Ren, Chuansen and MacKenzie, Rob (2007) Closed-form approximations to the Error and Complementary Error Functions and their applications in atmospheric science. Atmospheric Science Letters, 8 (3). pp. 70-73. ISSN 1530-261X
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.