### Abstract

This technical note introduces some corrections to the Lagrangian particle dispersion model of Rotachetal. (Q J R Meteorol Soc 122:367-389,1996). Careful mathematical derivation following the detailed explanations in that paper uncovered some unit inconsistencies that were the result of mistaken function definitions. Errors are noted in the drift correction, or "probability current" of the particle dispersion model as well as in parameterization of turbulence terms, which are necessary inputs to the model. The probability current comprises Gaussian, convective, and solenoidal components, with derivation errors discovered in the latter two components. All errors are presented along with new formulations that are mathematically consistent, correct the original problems, and adhere to the underlying Gaussian nature of the particle dispersion phenomenon. The corrections shown here should provide more accurate results for particle dispersion models based upon the work of Rotach et al., as well as resolve points of confusion for future researchers referring to that work.

Original language | English (US) |
---|---|

Pages (from-to) | 399-406 |

Number of pages | 8 |

Journal | Boundary-Layer Meteorology |

Volume | 145 |

Issue number | 2 |

DOIs | |

State | Published - Jul 3 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- Atmospheric turbulence
- Dispersion mode
- Lagrangian models
- Numerical simulation

### ASJC Scopus subject areas

- Atmospheric Science

### Cite this

**Corrections to the mathematical formulation of a backwards lagrangian particle dispersion model.** / Gibson, Max; Sailor, David.

Research output: Contribution to journal › Article

*Boundary-Layer Meteorology*, vol. 145, no. 2, pp. 399-406. https://doi.org/10.1007/s10546-012-9739-0

}

TY - JOUR

T1 - Corrections to the mathematical formulation of a backwards lagrangian particle dispersion model

AU - Gibson, Max

AU - Sailor, David

PY - 2012/7/3

Y1 - 2012/7/3

N2 - This technical note introduces some corrections to the Lagrangian particle dispersion model of Rotachetal. (Q J R Meteorol Soc 122:367-389,1996). Careful mathematical derivation following the detailed explanations in that paper uncovered some unit inconsistencies that were the result of mistaken function definitions. Errors are noted in the drift correction, or "probability current" of the particle dispersion model as well as in parameterization of turbulence terms, which are necessary inputs to the model. The probability current comprises Gaussian, convective, and solenoidal components, with derivation errors discovered in the latter two components. All errors are presented along with new formulations that are mathematically consistent, correct the original problems, and adhere to the underlying Gaussian nature of the particle dispersion phenomenon. The corrections shown here should provide more accurate results for particle dispersion models based upon the work of Rotach et al., as well as resolve points of confusion for future researchers referring to that work.

AB - This technical note introduces some corrections to the Lagrangian particle dispersion model of Rotachetal. (Q J R Meteorol Soc 122:367-389,1996). Careful mathematical derivation following the detailed explanations in that paper uncovered some unit inconsistencies that were the result of mistaken function definitions. Errors are noted in the drift correction, or "probability current" of the particle dispersion model as well as in parameterization of turbulence terms, which are necessary inputs to the model. The probability current comprises Gaussian, convective, and solenoidal components, with derivation errors discovered in the latter two components. All errors are presented along with new formulations that are mathematically consistent, correct the original problems, and adhere to the underlying Gaussian nature of the particle dispersion phenomenon. The corrections shown here should provide more accurate results for particle dispersion models based upon the work of Rotach et al., as well as resolve points of confusion for future researchers referring to that work.

KW - Atmospheric turbulence

KW - Dispersion mode

KW - Lagrangian models

KW - Numerical simulation

UR - http://www.scopus.com/inward/record.url?scp=84946478868&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946478868&partnerID=8YFLogxK

U2 - 10.1007/s10546-012-9739-0

DO - 10.1007/s10546-012-9739-0

M3 - Article

AN - SCOPUS:84946478868

VL - 145

SP - 399

EP - 406

JO - Boundary-Layer Meteorology

JF - Boundary-Layer Meteorology

SN - 0006-8314

IS - 2

ER -