Regularized inversion of aerosol hygroscopic growth factor probability density function: application to humidity-controlled fast integrated mobility spectrometer measurements

• Published in: Atmospheric measurement techniques Vol. 15; no. 8; pp. 2579 - 2590
• Main Authors: Zhang, Jiaoshi, Wang, Yang, Spielman, Steven, Hering, Susanne, Wang, Jian
• Format: Journal Article
• Language: English
• Published: Katlenburg-Lindau Copernicus GmbH 28.04.2022; Copernicus Publications
• Subjects: Aerosols; Algorithms; Convolution; Distribution (Probability theory); Efficiency; Environmental Sciences; Growth factors; Humidity; Hygroscopicity; Ill posed problems; Inversion; Inversions; Kernel functions; Least squares; Measurement; Methods; Mobility; Probability density function; Probability density functions; Probability theory; Radiation; Regularization; Regularization methods; Relative humidity; Specific gravity
• DOI: 10.5194/amt-15-2579-2022
• ISSN: 1867-8548; 1867-1381

Aerosol hygroscopic growth plays an important role in atmospheric particle chemistry and the effects of aerosol on radiation and hence climate. The hygroscopic growth is often characterized by a growth factor probability density function (GF-PDF), where the growth factor is defined as the ratio of the particle size at a specified relative humidity to its dry size. Parametric, least-squares methods are the most widely used algorithms for inverting the GF-PDF from measurements of the humidified tandem differential mobility analyzer (HTDMA) and have been recently applied to the GF-PDF inversion from measurements of the humidity-controlled fast integrated mobility spectrometer (HFIMS). However, these least-squares methods suffer from noise amplification due to the lack of regularization in solving the ill-posed problem, resulting in significant fluctuations in the retrieved GF-PDF and even occasional failures of convergence. In this study, we introduce nonparametric, regularized methods to invert the aerosol GF-PDF and apply them to HFIMS measurements. Based on the HFIMS kernel function, the forward convolution is transformed into a matrix-based form, which facilitates the application of the nonparametric inversion methods with regularizations, including Tikhonov regularization and Twomey's iterative regularization. Inversions of the GF-PDF using the nonparameteric methods with regularization are demonstrated using HFIMS measurements simulated from representative GF-PDFs of ambient aerosols. The characteristics of reconstructed GF-PDFs resulting from different inversion methods, including previously developed least-squares methods, are quantitatively compared. The result shows that Twomey's method generally outperforms other inversion methods. The capabilities of Twomey's method in reconstructing the pre-defined GF-PDFs and recovering the mode parameters are validated.