Regularized Inversion of Aerosol Hygroscopic Growth Factor Probability Density Function: Application to Humidity-Controlled Fast Integrated Mobility Spectrometer Measurements
Abstract
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.
Recommended Citation
J. Zhang et al., "Regularized Inversion of Aerosol Hygroscopic Growth Factor Probability Density Function: Application to Humidity-Controlled Fast Integrated Mobility Spectrometer Measurements," Atmospheric Measurement Techniques, vol. 15, no. 8, pp. 2579 - 2590, European Geosciences Union; Copernicus Publications, Apr 2022.
The definitive version is available at https://doi.org/10.5194/amt-15-2579-2022
Department(s)
Civil, Architectural and Environmental Engineering
International Standard Serial Number (ISSN)
1867-8548; 1867-1381
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2022 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
28 Apr 2022
Comments
We acknowledge the funding support from the US Department of Energy’s Atmospheric System Research (ASR; award no. DE-SC0021017), Small Business Innovation Research (SBIR; award no. DE-SC0013103), and Small Business Technology Transfer (STTR; award no. DESC0006312) programs.