Statistical Inverse Modelling of Aerosol Size Distributions
The uncertainty in the radiative forcing caused by aerosols is considered the main factor limiting our understanding of past and future climate changes. Some of this uncertainty is because the processes governing the aerosol dynamics are not fully known, and some uncertainty is because current climate models use crude approximations of the aerosol dynamics due to high computational costs when incorporated with other climate models. In this research we investigate the statistical inversion approach to estimating the aerosol size distribution and aerosol dynamical parameters from aerosol observations. Specifically, we consider the state space framework to simultaneously estimate and quantify the uncertainty of the size distribution, condensation, deposition, and nucleation rates from aerosol particle count measurements, and with lower computational costs compared to previous studies. The aerosol observation model is based on a differential mobility particle sizer. The temporal-evolution model of the size distribution is modelled by applying a combined finite element method to the aerosol general dynamic equation. We apply the discontinuous-Galerkin finite element method to the condensation, deposition, and source terms, and the collocation finite element method to the coagulation term in the general dynamic equation. We show that our combined finite element method approach computes accurate estimates at lower computational costs compared to the standard finite element and upwind Petrov-Galerkin finite element methods. We obtain feasible estimates of the size distribution, condensation, deposition, and nucleation rates from aerosol observations with fewer particle size discretisation bins and larger time steps compared to previous studies. In our results we find that the fixed-interval Kalman smoother is significant to improving the estimation of the nucleation rate, but less significant for the condensation and deposition rates. The inclusion of the coagulation term in the evolution model is significant to improving the estimation of the nucleation and deposition rates, but not the condensation rate. Using higher-order autoregressive models for the nucleation evolution model improves the estimates. Lastly, we use the Bayesian approximation error approach to account for errors in model reduction and marginalisation of the aerosol dynamical parameters, and show it is a feasible approach to improving the estimation of the size distribution, condensation, deposition, and nucleation rates.
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