A Parametric Radiative Forcing Model for Contrail Cirrus

Abstract

A new parameterized analytical model is presented to compute the instantaneous radiative forcing (RF) at the top of the atmosphere (TOA) produced by an additional thin contrail cirrus layer (called ‘‘contrail’’ below). The model calculates the RF using as input the outgoing longwave radiation and reflected solar radiation values atTOAfor a contrail-free atmosphere, so that the model is applicable for both cloud-free and cloudy ambient atmospheres. Additional input includes the contrail temperature, contrail optical depth (at 550 nm), effective particle radius, particle habit, solar zenith angle, and the optical depth of cirrus above the contrail layer. The model parameters (5 for longwave and 10 for shortwave) are determined from least squares fits to calculations from the ‘‘libRadtran’’ radiative transfer model over a wide range of atmospheric and surface conditions. The correlation coefficient between model and calculations is larger than 98%. The analytical model is compared with published results, including a 1-yr simulation of global RF, and is found to agree well with previous studies. The fast analytical model is part of a larger modeling system to simulate contrail life cycles (‘‘CoCiP’’) and can allow for the rapid simulation of contrail cirrus RF over a wide range of meteorological conditions and for a given size-dependent habit mixture. Ambient clouds are shown to have large local impact on the net RF of contrails. Net RF of contrails may both increase and decrease and even change sign in the presence of higher-level cirrus, depending on solar zenith angle.