Aerosol particles in the atmosphere interact with solar radiation through scattering and absorption. Accurate aerosol optical properties are needed to reduce the uncertainties of climate predictions. The aerosol optical properties can be obtained via optical modeling based on the measured particle size distribution. This approach requires knowledge or assumptions on the particle refractive index and shape. Meanwhile, integrating nephelometry provides information on the aerosol scattering properties directly. However, their measurements are affected by angular non-idealities, and their data need to be corrected for angular truncation and illumination to provide the particle scattering coefficient. We performed an extensive closure study, including a laboratory and a simulated experiment, aiming to compare different nephelometer angular truncation and illumination corrections (further referred to as “angular corrections”). We focused on coarse-mode irregularly shaped aerosols, such as mineral dust, a worldwide abundant aerosol component. The angular correction of irregular particles is found to be only

The atmosphere contains aerosol particles that scatter or absorb the solar radiation (direct effect) and act as cloud condensation nuclei (indirect effect), influencing the Earth's energy budget and thus the climate system. The aerosol radiative forcing constitutes one of the largest uncertainties in climate predictions

Different measurement techniques and models could be used to independently derive the same parameters of an aerosol. This practice, called “closure experiment”, aims not only to characterize a specific parameter but also to minimize the measurement uncertainties

The largest uncertainty of nephelometer measurements is the impossibility of measuring the light scattered by particles and air in the whole angular range, the angular truncation error

An empirical angular correction, exploiting the wavelength dependence of scattering, was developed by

Another method of calculating the angular correction uses Mie theory and the angular sensitivity function, which takes into account the geometrical limitations of the nephelometer

This work aims to evaluate and compare different nephelometer angular truncation and illumination corrections with a focus on mineral dust aerosol. We used the Ecotech Aurora 4000 polar nephelometer, which measures the light scattering in 18 different angular sectors in addition to the total scattering coefficient.

Very recently, when our data were already processed, a new angular correction was proposed by

We conducted an extensive closure study, including a laboratory and a simulated experiment, focusing on coarse-mode irregularly shaped particles (mineral-dust-like). Laboratory test aerosols were generated using polystyrene latex (PSL) particles, ammonium sulfate (AS), and soil dust samples. Their extinction, scattering, and absorption properties, as well as the particle number concentration and size distribution, were measured by seven instruments in parallel. To better interpret the results of the laboratory experiment, we performed a simulated closure experiment randomly selecting several size distributions, refractive indices, and shapes (e.g., irregularly shaped dust-like particles

In Sect.

The Aurora 4000 polar nephelometer is a three-wavelength integrating nephelometer. Integrating nephelometers measure the light scattered by particles and air in a volume.
The light detector is placed orthogonally to a nearly Lambertian light source

A light source is Lambertian if the emitted radians are proportional to

The Aurora 4000 polar nephelometer uses as light sources three
light-emitting diodes (LEDs) at different wavelengths: blue (

Calibration with particle-free gases of known Rayleigh scattering coefficient leads to the constant of calibration

In an ideal nephelometer, the light source is perfectly Lambertian and the angular integration is complete from

Parameters of the Aurora 4000 angular sensitivity function given by

The angular limits of detection

The ideal particle scattering coefficient

Taking into account both the angular truncation and the non-Lambertian illumination, the angular correction

Different angular corrections for the particle scattering coefficient and their limitations.

In this work, we focus on the angular correction

The angular correction can be calculated on the basis of the definition Eq. (

A method to calculate the angular correction

Angular corrections for Aurora 4000 for the total scattering coefficient

Calculations are limited to weakly absorbing particles with the imaginary part of the refractive index

Further limitations of this method were found by

A new angular correction based on the specific feature of the Aurora 4000 that integrates the angular scattering function

In particular, the particle scattering coefficients

To test the different angular corrections for the Aurora 4000 polar nephelometer, we deploy several instruments to measure the optical and microphysical properties of laboratory-generated aerosol, both monodisperse and polydisperse.
The experimental set-up is shown in Fig.

Scheme of the laboratory closure experiment set-up. Different aerosol types, such as monodisperse polystyrene latex (PSL) spheres, ammonium sulfate (AS), and polydisperse powder (mineral dust, silica dust, and volcanic ash), were generated using three different aerosol generation and size selection systems (in the upper left). The aerosol generation and size selection systems were connected via the aerosol inlet to a dilution chamber, where the aerosol flow is mixed with particle-free dry air. The dilution chamber was operated at a pressure slightly above ambient. Seven measurement instruments were connected to the dilution chamber to measure extinction, scattering, and absorption aerosol properties as well as particle number concentration and size distributions.

Measurements were repeated twice, with and without a cyclone for size-selective sampling, in order to achieve different size distributions. Although the nominal aerodynamic size cut-off of the cyclone was

Before each measurement, the dilution chamber was filled in with particle-free dry air to remove any residual particles. Stable concentrations were required for at least

The data evaluation of the laboratory experiment had the overall aim of investigating the uncertainty of the particle scattering coefficient measurements by testing different angular corrections.
A summary of data evaluation from the raw data is provided in Fig.

Flow chart of the data evaluation for the laboratory closure experiment. All instruments involved in the laboratory closure experiment are on the top bar. The descending arrows illustrate the data elaboration to obtain from raw data the relevant quantities (in the yellow boxes) and the different angular corrections (in the red boxes). Thick black arrows indicate when data are used in the data processing of a different instrument.

The most important considerations of the data analysis of each instrument are summarized below. Further details of the data analysis are provided in the Supplement. All data were converted to standard temperature and pressure (STP:

The particle extinction coefficient

Since mineral dust is expected to absorb in the green and blue wavelengths, the particle absorption coefficient was measured by the TAP at three different wavelengths: blue (

The Horvath's polar nephelometer was deployed to measure the particle phase function

For each measurement, data were averaged along sequences with a constant number concentration or along the

The particle size distribution was obtained by merging the particle size distribution measured by the UHSAS in the range of 0.06–0.374

The particle size distribution was obtained assuming the PSL refractive index, e.g., the PSL-equivalent nominal diameter values for the bin boundaries provided by the manufacturer. The PSL equivalent size distribution was used to calculate the OPS particle scattering coefficient and the OPS particle phase function via optical simulations.
The optical simulations were performed with the program MOPSMAP

The four angular corrections

Result of the laboratory experiment for each angular correction. Ratio of the Aurora 4000 particle scattering coefficient corrected for angular truncation and illumination error (corrected

Results of the regression analysis (

The angular correction

The

The angular correction

The angular correction

The angular correction

To compare different angular corrections, we performed a correlation analysis among all the considered angular corrections. The slopes of linear regression through the origin and coefficients of determination obtained are reported in Table

Monodisperse aerosol: PSL and AS. Results of the regression analysis (

Polydisperse aerosol: mineral dust, silica dust, and volcanic ash. Results of the regression analysis (

The angular corrections

Flow chart for the simulated closure experiment. The input parameters are selected randomly among the values indicated in the left box. The “original” angular correction

The angular correction

In the case of the polydisperse aerosol measurements, the agreement within

We conducted a simulated closure experiment to answer the questions raised by the laboratory experiment result, in particular concerning the effect of particle shape on the determination of the particle scattering coefficient. We estimated the effect of the particle shape on the “original” angular correction

The flow chart for this simulated closure experiment is represented in Fig.

We selected 5000 random samples with particle size distributions and refractive indices similar to previous studies on the nephelometer angular correction

Additionally, we selected 1000 random samples with refractive indices
similar to mineral dust aerosol (e.g.,

The selected values of the refractive index for each case are referred to hereafter in the text as well as in Fig.

Calculations were performed on a diameter grid with size range corresponding to the TSI OPS detection limits. The OPS diameter detection limits corresponding to each

Although particles smaller than

For each randomly sampled set of particle size distribution, refractive index, and shape, the response of the TSI OPS 3330 was simulated (step 1–2–3, Fig.

The particle size distribution was obtained (step 4, Fig.

The particle size distribution was obtained (step 4, Fig.

The particle size distribution was obtained (step 4, Fig.

In addition, we calculated the angular correction

Further details of the method used for this sensitivity study are described in the Supplement.

To estimate the effect of the particle shape on the nephelometer angular correction, we compared the angular correction for randomly oriented mineral-dust-like irregular particles with the angular correction obtained for the volume-equivalent spheres with the same size distribution and refractive index (green arrow, Fig.

Comparison between the angular correction for irregular particles and for spherical particles. Calculations are performed for

The

non-absorbing spherical particles, with

non-absorbing spherical particles, with

weakly absorbing spherical particles with

absorbing spherical particles with

weakly absorbing spherical particles with mineral-dust-like refractive index

weakly absorbing irregular particles with mineral-dust-like shape and refractive index

Simulated closure experiment to assess the limitations and uncertainties of the angular correction obtained with Mie theory from the size distribution measured by an OPS. The comparisons for the angular correction

Simulated closure experiment to assess the limitations and uncertainties of the angular correction obtained with Mie theory from the size distribution measured by an OPS. The comparisons for the angular correction

Several observations can be made looking at the results represented in Figs.

Second, if the particle size distribution is calculated with the calibration refractive index, the use of the true refractive index in the optical modeling of the angular correction

Third, if the particle size distribution is calculated with the true refractive index, the agreement between

Fourth, in the case of absorbing aerosol, the

Finally, an interesting result is found in the case of irregular particles when no size cut-off is considered (last panel row of Fig.

Integrating nephelometer measurements require an angular correction to provide the particle scattering coefficient. Several methods to calculate the angular correction are available in the literature and are covered by our laboratory and modeling study. The applicability and uncertainty of these corrections depend on the particle type and the availability of other measurements.

The angular correction

The angular correction

The overall higher uncertainty of the angular correction

Nevertheless, the angular correction

The angular correction

The direct effect of particle shape on the angular correction itself (i.e., original

If the true refractive index is assumed for the particle size distribution retrieval, the

In the case of irregularly shaped particles, the angular correction

Results of the simulated closure experiment show that the angular correction

Optical closure studies, where the aerosol optical properties measured directly are compared with the aerosol optical properties simulated using the measured size distribution and optics theory, allow not only the evaluating and minimizing of the measurement uncertainties but also constraining specific parameters. Iteratively comparing the measured particle scattering and absorption coefficient with the corresponding derived quantities, it is possible to retrieve the aerosol refractive index

If the instruments' uncertainties are comparatively high, it is difficult to achieve a perfect closure, and the refractive index retrieval might fail. For instance,

Our study suggests that while the particle shape affects the angular correction

Measurement uncertainties of the measurement instruments Aurora 4000, CAPS PM

Differences in the angular sensitivity function of the Aurora 4000 and the Aurora 3000

In our data analysis, we introduced some circularity when the CAPS PM

A method to evaluate the accuracy of the angular sensitivity function could consist of considering the angular correction

We performed an extensive closure study, including laboratory and modeling effort, to evaluate and compare different angular corrections for the Aurora 4000 polar nephelometer. We focused on their performance for coarse-mode irregularly shaped aerosol such as mineral dust, which is the most abundant aerosol worldwide in terms of dry mass

We compared the particle scattering coefficients corrected with each angular correction with the reference particle scattering coefficient obtained as the difference between the measured particle extinction and absorption coefficients.
As a result, we found that the angular correction

To interpret these results, we performed an extensive modeling effort, simulating a closure experiment for randomly selected particle size distributions, refractive indices, and shapes.
First, we estimated the effect of the particle shape on the original angular correction

Flow chart to decide which angular correction is appropriate in different situations. The uncertainty related to the appropriate angular correction is identified on the basis of the results of the sensitivity study reported in Figs.

The angular correction

Based on the current knowledge and the present work, we conclude that there is no generally “best” method to calculate the angular correction. Rather the angular correction should be selected depending on the aerosol type and the investigated size range. The angular correction

We provide uncertainties for different approaches to calculate the angular correction from the measured particle size distribution, and we indicate the least uncertain approach for several situations. The reported uncertainties are calculated on the basis of the simulated closure experiment and do not consider the uncertainty of the angular sensitivity function.
We recommend the procedure shown in the flow chart in Fig.

If the measurements are performed with a sub-micrometer cut-off or if the aerosol scattering is dominated by sub-micrometer aerosols,

and the nephelometer provides the scattering coefficient for various angular ranges (in particular

and the nephelometer does not provide the scattering coefficient for various angular ranges, the angular correction can be calculated with the

If the measurements are performed without a sub-micrometer cut-off or if the aerosol scattering is dominated by coarse-mode aerosols,

the size distribution is not measured over a relevant size range, or the aerosol type is not known, the angular correction can be calculated with the

the aerosol type is known, the particles are spherical, and the size distribution is measured over a relevant size range, the best method is the

the aerosol type is known and the particles are mineral dust, the angular correction

the aerosol type is known to be non-spherical but it is not mineral dust, more investigation is needed on the angular correction. However,

By improving the understanding of the nephelometer angular correction for irregularly shaped coarse particles – in particular mineral dust – this study reduces uncertainties in observations of aerosol scattering properties. Future studies with the aim of further reducing the uncertainty of scattering measurements should focus on environments with a high load of absorbing particles like urban sites or moderately absorbing mixtures such as mixtures of mineral dust and black carbon.

Data of the laboratory study shown in this paper are available on request to bernadett.weinzierl@univie.ac.at and marilena.teri@univie.ac.at.

The supplement related to this article is available online at:

MT, TM, and BW designed the study. MT, SV, and BW prepared the experiment. MT, SV, TM, and HH tested the experimental set-up and performed the measurements. MT analyzed the data with support from BW, TM, and JG. HH analyzed and provided Horvath's polar nephelometer data. MT performed the simulated closure experiment with contributions from AW for the Mie code reproducing the TSI OPS signal and JG for the ADDA calculations. The interpretation of the results is the outcome of numerous discussions among MT, TM, JG, SV, HH, RV, PB, AW, and BW. MT wrote the paper with contributions from JG, PB, and BW. All co-authors read and commented on the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The research leading to these results has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreement no. 640458, A-LIFE). We acknowledge financial support by the Vienna Doctoral School in Physics (VDSP). The Erasmus+ Traineeship Programme is also acknowledged for the financial support to Sara Valentini. The authors thank Scott Prahl and Maxim Yurkin for providing their optical modeling codes.

This research has been supported by the European Research Council, H2020 (A-LIFE (grant no. 640458)), Vienna Doctoral School in Physics (VDSP), and Erasmus+ Traineeship Programme.

This paper was edited by Mingjin Tang and reviewed by two anonymous referees.