Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science
Closed‐form approximations to the error and complementary error functions and their applications in atmospheric science
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误差和互补误差函数的闭式逼近及其在大气科学中的应用
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
A. MacKenzie
中科院分区：
文献类型：
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作者：
C. Ren;A. MacKenzie
误差函数以及相关函数出现在大气科学的许多部分的理论方面。本文给出了误差函数、互补误差函数和比例互补误差函数的闭合近似，最大相对误差在0.8%以内。与其他近似解不同，这个单一方程给出了真实的变量x ∈ [0∞）的规定精度内的答案。这种近似方法在解决大气科学问题时提供了解析解，是非常有用的。近似的实用性的例子是：计算卷云物理在大气环流模型，正态和对数正态分布的累积分布函数，以及风险评估的重现期。版权所有© 2007皇家气象学会
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 x ∈ [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