In this work, we developed a numerical method to investigate the effects of black carbon (BC) morphology on the estimation of brown carbon (BrC) absorption using the absorption Ångström exponent (AAE) methods. Pseudo measurements of the total absorption were generated based on several morphologically mixed BC models, then the BrC absorption was inferred based on different BC AAE methods. By investigating the estimated BrC absorption at different parameters, we have demonstrated under what conditions the AAE methods can provide good or bad estimations. As recent studies have shown that both externally and internally mixed BC still exhibits a relatively small fractal dimension value, the AAE

Carbonaceous aerosols, a main source of the light-absorbing aerosols, have great effects on the climate. Carbonaceous aerosols mainly include black carbon (BC) and organic carbon (OC). BC was considered the dominant absorbing aerosol in the atmosphere, which greatly absorbs light from ultraviolet (UV) wavelengths to near-infrared wavelengths, and it contributes to large warming effects on the climate

Laboratory measurements based on the extraction of filter samples were widely used to measure BrC absorption, while it is difficult to provide global, continuous measurements. Thus, an increasing number of studies used measurements based on remote sensing and in situ techniques. However, the observed absorptions commonly come from the mixing of different aerosols. To separate the contributions of different aerosols, some attempts were made to derive the BrC contribution from the total absorption

As measurements in the atmosphere are caused by many factors including particle size, refractive index, mixing states, morphologies, etc., it is difficult to figure out how BC morphologies affect BrC absorption derivation. Moreover, it is hard to quantify the deviations due to the effects of aerosol composition and size distributions

Numerical tools have an edge on revealing the complex factors that affect the measurements and can be the supplements for the measurements. In this work, we replaced the complex measurements in the atmosphere with the well-constrained pseudo absorption “measurements” computed using morphologically realistic mixed models,
and the inferred BrC absorptions based on the BC AAE

If BC presents a complex morphology, how large will deviations in the estimation of BrC absorption caused by the commonly used AAE methods be?

Under what conditions can the simplified methods provide bad or good estimations?

How are the deviations between the true and the estimated BrC absorption using simplified models caused?

The estimation of BrC absorption.

Non-spherical aerosol models show more excellent performance on reproducing the measurements even though the Mie theory was commonly used in remote sensing and climate modeling

The pseudo measured absorptions were calculated based on the morphologically realistic BC models. For the externally mixed particles, a fractal morphology was assumed for BC, and the structures satisfy the fractal law

For the internally mixing particles, the BC-containing morphologies were generated based on the models proposed by

The second coating method adds the coating materials based on another parameter

The absorption cross sections of spherical BC calculated using the Mie theory, MSTM, and DDA. For the BC core sphere, the ratio of the shell radius to the core radius was assumed to be 1.5.

BC morphologies considered in this work. The internally mixed particles were generated using the models developed by

The Mie theory

In MSTM and DDSCAT, the total absorption efficiency (

To verify the accuracy of MSTM and DDSCAT, we have compared the

In real circumstances, the total absorptions can be inferred from the observations or measurements. Thus, the total absorption cross section was used to provide pseudo measurements. For the internally mixed particles, the total absorption cross section can be directly obtained from the calculations based on the morphologically realistic models. For the externally mixed particles, the total absorption cross section is the sum of the absorption cross section of BC and BrC.

In the study of

The calculation of inferred BrC absorption is similar to the true case, while the difference in the

The total absorption observations at 440, 675, and 870 nm wavelengths can be commonly obtained in AERONET and other ground measurements. Based on the strong spectral dependence of BrC, BrC absorption at 675 and 870 nm wavelengths are commonly neglected, and the absorptions at 675 and 870 nm wavelengths come fully from the BC absorption. As BC absorption at 440 nm wavelength can be obtained based on the BC AAE, we can estimate the BrC absorption at 440 nm based on Eq. (

In addition,

As the BrC absorption estimation is significantly affected by the BC physical properties, we have also calculated the difference between true and the estimated BrC MAC:

Here we used a parameter

The BrC MAC significantly depends on the imaginary part of the BrC refractive index. The measured imaginary parts of BrC refractive indices varied greatly in different studies in the literature. For example,

The measured BrC MAC also varied in different studies. The range of from 1.26 to 1.79 m

The comparisons of the true and inferred BrC absorption for externally mixed particles are shown in Fig.

Comparison of the true and inferred BrC MAC (

The

The applicability of the BC AAE

Comparison of AAE and WDA between BC sphere and aggregates (

To dispose of the effects of particle size on the AAE method,

As BC and BrC are internally mixed, the morphologies become more complex. Not only the fractal parameters (such as

Variation in the true BrC absorption with different coating models (

The estimated BrC MAC also deviates significantly from the true BrC MAC for internally mixed particles. The Mie AAE methods can just provide relatively reasonable estimations for relatively small particles, and for large particles, the inferred BrC MAC based on the Mie AAE methods even deviates more significantly from true BrC MAC compared to the externally mixed particles. Fixing

Comparison of the true and inferred BrC absorption for internally mixed particles (Model A;

Similar to Fig.

The BC AAE

Sometimes the WDA method may even provide worse estimations than the BC AAE

Comparison of AAE and WDA between core-shell sphere model and Model A. Here WDA represents the AAE difference between the 440–675 nm wavelength pair and the 440–870 nm wavelength pair.

Even though the morphologically realistic models have not been used in the real cases, but based on the BC morphologies collected in the atmosphere, we believe that if we can know the detailed BC morphologies, we can improve the estimations. Some studies have been conducted to investigate the BC morphologies in different regions, which can provide information for the estimation of BrC absorption. For example, by exploring the three-dimensional (3D) electron tomography method,

Some previous studies have guessed that the AAE methods may not provide inaccurate estimations, but few studies have provided direct evidence to prove their guess. In this work, based on an inverse framework, we provide a relatively new insight to investigate the BC morphological effect on the estimation of BrC absorption. To focus on the effects of BC morphologies, pseudo measurements were generated based on some morphological mixed BC models, then the BrC absorption was inferred based on the AAE method. Even though the true BrC absorption is within the measured range, the inferred BrC absorption is significantly affected by the BC morphologies.

By investigating the estimated BrC absorption at different parameters, we have demonstrated under what conditions the AAE methods can provide good or bad estimations. Freshly emitted BC commonly presents a fluffy structure, and its AAE does not deviate significantly from 1, so the BC AAE

By comparing the AAE/WDA of spherical BC and detailed BC morphologically realistic models, we have provided explanations for why the good or bad estimations were caused. The AAE does not deviate significantly from 1 if BC presents a fluffy fractal structure, while it varies considerably with

Our calculations were performed using MSTM version 3.0 and DDSCAT 7.3. MSTM version 3.0 can be found online (

JL and QZ conceived the research idea. JL performed the computations and wrote the paper. YZ verified the simulation methods and results. QZ reviewed the paper and supervised the findings of this work. All authors discussed the results and contributed to the final paper.

The authors declare that they have no conflict of interest.

We particularly thank Daniel W. Mackowski and Michael I. Mishchenko for the MSTM code and thank Bruce Draine and Pjotr Flatau for the DDSCAT software. We also acknowledge the support of the super computing center of the University of Science and Technology of China.

This research has been supported by the National Natural Science Foundation of China (grant no. 41675024), the National Natural Science Foundation of China (grant no. U1733126), and the University of Science and Technology of China (grant no. WK2320000052).

This paper was edited by Christina McCluskeys and reviewed by two anonymous referees.