We have implemented a parameterization for forming ice in large-scale cirrus clouds that accounts for the changes in updrafts associated with a spectrum of waves acting within each time step in the model. This allows us to account for the frequency of homogeneous and heterogeneous freezing events that occur within each time step of the model and helps to determine more realistic ice number concentrations as well as changes to ice number concentrations. The model is able to fit observations of ice number at the lowest temperatures in the tropical tropopause but is still somewhat high in tropical latitudes with temperatures between 195°K and 215°K. The climate forcings associated with different representations of heterogeneous ice nuclei (IN or INPs) are primarily negative unless large additions of IN are made, such as when we assumed that all aircraft soot acts as an IN. However, they can be close to zero if it is assumed that all background dust can act as an INP irrespective of how much sulfate is deposited on these particles. Our best estimate for the forcing of anthropogenic aircraft soot in this model is -0.2 ± 0.06 W/m2, while that from anthropogenic fossil/biofuel soot is -0.093 ± 0.033 W/m2. Natural and anthropogenic open biomass burning leads to a net forcing of -0.057 ± 0.05 W/m2.
Keywords: cirrus cloud formation; climate forcing; gravity waves; heterogeneous ice nuclei.