Abstract
Abstract. 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.
Highlights
Atmospheric new particle formation and growth are important phenomena when considering global aerosol concentrations
We performed nucleation and growth experiments at 5◦ using oxidised organics from dark ozonolysis of alpha-pinene (Kirkby et al, 2016; Stolzenburg et al, 2018). Both experiments resulted in moderate new particle formation rate and in the Kalman smoother, we used DMA-train data that was averaged over 120 s time intervals
The methodology was shown to be able to predict new particle formation, growth, and loss rates from synthetic computergenerated aerosol size distribution evolution data, while here the method has been applied to real experimental data for the first time
Summary
Atmospheric new particle formation and growth are important phenomena when considering global aerosol concentrations. In non-linear and non-Gaussian cases, the rigorous choice is to use so-called particle filters and smoothers (Särkkä, 2013) Because these MCMC-based estimators are highly time consuming in large-dimensional cases, approximative methods are often used – such as the extended Kalman filter and smoother adopted in this paper. These recursive algorithms use sequential linearisation to approximate the nonlinear models and non-Gaussian probability distributions. Ten faced in atmospherically relevant nucleation studies, and third, the DMA train is, at the same time, an interesting and challenging instrument for detailed data analysis because of the gaps in the measured size spectrum
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