## 1 Introduction  
Atmospheric aerosols originate from a wide variety of natural and anthropogenic sources. A combination of various sources and physical and chemical processes generates these atmospheric aerosols. The optical properties of atmospheric aerosols play a key role in earth's radiation budget. They depend on size distribution, chemical composition, mass concentration, density, and wavelength. These optical properties are represented by the refractive index. For example, aerosol scattering is related to the real refractive index, and aerosol light absorption is related to the imaginary refractive index, and the refractive index depends on the above-mentioned conditions [1]. On the basis of the physical and chemical processes that generate aerosols, different source types can be distinguished. Knowledge of atmospheric aerosol optical characteristics depending on the source, such as aerosol extinction, scattering, and absorption, is necessary to enhance our understanding of how atmospheric aerosols impact the climate. Among many parameters that represent the optical properties of aerosols, the mass extinction efficiency (MEE) is a key index to estimate the aerosol extinction coefficient [2]. The MEE is the summation of the mass scattering efficiency (MSE) and mass absorption efficiency (MAE). Here, the MEE, MSE, and MAE are mass-related optical constants that are related to the specific masses and densities of aerosol components. These mass efficiencies (MEE, MSA, and MAE) are based on aerosol composition and are a function of the physico-chemical characteristics of aerosols, such as the aerosol refractive index and size distribution. However, for convenience, mass efficiencies are conventionally treated as constants [3]. According to [PERSON] [4], the MAE also depends on particle size. The conventionally used MAE of 10 m\({}^{2}\) g\({}^{-1}\) for elemental carbon (EC) is applicable to monodisperse carbon particles with radii of 0.08 \(\upmu\)m. For particle sizes larger than a few micrometers, the MAE of EC decreases to below 1 m\({}^{2}\) g\({}^{-1}\), which indicates that size distribution is an important factor to determine aerosol optical properties, such as mass efficiencies. Another important approach to understand aerosol characteristics is to investigate their sources. Source-based analysis provides important information to understand not only the characteristics, but also where emissions come from. The receptor model can provide contribution estimates for each source based on composition-dependent mass concentration. Receptor-oriented models infer source contributions by determining the best-fit linear combination between the emission source chemical composition profiles needed to reconstruct the measured chemical composition of ambient samples [5]. Although receptor models are able to show source-based mass concentrations and contributions, their source-based optical properties may have different contributions. These optical properties and the respective refractive indices depend on size distribution, chemical composition, and concentration of each source. For this reason, source-based optical properties, such as the source-based MEE, require consideration of their source-based mass concentrations and contributions, especially for polydisperse aerosol size distributions. A number of studies have investigated the optical properties of aerosols that are both size- and composition-dependent [6; 7; 8; 9]. However, owing to their complexity, studies that analyze the dependency of aerosol optical properties on both particle size and source are rare [10; 11; 12]. Generally, two types of receptor models, the Chemical Mass Balance (CMB) and Positive Matrix Factorization (PMF) models, have been widely used in the area of source apportionment studies of air pollution. Since PMF is a multivariate factor analysis tool that decomposes a matrix of speciated sample data into two matrices (factor contributions and factor profiles), source profiles are not necessary to run it [13].