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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 |
|---|---|
| Personen und Körperschaften: | , |
| In: | Atmospheric Science Letters, 8, 2007, 3, S. 70-73 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Wiley
|
| Schlagwörter: |
| author_facet |
Ren, C. MacKenzie, A. R. Ren, C. MacKenzie, A. R. |
|---|---|
| author |
Ren, C. MacKenzie, A. R. |
| spellingShingle |
Ren, C. MacKenzie, A. R. Atmospheric Science Letters Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science Atmospheric Science |
| author_sort |
ren, c. |
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Ren, C. MacKenzie, A. R. 1530-261X 1530-261X Wiley Atmospheric Science http://dx.doi.org/10.1002/asl.154 <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> Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science Atmospheric Science Letters |
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Atmospheric Science Letters |
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| title |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_unstemmed |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_full |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_fullStr |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_full_unstemmed |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_short |
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_sort |
closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| topic |
Atmospheric Science |
| url |
http://dx.doi.org/10.1002/asl.154 |
| publishDate |
2007 |
| physical |
70-73 |
| description |
<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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| author | Ren, C., MacKenzie, A. R. |
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| container_title | Atmospheric Science Letters |
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| description | <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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| imprint | Wiley, 2007 |
| imprint_str_mv | Wiley, 2007 |
| institution | DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1 |
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| spelling | Ren, C. MacKenzie, A. R. 1530-261X 1530-261X Wiley Atmospheric Science http://dx.doi.org/10.1002/asl.154 <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> Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science Atmospheric Science Letters |
| spellingShingle | Ren, C., MacKenzie, A. R., Atmospheric Science Letters, Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science, Atmospheric Science |
| title | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_full | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_fullStr | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_full_unstemmed | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_short | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_sort | closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| title_unstemmed | Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science |
| topic | Atmospheric Science |
| url | http://dx.doi.org/10.1002/asl.154 |