Note on the CoCiP-libRadtran contrail-cirrus radiative forcing model

Abstract. In 2012, we developed a parameterized analytical model to compute the instantaneous radiative forcing (RF) at the top of the atmosphere (TOA) produced by an additional thin cirrus or contrail layer. The model parameters were determined from least squares fits to calculations from the ‘‘libRadtran’’ radiative transfer model. In the course of coupling the contrail cirrus model CoCiP, which uses this RF model, with the global numerical weather prediction model ICON of the German Weather Service (DWD, Germany), we found that the libRadtran-based model shows a more linear function of RF versus the optical depth of the contrail (or added cirrus) than the results from ICON computed using the ecRad model of the European Center for Medium-Range Weather Forecasts (ECMWF). We therefore added a new model approximation allowing for a more nonlinear increase of RF with the solar optical depth values of the contrail and of any cirrus above the contrail. The former publication (RF2012) describes the models and the tests performed in detail. However, the set of libRadtran data used for setting up the RF model was not published so far.  This file contains the data, some test results, and the subroutines used to compute RF for given input parameters (effective radius Reff, top-of atmosphere longwave and shortwave radiation fluxes OLR and RSR, solar constant S₀, direct solar radiation SDR, contrail solar optical thickness TAU, contrail temperature T_C, and solar optical thickness TACI of cirrus above the contrail layer). We found that version 1 correctly approximates the given libRadtran data with a minimum number of model coefficients. Version 2 requires 4 more model coefficient but allows for a more nonlinear increase of RF with the solar optical depth values of the contrail and of any cirrus above the contrail, as suggested by ecRad results. It also provides a good fit to the libRadtran data though with very little smaller regression correlation values. We note that version 2 might give slightly larger RF values when most of the contrails have an optical depth below about 1.