNote = {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. We state the derivation of Yano is nothing new but the representation of PSDs in other variables.},

doi = {10.1175/JAS-D-18-0374.1},

journal = {Journal of the Atmospheric Sciences},

number = 12,

volume = 76,

place = {United States},

year = {2019},

month = {12}

}