Droplet activation parameterization: the population-splitting concept revisited

In this work, we postulate, implement and evaluate modifications to the population-splitting concept, introduced by Nenes and Seinfeld (2003), for calculation of water-condensation rates in droplet-activation parameterizations. The population-splitting approximation consists of dividing the population of growing droplets into two categories: those that experience significant growth after exposed to a supersaturation larger than their critical supersaturation, and those that do not grow much larger than their critical diameter. The modifications introduced here lead to an improved accuracy and precision of the parameterization-derived maximum supersaturation, s(max), and droplet-number concentration, N-d, as determined by comparing against those of detailed numerical simulations of the activation process. A numerical computation of the first-order derivatives partial derivative N-d/partial derivative chi(j) of the parameterized N-d to input variables chi(j) was performed and compared against the corresponding parcel-model-derived sensitivities, providing a thorough evaluation of the impacts of the introduced modifications in the parameterization ability to respond to aerosol characteristics. An evaluation of the parameterization computation of Nd and smax against detailed numerical simulations of the activation process showed a relative error of -6.0% +/- 6.2% for s(max), and -2.7% +/- 4.8% for N-d, which represents a considerable reduction in prediction bias when compared to earlier versions of the parameterization. The proposed modifications require only minor changes for their numerical implementation in existing codes based on the population-splitting concept.