### Abstract

Original language | English |
---|---|

Pages (from-to) | 4008-4012 |

Journal | Journal of the Atmospheric Sciences |

Volume | 45 |

Issue number | 24 |

DOIs | |

Publication status | Published - 1988 |

MoE publication type | A1 Journal article-refereed |

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### Cite this

*Journal of the Atmospheric Sciences*,

*45*(24), 4008-4012. https://doi.org/10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2

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*Journal of the Atmospheric Sciences*, vol. 45, no. 24, pp. 4008-4012. https://doi.org/10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2

**On the median volume diameter approximation for droplet collision efficiency.** / Finstad, Karen; Lozowski, Edward; Makkonen, Lasse.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - On the median volume diameter approximation for droplet collision efficiency

AU - Finstad, Karen

AU - Lozowski, Edward

AU - Makkonen, Lasse

PY - 1988

Y1 - 1988

N2 - In this note, we examine a shortcut for calculating the overall collision efficiency of a droplet spectrum, known as the “median volume diameter” (mvd) approximation. By calculating the overall collision efficiency of a circular cylinder for a variety of natural droplet spectra, first precisely using a spectrum weighting approach, and then as approximated using the mvd, as well as several other representative droplet sizes, we show by comparison that the mvd approximation is a good one, with an average absolute error of about 0.02. While trying to give some mathematical justification for why the mvd approximation works, we show that it can be derived from a single-point numerical integration formula, and that extension of this formula to 2, 3 or 4 points should give correspondingly better approximations. Detailed comparisons confirm that use of the 2-point formula reduces the average error by one-half, while the 3- and 4-point formulae can reduce it even more, depending on the type of spectrum.

AB - In this note, we examine a shortcut for calculating the overall collision efficiency of a droplet spectrum, known as the “median volume diameter” (mvd) approximation. By calculating the overall collision efficiency of a circular cylinder for a variety of natural droplet spectra, first precisely using a spectrum weighting approach, and then as approximated using the mvd, as well as several other representative droplet sizes, we show by comparison that the mvd approximation is a good one, with an average absolute error of about 0.02. While trying to give some mathematical justification for why the mvd approximation works, we show that it can be derived from a single-point numerical integration formula, and that extension of this formula to 2, 3 or 4 points should give correspondingly better approximations. Detailed comparisons confirm that use of the 2-point formula reduces the average error by one-half, while the 3- and 4-point formulae can reduce it even more, depending on the type of spectrum.

U2 - 10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2

DO - 10.1175/1520-0469(1988)045<4008:OTMVDA>2.0.CO;2

M3 - Article

VL - 45

SP - 4008

EP - 4012

JO - Journal of the Atmospheric Sciences

JF - Journal of the Atmospheric Sciences

SN - 0022-4928

IS - 24

ER -