Parameterization of cloud droplet formation in large-scale models: Including effects of entrainment

This work offers for the first time a comprehensive parameterization suitable for large-scale models which is robust, computationally efficient, and from first principles links chemical effects, aerosol heterogeneity and entrainment with cloud droplet formation. The parameterization is based on the entraining ascending parcel model framework; mixing of outside air is parameterized in terms of a per-length entrainment rate. The integration of the droplet growth is done using the population splitting'' concept of Nenes and Seinfeld (2003). Formulations for lognormal and sectional aerosol representations are given, as well as simplifications that allow the treatment of entrainment with high computational efficiency without loss of accuracy. The concept of critical entrainment,'' a value beyond which droplet activation is not favored, is introduced and shown that it is important for defining (1) whether or not entrainment effects have an impact on droplet formation and (2) the characteristic temperature and pressure for cloud droplet formation. The performance of the parameterization was evaluated against a detailed numerical parcel model over a comprehensive range of droplet formation conditions. The agreement is always very good (mean relative error 2.3% +/- 21%); errors tend to increase as entrainment approaches the critical value, but are never above 40%.