Inversion of data containing information on the aerosol particle size distribution using multiple instruments

An algorithm for inversion of data containing information on particle size distributions is presented that is designed to be true to the input data, does not need an initial guess, does not assume a shape of the size distribution function, yields the smoothest non-negative result consistent with the input data, calculates the uncertainty of the result based on the uncertainty of the input data, and is capable of combining data from more than one instrument type into one inversion result. To test the algorithm, synthetic data of aircraft payloads sensitive for particle diameters and combining a cascade of condensation particle counters (CPSA) with a differential mobility analyser (DMA), a passive cavity aerosol spectrometer probe (PCASP), and a parallel diffusion battery (PDB) are generated. The CPSA/DMA instrument combination retrieves the log-normal parameters of the Aitken-mode with <1% uncertainty while the CPSA/PDB combination reaches 4% and the CPSA/PCASP combination 8% uncertainty. Compared with the CPSA/DMA set-up, the CPSA/PDB and CPSA/PCASP combinations have advantages with respect to temporal resolution and space/weight demands, respectively. The algorithm is extendable to other instrument types and may also serve as a tool for optimising instruments or instrument packages with respect to specific scientific questions.