On the median volume diameter approximation for droplet collision efficiency

Karen Finstad, Edward Lozowski, Lasse Makkonen

    Research output: Contribution to journalArticleScientificpeer-review

    44 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)4008-4012
    JournalJournal of the Atmospheric Sciences
    Volume45
    Issue number24
    DOIs
    Publication statusPublished - 1988
    MoE publication typeA1 Journal article-refereed

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

    In: Journal of the Atmospheric Sciences, Vol. 45, No. 24, 1988, p. 4008-4012.

    Research output: Contribution to journalArticleScientificpeer-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

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    SN - 0022-4928

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