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Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science.

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Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science. / Ren, Chuansen; MacKenzie, Rob.
In: Atmospheric Science Letters, Vol. 8, No. 3, 31.08.2007, p. 70-73.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ren, C & MacKenzie, R 2007, 'Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science.', Atmospheric Science Letters, vol. 8, no. 3, pp. 70-73. https://doi.org/10.1002/asl.154

APA

Ren, C., & MacKenzie, R. (2007). Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science. Atmospheric Science Letters, 8(3), 70-73. https://doi.org/10.1002/asl.154

Vancouver

Ren C, MacKenzie R. Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science. Atmospheric Science Letters. 2007 Aug 31;8(3):70-73. doi: 10.1002/asl.154

Author

Ren, Chuansen ; MacKenzie, Rob. / Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science. In: Atmospheric Science Letters. 2007 ; Vol. 8, No. 3. pp. 70-73.

Bibtex

@article{976b43fdb98e4d858daf6a4582d273df,
title = "Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science.",
abstract = "The Error function, and related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementary error, and scaled complementary error functions, with maximum relative errors within 0.8%. Unlike other approximate solutions, this single equation gives answers within the stated accuracy for x between 0 and infinity . The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximations are: the computation of cirrus cloud physics inside a general circulation model, the cumulative distribution functions of normal and log-normal distributions, and the recurrence period for risk assessment.",
keywords = "Error function, complementary error function, scaled complementary error function, normal distribution, log-normal distribution, cumulative distribution function, recurrence interval",
author = "Chuansen Ren and Rob MacKenzie",
note = "This is a pre-print of an article published in Atmospheric Science Letters, 8 (3), 2007. (c) Wiley.",
year = "2007",
month = aug,
day = "31",
doi = "10.1002/asl.154",
language = "English",
volume = "8",
pages = "70--73",
journal = "Atmospheric Science Letters",
issn = "1530-261X",
publisher = "John Wiley and Sons Inc.",
number = "3",

}

RIS

TY - JOUR

T1 - Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science.

AU - Ren, Chuansen

AU - MacKenzie, Rob

N1 - This is a pre-print of an article published in Atmospheric Science Letters, 8 (3), 2007. (c) Wiley.

PY - 2007/8/31

Y1 - 2007/8/31

N2 - The Error function, and related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementary error, and scaled complementary error functions, with maximum relative errors within 0.8%. Unlike other approximate solutions, this single equation gives answers within the stated accuracy for x between 0 and infinity . The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximations are: the computation of cirrus cloud physics inside a general circulation model, the cumulative distribution functions of normal and log-normal distributions, and the recurrence period for risk assessment.

AB - The Error function, and related functions, occurs in theoretical aspects of many parts of atmospheric science. This note presents a closed-form approximation for the error, complementary error, and scaled complementary error functions, with maximum relative errors within 0.8%. Unlike other approximate solutions, this single equation gives answers within the stated accuracy for x between 0 and infinity . The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximations are: the computation of cirrus cloud physics inside a general circulation model, the cumulative distribution functions of normal and log-normal distributions, and the recurrence period for risk assessment.

KW - Error function

KW - complementary error function

KW - scaled complementary error function

KW - normal distribution

KW - log-normal distribution

KW - cumulative distribution function

KW - recurrence interval

U2 - 10.1002/asl.154

DO - 10.1002/asl.154

M3 - Journal article

VL - 8

SP - 70

EP - 73

JO - Atmospheric Science Letters

JF - Atmospheric Science Letters

SN - 1530-261X

IS - 3

ER -