Preprints
https://doi.org/10.5194/amt-2021-334
https://doi.org/10.5194/amt-2021-334

  01 Nov 2021

01 Nov 2021

Review status: this preprint is currently under review for the journal AMT.

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

Jiaoshi Zhang1, Yang Wang1,3, Steven Spielman2, Susanne Hering2, and Jian Wang1 Jiaoshi Zhang et al.
  • 1Center for Aerosol Science and Engineering, Washington University in St. Louis, St. Louis, Missouri, USA
  • 2Aerosol Dynamics Inc, Berkeley, California, USA
  • 3Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, Missouri, USA

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-square methods are the most widely used algorithms for inverting the GF-PDF from measurements of humidified tandem differential mobility analyzers (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 square 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 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-square methods, are quantitively compared. The result shows that Twomey’s method generally outperforms other inversion methods. The capabilities of the Twomey’s method in reconstructing the pre-defined GF-PDFs and recovering the mode parameters are validated.

Jiaoshi Zhang et al.

Status: open (until 08 Jan 2022)

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Jiaoshi Zhang et al.

Jiaoshi Zhang et al.

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Short summary
In this study, we present new nonparametric, regularized methods for inverting the growth factor probability density function (GF-PDF) from humidity-controlled fast integrated mobility spectrometer measurements. They do not require any prior assumptions of the GF-PDF distribution, reduce the error in inverted GF-PDF by eliminating noise amplification, and are more computationally efficient than before. And results show that Twomey’s method outperforms all other different inversion methods.