10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
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Estimation of Nucleation and Condensation Rates From Size Distribution Measurements Using Statistical Inverse Methodology
MATTHEW OZON, Aku Seppänen, Anton Laakso, Jari Kaipio, Kari Lehtinen, University of Eastern Finland
Abstract Number: 753 Working Group: Aerosol Modeling
Abstract Motivations Aerosols play a key role in the global radiative balance of the earth. Their number concentration, size distribution (SD) and chemical composition affect their ability to scatter and absorb solar radiation as well as the formation, properties and lifetimes of clouds. The same properties determine how particles enter the human lung and cause various public health problems. To quantify these effects, we need to be able to determine the rates of the key microphysical processes, aerosol formation and growth, from measurements of aerosol SD evolution.
Methods The estimation of nucleation rate and condensation rates still typically relies on rather simple visual analysis, regression methods or balance equations involving crude approximations. So far, e.g. determining both size and time dependence of condensation rates has been a challenge. In addition, the methods have not considered measurement uncertainty in a rigorous way. We propose an automated method based on the Kalman Filter (KF) — a very famous statistical, dynamical inversion method that is stable, minimizes the variance of the estimates and easy to implement. However, instead of using the KF only for filtering the SD, it is tweaked to also estimate the nucleation and condensation rates. This method requires no assumption of SD shape as it relies only on a physical evolution model — the aerosol General Dynamic Equation — and a measurement model — DMPS — that are both combined in the KF framework.
Results As a proof of concept of our method and a test of its performance we analyze synthetic data — SD — that are generated by solving the GDE with a sectional method. We simulate eight days with four having a new particle formation event. The size spectrum ranges from an arbitrary critical cluster size of 2nm to 2μm. One single vapor is responsible for condensational growth. The simulated data are corrupted by additive and multiplicative noise in order to resemble actual measured data. The tests are conducted on two versions of the method: 1) estimation of two parameters, the nucleation rate and the vapor concentration — assuming a model for the size dependence of the condensation rates — and 2) estimation of the nucleation rate along with all the condensation rates without any insight of the theory. The results are really promising;the first derivation of the method is resilient to the data quality and allows to retrieve the nucleation coefficient used for the simulation, and the second variation of the method gives similarly good estimates for the nucleation rate and fair evaluations of the growth rates — even though the condensation rates suffer discrepancies for poor data quality.