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Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science
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| Zeitschriftentitel: | Atmospheric Science Letters |
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| Personen und Körperschaften: | , |
| In: | Atmospheric Science Letters, 8, 2007, 3, S. 70-73 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Wiley
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| Schlagwörter: |
| Zusammenfassung: | <jats:title>Abstract</jats:title><jats:p>The error function, as well as 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 real variable <jats:italic>x</jats:italic> ∈ [0∞). The approximation is very useful in solving atmospheric science problems by providing analytical solutions. Examples of the utility of the approximation 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. Copyright © 2007 Royal Meteorological Society</jats:p> |
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| Umfang: | 70-73 |
| ISSN: |
1530-261X
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| DOI: | 10.1002/asl.154 |