Improved method of exponential sum fitting of transmissions to describe the absorption of atmospheric gases

For climate modeling and atmospheric research, such as investigations of global climate change, remote sensing of cloud properties, or the missing absorption problem in clouds, it is most important to describe adequately the absorption of radiation by atmospheric gases. An improved method for the exponential sum fitting of transmissions (ESFT) is developed to approximate this absorption accurately. Exponentials are estimated separately for any number of atmospheric-model layers, considering the pressure and temperature dependence of the absorption lines directly. As long as the error of the fit exceeds a limit of tolerance, the number of considered exponential terms is successively increased. The accuracy of the method presented yields a root-mean-square error of less than 0.03% for any atmospheric-model layer, whereas the commonly used one-layer techniques gain errors of up to 3% in the transmission functions for the upper layers. The commonly used ESFT methods consider only one atmospheric layer and introduce the pressure and temperature effects for the other model layers afterwards.