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, smax, and droplet-number concentration, Nd, as determined by comparing against those of detailed numerical simulations of the activation process. A numerical computation of the first-order derivatives ∂ Nd/∂ χj of the parameterized Nd to input variables χi 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 smax, and −2.7% ± 4.8% for Nd, 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.

Aerosol indirect effects in climate models strongly depend on the representation of the aerosol activation process. In this study, we assess the process-level differences across activation parameterizations that contribute to droplet number uncertainty by using the adjoints of the Abdul-Razzak and Ghan (2000) and Fountoukis and Nenes (2005) droplet activation parameterizations in the framework of the Community Atmospheric Model version 5.1 (CAM5.1). The adjoint sensitivities of Nd to relevant input parameters are used to (i) unravel the spatially resolved contribution of aerosol number, mass, and chemical composition to changes in Nd between present-day and pre-industrial simulations and (ii) identify the key variables responsible for the differences in Nd fields and aerosol indirect effect estimates when different activation schemes are used within the same modeling framework. The sensitivities are computed online at minimal computational cost. Changes in aerosol number and aerosol mass concentrations were found to contribute to Nd differences much more strongly than chemical composition effects. The main sources of discrepancy between the activation parameterizations considered were the treatment of the water uptake by coarse mode particles, and the sensitivity of the parameterized Nd accumulation mode aerosol geometric mean diameter. These two factors explain the different predictions of Nd over land and over oceans when these parameterizations are employed. Discrepancies in the sensitivity to aerosol size are responsible for an exaggerated response to aerosol volume changes over heavily polluted regions. Because these regions are collocated with areas of deep clouds, their impact on shortwave cloud forcing is amplified through liquid water path changes. The same framework is also utilized to efficiently explore droplet number uncertainty attributable to hygroscopicity parameter of organic aerosol (primary and secondary). Comparisons between the parameterization-derived sensitivities of droplet number against predictions with detailed numerical simulations of the activation process were performed to validate the physical consistency of the adjoint sensitivities.