Subdiffusive reflectance captured at short source-detector separations provides increased sensitivity to the scattering phase function and hence allows superficial probing of the tissue ultrastructure. Consequently, estimation of subdiffusive optical parameters has been the subject of many recent studies focusing on lookup-table-based (LUT) inverse models. Since an adequate description of the subdiffusive reflectance requires additional scattering phase function related optical parameters, the LUT inverse models, which grow exponentially with the number of estimated parameters, become excessively large and computationally inefficient. Herein, we propose, to the best of our knowledge, the first artificial-neural-network-based inverse Monte Carlo model that overcomes the limitations of the LUT inverse models and thus allows efficient real-time estimation of optical parameters from subdiffusive spatially resolved reflectance. The proposed inverse model retains the accuracy, is about four orders of magnitude faster than the LUT inverse models, grows only linearly with the number of estimated optical parameters, and can be easily extended to estimate additional optical parameters.

Abstract. Providing reliable observations of aerosol particles' absorption properties at spatial and temporal resolutions suited to climate models is of utter importance to better understand the effects that atmospheric particles have on climate. Nowadays, one of the instruments most widely used in international monitoring networks for in situ surface measurements of light absorption properties of atmospheric aerosol particles is the multi-wavelength dual-spot Aethalometer, AE33. The AE33 derives the absorption coefficients of aerosol particles at seven different wavelengths from the measurements of the optical attenuation of light through a filter where particles are continuously collected. An accurate determination of the absorption coefficients from the AE33 instrument relies on the quantification of the non-linear processes related to the sample collection on the filter. The multiple-scattering correction factor (C), which depends on the filter tape used and on the optical properties of the collected particles, is the parameter with both the greatest uncertainty and the greatest impact on the absorption coefficients derived from the AE33 measurements. Here we present an in-depth analysis of the AE33 multiple-scattering correction factor C and its wavelength dependence for two different and widely used filter tapes, namely the old, and most referenced, TFE-coated glass, or M8020, filter tape and the currently, and most widely used, M8060 filter tape. For performing this analysis, we compared the attenuation measurements from AE33 with the absorption coefficients measured with different filter-based techniques. On-line co-located multi-angle absorption photometer (MAAP) measurements and off-line PP_UniMI polar photometer measurements were employed as reference absorption measurements for this work. To this aim, we used data from three different measurement stations located in the north-east of Spain, namely an urban background station (Barcelona, BCN), a regional background station (Montseny, MSY) and a mountaintop station (Montsec d'Ares, MSA). The median C values (at 637 nm) measured at the three stations ranged between 2.29 (at BCN and MSY, lowest 5th percentile of 1.97 and highest 95th percentile of 2.68) and 2.51 (at MSA, lowest 5th percentile of 2.06 and highest 95th percentile of 3.06). The analysis of the cross-sensitivity to scattering, for the two filter tapes considered here, revealed a large increase in the C factor when the single-scattering albedo (SSA) of the collected particles was above a given threshold, up to a 3-fold increase above the average C values. The SSA threshold appeared to be site dependent and ranged between 0.90 to 0.95 for the stations considered in the study. The results of the cross-sensitivity to scattering displayed a fitted constant multiple-scattering parameter, Cf, of 2.21 and 1.96, and a cross-sensitivity factor, ms, of 1.8 % and 3.4 % for the MSY and MSA stations, respectively, for the TFE-coated glass filter tape. For the M8060 filter tape, Cf values of 2.50, 1.96 and 1.82 and ms values of 1.6 %, 3.0 % and 4.9 % for the BCN, MSY and MSA stations, respectively, were obtained. SSA variations also influenced the spectral dependence of C, which showed an increase with wavelength when SSA was above the site-dependent threshold. Below the SSA threshold, no statistically significant dependence of C on the wavelength was observed. For the measurement stations considered here, the wavelength dependence of C was to some extent driven by the presence of dust particles during Saharan dust outbreaks that had the potential to increase the SSA above the average values. At the mountaintop station, an omission of the wavelength dependence of the C factor led to an underestimation of the absorption Ångström exponent (AAE) by up to 12 %. Differences in the absorption coefficient determined from AE33 measurements at BCN, MSY and MSA of around 35 %–40 % can be expected when using the site-dependent experimentally obtained C value instead of the nominal C value. Due to the fundamental role that the SSA of the particles collected on the filter tape has in the multiple-scattering parameter C, we present a methodology that allows the recognition of the conditions upon which the use of a constant and wavelength-independent C is feasible.

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