Simultaneous MPSS data inversion and aerosol process rate estimation with uncertainty quantification via Bayesian state-space methods

Aerosol particles influence climate both directly, by scattering and absorbing solar radiation, and indirectly, by acting as cloud condensation nuclei. However, the magnitude of these effects remains highly uncertain, largely due to limitations in how aerosol dynamics are represented in global climate models. Current models often rely on simplified process rate approximations and coarse aerosol dynamics, as more accurate simulations are computationally prohibitive.

To improve parameterizations in climate models, there is a need for robust methods to estimate aerosol process rates, such as condensation, formation, and deposition, from both chamber and atmospheric data. These rates are not well constrained, as the underlying physical mechanisms are not yet fully understood. Nevertheless, they are key drivers of aerosol size distribution evolution, which varies with atmospheric conditions.

Bayesian state-space methods offer a way to simultaneously estimate size distribution evolution and process rates from Mobility Particle Sizer Spectrometer (MPSS) data. In addition, Bayesian methods account measurement and process uncertainties directly into the estimation framework, enabling inherent uncertainty quantification.

In this study, we use the extended Kalman Filter (EKF) to estimate the state of the system, i.e., the expected values and credibility intervals of the size distribution and process rates. At each time step, the EKF predicts the next state based on a model of the system dynamics and updates this prediction with new measurements. In the evolution step, we use a finite element approximation of the General Dynamic Equation of Aerosols. We model the process rates as Markov processes. In this work, the measurements consist of time-series of counts given by the MPSS. The Fixed Interval Kalman Smoother (FIKS) back-iterates the EKF estimates refining them in the process by applying information about the future measurements. The inference of process rates using EKF and FIKS was tested both with synthetic and experimental data. The simulated MPSS data are generated by transforming a known aerosol distribution evolution to the output of the MPSS with a system matrix which maps size distributions to counts measured by a condensation particle counter. In the chamber measurement, 𝛼-pinene and ozone reacted chemically forming organic compounds, which caused ammonium sulfate particles to grow due to condensation. The data was measured with scanning mobility particle sizer (SMPS).

The EKF and FIKS captures the true process rates from the simulated data as the true value lies constantly inside the 95-% credibility interval of the estimated process rates. In the chamber measurements, the growth estimates obtained with the EKF and FIKS are close to the estimates obtained with the maximum concentration method. Notably, the EKF and FIKS give estimates for the each particle size at each time step which is not the case with the customary methods. Furthermore, a major strength of the proposed methods is that, in addition to estimates of the mean values, credibility intervals for the variables of interest are obtained simultaneously.