A simple model for the time evolution of the condensation sink in the atmosphere for intermediate Knudsen numbers

Transformation of the mass flux towards the particle from the kinetic regime to the continuum regime is often described by the Fuchs-Sutugin coefficient. Kinetic regime can be obtained as a limiting case when only one term of the expansion of the Fuchs-Sutugin coefficient at small 1/Kn is considered. Here we take the two first terms into account, and get a mass flux which agrees well with the full mass flux down to Kn similar to 0.5. This procedure allows an analytical solution of the condensation equation valid for the range of intermediate Knudsen numbers to be obtained. The expansion is further applied to analytically calculate the condensation sink. The formula for the condensation sink is tested against field observations. The relative contribution of different aerosol modes to the condensation sink is discussed. Furthermore, we present a simple model describing the coupled dynamics of the condensing vapour and the condensation sink. The model gives reasonable predictions of condensation sink dynamics during the periods of the aerosol modes' growth by condensation in the atmosphere.Peer reviewe

Aerosol formation and growth rates from chamber experiments using Kalman smoothing

Bayesian state estimation in the form of Kalman smoothing was applied to differential mobility analyser train (DMA-train) measurements of aerosol size distribution dynamics. Four experiments were analysed in order to estimate the aerosol size distribution, formation rate, and size-dependent growth rate, as functions of time. The first analysed case was a synthetic one, generated by a detailed aerosol dynamics model and the other three chamber experiments performed at the CERN CLOUD facility. The estimated formation and growth rates were compared with other methods used earlier for the CLOUD data and with the true values for the computer-generated synthetic experiment. The agreement in the growth rates was very good for all studied cases: estimations with an earlier method fell within the uncertainty limits of the Kalman smoother results. The formation rates also matched well, within roughly a factor of 2.5 in all cases, which can be considered very good considering the fact that they were estimated from data given by two different instruments, the other being the particle size magnifier (PSM), which is known to have large uncertainties close to its detection limit. The presented fixed interval Kalman smoother (FIKS) method has clear advantages compared with earlier methods that have been applied to this kind of data. First, FIKS can reconstruct the size distribution between possible size gaps in the measurement in such a way that it is consistent with aerosol size distribution dynamics theory, and second, the method gives rise to direct and reliable estimation of size distribution and process rate uncertainties if the uncertainties in the kernel functions and numerical models are known.Bayesian state estimation in the form of Kalman smoothing was applied to differential mobility analyser train (DMA-train) measurements of aerosol size distribution dynamics. Four experiments were analysed in order to estimate the aerosol size distribution, formation rate, and size-dependent growth rate, as functions of time. The first analysed case was a synthetic one, generated by a detailed aerosol dynamics model and the other three chamber experiments performed at the CERN CLOUD facility. The estimated formation and growth rates were compared with other methods used earlier for the CLOUD data and with the true values for the computer-generated synthetic experiment. The agreement in the growth rates was very good for all studied cases: estimations with an earlier method fell within the uncertainty limits of the Kalman smoother results. The formation rates also matched well, within roughly a factor of 2.5 in all cases, which can be considered very good considering the fact that they were estimated from data given by two different instruments, the other being the particle size magnifier (PSM), which is known to have large uncertainties close to its detection limit. The presented fixed interval Kalman smoother (FIKS) method has clear advantages compared with earlier methods that have been applied to this kind of data. First, FIKS can reconstruct the size distribution between possible size gaps in the measurement in such a way that it is consistent with aerosol size distribution dynamics theory, and second, the method gives rise to direct and reliable estimation of size distribution and process rate uncertainties if the un-certainties in the kernel functions and numerical models are known.Peer reviewe

Combining instrument inversions for sub-10 nm aerosol number size-distribution measurements

Resolving aerosol dynamical processes in the sub-10 nm range is crucial for our understanding of the contribution of new particle formation to the global cloud condensation nuclei budget or air pollution. Accurate measurements of the particle size distribution in this size-range are challenging due to high diffusional losses and low charging and/or detection efficiencies. Several instruments have been developed in recent years in order to access the sub-10 nm particle size distribution; however, no single instrument can provide high counting statistics, low systematic uncertainties and high size-resolution at the same time. Here we compare several data inversion approaches that allow combining data from different sizing instruments during the inversion and provide python/Julia packages for free usage of the methods. We find that Tikhonov regularization using the L-curve method for optimal regularization parameter estimation gives very reliable results over a wide range of tested data sets and clearly improves standard inversion approaches. Kalman Filtering or regularization using a Poisson likelihood can be powerful tools, especially for well-defined chamber experiments or data from mobility spectrometers only, respectively. Nullspace optimization and non-linear iterative regression are clearly inferior compared to the aforementioned methods. We show that with regularization we can reconstruct the size-distribution measured by up to 4 different mobility particle size spectrometer systems and several particle counters for datasets from Hyytiala and Helsinki, Finland, revealing the sub-10 nm aerosol dynamics in more detail compared to a single instrument assessment.Peer reviewe

Growth of atmospheric clusters involving cluster-cluster collisions : comparison of different growth rate methods

We simulated the time evolution of atmospheric cluster concentrations in a one-component system where not only do clusters grow by condensation of monomers, but cluster-cluster collisions also significantly contribute to the growth of the clusters. Our aim was to investigate the consistency of the growth rates of sub-3aEuro-nm clusters determined with different methods and the validity of the common approach to use them to estimate particle formation rates. We compared the growth rate corresponding to particle fluxes (FGR), the growth rate derived from the appearance times of clusters (AGR), and the growth rate calculated based on irreversible vapor condensation (CGR). We found that the relation between the different growth rates depends strongly on the external conditions and the properties of the model substance. The difference between the different growth rates was typically highest at the smallest, sub-2aEuro-nm sizes. FGR was generally lower than AGR and CGR; at the smallest sizes the difference was often very large, while at sizes larger than 2aEuro-nm the growth rates were closer to each other. AGR and CGR were in most cases close to each other at all sizes. The difference between the growth rates was generally lower in conditions where cluster concentrations were high, and evaporation and other losses were thus less significant. Furthermore, our results show that the conventional method used to determine particle formation rates from growth rates may give estimates far from the true values. Thus, care must be taken not only in how the growth rate is determined but also in how it is applied.Peer reviewe

Terpene Composition Complexity Controls Secondary Organic Aerosol Yields from Scots Pine Volatile Emissions

Secondary organic aerosol (SOA) impact climate by scattering and absorbing radiation and contributing to cloud formation. SOA models are based on studies of simplified chemical systems that do not account for the chemical complexity in the atmosphere. This study investigated SOA formation from a mixture of real Scots pine (Pinus sylvestris) emissions including a variety of monoterpenes and sesquiterpenes. SOA generation was characterized from different combinations of volatile compounds as the plant emissions were altered with an herbivore stress treatment. During active herbivore feeding, monoterpene and sesquiterpene emissions increased, but SOA mass yields decreased after accounting for absorption effects. SOA mass yields were controlled by sesquiterpene emissions in healthy plants. In contrast, SOA mass yields from stressed plant emissions were controlled by the specific blend of monoterpene emissions. Conservative estimates using a box model approach showed a 1.5- to 2.3-fold aerosol enhancement when the terpene complexity was taken into account. This enhancement was relative to the commonly used model monoterpene, "alpha-pinene". These results suggest that simplifying terpene complexity in SOA models could lead to underpredictions in aerosol mass loading.Peer reviewe