Estimating Particle Number Size Distributions from Multi-instrument Observations with Kalman Filtering

Atmospheric aerosol particles have several important effects on the environment and human society. The exact impact of aerosol particles is largely determined by their particle size distributions. However, no single instrument is able to measure the whole range of the particle size distribution. Estimating a particle size distribution from multiple simultaneous measurements remains a challenge in aerosol physical research. Current methods to combine different measurements require assumptions concerning the overlapping measurement ranges and have difficulties in accounting for measurement uncertainties. In this thesis, Extended Kalman Filter (EKF) is presented as a promising method to estimate particle number size distributions from multiple simultaneous measurements. The particle number size distribution estimated by EKF includes information from prior particle number size distributions as propagated by a dynamical model and is based on the reliabilities of the applied information sources. Known physical processes and dynamically evolving error covariances constrain the estimate both over time and particle size. The method was tested with measurements from Differential Mobility Particle Sizer (DMPS), Aerodynamic Particle Sizer (APS) and nephelometer. The particle number concentration was chosen as the state of interest. The initial EKF implementation presented here includes simplifications, yet the results are positive and the estimate successfully incorporated information from the chosen instruments. For particle sizes smaller than 4 μm, the estimate fits the available measurements and smooths the particle number size distribution over both time and particle diameter. The estimate has difficulties with particles larger than 4 μm due to issues with both measurements and the dynamical model in that particle size range. The EKF implementation appears to reduce the impact of measurement noise on the estimate, but has a delayed reaction to sudden large changes in size distribution.